Cosmic Ray Bombardment of Molecular Cores Near Supernova Remnants

The Cold, the Dense and the Energetic: Cosmic Ray Bombardment of Molecular Cores Near Supernova Remnants

Nigel Maxted School of Chemistry & Physics The University of Adelaide

21-04-2013 x

1 Contents

0.1 Abstract...... 5 0.2 DeclarationofOriginality ...... 6 0.3 Acknowledgements ...... 7

1 High Energy Astrophysics 9 1.1 IntroductionandMotivation ...... 9 1.2 CosmicRays...... 10 1.2.1 TheCosmicRaySpectrum...... 10 1.2.2 CosmicRayPropagation...... 12 1.2.3 CosmicRayAcceleration...... 13 1.2.4 SupernovaRemnants ...... 19 1.3 Processes Responsible for High Energy Emissions ...... 20 1.3.1 SynchrotronEmission ...... 21 1.3.2 InverseComptonScattering ...... 21 1.3.3 Relativistic Bremsstrahlung ...... 22 1.3.4 NeutralPionDecay...... 23 1.3.5 Energy-loss Timescales ...... 23 1.4 Gamma-Ray Astronomy with H.E.S.S...... 28 1.4.1 ExtensiveAirShowers ...... 28 1.4.2 CherenkovImaging ...... 31 1.4.3 Image Parameterisation and HESS Performance ...... 33 1.4.4 Gamma-rays from Supernova Remnants ...... 33

2 Millimetre-wavelength Molecular Spectroscopy 34 2.1 MolecularEnergylevels ...... 34 2.2 Einstein Coeﬃcients and Critical Density ...... 36 2.3 Radiative Transfer and Physical Parameters ...... 38 2.3.1 Intensity, Flux and Luminosity ...... 38 2.3.2 ThermalRadiation ...... 39 2.3.3 EquationofRadiativeTransfer ...... 40 2.4 MolecularPopulationModels ...... 41 2.4.1 The Local Thermodynamic Equilibrium Model ...... 41 2.4.2 Statistical Equilibrium Models ...... 42 2.5 ColumnDensityCalculation ...... 43 2.5.1 OpticalDepthCalculation ...... 44 2.6 RADEXModelling ...... 44 2.7 SingleDishmm-Astronomy ...... 48

2 2.7.1 Mopra ...... 48 2.7.2 Nanten2 ...... 49 2.8 GalacticKinematicDistances ...... 50 2.8.1 TheDopplerEffect ...... 50 2.8.2 RotationalMotionoftheMilkyWay ...... 51 2.9 LineProfiles...... 52 2.9.1 LorentzianLineShape ...... 52 2.9.2 GaussianLineShape ...... 53 2.9.3 OtherEffectsonLineShape ...... 54 2.10 Whatarewelookingfor?...... 54

3 Gas Tracers 55 3.1 CO...... 55 3.1.1 X-factor ...... 56 3.1.2 GalacticCO Isotopologue Distribution ...... 56 3.2 CS ...... 58 3.2.1 OpticalDepthandIsotopologues ...... 58 3.3 DarkMolecularGas ...... 59 3.4 NH3 ...... 60 3.5 OH...... 65 3.6 SiO...... 66 3.6.1 GrainSputteringModels ...... 67 + 3.7 N2H ...... 68 3.8 HI ...... 70 3.8.1 SpectralLineAnalysis ...... 70

4 Supernova Remnant RX J1713.7 3946 71 4.1 3 to 12 millimetre studies of dense− gas towards the western rim of supernova remnant RX J1713.7 3946...... 71 4.2 Dense Gas Towards− the RX J1713.7 3946Supernova Remnant (1) ...... 89 4.3 Dense Gas Towards the RX J1713.7−3946Supernova Remnant (2) ...... 96 − 5 Supernova Remnant CTB 37A 117 5.1 Interstellar gas towards CTB 37A and the TeV gamma-ray source HESS J1714 385117 − 6 Cosmic Ray Diffusion 138 6.1 DiffusionofCosmicRaysintoGas...... 138 6.1.1 TheDiffusionCoefficient ...... 138 6.1.2 TheDiffusionEquation...... 140 6.1.3 Solving the Diffusion Equation ...... 141 6.2 Diffusion into an Inhomogeneous Core ...... 145 6.2.1 CosmicRayDistribution ...... 145 6.2.2 The Molecular Core in the Gamma-rays ...... 146 6.2.3 Injected Cosmic Ray Spectrum ...... 147 6.2.4 FutureWork...... 147

7 Summary and Final Remarks 148

3 A Appendices 156 A.1 CosmicRays...... 156 A.1.1 1storderFermiAcceleration ...... 156 A.1.2 Hypernovae ...... 158 A.2 HESSAnalyses ...... 159 A.2.1 Cosmic Ray Event Rejection in HESS Analyses ...... 159 A.2.2 Cosmic Ray Background Models ...... 160 A.3 Erratum:Chapter4 ...... 163 A.3.1 3 to 12 millimetre studies of dense gas towards the western rim of supernova remnant RX J1713.7 3946...... 163 − A.4 CosmicRayDiﬀusion...... 166 A.4.1 Cosmic Ray Distribution Inside a Molecular Core ...... 166 A.4.2 Cosmic Ray Diﬀusion Software ...... 167

4 0.1 Abstract

One of the oldest unsolved mysteries in astrophysics is the origin of cosmic rays, particles that travel at speeds close to the speed of light. A plausible theory to explain the acceleration of these particles is shock-acceleration in the expanding shells of supernova remnants (SNRs) within our galaxy. In this thesis, the interstellar medium towards supernova remnants that display indicators of particle acceleration, ie., gamma-ray emission, are investigated. More specifically, results from mm-wavelength molecular gas surveys towards two gamma-ray emitting SNRs, RX J1713.7 3946 and CTB 37A are presented. Chapter 1 summarises astrophysics at high energies, including− what cosmic rays are, how they may be accelerated, their connection to gamma-ray emission and how gamma-ray astronomy is performed from the ground. On the opposite (low-energy) side of the energy spectrum, Chapter 2 describes some of the theory of single dish radio astronomy, which allows us to probe molecular environments. By tuning the receiver to home-in on particular molecular species, different interstellar envi- ronoments can be targeted. Some specific molecular species are outlined in Chapter 3, before utilising these species in following chapters. The bulk of chapters 4 and 5 are composed of published articles presenting interstellar gas observations and investigation. Chapter 4 is an in-depth analysis of the molecular environment towards the supernova remnant RX J1713.7 3946 (in 3 articles) using several independent − + molecular gas tracers, including transitions of the CS, NH3 and N2H molecules. In addition to various specific mm-phenomena, the presence of dense gas was confirmed via our observations. The issue of cosmic ray transport into dense star-forming cores was then addressed. Due to enhanced magnetic turbulence, cosmic ray propagation may be slower than the galactic average, so predictions for several slow-diffusion scenarios are made. Through modeling, scenarios where low energy cosmic rays are excluded from the centres of molecular cores were identified. Such cases may result in a lower proportion of low energy gamma-rays coming from core centres relative to higher energy gamma-rays (ie. a hardening of the gamma-ray spectrum). Chapter 5 is an overview of the molecular gas towards the entire gamma-ray emission region of the supernova remnant CTB 37A (in 1 article), allowing the estimation of the mass of cosmic- 4 ray target material, found to be 10 M⊙. In a hadronic scenario for gamma-ray emission, this corresponds to a cosmic ray density∼ of 80-1100 times that seen Earth. This may have ∼ implications for the supernova remnant energetics, distance and age, which are discussed. Finally, in Chapter 6, an investigation of the subtleties of cosmic ray diffusion near supernova remnants is carried out, and techniques to simulate effects that may result from diffusion into molecular gas are outlined. Hard conclusions concerning the spectrum of gamma-rays resulting from molecular cores are left for future work.

5 0.2 Declaration of Originality

I, Nigel Maxted, certify that this work contains no material which has been accepted for the award of any other degree or diploma in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. I give consent to this copy of my thesis when deposited in the University Library, being made available for loan and photocopying, subject to the provisions of the Copyright Act 1968. The author acknowledges that copyright of published works contained within this thesis (as listed below*) resides with the copyright holder(s) of those works. I also give permission for the digital version of my thesis to be made available on the web, via the University’s digital research repository, the Library catalogue and also through web search engines, unless permission has been granted by the University to restrict access for a period of time.

*Published works contained within this thesis:

Maxted N., Rowell G., Dawson B., Burton M., Nicholas B., Fukui Y., Walsh A., Kawa- mura A., Horachi H. & Sano H., 2012, MNRAS, 419, 251-266

Maxted, N., Rowell G., Dawson, B., Burton, M., Kawamura, A., Walsh, A., Sano, H., Lazendic, J., 2012, eds. F. Aharonian et al., AIP Conf. Proc. Vol. 1505, High Energy gamma-ray Astronomy Am. Inst. Phys., New York, p. 253

Maxted N., Rowell G., Dawson B., Burton M., Nicholas B., Fukui Y., Walsh A., Kawa- mura A., Horachi H., Sano H., Yoshiike S. & Fukuda T., 2013, MNRAS, in press

Maxted N., Rowell G., Dawson B., Burton M., Nicholas B., Fukui Y., Lazendic J., Kawa- mura A., Horachi H., Sano H., Walsh A., Yoshiike S. & Fukuda T., PASA, Manuscript being ﬁnalised

Signature Date

6 0.3 Acknowledgements

Like a cosmic ray moving through magnetic turbulence, my PhD candidature was not without its ups, downs and other unexpected directions, but a number of people helped to keep my path rigid. Firstly, I would like to thank my supervisor Dr Gavin Rowell, who managed to find enough time between raising two children (8 or 9 if you include honours, masters and PhD students) to guide me over the past few years. He was very generous with his time and knowledge, and I very much appreciate the opportunity to not only learn from an expert in the field, but also to travel to locations in Australia, Africa and Europe. Of course, anyone who is part of the astrophysics group in Adelaide will inevitably end up owing Professor Bruce Dawson a great deal of gratitude for always possessing the will to consider any problem very deeply, often revealing layers of complexity previously over-looked in hours of independent pondering. But, I had the additional pleasure of having him as a co-supervisor who would take it upon himself to commit to reading through my drafts over his, perhaps otherwise free weekends, while cheerfully pouring me schooners of beer (un-tampered-with) at the staff club on many Friday nights. Fellow student, Brent Nicholas can perhaps be considered as a third supervisor in some ways. My research sometimes directly stood on the shoulders of his, allowing me to withdraw from his knowledge-bank of mathematical and computational techniques. Brent, having already gone through code-writing and painful trial and error processes, undoubtedly saved me time in the office equivalent to months (minus the time taken for extra coffee + doughnut breaks). Dr Andrew Koerber, from the department of mathematics at the University of Adelaide, was particularly helpful when considering the solution to the diffusion equation. It seems that what was, for me, a relatively difficult procedure, was rather straight forward for Adrian, who was very patient in explaining the process and coding the very first version of what later became my diffusion code (although I still consider it his when things don’t work as expected). Extending my gratitude to the Eastern states, I would like to acknowledge Professor Michael Burton (The University of New South Wales) and Dr Andrew Walsh (James Cook University, Townsville) for their invaluable guidance towards/through the very inhumane, but important process, of peer-review. Michael especially made sure to never leave questions half-answered, always inching my research beyond previous self-imposed limits. Following the Eastern states, I must thank the ‘East’. Professor Yasuo Fukui (The Uni- versity of Nagoya) and his group, partly comprised of Akiko Kawamura, Hirotaka Horachi and Hidetoshi Sano were very important collaborators, never hesitating to send Nanten and Nanten2 radio telescope data to the Adelaide group, while aiding in the editing process of submitted papers. I must make a special mention of Hidetoshi Sano, who checked calculations and generated new data for me. It was very helpful to have the option of walking into office 413, where fellow PhD students, Mathew Cooper, Alexander Herve and Tom Harrison were always willing to pause work (or other miscellaneous activities) to solve a programming problem of mine. I must particularly mention Mat’s outstanding C++ coding ability. I must thank all other people around the university for making the environment a friendly and productive one. Professor Roger Clay for making the whole operation run smoothly and his wife Marianne for her moral support and interesting discussions. Furthermore I must thank all the other staff and students who I ate lunch with, drank coffee/beer with and even occasionally went jogging with: Jarrad Denman, Justin Bray, Phoebe de Wilt, Mark Aartsen, Cheryl Au,

7 Phillip Wahrlich, Ben Whelan, Kerri Budd, Vanessa Holmes, Peter Warland, Fabien Voison, Jaryd Hawkes, Gary Hill, Jose Belido, Greg Thornton, Max Malacari, Steven Saﬃ and Tristan Sudholtz. All of you made the astrophysics group a fun and productive collective. Finally, I must thank my mother and father, Elizabeth and Raymond Maxted, who were always very willing to make sacriﬁces and encourage me through my education. Without them, I certainly wouldn’t have written this thesis.

8 Chapter 1

High Energy Astrophysics

1.1 Introduction and Motivation

Our Earth is under constant bombardment by cosmic rays, protons and nuclei that travel

at speeds close to that of light (see § 1.2). Although these are mysterious in origin, clues can be found through the use of detectors that observe particle showers initiated inside our atmosphere (see e.g. the caption of Figure 1.2). A probable source of galactically-accelerated cosmic rays is first order Fermi acceleration in the shocks of supernova remnants (SNRs), as this scenario is consistent with the observed cosmic ray spectrum both energetically and spectrally (e.g. Blandford & Ostriker, 1978). The link between SNRs and galactic cosmic rays cannot easily be proven via cosmic ray experiments that examine arrival directions, as path deviations caused by the galactic microgauss-order magnetic fields are significant (with cosmic rays having a gyroradius of 1pc at 1015 eV). This means that particles retain little or no directional ∼ information, hindering the possibility of simply observing arrival directions to obtain source positions. Alternately, cosmic ray collision by-products such as neutrinos and gamma-rays (see

§ 1.3) are potentially useful as markers of cosmic ray acceleration because they travel in straight paths, retaining information about their origin. Of these two by-products, gamma-rays have so far proved to be the most useful in galactic observations, being considerably easier to detect.

H.E.S.S., a gamma-ray observation experiment (see § 1.4) located in Göllschau, Namibia, is able to acquire gamma-ray (few hundred GeV to hundreds of TeV) source directions and has managed to trace a significant gamma-ray excess associated with several SNRs and SNR candidates. Sometimes these gamma-ray detections even display shell-like characteristics, but much information is needed about the structures and local environments before the precise mechanisms that gives rise to the gamma-ray emission can be concluded with certainty. Obser- vations at other wavelengths should aid in deciding whether HESS gamma-ray detections are due to leptonic (inverse Compton) or hadronic (neutral meson decay) processes (or indeed a combination of both). Observations of matter (atomic and molecular) around source regions are a key ingredient in the study of cosmic ray acceleration for several reasons. Firstly, first-order fermi acceleration of cosmic rays within SNRs requires the supernova blast-wave to interact with matter to create a shocked environment. Secondly, matter may act as target material for cosmic ray protons, creating gamma-ray emission, so gamma-ray emissivity is intrinsically linked to the mass of gas. Finally, the dynamics of magnetic fields, which alter the motion (and sometimes the energy) of energetic charged particles, can be linked to interstellar gas. To build a complete picture of cosmic ray acceleration, this thesis examines the gas towards SNRs.

9 On a large scale, the Milky Way contains matter in forms that range from hot ionised gas and plasma, to sparse atomic gas, to dense organic molecules and dust.This thesis puts

particular emphasis on the detection of molecules using Earth-based radio telescopes (see § 2),

especially the Mopra instrument (§ 2.7.1) located in New South Wales, Australia. With this telescope, dense gas can be located and molecular gas parameters can be calculated. Using this knowledge, the gas mass (which may be linked to gamma-ray emissivity) may be calculated, allowing an investigation of the cosmic ray density towards SNRs. Furthermore, an examination of the transport of cosmic rays into dense gas can be undertaken, allowing the prediction of possible observable features in gamma-rays and inferences about the local high energy particle populations (electrons/protons). A multi-wavelength approach can build a picture of the high energy particle density, matter distribution, magnetic ﬁeld strengths and shock-structure towards SNRs and SNR candidates, allowing cosmic ray diﬀusion properties to be constrained and a more detailed description of the nature of distant high energy processes. This may bring us closer to a model for the origin of galactic cosmic rays.

1.2 Cosmic Rays

Ever since Victor Hess ascended in a hot air balloon to measure an atmospheric ionisation rate that increased with altitude (Hess, 1912), people have been aware of cosmic rays (CRs), protons and nuclei that travel at speeds close to that of light (in this thesis, we will refer only to high energy hadrons, ie protons and nuclei, as CRs, and specify when discussing high energy leptons, ie electrons and positrons). The energies of detected particles can exceed 1020 eV ∼ (e.g. Abreu et al., 2010; Abu-Zayad et al., 2012), although the ﬂux of these particles can be seen to drastically decrease with energy, with CRs above GeV (109 eV) energies being more frequent than 1 m−2 s−1 and CRs above 1020 eV being less frequent than 1 km−2 century−1 (solid angle π sr). It follows that CR experiments∼ require large collecting areas to study the the highest energy∼ CRs. Figure 1.1 includes a visual representation of the electromagnetic spectrum. A typical high- school text book will often have a scale that concludes at wavelengths as small as λ 10−12 m (gamma-ray wavelengths), but this can be considered as cutting the spectrum in half∼ (in log- space) from the point of view of astrophysicists working in high energy ﬁelds! At these wavelengths, speaking in terms of energy is more appropriate. The spectrum (Figure 1.1) has been extended to include the high-energy regime of physics. Although cosmic rays are by no means part of the electromagnetic spectrum, they, like light, transmit information over large distances and expand the scale of energies accessible by astronomers to 24 orders of magnitude. Fur- ∼ thermore, cosmic rays encapsulate an energy density similar to that of starlight ( 1 eV cm−3), so cannot be ignored when considering the dynamics of the galaxy and indeed, the∼ universe.

1.2.1 The Cosmic Ray Spectrum Figure 1.2 illustrates the power law nature of the CR energy spectrum observed from Earth. The diﬀerential energy spectrum may be represented as dN E−γ (1.1) dE ∝

10 Visible Light

VHFVHF UHF FM Radio Radiotelescopes

Wavelength (m)

3 1 −1 −3 −5 −7−9 −11 10 10 10 10 10 10 10 10 Radio waves Ultraviolet Microwaves γ rays Infrared Xrays

5 7 9 11 13 15 17 19 10 10 10 10 10 10 10 10 Frequency (Hz)

The Large Hadron Collider Medical Xray Extragalactic Machines Uranium Fission Galactic Cosmic Rays Cosmic Rays Energy Release And γ rays

3 5 7 9 12 15 17 19 21 10 10 10 10 10 10 10 10 10 Energy (eV)

Figure 1.1: The electromagnetic spectrum (middle) that includes naming conventions for different wavelengths/frequencies of electromagnetic radiation. At the highest frequencies, it is more typical to use units of energy (bottom). Note that cosmic rays are composed of matter and not part of the electromagnetic spectrum. where N is the CR count, E is the CR energy and γ is the spectral index. Equation 1.1 describes the drastic reduction in CR flux for higher CR energies. The CR spectral index at Earth changes slightly with energy, but it generally stays between 2.5 and 3 in the energy range displayed, so in Figure 1.2 the flux, dN/dE, has been multiplied∼ by E2∼. This allows spectral variations usually less apparent on the CR energy spectrum to be highlighted. Of particular relevance are the ‘knee’, ‘ankle’ and high-energy cut-off. In Figure 1.2, the CR spectral index is γ =2.7 until the knee at an energy of 4 PeV (4 1015 eV), where there is a transition to a steeper ∼ × spectrum of spectral index γ 3.3 (Abraham, 2010). At the ankle, at 4.1 EeV (4.1 1018 eV), the spectrum flattens to γ ∼2.6 (Abraham, 2010), before a steep (γ∼ 4.3) cut-off× occurs at 29 EeV. ∼ ∼ ∼ The knee and ankle features of the CR spectrum are suggestive of a superposition of more than one source population. It’s possible that galactic sources such as shell-type supernova rem-

nants (SNRs, see § 1.2.4) and pulsar wind nebulae (PWN) produce CRs in the 1 GeV-100 TeV energy range, while extragalactic sources such as Active Galactic Nuclei (AGN) produce the highest energy CRs. Effects of propagation through galactic magnetic fields may also contribute to some of these spectral features, as CRs either escape or are retained within our local magnetic region. CRs may also interact with particles and photons in different, energy-dependent ways. This thesis mainly addresses CRs accelerated within the galaxy (1 GeV-100 TeV energy range).

11 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 1.2: Taken from Olinto (2012), this shows the diﬀerential cosmic ray energy spectrum as observed by the CR experiments, ATIC (Ahn et al., 2008), PROTON (Grigorov et al., 1971), RUNJOB (Apanasenko, 2001), Tibet ASγ (Cheng, 2008), KASCADE (Kampert, 2004), KASCADE-Grande (Apel, 2011), HiRes-I (Abbasi, 2009), HiRes-II (Abbasi, 2008), and Auger (Abraham, 2010; Kotera et al., 2011). The x-axis is the logarithm of the CR energy, while the y-axis is the CR ﬂux (count m−2 s−1 sr−1 eV−1) multiplied by the square of the energy (see text for explanation) .

1.2.2 Cosmic Ray Propagation Cosmic rays (CRs) are generally charged particles, as a charge is presumably necessary in the acceleration process. Neutrons can be CRs, but only resulting from CR collision by-products. Even so, the short mean life of a free neutron (885.7 0.8s in the particle’s rest frame, Yao ± et al., 2006) sets limits on the distance a CR neutron can travel before beta-decaying into a proton (although due to relativistic eﬀects, this range increases with energy). Thus, it is reasonable to assume that most CRs are charged. Charged particles are susceptible to the eﬀects of electromagnetic force, as described by the Lorentz equation,

F = q(E + v B) (1.2) × where q is the cosmic ray charge, E is the electric field vector, B is the magnetic field vector and v is the cosmic ray velocity vector. In the galactic medium, magnetism is usually the dominant force, so the electric field term in Equation 1.2 can be neglected (with the exclusion of the local regions of pulsars). To derive an approximation for the expected deviation of a cosmic ray from a rigid path due to a perpendicular magnetic field, B⊥, the equation for centripetal

12 force, Equation 1.3, can be inserted into Equation 1.2. mv2 F = (1.3) r As cosmic rays are relativistic particles, we let v c and m E/c2, where c is the speed of light, yielding gyroradius, → → (E/[J]) (E/[J]) (E/[eV]) rg = = = (1.4) qcB⊥ ZecB⊥ ZcB⊥ where Z is the atomic number of the cosmic ray nucleus and e is the charge of a proton (Note the switch between J and eV, when 1/e was absorbed into E). The gyroradius is the radius of the circular path made by a charged particle under the influence of a constant, perpendicular magnetic field. The magnetic field present in the galaxy can be composed of regular and turbulent components of order 1 µG and above (Han, 2009), corresponding to a gyroradius of 1pc for a cosmic ray with an∼ energy of 1015 eV. If the gyroradius is a good indicator of the expected∼ level of deviation of a cosmic ray from a straight path, it is likely that cosmic rays retain little to no directional information for galactic cosmic ray energies. As a consequence, the possibility of simply observing arrival directions to obtain source positions is not feasible. Alternately,

cosmic ray collision by-products such as neutrinos and gamma-rays (§ 1.3) are potentially useful as markers of cosmic ray acceleration, because they travel in straight paths. By observing

gamma-rays with instruments such as HESS (§ 1.4), the nature of high energy particle populations in other parts of the galaxy can be studied, particularly in the vicinity of suspected cosmic ray-acceleration sites.

1.2.3 Cosmic Ray Acceleration One of the great unsolved mysteries in astrophysics is the origin of cosmic rays; where and how particles are accelerated up to energies above 1020 eV. Much of this section addressing the issue of CR acceleration is taken from Protheroe (2000). On examining Equation 1.2, it becomes clear that since magnetic forces do not change the energy of particles, electric fields must be responsible for cosmic ray acceleration, but a strong electric potential, like that required to do so, would be difficult to maintain in a place where free ions can quickly move to neutralise such strong electrostatic fields. The solution to this dilemma is given by the Maxwell-Faraday (Faraday’s law of induction) equation, which describes the electric fields induced by changing magnetic flux. The integral form of this equation is ∂ E(r,t) dl = B(r,t) dA (1.5) · −∂t · IS ZS where dl is the path around a surface, S, through which there is a changing magnetic flux, and A is the cross-sectional area of the surface, S. This may be applicable to astrophysical situations where magnetic fields, frozen-into moving gas, may also be transported with the gas. Noting that the area, A, of an expanding surface, S, swept up by segment, dl, when moving at velocity, v , is given by dA = dl v dt, we get bulk × bulk E(r,t) dl = B(r,t) (dl v ) (1.6) · − · × bulk IS IS

13 A simple rearrangement using vector identities X (Y Z)= Y (Z X) and X Y = Y X yields · × · × × − × E(r,t) dl = v B(r,t) dl (1.7) · bulk × · IS IS Assuming that the magnetic field is constant and moving in a direction perpendicular to itself (which might be the case for an expanding magnetic field of a SNR), we can estimate that the maximum electric field able to be produced by a moving magnetic field is

dE d = (F ds) dt dt · = F v · = qE v (1.9) · where v is the velocity of the particle. By combining Equations 1.8 and 1.9, an expression for the maximum energy-gain rate can be approximated as qvvbulk B . By making the particle and magnetic flux-carrying material velocities equal to c,∼ a maximum| | acceleration-rate can be approximated, dE = ξZec2 B (1.10) dt | | acc where we have used q = Ze and where ξ <1 is called the “acceleration rate parameter” and is dependent on the source type. This approximation allows an estimate for the possible change in energy of a particle due to the influence of a magnetised astronomical body, within a period of time. This is merely a guide and does not take into account the size of a magnetic structure, nor possible mechanisms that cause energy-loss, but we can insert plausible values corresponding to a SNR into the above equation (∆t = 103 yr, B = 10 µG= 10−9 T) to get a change in energy of ∆E 1018(ξZ) eV. It follows that SNRs are plausible sites for CR acceleration up to energies of 1018∼eV. ∼ 2nd-order Fermi acceleration (in clouds) It has been established that moving magnetic fields (tracing gas) are a likely cosmic ray acceleration mechanism. SNRs were proposed as a possible acceleration site, but before this was seen as plausible, a formulation involving moving clouds was suggested and we consider this first for reasons that will become clear later. Fermi (1949) proposed a mechanism where particles enter moving magnetic clouds, are scattered at random, and some exit with a net gain in energy. Diffuse regions of gas inhabit the Galactic medium. These clouds often have local random velocities of 15 kms−1 and contain magnetic fields ‘frozen-in’ to associated ions and plasma ∼ (e.g. see Crutcher, 1999). A charged particle with energy, Ei enters a cloud that is moving at velocity V at an angle θi with respect to the cloud velocity (see Figure 1.3). The particle is scattered at random, eventually escaping the cloud at angle θf , with energy Ef . In the cloud frame, E′ = γ E (1 β cos θ ) (1.11) i cloud i − cloud i 14 V

Ef E f'

θ i θ f θ ' θ f' V i

Ei E i' Lab Frame Cloud Frame

Figure 1.3: A gas cloud containing magnetic turbulence is moving at velocity V as a charged particle with energy Ei enters at angle θi. The particle is scattered by magnetic turbulence, and exits with energy Ef at angle θf . Both the inertial frame of the ‘lab’ (left) and the cloud (right) are displayed.

2 where βcloud = V/c and γcloud =1/ 1 βcloud, and the scattering is collisionless, so no energy is gained by the particle, i.e. − p ′ ′ Ef = Ei = γ E (1 β cos θ ) (1.12) cloud i − cloud i But in the laboratory frame,

′ ′ Ef = γcloudEf (1 + βcloud cos θf ) ∴ E = γ2 E (1 β cos θ )(1 + β cos θ′ ) (1.13) f cloud i − cloud i cloud f Therefore, there is a change in energy in the lab (our) frame. The fractional change in energy of a charged particle between entering and exiting the cloud can be represented by ∆E E E = f − i Ei Ei ′ 2 ′ 1 βcloud cos θi + βcloud cos θ β cos θi cos θ = − f − cloud f 1 (1.14) 1 β2 − − cloud ′ Equation 1.14 is the fractional change in energy given some values of θi and θf , and ∆E/Ei can be positive or negative. The behaviour of entire populations of particles is more useful, so the average values of the various terms are considered. Assuming that the charged particle’s direction of travel on exiting the cloud is perfectly randomised due to multiple scattering events, ′ we can use cos θf =0. Calculating cos θi is a little more involved. Intuitively, ‘head-on’ collisions (i.e. particles travelling in theh oppositei direction to the gas cloud) may be expected to be more likely than ‘over-taking’ collisions.

15 Interstellar cloud V t θ i

v t L CP

Charged Particle

Figure 1.4: A charged particle at some distance, L, from a moving cloud, moves at velocity, ∼ vCP , to collide with the cloud at angle, θi.

Referring to Figure 1.4, we can ﬁnd the distance, L, in terms of the velocity of the cloud, V , velocity of the charged particle, vCP , time, t, and the angle of the charged particle path with respect to the cloud velocity vector as it enters the cloud, θi, (via the cosine rule) L2 =(Vt)2 +(v t)2 2V v t2 cos θ (1.15) CP − CP i

For a charged particle speed much greater than that of the cloud (for V vCP ), this can be approximated by, ≪ L (v V cos θ ) t (1.16) ≈ CP − i The rate of collision, R, can then be written n Lσ R = CP = n (v V cos θ ) σ (1.17) t CP CP − i where nCP is the moving free charged particle density and σ is the cross-sectional area of the cloud. Considering charged particles that are moving at speeds close to that of light, v c, CP → the collision probability, Pcol becomes P (1 β cos θ ) (1.18) col ∝ − cloud i The average value of variable, x, in a continuous function, f (x), is equal to xf (x) dx/ f (x) dx. Applying this to find the average value of cosθ , i R R cos θ P d(cos θ ) cos θ = i col i h ii P d(cos θ ) R col i cos θ (1 β cos θ ) d(cos θ ) = R i − cloud i i (1.19) (1 β cos θ ) d(cos θ ) R − cloud i i R 16 For -1< cos θi <1, this simplifies to β cos θ = − cloud (1.20) h ii 3 ′ Inserting Equation 1.20 and cos θf =0 (see above) into Equation 1.14, ∆E 4β2 h i cloud (1.21) Ei ≈ 3 Thus the average energy change is positive, and a population of particles will, on average, be accelerated. Since the energy gain of the particle population is proportional to the square of βcloud, this process was named ‘2nd-order’ Fermi acceleration. This process likely occurs in nature, but the average energy gain is so small (because βcloud is <<1) that it cannot account for the observed flux of CR rays. Despite this, the theory is a good starting point on which to base a more efficient acceleration theory.

1st-order Fermi acceleration (in shocks) In 2nd-order acceleration, particles gain energy in an approaching collision and lose energy in an ‘over-taking’ collision. Because particles are more likely to have head-on collisions than over-taking, the overall result is a slow gain in energy of a population of particles. 1st-order acceleration in astrophysical shocks, on the other-hand, doesn’t include over-taking collisions, so all collisions impart a positive energy gain. Rather than rely on energy-gain collisions out- numbering energy-loss collisions, like in the 1st-order fermi process, the 2nd-order fermi process involves only energy-gain collisions. This and the larger velocities involved (shock front vs cloud motion) in the 2nd-order process mean that 2nd-order fermi is a faster acceleration mechanism.

Figure 1.5 is a cross-section of an astrophysical shock which contains many magnetic inhomogeneities that act to inelastically scatter charged particles on a small-scale. Such scatterers may have the eﬀect of forcing the particles to cross the shock-front from upstream (in the region forward of the shock motion) to downstream (in the region behind the shock motion) and back again. The particle may cross the shock many times until it escapes the system. The rate (in units of m−2s−1) that charged particles cross from upstream to downstream, RU−D, and downstream to upstream, RD−U , can be expressed as R (θ )= n v cos(θ ) U−D i − CP CP i ′ ′ RD−U θf = nCP vCP cos θf (1.22) where nCP is the density of charged particles, vCP is the velocity of the charged particles, θi is the angle between the directions of the particle and shock motion upon moving downstream ′ in the lab frame (π/2 < θi < π) and θf is the angle between the directions of the particle and ′ shock motion upon moving upstream in the frame of the shock (0 < θf < π/2). On average, the relative change in energy of a charged particle (Equation 1.14) crossing a shock becomes ′ 2 ′ ∆E 1 βejecta cos θi + βejecta cos θ β cos θi cos θ h i = − h i h f i− ejectah ih f i 1 (1.23) E 1 β2 − i − ejecta ′ where βejecta = Vejecta/c. It can be shown that cos θi = 2/3 and cos θf = 2/3. Following the same logic as with Equation 1.14, the aboveh equationi simp− liﬁes toh i

∆E 4 4 Vejecta h i = βejecta = (1.24) Ei 3 3 c

17 Upstream Shock Downstream

Vejecta

E E i i θ i

E Vejecta i

Vejecta

Ef θ f

Vejecta Vejecta Ef Vshock V shock R

Figure 1.5: CR-scattering magnetic inhomogeneities in a shocked region. Mass ejecta and shock velocities are represented by Vejecta and Vshock respectively. Vshock/R is the velocity of matter downstream of the shock, where R is the compression ratio. Note that the particle crosses the shock many times, but for simplicity, in the diagram the particle is shown to cross the shock only twice.

Thus, the energy gain is proportional to the speed of the ejecta material. By relating the ejecta speed to the shock speed and calculating the likelihood of particles escaping the shock as a

function of energy (see §A.1.1), the resultant integral and diﬀerential CR energy spectra can be found, 3 Q ( k) E R−1 (1.25) ≥ ∝ and

3 −1 Q (k) E( R−1 ) ∝ − 2+R E R−1 (1.26) ∝ respectively, where Q is the energy spectrum of a population of particles and R is the com-

pression ratio (the ratio of the shocked gas density to the unshocked gas density, see §A.1.1 for details). The CR differential spectral index is thus modelled as, 2+ R Γ= (1.27) −R 1 − The compression ratio is R = 4 for strong shocks, so the theoretical CR source spectrum has a differential spectral index of Γ 2. Some discrepancy in source spectral index can be expected ∼ 18 between models due to uncertainties in the dynamics of shocks and the interstellar medium (e.g. Marcowith et al. (2006) with Γ 2.3). On Earth, however, the observed CR spectrum has a spectral index of 2.7. The collective∼ effect of numerous CR sources may contribute to this ∼ discrepancy, but energy-loss mechanisms during the propagation from source to Earth are also significant. Heavy CR nuclei (e.g. Fe, C, O) are expected to spallate in collisions, producing lighter secondary CR nuclei (e.g. Li, Be, B). This acts to steepen the CR energy spectrum. The theory above, at the very least, demonstrates that astrophysical shocks can produce power-law spectra, with slopes close to that observed. More detailed theories are beyond the scope of this thesis. The discussion does illustrate the potential connection between CRs and astrophysical shocks, and motivates observations of supernova remnants.

1.2.4 Supernova Remnants Arguably, one of the most obvious places to search for evidence of ﬁrst-order Fermi acceler-

ation in astrophysical shocks and the origin of CRs (§ 1.2), is towards the remains of some exploded massive stars (&9 M⊙), shell-type supernova remnants (SNRs). Such explosions feature a rapidly expanding magnetised shock that may interact with gas to create the conditions

necessary for 1st-order Fermi acceleration (see § 1.2.3). The energy ﬂux of cosmic rays escaping the Galaxy is 3 1040 erg s−1 (Mewaldt, 1983), thus, if we assume that SNRs are the primary source of CRs,∼ the× Galactic SN rate of 3 104 My−1 would imply that 3 1049 erg of energy must be injected into CRs by each Galactic∼ SNR× to keep × the total Galactic CR energy content constant (Blandford & Eichler, 1987). A SN explosion releases an energy of 1051 erg into its ejecta mass, so only 3% of its energy is required to ∼ ∼ be transferred into the CR energy spectrum for SNRs to plausibly be the primary source of

Galactic CRs. First-order fermi acceleration (see §1.2.3) may be responsible for such a transfer of energy.

Core-collapse supernova (Type Ib, Ic and II):

A star of mass 9-20 M⊙ goes through various stages of fusion until an inert core of iron and nickel grows∼ in size to a point when gravitational forces within the core overcome the electron-degeneracy pressure. The core quickly collapses until electrons and protons merge to form neutrons and the core becomes supported by neutron degeneracy pressure, halting the collapse. The infalling outer layers of the star ‘bounce’ as energetic neutrinos (as a copious product of neutron production) are produced and move outwards (e.g. Woosley & Janka, 2005), triggering a powerful shockwave that accelerates the surrounding star mass to speeds on the order of 10 000 kms−1. Such radially-expanding ejecta interacts with the surrounding ∼ interstellar medium and is referred to as a supernova remnant. The diﬀerent classiﬁcations (types Ib, Ic and II) for core-collapse supernovae are based on observational spectral information, which depends on elemental abundances of supernovae ejecta (e.g. Woosley & Janka, 2005). For stars with mass greater than 20 M , core collapse is not expected to be halted by ∼ ⊙ neutron-degeneracy pressure, but continues until the centre compresses under gravity to form a black hole. Above 40 M , models predict that gravitational forces may even be so large that ∼ ⊙ no ejecta would be released (i.e., no supernova remnant) (Fryer, 1999).

19 Type Ia supernovae Type Ia supernova remnants are caused by white dwarves that accrete matter from a neighbouring star (like one that is part of a binary star system) until carbon fusion is initiated and a supernovae explosion occurs (Wheeler & Harkness, 1990). These explosions are consistently 5 ∼ billion times brighter than the sun and can be used as ‘standard candles’ to calculate distances by using Equation 2.25 (or some variation of this equation). Type Ia, Ib, Ic and II supernova remnants can all potentially result in shell-type supernova remnants, possibly capable of accelerating CRs.

Hypernovae Hypernovae are a class of supernovae observed to have blast energies 5-50 larger than ∼ × ordinary supernova explosions. The term ‘hypernova’ is commonly linked to the speciﬁc case of an over-luminous Ic explosion (Iwamoto et al., 1998, 2000; Mazzali et al., 2002), but may also be linked to type II events with speciﬁc H spectral features (Type IIn SN) (Smith, 2010).

Further details about hypernovae are presented in §A.1.2.

Pulsar Wind Nebulae In a supernova event that results in the formation of a neutron star, angular momentum is conserved during the collapse of the progenitor core, so the neutron star spins rapidly. These neutron stars emit pulses of radiation and are referred to as pulsars. Pulsars are highly magnetized and may accelerate particles near the surface via voltages between separated charges at either the pulsar polar caps or in regions near these areas, although the exact mechanism is not well-understood (Gaensler & Slane, 2006). Rotational energy from the pulsar is gradually transferred into a wind of changed particles that ﬂows radially outwards, interacting with surrounding ISM gas or SNR ejecta, creating a termination shock that may

produce synchrotron radiation (see §1.3.1). This shock wave may accelerate particles to create gamma-ray emission, like in the case of the Crab Nebula (e.g. Aharonian et al., 2006).

1.3 Processes Responsible for High Energy Emissions

In astronomy, much of the electromagnetic radiation that we observe is from thermal sources that adhere to black-body spectra (Equation 2.27). Thermal masses emit radiation with peak frequencies proportional to temperature and total intensity proportional to the fourth power of

temperature (see § 2.3). Sometimes, observed radiation does not actually ﬁt this thermal picture and the population of emitting particles does not conform to a Boltzmann distribution. Such sources are referred to as ‘non-thermal’. Some common non-thermal energy-loss processes, both leptonic (from electrons and positrons) and hadronic (from protons and nuclei) are outlined in this section, which is composed of material referenced from Rybicki & Lightman (1979), Stanev (2004) and Gabici et al. (2009).

20 1.3.1 Synchrotron Emission Synchrotron emission occurs as high energy charged particles are accelerated by magnetic ﬁelds, and is most signiﬁcant for leptons. The average energy loss by a charged particle of Energy, E, via synchrotron emission is dE 4 = σ cU γ2 (1.28) dt −3 T B 2 where UB = B /2µ0 is the magnetic energy density, γ is the Lorentz factor of the particle 2 (E/mc ) and σT is the Thomson cross section,

8π q2 σ = (1.29) T 3 4πǫ mc2 0 where q is the particle charge, m is the particle mass and ǫ0 is the permittivity of free space. −29 2 For electrons, σT = 6.65 10 m . Equation 1.28 can be derived by finding the relativistic motion of a particle in a magnetic× field, calculating the acceleration perpendicular to the particle motion and averaging the resultant equation over all possible angles relative to the magnetic field direction (see for e.g. Rybicki & Lightman, 1979). The characteristic frequency of photons produced by this energy-loss mechanism is, 3 qB ν = γ2 sin θ (1.30) c 4π mc Synchrotron photons from TeV leptons are generally in the X-ray band and those from GeV leptons are generally in the microwave bands (for B 1 mG), although there is much variation for GeV electrons as they can traverse varied magnetic∼ field strengths (µG to mG), because they

can travel far from their sources (due to smaller cooling times, see §1.3.5) such that they can often be responsible for photons anywhere between radio and UV bands. Synchrotron radiation generally has a power law spectrum, reflecting the power law form of the population of leptons causing their emission. It can be shown (Rybicki & Lightman, 1979) that the ‘uncooled’ electron population spectral index, p, and the synchrotron emission spectral index, s, are related by, p 1 s = − (1.31) 2 Although, as the electron population evolves, higher energy radiation becomes less prominent, and synchrotron spectra gain a characteristic turn-over in power-law behaviour. Synchrotron radiation is a good indicator of the presence of magnetic fields, but will sometimes be super- imposed with thermal spectra, making it more difficult to identify components.

1.3.2 Inverse Compton Scattering Inverse Compton Scattering is a process (more signiﬁcant to leptons than hadrons in astrophysics) that involves the transfer of energy from an energetic particle to a photon. The average energy loss rate via inverse Compton scattering inside an isotropic radiation ﬁeld (such as the cosmic microwave background) is (Moderski et al., 2005)

dE 4 = σcU γ2 (1.32) dt −3 rad

21 where Urad is the radiation density, γ is the electron Lorentz factor and σ is the interaction cross- section, which is equal to the Thompson cross-section, σT (Equation 1.29), when the electron energy is much less that the rest mass energy. If this is not the case, we must move into the Klein-Nishina regime, where a high-energy suppression is imposed (Moderski et al., 2005), producing a high energy cut-oﬀ in the gamma-ray spectrum at 50 TeV (for CMB photons). ∼ The total Klein-Nishina cross-section (Longair, 2011) is, 1 2(x + 1) 1 4 1 σ = πr2 1 ln(2x +1)+ + (1.33) KN e x − x2 2 x − 2(2x + 1)2 2 2 2 where x = ~ω/mec and the classical electron radius is re = e /(4πǫ0mec ). The Klein-Nishina cross-section can be approximated as, 1 1 σ = πr2 ln(2x)+ (1.34) KN e x 2 in the ultrarelativistic (γ >> 1) limit. The approximate resultant photon energy from inverse-Compton scattering is,

E γ2ǫ (1.35) γ ≃ i where Eγ is the emitted gamma-ray energy and ǫi the initial photon energy. Like with synchrotron radiation, the inverse Compton energy spectrum reflects the energy spectrum of the emitting population. In regions with strong magnetic fields, less of the total electron population energy can flow to inverse Compton scattering, as Synchrotron losses become the dominant form of lepton energy loss. Taking the ratio of the energy loss rates due to inverse Compton (of CMB photons) in the Thompson regime and synchrotron processes, respectively, Aharonian et al. (1997) derive an approximation (for delta-function interaction cross-sections) relating the inverse Compton and synchrotron fluxes for a given magnetic field strength, F F sync (1.36) IC ∼ 10(B/10 µG)2 where FIC is the inverse Compton gamma-ray flux and Fsync is the synchrotron emission flux. Note that when magnetic field strength, B, is large ( 10 µG) synchrotron emission dominates. ∼ 1.3.3 Relativistic Bremsstrahlung Relativistic Bremsstrahlung (German for ‘braking’) radiation is emitted when high energy particles are accelerated by the electric fields of matter. The electron energy loss rate due to Bremsstrahlung radiation is

6 dE nZZ (Z +1.3) e 183 1 Eeρc = Ee 3 3 4 2 ln 1 + = (1.37) dt − 16π ǫ c m 3 8 − X 0 e Z 0 where Z is the atomic number of the target material, nZ is the number density of the target material, Ee is the electron energy, ρ is the density and X0 is the Bremsstrahlung radiation −2 length. X0 = 61.28 g cm for H2 (Z =1). In Galactic molecular clouds, synchrotron radiation tends to be the dominant mechanism for energy loss of TeV-energy electrons, because magnetic ﬁeld lines are generally ‘frozen-in’ to gas (Crutcher, 1999).

22 1.3.4 Neutral Pion Decay Pions are hadrons composed of two quarks (as opposed to protons, which have three). Three types of pions exist: positively charged, negatively charged and neutral. The charged variety quickly (mean life 10−8 s) decay into a muon and muon neutrino, but the neutral variety ∼ even more quickly decays into two gamma-ray photons (mean life 10−16 s, Schlickeiser, 2002). When a cosmic ray collides with a proton or nucleus, a shower of secondary∼ particles is produced. A significant proportion of the secondary particles produced are pions, with the population being roughly equally split between the 3 varieties (Allan et al., 1971). The average energy and typical number of pions produced depends on the energy of the initial interaction. The average energy loss-rate for a cosmic ray due to proton-proton collisions can be described by, dE =(n σ fc)E (1.38) dt p pp p where np is the target proton density, σpp is the total interaction cross section and f is the inelasticity for single interactions (f 0.5, Allan et al., 1971). f 0.5 implies that half of the ∼ ∼ cosmic ray energy goes into the creation of 10−5√E secondary particles (for cosmic ray energy >1 TeV) (Allan et al., 1971). ∼ Assuming a pure power law cosmic ray population producing pions via collisions, a resultant gamma-ray flux will tend to have a power law with an energy-dependent spectral index. Above a peak in the hadronic gamma-ray energy spectrum, at a few GeV (only accessible by low- spatial resolution space-based gamma-ray telescopes), the spectrum can appear to be a pure power law. This can cause difficulties when distinguishing a hadronic pion-decay scenario from a leptonic inverse Compton scattering scenario.

1.3.5 Energy-loss Timescales The above energy loss rates can be compared to one another by considering the approximate time taken for a particle to lose all its energy (assuming a constant energy loss rate), τ i ∼ E/(dE/dt), via some mechanism, i. This is referred to as a ‘cooling time’: synchrotron emission (leptons),

E −1 B −2 τ 1.3 105 [yr] (1.39) sync ∼ × TeV 10 µG inverse Compton emission (leptons),

−1 −1 8 Urad E τIC 3 10 [yr] (1.40) ∼ × eVcm−3 GeV bremsstrahlung (leptons),

n −1 τ 4 107 [yr] (1.41) brem ∼ × cm−3 and proton-proton scattering (hadrons)

n −1 τ 5.3 107 [yr] (1.42) pp ∼ × cm−3 23 When considering leptons with TeV energies in the ISM, bremsstrahlung emission is often not significant given such low gas densities (n 1 cm−3), and the synchrotron and inverse-Compton processes compete. In strong magnetic fields∼ (>10 µG), the synchrotron process can dominate and high energy electrons can emit non-thermal X-rays. In the absence of such strong magnetic fields, electrons may preferentially scatter low-energy photons to gamma-ray energies. Difficulties can arise, when attempting to discern between gamma-rays produced via inverse- Compton scattering by electrons and the decay of pions produced in proton-proton interactions. In the latter case, since CR hadrons require target particles to interact with, observations of interstellar gas (potential CR hadron target material) can help to distinguish between leptonic (electrons via inverse-Compton scattering) and hadronic (CR-hadrons via neutral pion production and decay) gamma-ray emission, via correlation studies of gamma-ray emission and gas. Hadronic gamma-ray emission is expected to exhibit overlap with gas, and be dimin- ished/absent towards regions with little/no gas. This is in addition to the examination of spectral characteristics, which may hold clues about the local particle population.

Shell-Type SNRs: Young vs Old When a shell-type SNR is young ( 103 yr), it has a small radius, so the blast energy and shock ∼ magnetic field are concentrated in a small volume, resulting in a fast ( 10000kms−1), highly- magnetised ( 0.1 mG) shock. During this phase, one might expect a∼ large local high energy particle enhancement∼ due to the shock . A high energy electron enhancement can be observed via strong non-thermal X-ray emission (see Chapter 4) and it’s possible that the same electron acceleration mechanism can accelerate hadrons too. High energy gamma-ray emission, which is often associated with young shell-type SNRs, may be expected from the inverse Compton mechanism, but this explanation is problematic, due to the presence of such strong magnetic fields making synchrotron radiation a more likely energy- loss mechanism. Figure 1.6 is a spectral energy distribution for a young SNR, RX J1713.7 3946. Leptonic models seem to provide a better fit to data than hadronic models, because the− latter predict a larger GeV flux than what is observed. This problem with hadronic models for RX J1713.7 3946 may be resolvable by accounting for the effects of dense gas (see Chapter 4) or by varying− the estimated CR source spectrum. As a shell-type SNR ages ( 104 yr), the shock speed and magnetic field strength decrease, and, with acceleration of particles∼ to TeV energies ceasing, the local population of high energy electrons is lower in energy due to synchrotron losses, and emit at lower frequencies. This means non-thermal emission from older remnants can be more prominent at radio wavelengths. Also, the shock has had more time to sweep through surrounding gas, transferring shock kinetic energy into turbulence and heat. It follows that at X-ray wavelengths, older remnants have a dominant thermal component.

For the cases of SNRs CTB 37A (see §5) and W28 (spectral energy distribution, Figure 1.7), there appears to be a strong case for a hadronic scenario, with the local CR enhancement remaining prominent relative to the high energy non-thermal electron enhancement (due to CRs not experiencing synchrotron losses, like electrons do). Furthermore, spatial variations in gamma-ray emission suggest a population of cosmic rays that has escaped the W28 SNR region, and moved into surrounding clouds (Aharonian et al., 2008). Recently, two GeV-bright shell-type SNRs W44 and IC443 were shown to have gamma-ray spectra consistent with hadronic origin mechanisms (Ackermann et al., 2013), providing the strongest evidence yet of a SNR origin for galactic CRs. Furthermore work by Uchiyama et al.

24 (2012) showed that the large spatial extent of GeV emission associated with W44 could not be explained via leptonic processes due to the non-detection of synchrotron radiation. The authors estimated a total kinetic energy of 0.3-3 1050 erg channelled into CRs escaping W44. × In this thesis, we use molecular spectroscopy to investigate the distribution of gas towards two SNRs, the young (age 103 yr) RXJ1713.7 3946 and the old (age 104 yr) CTB 37A. An ∼ − ∼ understanding of gas distribution may aid in the understanding of features seen in gamma-ray emission.

25 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 1.6: Two Spectral Energy Distributions (SEDs) taken from Abdo et al. (2011). Images include HESS and Fermi gamma-ray data points. The top image includes hadron-dominated SED models (authors indicated) predicted from HESS data, whereas the the bottom image includes lepton-dominated SED models (authors indicated) predicted from HESS data. The modeled SEDs pre-date the Fermi data-points, so may be considered predictions for the level of gamma-ray emission in the 1-100 GeV range. ∼

26 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 1.7: Spectral Energy Distributions (SEDs) taken from Abdo et al. (2010). Left) Mod- eled SEDs for W28 north-east. Right) Modeled SEDs for W28 south. In both SEDs, red points/regions represent Fermi data and black points indicate HESS data.

27 1.4 Gamma-Ray Astronomy with H.E.S.S.

The High Energy Stereoscopic System (H.E.S.S.) is an array of Cherenkov light detectors located in the Khomas Highland of Namibia. Four 13 m-diameter circular arrangements of mirrors collect light produced by secondary particles created by extra-terrestrial gamma-ray photons, allowing the direction and energy of the initial photon to be estimated. The HESS facility is shown in Figure 1.8. TeV gamma-rays cannot be observed directly from Earth’s surface like optical or radio- wavelength electromagnetic radiation due to the attenuative properties of the atmosphere, but unlike X-rays and low energy gamma-rays, TeV photons are too low in ﬂux to be success- fully detected by aperture-limited satellite-based detectors. To observe TeV photons, detectors that monitor the Cherenkov light from secondary particles of photon-initiated atmospheric air- showers are employed. Air-shower simulations allow parameters associated with Cherenkov

images (see § 1.4.2) to be separated into a ‘signal’ and a ‘background’, to eﬀectively do gamma- ray astronomy of sources where the statistics are favourable (i.e. a large enough gamma-ray ﬂux). With the Earth’s atmosphere as an aperture, the HESS gamma-ray telescope has a 5 2 collecting area of 10 m (due to a broad Cherenkov light pool, see § 1.4.2). ∼

A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 1.8: (HESS website, 2009) The four Cherenkov light detectors of the High Energy Stereoscopic System (HESS 1) in the Khomas Highland of Namibia. These instruments are placed on the corners of a square with sides of 120m at an altitude of 1.8km (Aharonian et al., 2006).

1.4.1 Extensive Air Showers High energy cosmic rays and gamma-rays inevitably interact with the Earth’s atmosphere and trigger secondary showers of particles in the atmosphere. Cosmic-ray initiated showers diﬀer in composition to gamma-ray initiated showers. Examples of the two types of extensive air shower can be viewed in Figure 1.9. Before gamma-ray sources can be found, cosmic ray events must be identiﬁed and preferentially discarded.

Electromagnetic Extensive Air Showers Secondary showers initiated by gamma-ray photons are entirely comprised of an electromagnetic component, where gamma-ray photons interact with an atmospheric nucleus via the pair production mechanism to create electron-positron pairs, and these electrons and positrons interact

28 Figure 1.9: Taken from V¨olk & Bernl¨ohr (2009). Black lines represent the path of secondary particles and photons. Left: A simulation of a 300 GeV gamma-ray-initiated extensive air shower, which consists of an electromagnetic component. Right: A simulation of a 1 TeV cosmic ray proton-initiated extensive air shower, which consists of not only an electromagnetic component, but a hadronic component.

with atmospheric nuclei via the Bremsstrahlung process (see § 3.13) to create more gamma-ray photons, in a cyclic process. This process persists, exponentially inﬂating the total number of shower particles/photons until the particle energies become less than a critical value, where lower energy processes such as ionisation begin to dominate. The Heitler model (Heitler, 1954) is a simpliﬁcation of a secondary shower, useful for modelling purposes. In the Heitler model, the interaction length, λ (in g cm−2), for the Bremsstrahlung and pair production processes are assumed to be equal (true to within 25%), and it is assumed that energy is always split evenly between particles/photons in any∼ single interaction, i.e., that a Bremsstrahlung photon carries away half of a lepton’s energy, while pair production results in two leptons of equal energy (half that of the photon, minus the electron and positron rest energy). Figure 1.10 is an illustration of the Heitler model of an electromagnetic extensive air shower. The number of secondary particles/photons in the shower doubles after each interaction length, λ, so it grows exponentially, with the number of secondary particles/photons being 2n, where n is the number of interaction lengths, λ. It follows that the energy of the secondary particles/photons is E E(n)= 0 (1.43) 2n

When particle/photon energy, E(n), reaches a critical energy, Ec, where ionisation losses begin

29 Figure 1.10: The Heitler model for electromagnetic air showers. X is the shower depth in terms of interaction length, λ, and E0 is the energy of the primary incident gamma-ray. Image courtesy of Nicholas (2012b). to dominate, the number of particles/photons comprising the shower begins to decline, thus the maximum number of particles/photons in the shower is,

Nmax = E0/Ec (1.44)

This expression demonstrates that Nmax is proportional to the initial energy of the gamma- ray, E0, an important result for the approximation of energy by studying secondary particles. By noting that the maximum depth of the shower is, Xmax = nλ, we can derive an alternate expression for maximum particle/photon number,

Xmax Nmax =2 λ (1.45) and use these two expressions for Nmax to derive an expression for the maximum depth of the shower, log E0 Ec X = λ (1.46) max log(2) This demonstrates that the atmospheric depth at shower maximum is approximately proportional to log(E0), a result that is important for energy reconstruction.

Hadronic Extensive Air Showers Cosmic rays, like gamma-rays, also give rise to showers of secondary particles, but these tend to diﬀer in composition due to the additional hadronic mechanisms involved (meson production and decay). The diﬀerence occurs because cosmic rays, being protons or nuclei, can interact via strong nuclear force, creating a hadronic component, which itself spawns an electromagnetic component. The processes involved in the hadronic component of a shower have longer

30 interaction lengths than those involved in electromagnetic showers, meaning that generally the maximum particle number of a shower is reached lower in the atmosphere than for gamma-ray initiated showers. Initially, a p-p interaction produces charged pions, π±, and neutral pions, π0, and other nucleons. The nucleons can subsequently interact via p-p interactions in a similar way. The charged pions decay into a charged muon-neutrino pair. The charged muons can then decay into electrons/positrons, while neutrinos are unlikely to interact. The neutral pions quickly decay into gamma-ray photons (2 per neutral pion), which can pair-produce to spawn electron- positron pairs, and an electromagnetic component to the secondary shower. Figure 1.11 is a diagram of a hadronic shower. The inelastic processes occurring in the hadronic component of

Figure 1.11: The Heitler model for hadronic air showers. Image courtesy of Nicholas (2012b). a shower lead to more of a lateral spread in the shower structure, allowing cosmic-ray initiated showers to be distinguished from gamma-ray initiated showers, although a large variation in the structure of cosmic-ray initiated showers does result in some ‘gamma-ray-like’ (CR initiated events that have characteristics of gamma-ray initiated events) events, which are diﬃcult to identify.

1.4.2 Cherenkov Imaging Along the path traced by a high-energy charged particle, electrons in atmospheric molecules are displaced by the electromagnetic disturbance. These electrons emit photons as they return to their equilibrium positions. In normal circumstances (velocity of particles < c) destructive interference occurs between these photons, but if the particle is moving faster than the speed of light in the local medium, constructive interference occurs in a scenario analogous to a sonic boom. This light, known as Cherenkov light, can be utilised in gamma-ray observatories like HESS. From classical geometrical arguments, Cherenkov light from a single particle can be shown to be emitted in a conical shape adhering to equation 1.47.

31 1 c c cos θ = , forv> (1.47) v n n c where c is the speed of light in a vacuum, n is the refractive index of the atmosphere (making n the velocity of light in the atmosphere), v is the velocity of the particle and θ is the angle of the direction of Cherenkov light propagation relative to the particle trajectory. For the refractive index of the atmosphere at sea-level, θ does not exceed 1.3◦. The smaller refractive index at larger altitudes means that this angle is less than this value. The combined Cherenkov light from many secondary particles will produce a 5 to 200 ns burst of light that can be observed on clear, moonless nights by detectors such as HESS. After reﬂection from a 13 m diameter mirror, the 960 photomultiplier-tube-pixels of a HESS Cherenkov telescope can view the light emitted from a shower of secondary particles. The light cone appears as an illuminated elliptical shape when projected onto the 2 dimensions of the camera image (see Figure 1.12).

Gamma−ray interaction

Photomultiplier tubes

Mirrors Cherenkov light

Single telescope image

Figure 1.12: The Cherenkov light from a gamma-ray initiated secondary shower is seen by a HESS telescope. The light is reﬂected from the mirrors onto an arrangement of photomultiplier tubes, creating a Cherenkov image for analysis.

32 1.4.3 Image Parameterisation and HESS Performance Light from a gamma-ray shower appears as an elliptical image in a HESS telescope and several of these elliptical images can be acquired if several telescopes are used, improving shower reconstruction. From geometrical arguments the length, l, and width, w, (semi-major and

semi-minor axes, see §A.2) describing the ellipse of Cherenkov light projected onto the HESS camera can be calculated. Figure A.2 illustrates the parameters of shower Cherenkov images. The mean-scaled-width is an important parameter for the successful rejection of the cosmic ray hadron background, which comprises about 99.9% of all triggered events. Cosmic ray- initiated shower images are less ‘tight’ than gamma-ray-initiated shower images, so can be

largely discriminated. This process is described in some detail in §A.2. The HESS instrument has a field of view of 5◦, and after processing, gamma-ray data generally has an angular resolution finer than 0.1∼◦. Between a few hundred GeV and a few ∼ tens of TeV, HESS can achieve a sensitivity of 1% of the gamma-ray flux of the Crab Nebula after an observation duration of 25 h. ∼ ∼ 1.4.4 Gamma-rays from Supernova Remnants Using HESS and the technique described above, gamma-rays of TeV energies can effectively be observed at ground level. Often these gamma-rays are likely generated by CRs via the processes

outlined in §1.3, so the HESS observatory is a good tracer of CRs and high energy electron enhancements in the galaxy. It follows that the HESS telescope is able to see gamma-rays from SNRs with associated high energy particle populations, a key step to investigating the CR acceleration potential of SNRs in the Milky Way. Gamma-ray sources may be identiﬁed with HESS, but gamma-ray emission alone can’t yield distance solutions to potential CR acceleration sites (like shell-type SNRs), and more information may be required to discern the nature of emitting particle populations. Observations of molecular gas tracers, as explained in the following chapters, may help to solve these questions.

33 Chapter 2

Millimetre-wavelength Molecular Spectroscopy

Radio emission from gas can travel large distances across the Galaxy, making radio astronomy a key tool for studying gas from our otherwise limited vantage point. This chapter, which incorporates material from Townes & Schawlow (1955), Rybicki & Lightman (1979), Goldsmith & Langer (1999), Wilson (2009) and other more speciﬁc sources (cited in-text), discusses the theory associated with radio astronomy and molecular spectroscopy.

2.1 Molecular Energy levels

Ignoring kinetic energy, the total energy of a molecule is simply the sum of rotational, vibrational and electronic components,

Etot = Erot + Evib + Eelec (2.1) The temperature of molecular clouds and diﬀuse gas inside the Galaxy generally doesn’t exceed 100 K, so rotational emissions usually only requiring tens-of-kelvin magnitude temperatures for adequate excitations are the most useful for observing these regions. These rotational transitions fall within the radio/microwave-band of the electromagnetic spectrum (as opposed to vibrational transitions that may fall within infrared bands), so we place an emphasis on rotational transitions. The rotational component of energy is related to angular momentum, J, by J 2 E = , (2.2) rot 2I where the moment of inertia is,

I = miri (2.3) where mi is the mass of a constituent atom, iX, within a molecule and ri is the distance of that atom from the molecular axis. Decomposing this into its components, we get

2 2 2 Jx Jy Jz Erot = + + (2.4) 2Ix 2Iy 2Iz where subscripts indicate x, y and z components. The rotational energy can also be written as 1 E = I ω2 + I ω2 + I ω2 (2.5) rot 2 x x y y z z 34 where ωi is the angular velocity of component i. Simple molecules can often be categorised as one of the following ‘rotors’, based on the number of rotational dimensions.

Classiﬁcation Conditions Examples + + Linear Rotor Ix = Iy = Iz CO, HCO ,N2H Spherical Rotor Ix = 0, Iy = Iz CH4, SiH4 Symmetric Rotor Ix = Iy = Iz NH3, CH3CN Asymmetric Rotor I = I =6 I H O, CH OH x 6 y 6 z 2 3 Linear Rotor

Taking the simplest example of a linear rotator (one rotational axis), such as CO (see §3.1), we only need to consider the rotation perpendicular to the rotation axis. It follows that for CO, Equation 2.4 reduces to, 2 J⊥ Erot = (2.6) 2I⊥ where J⊥ is the angular momentum perpendicular to the rotation axis and I⊥ is the moment of inertia. Moving into a quantum regime, we can use the correspondence principle to replace the square of the angular momentum with

J 2 J(J + 1)ℏ2 (2.7) → where J now represents the angular momentum quantum number, an integer. Equation 2.6 becomes, ℏ2 E = J (J +1) (2.8) rot 2I This equation allows the calculation of the rotational energy levels of a linear rotor molecule, with the moment of inertia, I, being unique to the molecule. For a simplistic case of a change in rotational energy of a linear rotor molecule, the frequency of the absorbed or emitted photon can be described as ν = ∆Erot/2πℏ, where ∆Erot is the energy diﬀerence between rotational levels. Since photons have spin of 1, absorption/emission transitions are restricted to ∆J = 1. It follows that Equation 2.8 becomes, ± ℏ ν = (J +1) (2.9) 2πI l where Jl is the lower rotational quantum number.

Symmetric Rotor

Another rotor type molecule exploited in this thesis is the symmetric rotor (NH3, see §3.4). Symmetric rotors are symmetric about an axis, referred to as the principal (or symmetry) axis and have the other two axes being equivalent. The total angular momentum can be described by, 2 2 2 2 J = Jx + Jy + Jz (2.10) which can be rearranged to get J 2 + J 2 = J 2 J 2 (2.11) x y − z

35 For symmetric rotors, I = I = I , so we make the moment of inertia perpendicular to the x y 6 z principal axis, I⊥ = Ix = Iy and the moment of inertia parallel to the principal axis Ik = Iz. This allows us to rewrite Equation 2.4 as,

2 2 2 Jz Jx + Jy Erot = + (2.12) 2Ik 2I⊥ Now we combine this equation with Equation 2.11 and rearrange to get J 2 1 1 E = + J 2 (2.13) rot 2I 2I − 2I z ⊥ k ⊥ Again, Equation 2.7 can be used to transform the equation into a quantum regime, but this 2 2 time we also replace the projection of the angular momentum in the principal axis, Jz K ℏ , where K is an integer quantum number between J. → ± ℏ2 1 1 E = J(J +1)+ ℏ2 K2 (2.14) rot 2I 2I − 2I ⊥ k ⊥ This equation allows the calculation of the rotational energy levels of a symmetric rotor molecule, with the moments of inertia, I⊥ and Ik, being unique to the molecule. Note that Equation 2.8 is retrieved for the special case of the symmetric rotor where K=0, i.e. the rotation vector is perpendicular to the principal axis. If J = K, the rotation vector is parallel to

the principle axis (e.g. for the ammonia inversion transitions, see §3.4).

Degeneracy Within each rotational energy level there is a degeneracy, g, of 2J + 1, due to the number of diﬀerent values of the magnetic quantum number, M, which range between J. Often these diﬀerent levels overlap, so a population of molecules produce overlapping spectral± lines, but sometimes magnetic splitting can occur, leading to a population of molecules that can produce

multiple spectral lines separated closely in frequency-space (see for example §3.4).

2.2 Einstein Coeﬃcients and Critical Density

As described in Section 2.1, molecules often have multiple energetic states that are associated with various rotational and vibrational modes. Einstein coefficients describe the rate that transitions between these states occur via different mechanisms. The A-coefficient (s−1) gives the spontaneous transition rate, the rate of molecular transitions not triggered by outside influences. This only applies for downward-going (decreasing energy states) transitions. The B-coefficients (cm3 J−1 s−1 Hz) describe transitions of absorption and stimulated emission. Molecular absorption occurs when a photon loses all of its energy, raising the energetic state of the receiving molecule. Stimulated emission can occur when a photon interferes with the electric field of an already excited molecule, stimulating the emission of a second photon of equal energy. The −3 −1 B-coefficients must be multiplied by the specific radiation density, uν (J cm Hz ), to yield a rate (s−1). The A and B-coefficients for spontaneous and stimulated emission, and absorption are related by equations 2.15 and 2.16 (Elitzur, 1992),

3 Aij 2hνij = 2 (2.15) Bij c

36 giBij = gjBji (2.16) where νij is frequency, and the subscript ij indicates a transition from state i to j. gi and −1 gj are the statistical weights of states i and j respectively. The C-coefficients (s ) are rates of excitation and de-excitation of molecules by collisions. Theses rates are proportional to the hydrogen number density, nH (assuming that H is the dominant form of gas). Equation 2.17 relates the C-coefficient to a density-independent value, k (cm3 s−1), that is unique for a given molecule, taking into account particle cross sections and collision speeds (ie kinetic temperature), Cij = kij(T )nH (2.17) It is useful in radio astronomy to define a condition where the rate of spontaneous emission of the transition i i 1 is equal to competing de-excitation processes that don’t result in → − radiative emission of νi→i−1 photons, ie collisional de-excitation.

Ai→i−1 = Cij (2.18) j

Ai→i−1 ncr = (2.19) j

§3). The Einstein A-coefficient for transition i j can be derived from the classical Larmor formula for the power emitted by an accelerating→ charge (see Elitzur (1992) for details), 64π4 ν3 A = ij µ 2 (2.20) ij 3c3 h | | where νij is the frequency of the transition and µ is the dipole moment of the molecule (which may depend on the vibrational/electronic state). It can be observed that the critical density is dependent on both the cube of the transition frequency and the square of the electric dipole moment. CO is one of the most commonly exploited gas tracers, as its low electric dipole moment ( µ =0.122 D [1 Debye=10−18 statC cm] Huzinaga et al., 1993) leads to comparatively low critical| | densities, making CO ideal for general gas surveys. When denser regions are to be probed, high-electric dipole moment molecules such as CS ( µ = 1.958 D, Huzinaga et al., 1993) are better suited. Chapter 3 discusses these characteristics| in| greater detail. Einstein coefficients can be useful in expressing the emission and absorption coefficients (defined in Equation 2.32) in terms of physically understandable quantities. hν j = ij n A φ(ν) (2.21) ν 4π i ij hν α = ij (n B n B ) φ(ν) (2.22) ν 4π j ji − i ij

where i > j and φ(ν) is the normalised line proﬁle (discussed in §2.9). It can be seen that Equations 2.21 and 2.22 are simply derived from the photon energy (hνij), the number of emitters/absorbers (ni/nj) and the emission and absorption rates (Aij, Bij, Bji), with these coeﬃcients being normalised to solid angle (1/4π).

37 2.3 Radiative Transfer and Physical Parameters

In order to investigate environments outside the Earth via electromagnetic radiation, one must ﬁrst consider how that electromagnetic radiation reaches us and how it may change in transit. Radiative transfer, a mathematical description of the properties of light, are described in this section, which is largely taken from Rybicki & Lightman (1979).

2.3.1 Intensity, Flux and Luminosity Intensity Emission of radiation of frequency between ν and ν + dν from direction Ωˆ can be described by the speciﬁc intensity (or brightness),

dE I (Ω)ˆ = (2.23) ν dAdtdνdΩ where dE is the energy of radiation of frequency ν to ν + dν received on area dA in the time interval dt from the solid angle dΩ about the direction Ω.ˆ The SI units used for this quantity are [W m−2 Hz−1 sr−1], but it is not unusual to use the cgs units [erg s−1 cm−2 Hz−1sr−1], where one erg is equivalent to 10−7 joule.

Flux When using a detector such as a radio telescope, where the detector is pointed directly at a source, it can be useful to express the energy being emitted from the source as a specific flux, which can be simply thought of as the integral of specific intensity, Iν, with respect to solid angle, Ω. dE F = (2.24) ν dAdtdν If the solid angle, Ω,ˆ subtended by the source is small, which is often the case, specific flux can −2 −1 be approximated by Fν Iν∆Ω. The SI units for specific flux are [W m Hz ], but as this is often a small value, the≈ Jansky [Jy] is often used, where 1 Jy = 10−26 W m−2 Hz−1. This also serves to simplify the units of specific flux. Both specific intensity and specific flux can be integrated with respect to some frequency range that is chosen depending on the type of emission being observed. If the entire frequency range is integrated over, the result is the ‘bolometric’ intensity (with SI units of W m−2 sr−1) or ‘bolometric’ flux (with SI units of W m−2).

Luminosity The total radiative energy emitted from a source between ν and ν +dν is the specific luminosity, −1 −1 −1 Lν. This quantity has units [W Hz ] or [erg s Hz ] and can also be integrated with respect to frequency to get the bolometric luminosity, with units of [W] or [erg s−1]. For sources that emit radiation isotropically (equally in all directions), the flux (whether specific or bolometric) depends on the distance from the source. One can think of an isotropically emitting source in terms of an expanding spherical front, with the radiative energy being distributed evenly around the source on a sphere of surface area 4πd2, where d is the distance

38 from the source. This allows a relationship between flux and luminosity to be defined (assuming an isotropic flux), 2 2 Lν =4πd Fν , L =4πd F (2.25) Luminosity is independent of distance, whereas flux is dependent on distance. The assumption of isotropy allows one to simplify intensity by instead using mean intensity, 1 J = I (Ω)dΩ ν 4π ν 1 Z J = I(Ω)dΩ (2.26) 4π Z where we have integrated intensity, I, over all solid angles, Ω.

2.3.2 Thermal Radiation Thermal radiation is the radiation emitted by particles due to their thermal motions. For matter in thermal equilibrium at some temperature, T , the intensity of thermal radiation of frequency, ν, for a blackbody can be described by Planck’s law, 2hν3 1 Bν(T )= 2 hν (2.27) c e kT 1 − where h is Planck’s constant (6.626 10−34 J s), c is the speed of light (3 108 m s−1) and k is × × Boltzmann’s constant (1.380 10−23 J K−1) By integrating Equation× 2.27 with respect to solid angle and over the entire frequency range, the Stefan-Boltzmann law which describes the total radiative ﬂux from a blackbody (an idealised material that absorbs all incident radiation independent of angle of incidence and frequency) can be derived, F = σT 4 (2.28) where σ is the Stefan-Boltzmann constant (5.670 10−8 W m−2 T4). By using the derivative of Equation 2.27 to× pinpoint the maximum of the function, the wavelength of maximum intensity emission, λpeak, can calculated with Weins displacement law, b λ = (2.29) peak T where b is the is the constant of proportionality (2.898 10−3 m K). × Brightness Temperature In the limit where ν kT/h, a Taylor series expansion (exp [hν/kT] 1+ hν/kT) allows Equation 2.27 to be reduced≪ to the Rayleigh-Jeans relation, ∼ 2ν2kT B (T )= (2.30) ν c2 This relation is often applicable to astronomical measurements made at radio wavelengths. It is common practice for radio astronomers to measure intensities in terms of the temperature of matter required to excite a thermal emission of equivalent intensity. This value is deemed brightness temperature, c2 T (ν)= I (2.31) b 2ν2k ν

39 2.3.3 Equation of Radiative Transfer The propagation of radiation through the interstellar medium can be described by, dI ν = α (s)I (s)+ j (s) (2.32) ds − ν ν ν where αν(s) and jν (s) are the coeﬃcients of absorption and emission at frequency ν, respectively, and s is the distance travelled through the medium. These coeﬃcients describe the way that particles along the line of sight of a beam of radiation can either absorb photons, decreasing the intensity, or emit photons, increasing the intensity. As illustrated in Figure 2.1, particles

I (s) + dI Iν (s) dA ν ν

Figure 2.1: A cylindrical column of particles with cross-sectional area dA and length ds. Radi- ation of frequency ν and intensity Iν enters on the left. Particles along this column will effect the intensity of radiation, changing it by dIν. along the path of a beam of radiation may act to alter the intensity. The column density, N, is the number of particles along the line of sight within some cross-sectional area, dA. Assuming a constant number density of a given absorber, na, and a constant absorption cross-section, σν , the absorption coefficient is given by αν = naσν. Sometimes the absorption coefficient is −3 −1 2 written in terms of mass density, ρ (g cm ), and opacity, κν (g cm ): αν = ρκν . −1 The inverse of the absorption coefficient is the absorption mean free path, lν = αν , or the expected distance photons will travel in a medium before 63% (or 1/e) are absorbed. When observing an astronomical source, the absorption coefficient is not a directly measurable quantity and there is significant uncertainty in s, the length of emission/absorption along the line of sight. This is why the parameter ‘optical depth’, τν , defined by dτν = αν ds, is particularly useful. By dividing Equation 2.32 by the absorption coefficient, the equation can be rewritten in terms of optical depth, dIν = Iν (τν)+ Sν(τν ) (2.33) dτν − where Sν(τν)= jν(τν )/αν(τν ) is defined as the source function. Equation 2.33 is a 1st Order Linear Differential Equation, that can be readily solved to produce, τν ′ −τν −(τν −τν ) ′ ′ Iν (τν)= Iν(0)e + e Sν(τν )dτν (2.34) Z0 The first term in Equation 2.34 represents radiation from a background source Iν (0) that suffers attenuation in transit across a medium. The second term represents the radiation originating

40 from the medium itself (if Sν = 0, this term is zero). If the source function is constant throughout the source, Equation 2.34 becomes

I (τ )= S + e−τν [I (0) S ] (2.35) ν ν ν ν − ν Expressing Equation 2.35 in terms of brightness temperature yields

T (ν)= T + e−τν [T (ν) T ] (2.36) b s bg − s where Ts and Tbg are the source and background brightness temperatures. Generally, when performing emission line astronomy, the instrument is not only pointed towards the region under scrutiny, but also towards a region that is known to not emit emission lines. This position is referred to as the ‘background’ position and its measured spectrum can be subtracted from that of the source, thus reducing noise common to both locations. We subtract the brightness temperature of the background reference position to yield an expression including the optical depth of a transition.

T (ν)= T + e−τν [T T ] T b s bg − s − bg = (1 e−τν )(T T ) (2.37) − s − bg This is referred to as the detection equation.

2.4 Molecular Population Models

When spectral line observations are taken, only a sample of the particular targeted molecular species are directly observed - those that happen to transit between the energy levels corresponding to the frequency observed at the time of observation. We must have methods to convert electromagnetic radiation data into physical quantities such as density and temperature.

2.4.1 The Local Thermodynamic Equilibrium Model A Local Thermodynamic Equilibrium model (hereafter an LTE model) is the simplest of the population models. Equation 2.38 can be used to easily estimate the energy level distribution of a species given a kinetic temperature, Tkin, n g hν j = j exp i→j (2.38) n g − kT i i kin where ni, gi, nj and gj are the number densities and degeneracies of states i and j respectively, νi→j is the frequency of the transition and Tkin is the kinetic temperature. Equation 2.38 is simply derived from the partition function, describing the distribution of energetic states within a population of molecules, N E Q(X)= g exp i (2.39) i −kT i=0 kin X where Q(X) is the sum of the proportions of a population of molecules, X, in the state i. This means that Q(X)=1 when N is the total number of energetic states. The degeneracies depend

41 on the conﬁguration of molecule X. Equation 2.38 assumes that the population is in thermodynamic equilibrium and that the energy level population distribution follows a Boltzmann distribution, which is often not the case. Due to the LTE method’s simplicity, it is widely applied as a ﬁrst approximation to convert column densities of one or several energetic states of a molecule to the total column density of the molecule.

Rotational Temperature If two molecular transitions of the same molecule are observed, minimal modification of Equa- tion 2.38 allows an expression relating the relative abundance of those two states to the temperature that would naturally achieve that relative abundance given a time greater than the relaxation time. A temperature calculated in this way is called a rotational temperature, Trot, and is approximately equal to the kinetic temperature when the gas is in thermal equilibrium. N g E E j = j exp j − i N g − kT i i rot g N T = (E E )/ k ln i j (2.40) rot − j − i g N j i where Ni and Nj are the column densities of the i and j states respectively, and Ei and Ej are the energies of the i and j states respectively. Care must be taken when applying this method because if different spectrometers are used to calculate the two different column densities, systematic errors may dominate.

2.4.2 Statistical Equilibrium Models Molecular distribution models based on collision coefficients have a number of advantages over LTE models. No assumption of thermodynamic equilibrium is needed and time dependencies can be imposed. Different radiation fields and collision scenarios can also come into play. An initial set of density values, which can be guessed from some other method to speed up the computational process, can be used in a multi-state solution, where transitions to and from all states are considered. Equation 2.41 (Gusdorf et al., 2008a) is applied numerous times, normalising the total number density data set to the desired molecular density after each iteration. dn i = n [A + B u ]+ n [B ] dt i+1 i+1→i i+1→i ν i−1 i−1→i n [A + B u + B u ] − i i→i−1 i→i+1 ν i→i−1 ν + [C n C n ] (2.41) j→i j − i→j i Xj6=i where ni is the number density of the i-th rotational state of a given molecule. The system moves closer to an equilibrium with each iteration, allowing each energetic state density to converge on its equilibrium value. This process often forms the basis of models referred to as ‘non-LTE’. Non-LTE models may be useful for cases when a parcel of gas is not in thermal equilibrium, like when the relaxation time of the gas has not been reached. In other cases, one can cater the B and C coefficients for situations where there is a unique environment, such as a particular background photon spectrum (eg. an ultra-violet-dominated region associated with high-mass stars) or a non-thermal distribution of gas velocities (eg. an astrophysical shock interaction).

42 2.5 Column Density Calculation

A key goal in molecular spectral line studies is often to investigate the amount of gas within a distant region. To this end, a column density derivation from Goldsmith & Langer (1999) is presented here. By substituting Equations 2.15 and 2.16 into Equation 2.22, a new expression for absorption coeﬃcient can be derived. 2 c gu αν = 2 Aul(nl nu)φ(ν) (2.42) 8πνul gl − Note that the subscript ‘ij’ is simply replaced with ‘ul’ indicating ‘upper state’ to ‘lower state’. If the spectral line is thermally excited, a Boltzmann relation (Equation 2.38) between the populations nu and nl can be assumed.

2 c hνul kTkin αν = 2 Aulnu(e 1)φ(ν) (2.43) 8πνul − The absorption coeﬃcient is readily converted into optical depth by integrating along the line of sight. 2 c hνul τ = α ds = A N (e kTkin 1)φ(ν) (2.44) ν ν 8πν2 ul u − Z ul as nuds = Nu and the line shape function, φν, has unit area, φνds = 1. By ignoring background radiation and multiplying by τ /τ , Equation 2.36 becomes R ν ν R hν 2 ul c kTkin 8πν2 AulNu(e 1)φ(ν) −τν ul − Tb(ν)= Ts(1 e )   (2.45) − τν     hνul 2hν kTkin −1 If one assumes that the source is thermally excited, Ts = k (e 1) (Equations 2.27 and 2.31) can be substituted into Equation 2.45, yielding −

hc2 1 e−τν Tb(ν)= AulNu − φ(ν) (2.46) 8kπνul τν ν Noting that Tbdν = c Tbdv, where v is the Doppler-shift velocity (see §2.8), Equation 2.45 can be integrated with respect to velocity and be rearranged, R R 2 8kπνul τν Nu = Tbdv (2.47) A hc3 1 e−τν ul Z − In the above equation, Tb is the brightness temperature of the source and one must take care in correcting for the radio telescope beam response. The most simple correction takes into account only the beam ﬁlling factor, ie. the ratio of the antenna beam area, Ωa, and source area, Ω . Letting T (Ω /Ω )T yields, s b → a s b 2 Ωa 8kπνul τν Nu = Tbdv (2.48) Ω A hc3 1 e−τν s ul Z − Equation 2.48 is useful for calculating column density, but requires an independent method of τν calculating optical depth, although an optically thin assumption would make 1−e−τν 1 (from Taylor-expanding e−τ ). ∼

43 2.5.1 Optical Depth Calculation Given a pair of observed emission lines, if one knows the expected flux ratio and assumes that any deviation from this ratio is due to the effects of absorption, it is possible to derive an optical depth. This is the case for isotopologue pairs or molecules with hyperfine structure (for examples of these see Sections 3.2 and 3.4). Some molecules have one or many energy levels that are split due to electric/magnetic hyperfine structure, resulting in closely spaced emission lines that have very similar associated emission parameters (frequency, dipole moment, critical density, etc.). This is referred to as hyperfine structure. Isotopologues are molecules that differ only in the isotopic composition of their constituent atoms. Since the mass numbers of isotopes of a given element can generally only vary by 1 or 2, analogous transitions of isotopologues atoms, like hyperfine-split transitions, have very similar emission parameters and can be utilised in finding optical depth. By taking the ratio of the upper-state column densities (Equation 2.47) of the energetic species responsible for two transitions, Equation 2.49 can be found. To keep the relation general, variables are given either a ’t1’ or ’t2’ subscript representing transitions ’t1’ and ’t2’ respectively. (N ) ν 2 (A ) (T ) dv τ 1 e−τt2 u t1 = t1 ul t2 b t1 t1 − (2.49) (N ) ν (A ) (T ) dv τ 1 e−τt1 u t2 t2 ul t1 R b t2 t2 − In some cases, a factor a, the relative line strengthR in the case τ 0, can be assumed, such that the following conditions are met, → (N ) u t2 = a−1 (Nu)t1

aτt2 = τt1 (2.50) In such a case, Equation 2.49 would yield Equation 2.51, allowing the optical depth to be calculated numerically. 2 (T ) dv ν (A ) 1 e−τt2 b t2 t1 ul t2 − =0 (2.51) (T ) dv − ν (A ) 1 e−aτt2 R b t1 t2 ul t1 − For isotopologues a mayR be estimated from an isotopic abundance ratio, whereas for molecules with hyperﬁne structure the value of a may simply reﬂect the relative degeneracies of energy levels involved in the transitions. Examples of this method are present in Sections 3.2 and 3.4.

2.6 RADEX Modelling

RADEX is a commonly-used computer model that simulates molecular line emission strengths that can be compared with real-life measurements in an iterative fashion. The properties of molecular emission from a homogeneous region of a speciﬁed shape (eg.

sphere), with speciﬁed local gas parameters is calculated by RADEX. The program incorporates § both statistical equilibrium calculations (see § 2.4.2) and radiative transfer equations (see 2.3), but due to the depth of the calculations, a comprehensive explanation of RADEX is largely beyond the scope of this thesis, and RADEX is mainly used for comparison with other methods. The formalism adopted in RADEX is summarised in Van der Tak et al. (2007). The way RADEX was incorporated into this project is brieﬂy described in this section. At the most basic level, one provides RADEX with the following inputs:

44 A file containing collision coefficient (§2.2) data, • output file name, • range of frequencies to be considered (GHz), • kinetic temperature (K), • number of collision partners (molecule collisionally causing excitation/de-excitation), • main collision partner (usually H ), • 2 number density of main collision partner (cm−3), • background temperature (K, CMB=2.73 K), • molecular column density (cm−2), • line-width (km s−1) • another trial? (0=no, 1=yes) • RADEX will then return an output file that contains the expected optical depth and flux for the transitions of the scrutinised molecule within the range specified (as well as several other quantities). Figure 2.2 is an example of an output file from RADEX. The outputs of RADEX

Figure 2.2: An example of an output ﬁle from the RADEX simulation. See Van der Tak et al. (2007) for details.

(Figure 2.2) aren’t immediately useful for analyses of observational data for several reasons. Firstly, because its backwards in the sense that we have to input the useful physical quantities that we want to know (temperature, density, column density) in order to yield the observational values that we may already have (spectral line flux). This is why the program is intended to be ‘looped’ over in an iterative process, effectively guessing the input parameters and varying them until consistent outputs are found (see Figure 2.3). A second problem is the very large systematics introduced by assumptions that aren’t explicitly true (eg. the homogeneity assumption, spherical region assumption and isothermal region assumption), while a third problem is that the solutions are expected to be degenerate. To fix both of these problems, one must find a way to cancel-out systematics. This may be

45 achieved by observing numerous transitions of the same molecule or isotopologue molecules (see Figure 2.3) and comparing the ratio of line intensities, not their individual magnitudes. Figure 2.3 describes (through example) how RADEX simulations were used in conjunction with real data to estimate gas parameters. The input parameters of temperature, density and CS column density were varied, with a RADEX simulation being executed for each parameter set. Simultaneously, another RADEX simulation is executed for a CS isotopologue (e.g. C34S), for an assumed abundance ratio (e.g. CS/C34S). The emission line ﬂux ratio was calculated for the simulated data, and compared to that of the real, observational data. If the data were consistent, the initial input parameters were saved for a later analysis. In this manner, a set of gas parameters consistent with observational data can be constructed, allowing density and temperature ranges to be estimated.

46 Other Parameters CS CS isotopologue Observables: (density, temperature, etc.) Column Density Abundance Assumptions Flux Ratios

CS isotopologue Column Density

Input Parameters Input Parameters

RADEX RADEX

Simulated (eg. CS/C34S) Flux Ratios

Are Simulated and Observed Ratios Consistent?

Yes No

Save Inputs Discard Inputs

Back to start

Figure 2.3: A logic tree describing the way RADEX was employed to analyse CS isotopologue data.

47 2.7 Single Dish mm-Astronomy

The digital cameras that most people are familiar with record an optical image composed of multiple pixels (>106). A radio telescope that measures the intensity at radio wavelengths generally can produce only one pixel (although next-generation multi-pixel receivers do exist, eg. Parkes Multi-beam, Staveley-Smith et al., 1996; ASKAP phased-array feed, Chippendale et al., 2010). This does not limit the instrument to only looking in one direction because by panning the field-of-view across the sky, multi-pixel images can be generated. Included in the measured signal flux is a component of noise that is largely systematic (radio interference and atmospheric effects). This component, being present within all measurements within a small solid angle can be subtracted by recording the intensity towards a suitable ‘OFF’ position to use as a reference. This ‘OFF’ position represents the background intensity and can be subtracted from the ‘ON’ position (the position being investigated) to retrieve the signal, ie. Isignal = ION IOFF . This section discusses− two single dish radio-telescopes employed in this study, Nanten2 and Mopra.

2.7.1 Mopra Mopra is a 22 m diameter radio-telescope located at the edge of the Warrumbungle Mountains near Coonabarabran, Australia. It is generally operated remotely from the Paul Wild obsert- vatory, the location of the CSIRO Australia Telescope Compact Array, or Marsﬁeld, NSW.

A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 2.4: (Mopra website, 2012) The Mopra radio-telescope framed by the Warrumbungle Mountains.

MOPS The Mopra back-end produces two 8 GHz-wide bands, one per polarisation. MOPS (the Mopra spectrometer) can operate at bands around three frequencies: 76-117 GHz (3 mm), 30-50 GHz (7 mm) and 16-27 GHz (12 mm). MOPS has two main operating modes: ‘wideband’ and ‘zoom’. Wideband consists of four overlapping 2.2 GHz sub-bands (8.3 GHz range) with 8096 channels/polarisation. In zoom mode, these four sub-bands are further divided into four zoom bands, or ‘windows’, of 137.5 MHz width, composed of 4096 channels/polarisation. This makes sixteen bands which can be tuned to sixteen spectral lines. Table 2.1 displays the bandwidth, spectral resolution and beam FWHM (full-width-half-maximum) of the Mopra radio-telescope in its three observation bands and Table 2.1 displays a sample of molecular transitions observable with MOPS.

48 Table 2.1: The bandwidth and spectral resolution of the Mopra Spectrometer, MOPS, in both wide and zoom-band modes, at 3, 7 and 12 mm. The beam FWHM (full-width-half-maximum) of the Mopra radio telescope is also displayed (Ladd et al., 2005; Urquhart et al., 2010). Bandwidth (km/s) Spectral Resolution (km/s) Beam FWHM (′′) Band (centre freq.) Wide Zoom Wide Zoom 3 mm (90 GHz) 30 378 505 0.915 0.11 40 7 mm (42 GHz) 56 025 932 1.69 0.21 80 12mm (24GHz) 112 050 1863 3.38 0.41 120

Table 2.2: A sample of molecular transitions accessible to the Mopra Spectrometer, MOPS, at 3, 7 and 12 mm. The transitions and rest frequencies are displayed. 3 mm 7 mm 12 mm Molecular Line Molecular Line Molecular Line Emission Line Frequency Emission Line Frequency Emission Line Frequency (GHz) (GHz) (GHz) CS(J=2-1) 97.980953 30SiO(J=1-0,v=0) 42.373365 H69α 19.59111 SO(J=21 3- 2) 99.299905 SiO(J=1-0,v=3) 42.519373 H 20(J=61,6-52,3) 22.235253 34 C S(J=2-1) 96.412950 SiO(J=1-0,v=2) 42.820582 C 2S(J=21-10) 22.344030 29 CH 3OH(J=2-1, E) 96.739363 SiO(J=1-0,v=0) 42.879922 H65-α 23.40428 CH3OH(J=2-1, A++) 96.741377 SiO(J=1-0,v=1) 43.122079 NH 3(1,1) 23.6944709 + N2H (J=1-0) 93.171881 SiO(J=1-0,v=0) 43.423864 NH 3(2,2) 23.7226336 CH 3OH(70-61 A++) 44.069476 NH 3(3,3) 23.8701296 HC 7N(J=40-39) 45.119064 NH 3(6,6) 25.056025 HC 5N(J=17-16) 45.26475 HC 5N(J=10-9) 26.626533 HC 3N(J=55-44) 45.488839 H62α 26.93917 13 CS(J=1-0) 46.24758 HC 3N(J=3-2) 27.294078 HC 5N(J=16-15) 47.927275 NH 3(9,9) 27.477943 C34S(J=1-0) 48.206946 OCS(J=4-3) 48.651604 CS(J=1-0) 48.990957

2.7.2 Nanten2 Nanten2 is the recently upgraded (2006) version of the Nanten observatory. The 5 km altitude and clear desert skies of the Atacama Desert in Northern Chile allow superb conditions for radio astronomy. The 4 m diameter radio-telescope operates in the 110 to 345 GHz range, as well as the high frequency atmospheric windows of 460-490 and 809-880 GHz. A picture of Nanten2 is displayed in ﬁgure 2.5.

A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 2.5: (Nanten website, 2012) The Nanten2 high-altitude radio-telescope amid the Ata- cama Desert.

49 The Nanten2 telescope can be tuned to the rest frequencies of the low to mid-frequency rotational lines of the CO and 13CO molecules and also atomic carbon lines.

Table 2.3: The frequencies/wavelengths accessible by the Nanten2 radio telescope and the angular resolution at those frequencies/wavelengths. The bandwidth is 1 GHz. Observed Frequency Wave length Angular resolution∼ (GHz) (µm) (′′) 115 2600 180 230 1300 90 345 870 60 460 650 45 490 610 40 809 370 25 880 340 22

2.8 Galactic Kinematic Distances

Knowing the distance to galactic sources is of utmost importance when observing in radio astronomy, as an accurate description of a 3-dimensional galaxy cannot be formulated with mere 2-dimensional measurements. Fortunately, line-of-sight information is transmitted in small, measurable frequency-shifts caused by the Doppler eﬀect.

2.8.1 The Doppler Effect The Doppler effect is the change in frequency of a wave caused by a velocity difference of a source relative to an observer in the direction of a line connecting source and observer (ie. line-of- sight). The equation describing this behaviour is referred to as the Doppler (or Doppler-Fizeau) equation, v + v ν = r ν (2.52) measured v + v 0 s where νmeasured and ν0 are the measured and source frequencies respectively and v, vr and vs are the velocities of the emitted waves, observer and source respectively. Equation 2.52 only applies for v > vr, vs (in this case v = c) and the direction of positive velocity, by convention, is from the receiver towards the source. The Doppler effect is commonly witnessed in electromagnetic radiation from astrophysical objects. When molecular emission or absorption lines are observed, small deviations from the precisely-known (laboratory) rest frequencies may be observed, allowing the velocity of distant

50 bodies with respect to Earth to be calculated via the expression,

∆ν = ν ν (2.53) measured − 0 c + v = ν r 1 0 c + v − s c + v c + v = ν r s 0 c + v − c + v s s v v = ν r − s 0 c + v s ν ∆v = 0 c where c is the speed of light, ∆v = v v . Figure 2.6 uses the example of CS(J=1-0) line s − r emission to illustrate the conversion of an emission line in frequency-space to that in velocity- space using Equation 2.53.

16 CS(J=1-0) 2.0 2.0

1.5 1.5

1.0 1.0

0.5 0.5 Brightness Temperature (K) Brightness Temperature (K)

0.0 0.0

48.92 48.94 48.96 48.98 49 49.02 49.04 -100 -80 -60 -40 -20 0 20 40 60 LSRK Frequency (GHz) LSRK RADIO velocity (km/s)

Figure 2.6: Left: A frequency spectrum from radio observations towards a molecular core. Right: The corresponding velocity spectrum of the same molecular core. A small variation in rest frequency of this CS(J=1-0) emission has translated into a line-of-sight velocity when Equation 2.53 was applied.

2.8.2 Rotational Motion of the Milky Way The rotational motion of our galaxy, the Milky Way, can be studied using radio observations and the Doppler eﬀect. Firstly, distances to stars can be found by comparing observed optical star intensities to their corresponding expected luminosities (see for example Vogt & Moﬀat, 1975). Brand & Blitz (1993) compiled 400 star distances found via this technique together with line-of- sight velocities found from line emission from HII regions associated with each star. Using the coordinates, line-of-sight velocity and distance for each star, a dynamic model of our Galaxy was constructed. Equation 2.54 expresses the local-standard-of-rest (LSR) velocity, vLSR, of an object within the plane of the Milky Way, assuming perfectly circular orbits.

ΘR0 vLSR = Θ sin l cos b (2.54) R − 0 51 Galactic object (l,b)

b Galactic Centre (0,0) Sun l The Galactic Plane

Figure 2.7: The plane of the Milky Way. The galactic coordinate system is deﬁned such that galactic longitude, l, is the angle between a line connecting the Sun and the centre of the galaxy and a projection in the Galactic Plane of a line connecting the Sun and source. Galactic latitude, b, is the angle between Galactic plane and a line connecting the Sun and source. where Θ and R are the circular rotation velocity and radius of the observed object, respectively, and Θ0 and R0 are the circular rotation velocity and radius of the Sun’s orbit around the Galactic centre. l and b are the galactic longitude and latitude coordinates, respectively (see −1 Figure 2.7). Assuming the IAU-recommended values of R0 =8.5kpc and Θ0 =220 kms (Kerr & Lynden-Bell, 1986), the value of the circular rotation velocity, Θ, was plotted as a function of R by Brand & Blitz (1993). A function of best ﬁt was then found,

R 0.0394 Θ=1.00767Θ +0.00712 (2.55) 0 R 0 Then, some simple trigonometry allows one to ﬁnd the radius of the observed object,

R2 =(d cos b)2 + R2 2R (d cos b) cos l (2.56) 0 − 0 where d cos b is the projection of the line between the galactic object and the Sun into the galactic plane. Equations 2.55 and 2.56 allow Equation 2.54 to be solved numerically to ﬁnd the distance to the object, d. For objects closer to the galactic centre than the Sun (R < R0), the solution is degenerate, giving one ‘near’ and one ‘far’ distance corresponding to the two intersection points of our line-of-sight with a smaller orbit. Thus, it is helpful to constrain the distance in a second way, such that one of the two solutions is ruled out. A recent metastudy by Vallee (2005) found that the distance between the Sun and Galactic centre, R , was equal to 7.9 0.1 kpc. Thus, distance measurements calculated using the Brand 0 ± & Blitz (1993) galactic rotation method with the assumption that R0 =8.5 kpc may need to be recalculated.

2.9 Line Proﬁles

2.9.1 Lorentzian Line Shape Spectral emission lines have an intrinsic ‘natural’ Lorentzian shape caused by the uncertainty in the energy and lifetime of the transition (Heisenberg’s Uncertainty Principle, ∆E∆t ~). This results in a Lorentzian line shape, ∼

(A + C)/4π2 φ(ν)= ij (2.57) (ν ν )2 +(A + C)/4π2 − 0 ij 52 where C is a constant value, Aij is the Einstein coefficient and ν0 is the emission line central frequency. Additional broadening from electromagnetic interactions between atoms and molecules as emission occurs also results in a Lorentzian line profile that largely dominates the intrinsic broadening. This is often referred to as ‘pressure broadening’ and includes the effects of, both, interactions interrupting the emission process, and interactions altering the energy levels between states.

2.9.2 Gaussian Line Shape The motion of gas molecules caused by thermal energy results in Doppler frequency shifts (see

§2.8.1) that yield a (normalised) Gaussian proﬁle (Equation 2.58).

mc2 (ν ν )2mc2 φ(ν)= exp − 0 (2.58) 2πkTν2 − 2kTν2 s 0 0 where m is the mass of the emitting molecule. Emission line shapes can be thought of as a convolution of both Lorentzian and Gaussian proﬁles, but generally the thermal Gaussian component dominates. To simplify the ﬁtting of a Gaussian function to real data in velocity- space (rather that frequency-space), it is common to use

2 (v vLSR) φ(v)= A exp − (2.59) − 2∆v2 where A is the emission line amplitude, ∆v is the 1σ line-width (containing 68.2% of emission) and vLSR is the velocity of peak intensity. The Full-Width-Half-Maximum (FWHM), ∆vFWHM, of the intensity, can be calculated by

∆vFWHM =2√2 ln 2∆v (2.60)

The FWHM is calculated from data acquired with an instrument using a discrete sampling interval, so one must deconvolve the measured FWHM, (∆vFWHM)m from the FWHM of the 2 2 instrument, (∆vFWHM)i. ie., the true FWHM is (∆vFWHM)m (∆vFWHM)i . It is not uncommon to encounter emission lines with Gaussian− widths that imply ridicu- p lously large temperatures when Equation 2.58 is assumed. This is usually caused by turbulent broadening eﬀects or the larger-scale motions of gas. This can be accounted for with a ‘micro- turbulent’ velocity term, Vt,

ν0 2kT 2 ∆vFWHM =2√2ln2 + Vt (2.61) c r m If emission line parameters are ﬁtted correctly, the formula for the area under a Gaussian,

Area = A∆v√2π

A∆vFWHM√π = (2.62) 2√ln 2 can be used to calculate the integrated (in velocity-space) intensity.

53 2.9.3 Other Effects on Line Shape In Equation 2.61, a microturbulence term was introduced to account for anomalous broadening. Encompassed in this, is turbulence injected at large-scales, that generate turbulent cells of decreasing size. This may be associated with star-formation, in/outflows or indeed, an expanding SNR. It follows that broadened lines may be evidence for the presence of a shock-gas interaction. Even more convincing evidence for the presence of a shock-gas interaction (possibly associated with an SNR) could be asymmetric line-profiles, where a shock causes a directional bias in velocity distribution of molecules, the components along the line of sight possibly being observable. Such phenomena can also occur towards in/outflows associated with star formation, or multiple line-of-sight gas components, so care must be taken in attributing an asymmetric line profile to SNR-shocks.

2.10 What are we looking for?

This chapter described some of the tools of radio astronomers, from the mathematics of radiative transfer to the hardware for the detection of that radiation, but hasn’t detailed what will physically be observed. Chapter 3 outlines the specific molecules/atoms targeted and how different species are useful for different scientific goals.

54 Chapter 3

Gas Tracers

Locating matter within the interstellar medium is often achieved by observing selected atomic or molecular emissions. The choice of observed atom or molecule, referred to as a ‘tracer’, depends on the conditions of the region in question. A tracer may even highlight very special cases of environmental condition. Table 3.1 summarises the transitions that are extensively used in this thesis. The properties of selected molecules are discussed in further detail in following sections.

Table 3.1: This table summarises the dipole moment, transition, frequency, critical density and use of the most important gas tracers employed in this research. Critical densities are quoted at a temperature of 20K. Molecule Dipole moment∼ Transition Frequency Critical Notes /atom/ion (Debye) (GHz) Density (cm−3) CO 0.122 J=1-0 115.271202 ∼1×103 General gas tracer 4

J=2-1 230.538000 ∼1×10 Very abundant ( §3.1) Usually optically thick CS 1.957 J=1-0 48.990955 ∼8×104 Dense gas and 5

J=2-1 97.980953 ∼3×10 hot cores ( §3.2) 4

SiO 3.098 J=1-0 43.423853 ∼6×10 Shock tracer ( §3.6) ∗ 3

NH3 1.48 J,K=1,1, F1−F1 23.694495 ∼2×10 Cold, dense gas ( §3.4) ∗ 3 J,K=2,2, F1−F1 23.722633 ∼4×10 ∗ 3 J,K=3,3, F1−F1 23.870129 ∼5×10 Warm, dense gas ∗ 3 J,K=6,6, F1−F1 25.056025 ∼7×10 Hot, dense gas + ∗ 5

N2H 3.40 J=1-0 93.173480 ∼7×10 Cold, dense core ( §3.7) CH3OH - J(n)=7(0)-6(1) A++ 44.069476 Good warm/hot core tracer (van Dishoek & Blake, 1998) −5

H (HI) - F=1-0 1.42040575177 ∼10 Tracer of atomic gas ( § 3.8). ∗Molecule has hyperﬁne structure, so the largest observable frequency (or ‘main’ line) is displayed.

When considering the suitability of a tracer, one must consider two important questions: 1) How does the gas-phase abundance of the considered tracer vary with local environment, whether due to chemistry or condensation onto grains? 2) What are the excitation conditions of the tracer in question?

3.1 CO

Carbon monoxide (CO 12C16O) is the most commonly exploited molecular gas tracer. This ≡ linear rotor (see §2.1) molecule has a low electric dipole moment (and hence relatively low

critical density transitions, see §2.2) making this molecule ideal for tracing diﬀuse gas. Denser regions are often not observable with this transition, because CO emission has a tendency to

55 become optically thick very quickly due to their large abundance, but this molecule is still a key transition in mm-wavelength astronomy.

3.1.1 X-factor

An X-factor, X, is a useful tool to simply convert intensity directly into H2 column density for large scale survey data, where small-scale optical depth and temperature-variations can be expected to average-out. The CO(J=1-0) X-factor is deﬁned as,

NH2 XCO10 (3.1) ≡ WCO10

where NH2 is the average H2 column density and WCO10 is the CO(J=1-0) intensity (often in units of K km s−1). Dame et al. (2001) carried out a large-scale CO(1-0) survey (488000 spectra) of the Galactic plane and compared the measured intensity distribution with that of a column density distri-

bution predicted from atomic HI emission (§3.8) and IRAS 100µm infrared emission from dust. 20 −2 −1 −1 The solution to the above equation was found to be XCO10 =(1.8 0.3) 10 cm (K km s ) , which is now commonly adopted for simplistic column density calculations.± × X-factors should be cautiously employed, as deviations due to variations in conditions (e.g. density and temperature) are expected (e.g. Dickman et al., 1986) and there may not only be small-scale ﬂuctuations, but also large-scale Galactic systematic variations. Dame et al. (2001) ◦ note little variation in X-factor inside of the central b 5 latitude, but do see XCO10 tend to 0.1 1020 cm−2(K km s−1)−1 near a latitude of b ∼±30◦. Via a method similar to that later ∼employed× by Dame et al. (2001), Sodroski (1995)∼ used ± 140/240µm infrared and CO(1-0) data to examine the longitudinal variation of the X-factor and found it to be a factor 3-10 lower in the central 400 pc of the Galaxy, and in a latter paper, Sodroski (1997) used the estimated hadronic target material and measured gamma-ray ﬂux to parametrise the X-factor as,

0.12D−0.34 20 −2 −1 −1 XCO10 = e [10 cm (K km s ) ] (3.2) where D is the Galactocentric distance (within the Galactic Plane) in kiloparsecs. If such a relation holds, a constant CO(1-0) X-factor assumption would result in an over-estimate of column density (and hence mass) in the inner-Galaxy and an under-estimate in the outer- Galaxy. Both small and large-scale variation in X-factor is a matter of continued investigation (see for e.g. Glover & Mac Low, 2011; Narayanan et al., 2011; Shetty et al., 2011).

3.1.2 Galactic CO Isotopologue Distribution The large abundance that helps to make low-rotational state CO transitions easy to observe, also means that regions often become optically thick to CO emission, so it is not ideal for probing regions deep inside molecular cores. Less abundant isotopologues of CO, such as 13CO and C18O (the two most common isotopologues after CO) are sometimes observed in such cases,

and can indeed be exploited via the method outlined in §2.5.1 to investigate optical depth. To do this, one needs to constrain the relative abundances of the isotopologue species. If one assumes that all isotopologue species of CO behave in the same manner chemically, one can

56 naively approximate that isotopologue abundances mirror elemental isotope abundances, [CO] [12C] [13CO] ∼ [13C] [CO] [16O] (3.3) [C18O] ∼ [18O] and the molecular abundances will simply reﬂect the isotopic composition of matter produced from stellar activity.

Galactic Gradient in [12C]/[13C] Elemental/isotopic abundances are not constant throughout the galaxy. The evolution of the distribution of elements/isotopes since the formation of the galaxy has not only been influenced by the star-formation rate, but also the types and generation of stars being formed (different stars can feature different nuclear reactions and byproducts). A relevant example would be the generation of 13C and C, products of secondary and primary processing, respectively. C is generally produced in massive stars at high temperatures via the triple-alpha process (fusion of 3 He nuclei), whereas 13C is formed as part of the CNO-cycle in AGB stars and is ejected into the ISM after being convected to the surface layers of the star. Milam et al. (2005) (and references therein) look at the C/13C gradient in the Galaxy using three tracers, CO(J=1-0), CN(N=1-0) and HCO+(J=1-1,2-2) (and respective 13C-isotopologue pairs), finding agreement in the 3 derived gradient functions, with a least-squared fit of, [C] D = (6 1) GC + (19 7) (3.4) [13C] ± kpc ± where DGC is the distance from the Galactic centre. Note that the fit derived purely from CO 13 and CO was (5 1)DGC +(19 8). ± 13± At the Galactic centre C/ C is 20, whereas in the local ISM (DGC 8 kpc) the above equation yields 67 12. The local ISM∼ value is actually different to that observed∼ within our solar system, C/13±C=89, but this discrepancy is likely the result of ongoing 13C-enrichment occurring in the local galaxy, while the solar system distribution of stable elements has remained relatively steady since the formation of the solar system 5 billion years ago. ∼ Isotopic Fractionation The caveat on the ratios given in Equation 3.3 is that isotopes behave in the same way chemically, but this is not strictly true. Isotopes of the same element may behave differently, and this phenomenon can be understood in terms of the zero point or ground-state energy of a molecule. Heavier isotopes will result in a lower molecular zero point energy, so will result in a larger release of energy than their lighter cousins, in forming a molecule in an exothermic reaction, or conversely, require less energy to form a molecule in an endothermic reaction. This effect will become most prominent when the difference between zero-point energies of the isotopologues is comparable to the temperature. In the case of CO and 13CO, the following reaction may be of consequence, 13C+ + 12CO ⇋ 13CO + 12C+ + ∆E (3.5) where ∆E is the energy released. The zero-point energies of CO and 13CO are 0.1345 eV and 0.1315 eV, respectively (Langer et al., 1984), so the energy difference is ∆∼E 3 meV ∼ ∼ 57 corresponding to a temperature of 35 K. The forward (13CO-producing) reaction rate is then ∼ a factor of exp( 35 K/kBT ) larger than the backward (CO-producing) reaction rate, where T is the temperature− (Langer et al., 1984). Certainly, this type of chemical fractionation is observed in CO towards some diffuse clouds (see for e.g. Visser, 2009, and references within) and observed isotopologue abundances are often explainable with the expected rates of CO photodissociation by UV light (driving the reaction in Equation 3.5), but Milam et al. (2005) found no large-scale correlation between temperature and CO-13CO ratio (nor for 2 other isotopologue pairs, nCN and HnCO+).There are even cases of 13CO abundance decreasing below that expected relative to CO, as 13CO is preferably dissociated by UV light while higher-abundance CO is better able to self-shield against photo-dissociating radiation (Bally & Langer, 1982).

CO Depletion The ﬁnal note on CO is that of depletion, where CO may ‘freeze-out’ onto dust grains in particularly dense or cold environments. This acts to lower the molecular gas-phase abundance, which if left unaccounted for may lead to an under-estimation of mass. This characteristic is common to all molecules, but in the case of CO, freeze-out may occur for densities that have a

minimal effect on other tracers such as NH3 (see §3.4). One example of this behaviour is the starless core L1544 (Caselli et al., 1999), where for densities above 105 cm−3 CO condenses onto dust grains, causing gas-phase CO abundance to drop by a factor∼ 10. Depletion is also evident in the double-peaked emission line profile ∼ of the closely-related (and optically-thin) species HC18O+ and D13CO+, highlighting regions foreground and background to the ‘depletion-zone’. Tafalla et al. (2002, 2004) examined the starless cores L1498 and L1517B in detail and found significant variation in CO and CS abundances with radius. A central 0.05 pc-radius CO/CS + ∼ abundance ‘hole’ corresponds to spatially-constant N2H abundance, and interestingly, a factor 3 increase in NH abundance. The authors suggest that nitrogen-containing molecules not ∼ 3 only survive in gas-phase for longer due to the lower energy for binding to dust grains of N2, but that the removal of C-containing molecules may allow for the more efficient production of NH3, a topic of continued investigation for the authors.

3.2 CS

Carbon monosulﬁude (CS 12C32S) is observed extensively in this work. Unlike CO, CS has a high dipole moment (1.957≡ D), such that the critical density for the lowest excitation is 8 104 cm−3. In addition to this characteristic, CS is considerably less abundant, with an ∼ × −9 abundance with respect to molecular hydrogen of [CS]/[H2] 1 10 (Frerking et al., 1980). It follows that the J=1-0 and J=2-1 transitions of CS, which∼ are×observable in mm-wavelengths, are ideal for probing dense molecular cores, where CO is optically thick.

3.2.1 Optical Depth and Isotopologues Although not as abundant as CO, emission from CS still suﬀer from optical depth eﬀects, which must be corrected for. To this end, optical depth can be calculated by observing a CS

58 isotopologue pair and solving Equation 2.51, which simpliﬁes to,

2 (T ) ν (A ) 1 e−τCS b CS = iso ul CS − (T ) ν (A ) 1 e−aτCS b iso CS ul iso − 1 e−τCS − (3.6) ∼ 1 e−aτCS − where subscript ‘CS’ refers to the J = u -(u 1) transition of CS, subscript ‘iso’ refers to the − −1 equivalent transition of a CS isotopologue, aτCS = τiso and NCS(J=u)/Niso(J=u) = a . In order to use this approximation effectively, the relative abundance between CS and its isotopologue pair, a, must be estimated. The two most common isotopologues of CS (after CS, itself) are 13CS and C34S. In a similar way to what was done for CO, one can naively approximate CS isotopologue abundances to 13 13 mirror elemental abundances, such that the discussion of C in § 3.1.2 similarly applies to CS. A key problem with this is that outside the inner few kiloparsec of the Galaxy, the abundance ratio, C/13C generally exceeds 50, making 13CS transitions relatively difficult to observe (not a problem for relatively abundant∼ 13CO). C34S transitions, on the other hand, can be more accessible by observations of a reasonably small exposure-time. Early studies of C34S (Wilson et al., 1976) compared the species to the next most common isotopologue, 13CS (using CS would have introduced systematics associated with optical depth) and the authors attributed the majority of variation of 13CS/C34S to variations in carbon isotope abundance, reasoning that since the nature of sulphur production is similar for each isotope (products of O-burning), the solar-system abundance of S/34S 22 probably generally held. Later work by Chin et al. (1996), which took the Galactic 13CS/C∼ 34S gradient into account (through a study prior to that which produced Equation 3.7), approximated (with correlation coefficient 0.84) a Galactic sulphur isotope gradient of, ∼ [S] D = (3 1) GC + (4 3) (3.7) [34S] ± kpc ± where DGC is the distance from the Galactic centre. It is difficult to find further literature about the sulphur isotope abundance in the Galaxy, but certainly, the equation above is consistent with a local (D 8 kpc) value of [CS]/ [C34S] 22. GC ∼ ∼ 3.3 Dark Molecular Gas

So-called ‘dark’ molecular gas, where carbon is in an atomic/ionic form (not in molecules such as CO or CS), and hydrogen is in molecular form (not atomic) probably exists in the transition regions between atomic and molecular gas, and this component can’t be traced by HI or CO. In the presence of ionising radiation, H2, like all other molecules (CO, CS, etc.) can be destroyed, but due to a high abundance, this molecule is better able to ‘self-shield’ against radiation of the corresponding ionisation energy range than other, less abundant molecules (like CO or CS). This gas may be traced by the ionic 157.7µm CII emission line via balloon experiments (Nordh et al., 1989) or the atomic 492 GHz CI emission line observable with the Antarctic Millimetre telescope (e.g. Stark et al., 1997) Wolﬁre et al. (2010) predict that the dark component might comprise 0.3 of the total mass of an average cloud and that this value increases for regions with enhanced∼ CR ionisation rates,

59 as this leads to an increase in CO-destruction rates. For a factor 10 CR ionisation enhancement, the dark gas fraction is predicted to increase to 0.4, so it is plausible that the dark gas fraction around a potential CR accelerator such as a shell-type∼ SNR may be similarly elevated.

3.4 NH3

Ammonia (NH3) is perhaps the 2nd most commonly exploited molecular gas tracer (after CO). The hyperﬁne structure of NH3 inversion transitions (see below) allows much information to be transmitted through the intensities of the various spectral emission components. Much of the background theory of this section is from the ammonia review paper Ho & Townes (1983) and a detailed summary of the analysis of ammonia emission appears in the appendix of Ungerechts et al. (1986).

NH3 Structure

N y^

H H

Figure 3.1: The ammonia (NH3) molecule, composed of one nitrogen and three hydrogen atoms. Covalent bonds are represented by solid lines. The principal rotation axis is shown as the vertical dotted line.

The four atoms that make up the ammonia molecule form a triangular pyramid, with the three H atoms forming an equilateral triangle at the base (Figure 3.1). This shape is a product of the repulsive forces between the covalent H-bonds and the nitrogen atom’s electron pair.

60 A line intersecting the N-nucleus and the centroid of the triangular base is referred to as the symmetry (or principle) axis. The rotation of the molecule can be represented by two quantum numbers, J, the quantum number for the magnitude of the total angular momentum, and K, the quantum number for the projection of the rotational momentum onto the symmetry axis

(see § 2.1). Thus these two numbers are constrained by the relation K J. | |≤ Ammonia can be sorted into two distinct groups based on spin: Ortho-NH3, where K is a multiple of 3, corresponding to all H-nuclei having parallel spin ( , ), and para-NH3, where K is not a multiple of 3, corresponding to one H-nuclei having↑↑↑ spin↓↓↓ anti-parallel to the other two ( , , , , , ). For a given molecule, the spontaneous transition between the ortho↑↑↓ ↑↓↑ and↓↑↑ para↑↓↓ states↓↑↓ is↓↑↓ so unlikely (rate 10−6 yr−1, Cheung et al., 1969, compared to −7 −1 −1 ∼ 10 s 5 yr for the 1,1 inversion transition, see §3.4) that it is referred to as a forbidden transition.∼ ∼ As the ammonia molecule is symmetric about the principle axis, the electric moment perpendicular to this axis is zero (assuming that there is no vibrational motion transverse to the symmetry axis). We can therefore treat the ammonia molecule as an electric dipole, with an electric moment along the symmetry axis. The dipole selection rules are therefore ∆K =0 and ∆J =0, 1. Thus, transitions between K-levels are usually forbidden, although vibrational motion can act± to create a small dipole moment perpendicular to the symmetry axis such that K-transitions are sometimes possible ( 10−2 yr−1, Ho & Townes, 1983). K-states are therefore referred to as metastable. Within each∼K-ladder, the non-metastable states, J > K, exist, but quickly decay (10−2 10−1 s−1) via far-infrared emissions until J = K. − Parity and the Inversion Transition

A third quantum variable that can be assigned to NH3 is parity (+ or -), denoting the direction of spin about the symmetry axis (right-handed or left-handed). For low J and K, the diﬀerence in energy between + and - parity is ∆E (23 GHz)h, where h is Planck’s constant, so a transition between parities or a so-called inversion∼ transition is observable at radio wavelengths. In such transitions, the nitrogen nucleus quantum mechanically tunnels through the potential barrier of the hydrogen plane, inverting the molecule while preserving the same J and K quantum numbers, ie., ∆J, ∆K =0. An inversion transition of an ammonia molecule with quantum numbers J and K is simply denoted NH3(J,K).

Hyperfine structure of NH3 Each (J,K,parity)-level is split into 3 by the interactions of the electric quadrupole moment of the nitrogen nucleus and the electron electric fields (see Figure 3.2). The total angular momentum is thus denoted by F1 = J + IN , where IN is the nitrogen spin. There are in total 6 allowed transitions between the 3 different quadrupole hyperfine levels of positive parity and the 3 different quadrupole hyperfine levels of negative parity. Figure 3.3 is an NH3(1,1) spectrum displaying the characteristic ‘5-finger’ hyperfine structure caused by electric quadrupole interactions. The relative intensities of the ‘5 fingers’ of NH3(J,K) emission depends on the probabilities of being in different molecular states. The relative strengths of these hyperfine lines (increasing in velocity-space) are [0.22, 0.28, 1, 0.28, 0.22] for NH3(1,1) and [0.05, 0.05, 0.80, 0.05, 0.05] for NH3(2,2). Further splitting occurs from weaker magnetic interactions, but this occurs on the order

61 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 3.2: Taken from Ho & Townes (1983), this image illustrates the various energy-levels within the J =1, K =1 state of NH3. of 40kHz, often unresolvable in radio observations. Figure 3.2 shows this ﬁner hyperﬁne ∼ splitting.

Typical NH3 Inversion Line Analysis

The inversion transitions of NH3 are very powerful tools for studying the galactic environment. If the ‘5 ﬁngered’-NH3(1,1) transition and at least the main NH3(2,2) transition is detected within a region, much can be implied about the temperature and column density of the gas (with some assumptions). Firstly, functions must be ﬁtted to the emission lines (usually Gaussians)

to provide usable values to describe the height, width and area of each emission line (see §2.9).

NH3(1,1) optical depth: The procedure outlined in Section 2.5.1 is used to estimate the NH3(1,1) optical depth, where Equation 2.51 reduces to

T (J, K, m) 1 e−τ(J,K,m) b − = 0 (3.8) T (J,K,s) − 1 e−ατ(J,K,m) b − where Tb(J, K, m) and Tb(J, K, s) are the main-line peak brightness temperature and a satellite- line peak brightness temperature respectively, τ(J, K, m) is the main-line optical depth and α is the expected intensity ratio between the main-line and the satellite-line being considered (ie, either 0.22 or 0.28). This equation (numerically solved) will yield 4 optical depths (one for each satellite-line), so a weighted average is used to ﬁnd the most likely main-line optical depth. Note that in going from Equation 2.51 to Equation 3.8 some simpliﬁcations were made:

62 NH3-(1,1)

0.30 F1 = 1−1

F1 = 2−2 0.25

0.20 F1 = 2−1 F1 = 1−2 0.15 F1 = 0−1 F1 = 1−0 0.10

0.05 Brightness Temperature (K)

0.00

-0.05

-100 -80 -60 -40 -20 0 20 40 60 LSRK RADIO velocity (km/s)

Figure 3.3: NH3(1,1) inversion emission spectrum towards Core C, coincident with RXJ1713.7- 3946 (See Chapter 4). Five distinct peaks can be observed, corresponding to diﬀerent transitions in F1-space. Note that further hyperﬁne-splitting is present, but not resolved in this example.

The first term goes from being an integrated intensity ratio to simply an intensity ratio, ie an assumption of equal NH3(1,1) hyperfine line-widths, dv, is applied. As the width of all the hyperfine lines are more generally greater than the width of small-scale magnetic splitting within each of the ‘5 fingers’, the assumption of equal line-widths is justified. In fact, assuming this at the line-fitting stage allows for a simpler χ2-minimisation process. Equation 3.8 yields the main-line optical depth, but as the main-line emission only represents some fraction, f(J, K, m), of the inversion emission, this value must be scaled by Equation 3.9 to find the total NH3(J,K) optical depth,

τ(J, K, m) τ tot = (3.9) J,K f(J, K, m) where f(1,1,m) and f(2,2,m) are 0.50 and 0.80, respectively.

NH3(2,2) optical depth: If NH3(2,2) satellite-lines are distinguishable, the NH3(2,2) optical depth can be found in the same way as that of the (1,1), but in practice the lower NH3(2,2) satellite-line intensities are at levels less than or comparable to the noise. An alternative

63 method to calculating optical depth is thus presented here. Rearranging the ‘detection equation’ (Equation 2.37), T τ = ln 1 b (3.10) ν − − T T s − bg Equation 3.9 can then be substituted to produce an expression for the total optical depth of the NH3(J,K) transition,

1 T (J, K, m) τ tot = − ln 1 b (3.11) J,K f(J, K, m) − T (J, K) T s − bg where Ts(J, K) is the temperature of the source of NH3(J,K) emission. Now speciﬁc to the case of NH3(2,2), we have,

1 T (2, 2, m) τ tot = − ln 1 b 2,2 f(2, 2, m) − T (2, 2, m) T s − bg 1 T (2, 2, m) T (1, 1, m) T = − ln 1 b s − bg (3.12) f(2, 2, m) − T (1, 1, m) T × T (2, 2, m) T s − bg s − bg

If we make the assumption that both NH3(1,1) and NH3(2,2) emission originates from the same region, it follows that the source temperature of each transition is the same, ie., Ts(1, 1) = Ts(2, 2). Therefore, 1 T (2, 2, m) τ tot = − ln 1 b (3.13) 2,2 f(2, 2, m) − T (1, 1, m) T s − bg The ‘detection equation’ (Equation 2.37) can once again be inserted to yield,

1 T (2, 2, m) τ tot = − ln 1 b (1 e−τ(1,1,m)) (3.14) 2,2 f(2, 2, m) − T (1, 1, m) − b Rotational & Kinetic Temperature

By substituting the NH3(1,1) and (2,2) level degeneracies, g1,1 =3 and g2,2 =5, and the NH3(1,1) and (2,2) energy diﬀerence, E /k E /k =41 K, into Equation 2.40, we get 2,2 − 1,1 3 N −1 T = 41 ln 2,2 (3.15) rot − 5 N 1,1 where N1,1 and N2,2 are the column densities of the (1,1) and (2,2) states of NH3. As stated in Section 2.4.1, the derivation of a rotational temperature presupposes that the region under scrutiny is in LTE. Tafalla et al. (2004) test this assumption, simulating NH3 emission from a model core of some kinetic temperature, Tkin, and calculating the observed rotational temperature to derive the following relation

Trot Tkin = [K] (3.16) 1 Trot ln 1+1.1 exp 16 − 42 − Trot h i which the authors claim to be accurate to 5% between temperatures of 5 and 20 K, but less reliable above temperatures of 20 K. ∼

64 Column Density

The (J,K)=(1,1) and (2,2) state column densities, N1,1 and N2,2, respectively, can be calculated with Equation 2.48. The total column density of Ammonia can then be calculated assuming LTE and ‘perfect correspondence’ between the NH3(1,1) and NH3(2,2) emission region by ex-

trapolating on the discussion in § 2.4.1,

N1,1 E1,1/kT −2 NNH3 = e Q(T ) [cm ] g1,1 1 22.7 5 −41.2 14 −100.3 9 −177.3 11 −272.18 26 −384.89 = N e T +1+ e T + e T + e T + e T + e T (3.17) 1,1 3 3 3 3 3 3 This analysis is powerful in its simplicity. With quite reasonable assumptions (LTE and perfect correspondence), 2 closely-spaced, easily-observable molecular transitions can yield optical depth, temperature and column density, allowing (with assumptions of structure) mass and density to be calculated towards dense environments.

3.5 OH

The OH (Hydroxyl) radical has relevance to this investigation through its role in tracing gas clouds shocked by SNR shocks. The OH molecule consists of an O nucleus covalently bonded to an H-nucleus, forming a diatomic molecule. In addition to this covalent bond, the O molecule has 2 electron pairs, and one free electron that is aligned along the molecular axis (a line drawn between the O and H nucleus). The ground ro-vibrational state (the only state of OH discussed here) of OH has an electronic orbital angular momentum along the molecular axis (l = +1), parallel to the electronic spin angular momentum (s = +1/2). This energy level is split by the interaction between the O nucleus rotation and the unpaired electron motion (Λ-doubling, ǫ = 1) (Oﬀer & van Dishoek, 1992). The transition between these states, OH(ǫ = +1 1) corresponds± to a wavelength of 18 cm. Additional splitting occurs in the ǫ = 1 levels→ − due to the interaction of the H ∼ ± nucleus rotation and the unpaired electron motion (F = 1, 2), creating four distinct possible ground-level transitions (F =2-2, 1-1, 2-1, 1-2).

The 1720 MHz Maser The OH(F =2-1) transition results in emission at 1720.530 MHz and is a maser transition commonly associated with SNR shock-gas interactions. Observations of this transition were ﬁrst discovered towards the SNRs W28 and W44 (Goss & Robinson, 1968), and Elitzur (1976) showed that it is possibly triggered by H2 collisions with OH in cooling post-shocked clouds (with temperatures of 25-200 K and densities of 103-105 cm−3). Since then, additional 1720 MHz OH masers have been discovered towards other SNRs (Frail et al., 1996; Koralesky et al., 1998), most of these SNRs having ages consistent with ‘slower’ (few 10 km s−1) shocks of &104 yr, supporting the notion of a shock-gas relation. × Two theories may explain the prominence of 1720 MHz emission towards SNRs (Frail et al., 1998), one involving a non-dissociative shock travelling through a high gas-density medium (104-105 cm−3), the other a dissociative shock travelling through a low gas-density medium (102-103 cm−3). The latter theory involves OH molecules being rapidly produced and emitting

65 at 1720 MHz, before being systematically destroyed, all in the post-shock region (Neufeld & Dalgarno, 1989). The former case of a non-dissociative shock propagating through high density material (104-105 cm−3) is considered to be particularly promising (Frail et al., 1998). This involves a high-temperature ( 1 000 K) post-shock region that produces a signiﬁcant column density of ∼ OH (Draine et al., 1983). As the gas cools (to 400 K) OH is converted into H2O, but the high OH column density can be maintained if conditions∼ are right for the simultaneous destruction of H2O molecules, possibly caused by X-ray emission from the inner SNR region (Wardle et al., 1998, 1999). This would allow for a population of OH molecules to be kept at a temperature of 100-200 K in the post-shock region. 1720 MHz OH masers are expected to be most intense perpendicular to the direction of the shock-motion because the column density of the shock-excited, population-inverted OH molecules is largest here, while the velocity-dispersion of the emitters is smallest. It follows that the line-of-sight velocity of these masers generally represent the systemic velocity of gas associated with the object that injected the shock.

3.6 SiO

When observing shocked/disrupted or energetic/hot environments, silicon monoxide (SiO) emission can be a potentially powerful tool, because gas-phase SiO abundance can actually increase by many orders of magnitude in such situations. Ziurys et al. (1989) discovered a distinct difference in gaseous SiO abundance between molecular clouds of different properties, with SiO(J=2-1) detections in the warm molecular star forming regions of Orion and NGC 7538 (with implied SiO abundances relative to H2 of up to 2 10−7 ) and an absence of detectable SiO emission towards the dark clouds TMC-1, L1551,∼ × −12 L134 N and B335 (with SiO/H2 . 10 ). Arguably, the most interesting instance of SiO emission was recorded in the SNR IC 443 (Ziurys et al., 1989), where the emission was triggered by a passing SNR shock. Since then, other examples have been observed (for e.g. W28, Nicholas et al., 2012a). It was claimed that these results may be representative of an energy barrier of 90K for endothermic SiO-producing reactions, restricting SiO production (and hence SiO emission)∼ to only hot/energetic regions. This observed temperature relation was reinforced by work done by Langer & Glassgold, 1990, who suggested that if SiO is formed by neutral reactions of Si with OH and O2, Si would need to initially be in the first rotational state. The gap between the ground and first rotational states of the silicon atom is 111K, consistent with observations. This effect was also said to occur for carbon in the formation of CO, but was less prominent due to the smaller J=0-1 energy gap of 23.6K. An additional mechanism that could feasibly explain SiO abundance enhancements is the ‘sputtering’ of dust grains, where energetic events release silicon from silicate-containing dusts. From observations of the J=2-1, J=3-2 and J=5-4 emission lines of SiO, Martin-Pintado et al. (1991) found that SiO is two orders of magnitude more abundant in regions where derived H2 densities are large (0.5-10 106 cm−3) compared to less dense, quiescent regions. This calculated abundance value increases× to three orders of magnitude inside a region of L1448, a molecular cloud with kinetic temperatures of merely 14K (Martin-Pintado et al., 1991 and references ∼ therein). It was suggested that the increased SiO abundance was likely due to molecular outflows manufacturing gaseous SiO in the field of view, a scenario supported in principle by

66 models. Overall, the gaseous SiO abundance was observed to vary from <4 10−12 in quiescent gas to up to 2 10−6 in shocked regions. × In Sagittarius× A and B, correlations between Fe 6.4 keV and SiO(J=1-0) emission further builds on the case for SiO as a shock tracer (Martin-Pintado et al., 2000). Martin-Pintado et al. proposed that shocks present in the region lead to both ionisation of Fe by hard X-rays and gaseous SiO production by grain destruction. A recent follow-up of the Sagittarius 6.4keV emission tests a low energy cosmic ray scenario against the X-ray hypothesis and found that an X-ray reflection nebula could best explain the correlation with the condition that a population of very small (615 10−10m), high silicate-concentration ( 10%) grains exist. These grains could be evaporated× by high energy photons, releasing locke∼d-up elements. It is likely that an energy threshold for the neutral SiO-producing reactions coupled with Si-liberating grain destruction mechanisms are responsible for increased SiO emission in shocks and hot environments. Irrespective of the relative significance of these processes, SiO can be confidently employed as a gas tracer in shocked or high temperature environments. For these reasons, SiO is utilized in the search for shocked matter in the region of supernova remnants.

3.6.1 Grain Sputtering Models At face value, SiO and CO seem like very similar molecules, with silicon (Si) being just below carbon (C), in the same group of the periodic table. But, an assumption of a simple elemental abundance scaling relation between the two molecular species (Si:C 10:1) does not ﬁt ∼ observational results (Schilke et al., 1997). CO emission is a popular choice of tracer in radio astronomy due to its high detectability in most molecular regions, whereas SiO emission is often absent due both to large fractions of Si depleting onto dust grains and the large dipole moment of SiO (µ = 3.087 D, Drira et al., 1997) resulting in a high critical density ( 6 104 cm−3). CO abundance can also suﬀer from C-depletion, but only by a factor of a few,∼ as× compared to several orders of magnitude for Si (Schilke et al., 1997). In shocks, Si is believed to be released by the impact of particles on silicate-containing grains. Models of this behaviour show a dependence on shock characteristics and uncertain grain properties (Gusdorf et al., 2008a,b; May et al., 2000; Schilke et al., 1997). Schilke et al. (1997) describes sputtering from two different sections of grains: the core and the outer mantle. From a sputtering model considering 4 7 only grain core contributions, it was found that for pre-shock densities of 10

67 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 3.4: (May et al., 2000) The fractional yield of Si from impact of various species on olivine dust grains as a function of shock speed produced from simulations (with pre-shock density 104 cm−3). Larger atoms can be seen to have a greater eﬀect on yield.

A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure 3.5: (May et al., 2000) Simulated Si and SiO column densities as a function of shock speed in a region with a pre-shock density of 104 cm−3.

+ 3.7 N2H

+ Diazenylium (N2H ) can be thought of as a tracer of molecular nitrogen (N2, itself, having no electric dipole moment, hence being undetectable by radio telescopes), as its primary means of 68 N2H+(J=1-0)

(F1 ,F)=(2,2)−(1,1) (F1 ,F)=(1,1)−(1,0) 1.0 (F ,F)=(2,3)−(1,2) 1 (F1 ,F)=(1,2)−(1,2)

(F1 ,F)=(1,0)−(1,1) 0.8 (F1 ,F)=(2,1)−(1,1)

0.6

(F1 ,F)=(0,1)−(1,2) 0.4 Brightness Temperature (K) 0.2

0.0

-30 -25 -20 -15 -10 -5 0 5 LSRK RADIO velocity (km/s)

+ Figure 3.6: The J=1-0 transition of the N2H ion towards CoreC of RXJ1713.7 3946 (see Chapter 4). Three distinct peaks can be viewed, but two of these peaks are actually− comprised of three individual hyperﬁne components (indicated).

+ production is likely via the reaction N2 + H2 N2H . We note that NH3 cannot similarly be said to be a tracer of molecular nitrogen, since−→ other main formation reactions exist that don’t directly involve N2 (Hotzel et al., 2004). + Rotational transitions of N2H have a distinct spectrum consisting of three quadrapole hyperfine lines (F1=0-1,2-1,1-1), with further, generally-unresolved magnetic (F =0,1,2) hyperfine- + splitting. Figure 3.6 is a spectrum of the hyperfine lines of N2H (1-0). But, like with NH3 inversion emission, if we treat this emission as 3 distinct lines, the relative degeneracies lead to line strengths of f [0.2, 1, 0.6] (increasing in velocity space, see Figure 3.6) (Womack et al., ∼ 1992) and calculate optical depth in the same way as is done for NH3 (§ 3.4). To calculate the column density, a process presented in Hotzel et al. (2004) is applied. First the excitation temperature can be calculated,

∆Ω T ∆Ω T = s mb + s T (3.18) ex ∆Ω (1 e−τ ) ∆Ω bg a − a where Tmb is the main beam intensity, Tbg is the background temperature (assumed to be 2.7 K), ∆ΩS is the solid angle of the source, ∆Ωs is the solid angle of the antenna and τ is the optical depth of the transition. Then the following equation which assumes a linear rotor molecule in

69 LTE is applied,

hν 3√πhǫ0 e kTex kTex 1 + NN2H = + ∆vFWHMτ (3.19) 2 2 hν 2π √ln 2µ + e kTex 1! hν 6 N2H − 

+ + where µN2H is the dipole moment of N2H ( 3.4 D). + ∼ The N2H abundance with respect to molecular hydrogen is generally noted to be constant at 5 10−10 (Pirogov et al., 2003) and no depletion is observed for this molecule, making ∼+ × N2H ideal for abundance studies of other similar-critical density molecules such as NH3 and CS (Tafalla et al., 2004; Hotzel et al., 2004).

3.8 HI

Colloquially referred to as the 21 cm line, HI is unique in this chapter as the only atomic gas tracer discussed (ie. it traces atomic H rather that molecular H2). A neutral H atom simply consists of an electron in orbit about a proton. Both the proton and electron have an associated spin and when these spins are aligned the magnetic interactions of the particles result in a higher energy state than when the spins are anti-parallel. Although a transition between these states is highly forbidden (2.9 10−15 s−1), atomic hydrogen has such large column densities in the × interstellar medium ( 1021 cm−2) that the HI transition is observable in both emission and, in the presence of a background∼ source, absorption.

3.8.1 Spectral Line Analysis For optically thick HI emission, optical depth and atomic column density are related by (Dickey & Lockman, 1990), N τ =5.2 10−19 H (3.20) × ∆vTs where ∆v is the emission line-width and Ts is the brightness temperature, which is often close to the kinetic temperature for optically thick HI emission. For the optically thin case, this 18 −3 relation can be rearranged to yield an X-factor (see §3.1.1) of X 1.823 10 cm . HI ∼ × Sometimes HI data will exhibit features of absorption and an optical depth calculation is necessary. Absorption produces a drop in intensity by a factor of e−τ , so, similar to previous optical depth calculation examples, with an estimate of the initial∼ source intensity an optical depth can be approximated. In the case of a background continuum source, the intensity before absorption is often identiﬁable in spectra at line-of-sight velocity not corresponding to any gas (ie. the ﬂat part of the spectrum). For HI self-absorption from an optically thick source, more complex arguments may be required, such as looking at the intensity of HI near (spatially or in velocity-space) the absorption region (e.g. Fukui et al., 2012). HI has been instrumental in mapping the Galactic spiral arms, estimating distances to radio continuum sources (via absorption) and detecting red-shifted extragalactic sources. In this investigation HI is important for mapping potential CR hadron target material in an atomic form, complementing targeted molecular tracers (e.g. CO and CS).

70 Chapter 4

Supernova Remnant RX J1713.7 3946 −

RX J1713.7 3946 (also known as SNR G 347.3-0.5) is one of the brightest sources in the HESS − TeV gamma-ray sky. As part of this PhD investigation, mm-wavelength observations towards this potential cosmic ray accelerator were carried out, spread across several years. The resultant data sets and in-depth analyses are presented in this chapter, which is comprised of one paper published in the Monthly Notices of the Royal Astronomical Society (3 to 12 millimetre studies of dense gas towards the western rim of supernova remnant RX J1713.7 3946), a proceedings − paper from the the 5th International Symposium on High Energy Gamma-ray Astronomy (Dense Gas Towards the RX J1713.7 3946 Supernova Remnant) and a draft to be submitted − for publication by Publications of the Astronomical Society of Australia (Dense Gas Towards the RXJ1713.7 3946 Supernova Remnant). − 4.1 3 to 12 millimetre studies of dense gas towards the western rim of supernova remnant RX J1713.7 3946 − The following paper was published in the peer-reviewed journal, Monthly Notices of the Royal

Astronomical Society (MNRAS). See §A.3 for an erratum describing a minor error in this article.

71 29/1/13

72 Mon. Not. R. Astron. Soc. 422, 2230–2245 (2012) doi:10.1111/j.1365-2966.2012.20766.x

3 to 12 millimetre studies of dense gas towards the western rim of supernova remnant RX J1713.7−3946

Nigel I. Maxted,1⋆ Gavin P. Rowell,1 Bruce R. Dawson,1 Michael G. Burton,2 Brent P. Nicholas,1 Yasuo Fukui,3 Andrew J. Walsh,4 Akiko Kawamura,3 Hirotaka Horachi3 and Hidetoshi Sano3 1School of Chemistry and Physics, University of Adelaide, Adelaide 5005, Australia 2School of Physics, University of New South Wales, Sydney 2052, Australia 3Department of Astrophysics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan 4Centre for Astronomy, School of Engineering and Physical Sciences, James Cook University, Townsville 4811, Australia

Accepted 2012 February 17. Received 2012 February 16; in original form 2011 December 21

ABSTRACT The young X-ray and gamma-ray-bright supernova remnant RX J1713.7 3946 − (SNR G347.3 0.5) is believed to be associated with molecular cores that lie within regions − of the most intense TeV emission. Using the Mopra telescope, four of the densest cores were observed using high critical density tracers such as CS(J 1–0, J 2–1) and its isotopologue = = counterparts, NH3(1, 1) and (2, 2) inversion transitions and N2H+(J 1–0) emission, con- 4 3 = firming the presence of dense gas 10 cm− in the region. The mass estimates for Core C range from 40 (from CS) to 80 M (from NH3 and N2H+), an order of magnitude smaller than published mass estimates from⊙ CO(J 1–0) observations. = We also modelled the energy-dependent diffusion of cosmic ray protons accelerated by RX J1713.7 3946 into Core C, approximating the core with average density and magnetic − 3 field values. We find that for considerably suppressed diffusion coefficients (factors χ 10− 5 = down to 10− the Galactic average), low-energy cosmic rays can be prevented from entering the inner core region. Such an effect could lead to characteristic spectral behaviour in the GeV to TeV gamma-ray and multi-keV X-ray fluxes across the core. These features may be measurable with future gamma-ray and multi-keV telescopes offering arcminute or better angular resolution, and can be a novel way to understand the level of cosmic ray acceleration in RX J1713.7 3946 and the transport properties of cosmic rays in the dense molecular cores. − Key words: diffusion – molecular data – supernovae: individual: RX J1713.7 3946 – ISM: − clouds – cosmic rays – gamma-rays: ISM.

et al. 2012), has previously been observed in CO(J 1–0) and 1 INTRODUCTION CO(J 2–1) with the Nanten and Nanten2 4-m telescope= (Fukui The origin of Galactic cosmic rays (CRs) is mysterious, but popular et al. 2003;= Moriguchi et al. 2005; Fukui et al. 2008), and more re- theories attribute observed fluxes to first-order Fermi acceleration in cently, H I in the Southern Galactic Plane Survey (SGPS; McClure- the shocks of supernova remnants (SNRs; e.g. Blandford & Ostriker Griffiths et al. 2005; Fukui et al. 2012). Three dense clumps, Cores 1978). One such potential CR accelerator is RX J1713.7 3946, a A, B and C (see Fig. 1), to the west of this void, and a fourth young, 1600-yr-old (Wang, Qu & Chen 1997) SNR that− exhibits clump, Core D, in the remnant’s northern boundary are coincident shell-like∼ properties at both X-ray (Pfeffermann & Aschenbach with regions of high TeV flux. The beam full width at half-maximum 1996; Koyama et al. 1997; Lazendic et al. 2003 ; Cassam-Chenai (FWHM) of 10 arcmin for the detection of gamma-rays with High et al. 2004; Tanaka et al. 2008; Acero et al. 2009) and TeV gamma- Energy Stereoscopic∼ System (HESS) would not be able to resolve ray energies (Aharonian et al. 2006, 2007). TeV features of the scale of these molecular cores ( 1 arcmin). A void in molecular gas, most likely created by the Three of the four stated cores (Cores A, C and∼ D) feature co- RX J1713.7 3946 progenitor star–winds (Inoue et al. 2012; Fukui incident infrared sources commonly associated with star formation − (Moriguchi et al. 2005). Core C displays a bipolar nature in CO(J 3–2) and CO(J 4–3) that may be attributed to protostellar activity= = ⋆E-mail: [email protected] or outflows (Moriguchi et al. 2005; Sano et al. 2010).

C 2012 The Authors C Monthly Notices of the Royal Astronomical Society 2012 RAS Dense gas towards SNR RX J1713.7 3946 2231 −

1 Figure 1. (a) Left: Nanten2 CO(J 2–1) integrated-intensity image (vLSR 18 to 0 km s ) (Sano et al. 2010) with HESS >1.4 TeV gamma-ray excess = =− − count contours overlaid (Aharonian et al. 2006). Contour units are excess counts from 20 to 50 in intervals of 5. All core names except ABm were assigned by Moriguchi et al. (2005). The dashed 18 18 arcmin2 box marks the area scanned in 7 mm wavelengths by Mopra (Fig. 2). (b) Right: XMM–Newton × 1 1 0.2–12 keV X-ray image with Nanten2 CO(J 2–1) (vLSR 18 to 0 km s ) contours. CO(J 2–1) contours span 5–40 K km s in increments of = =− − = − 5Kkms 1.TheXMM–Newton image has been exposure corrected and smoothed with a Gaussian of FWHM 30 arcsec. Two compact objects are indicated: − = 1WGA J1713.4 3949, which has been suggested to be associated with RX J1713.7 3946 and 1WGA J1714.4 3945, which is likely unassociated (Slane − − − et al. 1999; Lazendic et al. 2003; Cassam-Chenai et al. 2004).

RX J1713.7 3946 has a well-defined high-energy structure that peak also coincident with Core D’s boundary. Additional gas-keV is shell like at both− keV X-ray and TeV gamma-ray energies (Aharo- association may be seen in a line running along an X-ray fila- nian et al. 2006). The TeV emission contours displayed in Fig. 1(a) ment on the eastern border of Core A, Point ABm (midpoint of reveal a clear shell-like structure. The highest fluxes originate from Cores A and B) and Core B. These structures possibly suggest gas an arc-shaped region in the northern, north-western and western swept-up by the RX J1713.7 3946 shock or progenitor wind. Inoue parts of the remnant. The keV XMM–Newton image (Cassam- et al. (2012) modelled a SN− shock–cloud interaction and outlined Chenai et al. 2004) consists of extended emission regions that form the resultant high energy emission characteristics that were com- what appears to be two distinct arced shock fronts in the north, mon to both their model and RX J1713.7 3946. These included north-west and western parts of Fig. 1(b). Two separate shock parsec-scale keV X-ray correlation with CO− emission, subparsec structures seen at keV energies towards the north-west, believed X-ray anticorrelation with CO emission peaks, short-term variabil- to be dominated by synchrotron radiation from electrons within the ity of bright X-ray emission and stronger TeV gamma-ray emission RX J1713.7 3946 shock, have been considered as an outwards- in regions with stronger CO emission. Despite this strong evidence moving and− a reflected, inwards-moving shock (Cassam-Chenai for an association, a survey by Cassam-Chenai et al. (2004) that tar- et al. 2004). Various flux enhancements and filaments are evident geted shock-tracing 1720 MHz OH maser emission (Wardle 1999) along these fronts. recorded no detections towards this gas complex. This lack of an The RX J1713.7 3946 keV emission was first thought to origi- indication of a molecular chemistry consistent with a shock may nate from a distance− of 6 kpc due to an assumed association with point towards a scenario where the gas does not lie within the SNR ∼ 1 molecular gas at line-of-sight velocities, vLSR 70 to 90 km s− shell, but given the weight of evidence to the contrary (outlined (Slane et al. 1999), but later CO observations∼− and discussion− by in this section), the most probable explanations are, as suggested Fukui et al. (2003) placed the remnant inside a void in molecular by Cassam-Chenai et al. (2004), that the density is not sufficiently 1 gas at 1 kpc distance (vLSR 10 km s− ). This distance was large to cause OH maser emission or that a non-dissociative C-type consistent∼ with an initial estimate∼− based on an X-ray spectral fit and shock, like that required, does not exist in this region. a Sedov model (Pfeffermann & Aschenbach 1996), which was itself Fermi-Large Area Telescope (LAT) observations (Abdo et al. consistent with the SNR age (Wang et al. 1997). 2011) have recently shown that RX J1713.7 3946 exhibits a low Interestingly, keV X-ray emission peaks (Fig. 1b) seem to show but hard-spectrum flux of 1–10 GeV gamma-ray− emission, not some degree of anticorrelation with molecular gas peaks and cores predicted by early hadronic emission models (i.e. pion-producing 1 at vLSR 10 km s− , as traced by CO (Fig. 1b). Two synchrotron proton–proton collisions), but consistent with previously published intensity∼− peaks on the border of the densest central region of Core C lepton-dominated gamma-ray models (i.e. inverse Compton scat- are suggestive of compressions associated with the shock (Sano tering of TeV electrons) of RX J1713.7 3946 (Porter, Moskalenko et al. 2010), while a dip in non-thermal emission from Core C’s & Strong 2006; Aharonian et al. 2007;− Berezhko & Volk 2010; centre may imply that the electron population is unable to diffuse Ellison et al. 2010; Zirakashvili & Aharonian 2010). However, into the core and/or that keV photons cannot escape. A similar sce- a hadronic component is possible towards dense cloud clumps nario may also be applicable to Core D, with an X-ray intensity (Zirakashvili & Aharonian 2010), and perhaps more globally if

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS 2232 N. I. Maxted et al. one considers an inhomogeneous interstellar medium (ISM; Inoue Table 1. The window set-up for the MOPS at 7 mm. The centre frequency, et al. 2012) into which the SNR shock has expanded. Further sup- targeted molecular line, targeted frequency and total mapping noise (TRMS) port for a global hadronic component may come from consideration are displayed. of the molecular and atomic ISM gas together (Fukui et al. 2012). Another novel way to discern the leptonic and/or hadronic nature Centre Molecular Line Map frequency emission line frequency T of the gamma-ray emission is to make use of the potential energy- RMS (GHz) (GHz) (K ch 1) dependent diffusion of CRs into dense cloud clumps or cores (e.g. − Gabici, Aharonian & Blasi 2007), which may lead to characteris- 42.310 30SiO(J 1–0, v 0) 42.373365 0.07 = = ∼ tic features in the spectrum and spatial distribution of secondary 42.500 SiO(J 1–0, v 3) 42.519373 0.07 = = ∼ gamma-rays and synchrotron X-rays from secondary electrons. In 42.840 SiO(J 1–0, v 2) 42.820582 0.07 = = ∼ Section 6 we therefore looked at a simplistic model of the energy- 29SiO(J 1–0, v 0) 42.879922 = = 43.125 SiO(J 1–0, v 1) 43.122079 0.08 dependent diffusion of CRs into a dense molecular core similar to = = ∼ 43.395 SiO(J 1–0, v 0) 43.423864 0.08 Core C, in an effort to characterize the penetration depth of CRs in = = ∼ 44.085 CH3OH(7(0)–6(1) A ) 44.069476 0.08 the core and qualitatively discuss the implications for the gamma- ++ ∼ 45.125 HC7N(J 40–39) 45.119064 0.09 ray and secondary X-ray synchrotron emission. = ∼ 45.255 HC5N(J 17–16) 45.26475 0.09 CO observations, such as those already obtained towards = ∼ 45.465 HC3N(J 5–4, F 5–4) 45.488839 0.09 = = ∼ RX J1713.7 3946, are ideal for tracing moderately dense gas 46.225 13CS(J 1–0) 46.24758 0.09 3 3− = ∼ ( 10 cm− ), but they do not necessarily probe well dense regions 47.945 HC5N(J 16–15) 47.927275 0.12 ∼ 5 3 34 = ∼ and cores (10 cm− ) that may play an important role in the transport 48.225 C S(J 1–0) 48.206946 0.12 = ∼ and interactions of high-energy particles. Dense gas may also influ- 48.635 OCS(J 4–3) 48.651604 0.13 = ∼ ence SNR shock propagation. To gain a more complete picture, we 48.975 CS(J 1–0) 48.990957 0.12 = ∼ performed 7 mm observations of high critical density molecules to probe the inner regions of cores and search for evidence of ISM disruption by the SNR shocks and star formation. Towards this goal, we The velocity resolutions of the 7- and 12-mm zoom-mode and used the Mopra 22-m single dish radio telescope in a 7-mm survey 1 3-mm wideband-mode data are 0.2, 0.4 and 1kms− , respec- to observe bands containing the dense gas tracer CS(J 1–0), the ∼ ∼ ∼ = tively. The beam FWHM of Mopra at 3, 7 and 12 mm are 36 shock tracer SiO(J 1–0) (Schilke et al. 1997; Martin-Pintado 3, 59.4 2.4 and 123 18 arcsec, respectively, and the point-± et al. 2000; Gusdorf= et al. 2008a,b) and star formation tracers ± ± ing accuracies are 6 arcsec. The achieved TRMS values for 7-mm CH3OH and HC3N (van Dishoek & Blake 1998). We chose the maps and individual∼ 3, 7 and 12 mm pointings are stated in Tables 1 western region of RX J1713.7 3946 due to the evidence of shock − and 2. interactions with the molecular gas. On-the-fly (OTF) mapping and pointed observation data were Additionally, a 12-mm observation of NH inversion transitions 3 reduced and analysed using the ATNF analysis programs, LIVEDATA, and archival 3-mm observations of CS(J 2–1) provided further 1 GRIDZILLA, KVIS, MIRIAD and ASAP. information towards Core C. = LIVEDATA was used to calibrate each OTF-map scan (row/column) using the intermittently measured background as a reference. A linear baseline subtraction was also applied. GRIDZILLA then com- 2 OBSERVATIONS bined corresponding frequency bands of multiple OTF mapping runs into 16 three-dimensional data cubes, converting frequencies 2 An 18 18 arcmin region (see Fig. 1) centred on (l, b) into line-of-sight velocities. Data were weighted by the Mopra sys- (346.991,× 0.408) that encompasses Cores A, B and C was mapped= − tem temperature and smoothed in the Galactic l–b plane using a by the 22-m Mopra telescope in the 7-mm waveband on the nights Gaussian of FWHM 1.25 arcmin. of the 2009 April 22 and 23 and 2010 April 11 and 21. The Mopra MIRIAD was used to correct for the efficiency of the instrument Spectrometer (MOPS), was employed and is capable of recording (Urquhart et al. 2010) for map data and create line-of-sight velocity- 16 tunable, 4096-channel (137.5 MHz) bands simultaneously when integrated intensity images (moment 0) from data cubes. in ‘zoom’ mode, as used here. A list of measured frequency bands, ASAP was used to analyse pointed observation data. Data were targeted molecular transitions and achieved TRMS levels are shown time-averaged, weighted by the system temperature and had fitted in Table 1. polynomial baselines subtracted. Like mapping data, deep pointing In addition to mapping, 7-mm deep ON–OFF switched pointings spectra were corrected for the Mopra efficiency (Ladd et al. 2005; (pointed observations) were taken on selected regions on the nights Urquhart et al. 2010). of the 2009 April 23 and 2010 March 16–18, and a 12-mm pointed observation was taken on the night of the 2010 April 10. Archival 3-mm Mopra data on Core C were utilized in the analysis and were 3 LINE DETECTIONS taken on the 2007 April 30 in the MOPS wide-band mode (8.3-GHz This investigation involved six different species of molecule and band). all detections are displayed in Table 2. Our 7-mm survey found the The H2O Southern Galactic Plane Survey (HOPS; Walsh et al. dense gas tracers CS, C34Sand13CS in the J 1–0 transition and 2008) surveyed the entire Galactic longitudinal extent of 34 = HC3N(J 5–4) (C S(J 1–0) and HC3N(J 4–5) emission maps RX J1713.7 3946 down to a Galactic latitude of 0◦.5, reaching a are in Section= A1). Various= detections of CH= OH are indicative − 1 − 3 noise level of T 0.25 K channel (ch)− . From these data, only RMS ∼ that these cores have a warm chemistry. Deep 12-mm observations a weak NH3(1, 1) detection towards Core C was found. We took measured two lines of rotational NH3 emission. In addition to these deeper 12-mm pointed observations towards this region in response to the HOPS detection, revealing NH3(1, 1) and NH3(2, 2) emission of a sufficient signal-noise ratio to extract some gas parameters. 1 See http://www.atnf.csiro.au/computing/software/

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Table 2. Detected molecular transitions from pointed observations. Velocity of peak, vLSR, peak intensity, TPeak, and FWHM, vFWHM, were found by fitting Gaussians before deconvolving with the MOPS velocity resolution. Displayed values include the beam efficiencies (Ladd et al. 2005; Urquhart et al. 2010), after a linear baseline subtraction. Statistical uncertainties are shown, whereas systematic uncertainties are 7, 2.5 and 5 per cent for the 3, 7 and 12 mm ∼ ∼ ∼ calibration, respectively (Ladd et al. 2005; Urquhart et al. 2010). Band noise, TRMS, integrated intensity, Tmb dv, possible counterparts and 12 and 100 µm IRAS flux, F12 and F100, respectively, (where applicable), are also displayed.

Object Detected TRMS Peak vLSR TPeak vFWHM Tmbdv Counterparts 1 1 1 1 (l, b) emission line (K ch− )(kms− )(K)(kms− )(Kkms− )[F12/F100 (Jy)]

Core A CS(J 1–0) 0.06 9.82 0.02 0.92 0.04 1.25 0.06 17.0 0.9 IRAS 17082 3955 = − ± ± ± ± − (346.93, 0.30) HC3N(J 5–4, F 5–4) 0.04 9.76 0.04 0.29 0.02 1.07 0.11 4.6 0.6 [5.4/138] ◦ − ◦ = = − ± ± ± ± SiO(J 1–0) 0.03 – – – = Core B CS(J 1–0) 0.06 – – – – = (346.93, 0.50) SiO(J 1–0) 0.03 – – – – ◦ − ◦ = CS(J 1–0) 0.05 11.76 0.01 2.12 0.02 2.08 0.03 65.2 0.9 = − ± ± ± ± Core C CS(J 2–1) 0.10 11.62 0.08 1.49 0.08 2.94 0.21 64.8 2.0 IRAS 17089 3951 = − ± ± ± ± − (347.08, 0.40) C34S(J 1–0) 0.04 11.83 0.04 0.37 0.02 1.40 0.09 7.7 0.7 [4.4/234] ◦ − ◦ = − ± ± ± ± C34S(J 2–1) 0.07 11.78 0.20 0.34 0.06 1.89 0.49 9.5 1.4 = − ± ± ± ± 13CS(J 1–0) 0.03 11.70 0.10 0.10 0.02 0.88 0.22 1.3 0.5 = − ± ± ± ± HC3N(J 5–4, F 5–4) 0.02 11.65 0.03 0.32 0.01 1.74 0.08 8.2 0.6 = = − ± ± ± ± CH3OH(7(0)–6(1) A )0.02 10.21 0.17 0.07 0.01 2.13 0.32 2.2 0.6 ++ − ± ± ± ± CH3OH(2( 1)–1( 1) E) 0.07 11.75 0.17 0.33 0.13 0.99 0.90 4.8 1.7 − − − ± ± ± ± CH3OH(2(0)–1(0) A ) 11.86 0.14 0.43 0.08 1.44 0.46 9.2 1.5 ++ ′′ − ± ± ± ± SO(2,3–1,2) 0.07 11.77 0.09 0.65 0.07 1.74 0.25 16.7 1.4 a − ± ± ± ± N2H (J 1–0) F1 2–1 0.08 11.61 0.03 1.14 0.03 2.18 0.08 36.8 1.1 + = = − ± ± ± ± F1 0–1 0.40 0.04 1.58 0.23 9.4 1.1 = ′′ ′′ ± ± ± F1 1–1 ′′ ′′ 0.76 0.03 0.87 0.04 9.8 0.6 = a ± ± ± NH3((1,1)–(1,1)) F F 0.03 12.04 0.04 0.34 0.02 1.46 0.09 7.3 0.7 → − ± ± ± ± F F 1b 0.07 0.02 1.5 0.5 → − ′′ ′′ ± ′′ ± 0.13 0.02 2.8 0.5 ′′ ′′ ± ′′ ± F F 1c 0.13 0.02 2.8 0.5 → + ′′ ′′ ± ′′ ± ′′ ′′ 0.12 0.02 ′′ 2.6 0.5 a ± ± NH3((2,2)–(2,2)) F F 11.69 0.10 0.16 0.02 2.02 0.26 4.8 0.8 → ′′ − ± ± ± ± SiO(J 1–0) 0.03 – – – – = Core D CS(J 1–0) 0.10 9.06 0.11 0.47 0.04 2.50 0.29 17.4 1.3 IRAS 17078 3927 = − ± ± ± ± − (347.30, 0.00) 0.10 71.25 0.46 0.15 0.04 3.38 0.36 7.5 1.2 [2.0/739] ◦ ◦ − ± ± ± ± SiO(J 1–0) 0.06 – – – – = Point ABm CS(J 1–0) 0.04 8.89 0.43 0.09 0.02 4 15.31.1 = − ± ± ± ± (346.93, 0.38) SiO(J 1–0) 0.06 – – – – ◦ − ◦ = aCentre line; bOuter satellite lines; cInner satellites lines. molecules, archival 3-mm data revealed detections of the J 2–1 Core A exhibits symmetric narrow line CS(J 1–0) emission, of 34 = 1 = transitions of CS and C S, transitions of SO and N H+ and further v 1.25 km s− , suggesting that the inner, dense core is not 2 FWHM ∼ detections of CH3OH. under the influence of an exterior shock. Fig. 1(b) shows that the forward shock is coincident with the outskirts of Core A such that the inner CS(J 1–0)-emitting region probably remains unaffected J = 3.1 CS( 1–0) detections by the RX J1713.7= 3946 shock, consistent with our observations. − Fig. 2 is a CS(J 1–0) map of the Core A–B–C region of Core C displays the strongest CS(J 1–0) emission of this sur- = RX J1713.7 3946.= CS(J 1–0) emission can be seen to be orig- vey, implying that this region probably harbours the largest mass inating from− the two most= CO(J 2–1)-intense regions, Cores dense core. CO(J 4–3) observations by Sano et al. (2010) sug- = 1 = A and C at line-of-sight-velocities of 10 and 12 km s− , gested that Core C contains a bipolar outflow, but we find no ob- respectively, consistent with CO emission∼− line-of-sight-velocities.∼− vious asymmetries in the CS(J 1–0) emission line profile or = The Core C CS(J 1–0) emission is coincident with the Core C map data. We do, however find a significant difference between infrared source, but= the Core A CS(J 1–0) emission peak is offset the red and blueshifted sides of CS(J 2–1) emission. For deep = from the Core A infrared source. This= discrepancy of 1 arcmin, switched pointing spectra, fitted Gaussians were subtracted from the similar to the size of the 7-mm beam FWHM, is not∼ evident for observed spectra of CS(J 1–0, J 2–1) emission, and the resul- = = CO(J 2–1) emission. tant spectra were integrated over velocity ranges chosen, by eye, to Figs= 3–9 show CS(J 1–0) spectra from pointed observations to- represent red and blue-shifted line wings. Integrating CS(J 2–1) = 1 1 = wards Cores A, B, C and D, and Point ABm. Corresponding CO(J emission over 4.1 km s− wide bands, 3.0 km s− either side of the 1–0) spectra (Moriguchi et al. 2005) are also shown in these figures,= peak emission, highlights a 2–2.5σ intensity difference between but the CO beam FWHM of 180 arcsec, corresponding to 9 red- and blueshifted sides, possibly tracing manifestations of the the 7-mm solid angle, means∼ that neighbouring gas is probably∼ × Core C bipolar outflow seen by Sano et al. (2010) in CO emission included in the beam average. lines. No significant asymmetry (<1σ ) is viewed in CS(J 1–0) =

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Figure 2. Mopra CS(J 1–0) integrated-intensity image (vLSR 13.5 1 = =− 1 to 9.5 km s ) with Nanten2 CO(J 2–1) (vLSR 18 to 0 km s ) − − = =− − contours (black) and two 8 µm point sources indicated by crosses. CO(J 1 1 = 2–1) contours span 5–40 K km s− in increments of 5 K km s− .CS(J =1 1–0) contours (white) are also shown, spanning from 0.4 to 2.0 K km s− in increments of 0.4 K km s 1. The beam FWHM of Mopra at 49 GHz is − Figure 5. Core C: CS isotopologue spectra towards Core C. The position of displayed in the bottom left-hand corner. Core C is that displayed in Table 2.

Figure 3. Core A: CS(J 1–0) spectrum (top) and CO(J 1–0) spectrum = = (bottom) towards Core A. The position of Core A is that displayed in Table 2.

Figure 6. Core C: various CO spectra towards Core C (Fukui et al. 2003; Moriguchi et al. 2005; Fukui et al. 2008; Sano et al. 2010). The position of Core C is that displayed in Table 2.

that Core D harbours an IRAS point source more luminous than that of the other cores associated with RX J1713.7 3946 (Moriguchi et al. 2005), but Core D also lies on the northern shock− front, another possible source of disruption. Towards Core D, a second peak at 1 v 70 km s− ( 6 kpc) was detected. This Norma-arm LSR =∼− ∼ Figure 4. Core B: CS(J 1–0) spectrum (top) and CO(J 1–0) spectrum gas, initially suggested by Slane et al. (1999) to be associated with = = (bottom) towards Core B. The position of Core B is that displayed in Table 2. RX J1713.7 3946, is probably unassociated, given the preference for a 1 kpc distance− (see Section 1). emission spectra, while in the plane of the sky, there is no signiﬁ- Deep observations on a location at the midpoint of Cores A and cant offset between the red- and blueshifted CS(J 1–0) emission B, Point ABm, revealed weak and moderately broad CS(J 1–0) = = peaks. emission of FWHM, vFWHM 4 1, possibly indicating the In the northern part of the remnant, Core D exhibits a CS(J existence of a passing shock, as= there± is no evidence to support 1 = 1–0) emission line with a FWHM of 2.5 0.3 km s− , slightly star-formation towards this location. This scenario is qualitatively larger than that for Cores A and C. This might± be expected given supported by the positional coincidence of Point ABm with the

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Figure 9. Point ABm: CS(J 1–0) spectrum (top) and CO(J 1–0) spec- = = trum (bottom) towards Point ABm. CS(J 1–0) emission has been box-car- = smoothed over six channels. The position of Point ABm is that displayed in Table 2.

but also initiate non-dissociative subsidiary shocks in dense gas, as discussed by Uchiyama et al. (2010) for older SNRs. Given the existence of dense gas in the region, as indicated by this study, one might indeed expect such secondary shocks if the gas lies within the SNR shell. In such scenarios, it may be expected that Si is sputtered from dust grains, increasing the gas-phase abundance of SiO in the post-shock region (see for example Schilke et al. (1997)). As we do not detect SiO towards this region of RX J1713.7-3946, we conclude that, if the SN shock is indeed interacting with the surveyed gas as indicated by high energy emissions (see Section 1), it has not produced SiO at detectable levels. Detections of the organic molecules HC3NandCH3OH were recorded from Core C and HC3NfromCoreA.CH3OH is believed to be the product of grain-surface reactions. Weak emission from this molecule suggests that conditions within the core are capable of evaporating a signiﬁcant amount of the ice mantles of grains into Figure 7. Core C: various spectra towards Core C. The position of Core C gas phase. is that displayed in Table 2. N2H+ and NH3 were both detected inside Core C. NH3 is generally thought to be a tracer of cool, quiescent gas, as its main reaction pathways do not require high temperatures (Le Bourlot 1991). The main reaction pathway of N2H+ is through molecular nitrogen interacting with H3+ (Hotzel, Harjul & Walmsley 2004), so N2H+ can be thought as a tracer of molecular nitrogen.

4 MILLIMETRE EMISSION-LINE ANALYSES

Local thermodynamic equilibrium (LTE) analyses using NH3(1,1), NH3(2,2), CS(J 1–0), CS(J 2–1) and N2H+(J 1–0) were applied to estimate= gas parameters.= For brevity, the mathematics= of Figure 8. Core D: CS(J 1–0) spectrum (top) and CO(J 1–0) spectrum our molecular emission analyses is not presented here, but in Ap- = = (bottom) towards Core D. CS(J 1–0) emission has been box-car-smoothed pendix B. Optical depths were found by taking intensity ratios of = over six channels. The position of Core D is that displayed in Table 2. emission line pairs. Rotational (or excitation in the case of N2H+) temperatures could then be estimated from LTE assumptions allow- western shock-front (see Section 1), but the low signal-to-noise ratio ing total column densities to be calculated. The methods used are means that any conclusions drawn from this are low confidence. only briefly described here, but details are presented in references. Alternatively, small-scale unresolved clumps (perhaps from star After making some assumptions about core structure, masses and formation) may be responsible for the detection. densities were estimated. Gaussian functions were fitted to all emission lines using a χ 2 minimization method. Lines with visible hyperfine structure (NH 3.2 Other molecular species 3 and N2H+) had each ‘satellite’ line constrained to be a fixed dis- No emission from the shock tracer, SiO, was seen in maps or tance (in vLSR space) from the ‘main’ line. In addition to this, for pointed observations. The RX J1713.7 3946 shock-front likely ex- simplicity, all NH3(1,1) emission lines were assumed to have equal 1 − ceeds 1000 km s− , which may dissociate molecules in the region, FWHM.

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4.1 Optical depth corrects for the size of the source compared to the beam FWHM (Urquhart et al. 2010), where R is the source radius and θ is The NH (1,1) inversion transition has five distinctly resolvable mb 3 the main beam FWHM. The main beam FWHM for CS(J 2–1), peaks and the N H (J 1–0) rotational transition has three (fur- 2 + N H (J 1–0), CS(J 1–0) and detected NH lines are= 36 3, ther splitting is present= in both molecular transitions, but remain 2 + 3 36 3, 59.4= 2.4 and= 123 18 arcsec, respectively (Ladd et± al. unresolved due to line overlap). The relative strengths of these lines 2005;± Urquhart± et al. 2010). ±fK tends to 1 for beam sizes smaller (increasing in velocity space) are [0.22, 0.28, 1, 0.28, 0.22] for than the core size. NH3(1,1) (Ho & Townes 1983) and [0.2, 1, 0.6] for N2H+(J 1–0) (Womack, Ziurys & Wychoff 1992). Here, we refer to the= centre lines as ‘main’ lines and all others as ‘satellite’ lines. 4.4 LTE mass and density To estimate optical depths, τ,ofNH(1,1) and N H (J 1–0), 3 2 + LTE masses, M , were calculated assuming a spherical, homoge- any deviations from the aforementioned relative line strengths= of LTE neous core of radius, R, composed of molecular hydrogen. Average main and satellite emission peaks were assumed to be due to optical abundances with respect to H2 for CS, N2H+ and NH3 were as- depth effects, allowing the use of the standard analysis presented 9 10 sumed to be 1 10− (Frerking et al. 1980), 5 10− (Pirogov in Barrett, Ho & Myers (1977). Note that the optical depths quoted × 8 × et al. 2003) and 2 10− (Stahler & Palla 2005), respectively. for these two molecular transitions are those of the central emission × lines, which in both cases have unresolved structure. By assuming abundance ratios between CS and rarer isotopo- 4.5 Virial mass logue partners, C34Sand13CS, a similar method can be used to Under the assumption that turbulent energy balances gravitational estimate the optical depth of CS emission lines. Values of 22.5 energy within a core, a virial mass and 75 were assumed for the abundance ratios [CS]/[C34S] and [CS]/[13CS], respectively. CS emission without detected isotopo- R vFWHM Mvir k 1 [M ](2) logue pairs were approximated as being optically thin. = 1pc1kms− ⊙ Where multiple optical depth values were calculated (4 for can be calculated, where R is the radius of the core, vFWHM is NH (1,1), 2 for N H+(J 1–0), 3 for CS(J 1–0,2–1), respec- 3 2 = = the emission line full width at half-maximum and k is a coefficient tively), an average was taken, weighting by the inverse of the optical that depends on the density profile of the core. The coefficient k is depth variance. 444 for a Gaussian density profile (Protheroe et al. 2008), 210 for 2 constant density and 126 for density, ραR− profile (MacLaren, 4.2 Temperature and column density Richardson & Wolfendale 1988). Recent CO observations suggest that the latter is the best fit (Sano et al. 2010), so k 126 is assumed. Upper-state column densities, NU,forNH3(1,1), N2H+(J 1–0) A core radius consistent with previous beam dilution= assumptions and CS(J 1–0, J 2–1) were calculated via equation= (9) of = = is assumed. For CS emission, virial masses were calculated using Goldsmith & Langer (1999). the rarer isotopologue C34S to minimize the effect of optical depth broadening. NH3. The LTE analysis outlined in Ho & Townes (1983) and sum- As the virial mass is not always consistent with LTE mass, the marized in Ungerechts, Winnewisser & Walmsley (1986) was used molecular abundances that give an LTE mass equal to that of the to find rotational temperature, Trot, and total column density, Ntot, virial mass was calculated in each case. of NH3 from the NH3(1,1) and NH3(2,2) emission lines. Kinetic temperature, Tkin, was calculated from an approximation presented in Tafalla et al. (2004). 5 CORE PARAMETERS The critical density of the J 1–0 transition of CS is 8 N2H+. Given the smaller beam FWHM of the 3-mm observations 4 3 = ∼ × 10 cm− , implying that the density of regions traced by this emis- with Mopra (36 arcsec < 0.2 pc at 1 kpc), a filled-beam assumption sion, in this case, Cores A, C and D, is probably distributed around for the measured N H+(J 1–0) lines was used to estimate the 2 = this value. Cores A, C and D are coincident with infrared sources excitation temperature, Tex, in order to find the total column density (Moriguchi et al. 2005), so the detection of CS(J 1–0) emis- assuming an approximation of a linear, rigid rotator in LTE (Hotzel sion from these regions supports the notion that these= cores harbour et al. 2004). dense warm gas.

CS. Because of the small separation in energy ( 4.7 K), where both CS J 1andJ 2 column densities were∼ calculated, a 5.1 Core C weighted average= was taken= and assumed to represent the CS(J 1) = The 3, 7 and 12 mm observations on Core C revealed emission from column density (after a beam-dilution correction, see Section 4.3). six different molecular species (see Table 2). Using three of these Where possible, an NH3-derived temperature would be assumed, molecular species, detailed analyses were performed. Results are otherwise a temperature of 10 K was assumed and applied in an displayed in Table 3, and discussed in the following subsections. LTE approximation to calculate the total CS column density.

5.1.1 Core C size 4.3 Beam dilution Using CS(J 1–0) map data, we can estimate the core size by A beam dilution factor, f , and coupling correction factor, K, were deconvolving= the intensity distribution with a Gaussian of FWHM applied. Multiplying the column density by the factor equal to the 7-mm beam FWHM. We assume that the Core C radial 1 4R2 − density proﬁle is well approximated by a Gaussian and assume the fK 1 exp ln 2 (1) 2 2 2 = − − θ 2 relation r s r′ ,wherer, s and r′ are the observed radius, beam mb = +

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS Dense gas towards SNR RX J1713.7 3946 2237 − Table 3. Core C parameters derived from three different molecular species assuming a core radius 0.12 pc. Optical depth, rotational temperature, kinetic temperature, molecular column density, H2 column density, LTE mass, LTE density, virial mass and molecular abundance are denoted by τ, Trot,

Tkin, NX, NH2 , MLTE , nH, Mvir and χ vir. Statistical errors (rounded to the nearest signiﬁcant ﬁgure) for all variables independent of virial equilibrium assumptions are shown. Systematic errors are not displayed, but are discussed in the text.

a b,c b,c,d b,c,d b,c,d b a,b,c Emission τ Trot NX NH2 MLTE nH Mvir χ vir 13 2 22 2 5 3 lines (K) ( 10 cm− )(10 cm− )(M)(10 cm− )(M)[X]/[H2] × × ⊙ × ⊙ e 8 NH3(1,1) 1.81 0.51 21 6 210 40 11 28010 3 0.5 30 5 10 ± ± ± ± ± ± × − NH3(2,2) 0.40 0.08 ± b,f 10 N2H (J 1–0) 1.06 0.23 4.5 0.2 5 11138020 3 170510 + = ± ± ± ± ± ± × − CS(J 1–0) 2.71 0.29 5.5 0.4g 55 44032130h 1 10 9 h = ± ± ± ± ± × − CS(J 2–1) 50h 7 10 10 h = × − aEqual excitation temperature assumption; bAssuming a source of radius 25 arcsec ( 0.12 pc); cLTE assumption; dAssuming abundance ratios stated e f g ∼ h 34 in Section 4.4; Tkin 26 8; Tex; Assuming the temperature calculated from NH3; Using the optically thin isotopologue C S. = ±

half width at half-maximum (HWHM)and deconvolved radius, re- 1–0) and CS(J 2–1) is different to that emitting in NH3(1,1). spectively. By extending the definition of s to be the quadrature sum The systematic error= caused by this effect is difficult to quantify, of both the 7 mm HWHM (29.7 arcsec) and the Gaussian smoothing but given the factor 2 agreement between CS and NH3-derived core HWFM of our maps (37.5 arcsec), we obtained a dense core radius mass under a ‘perfect-correspondence’ assumption, it is expected of 25 arcsec. Thus, we assumed a core radius of 0.12 pc (25 arcsec to be small. at a∼ distance of 1 kpc) in our calculations, yielding correction fac- The CS J 1andJ 2 states are separated by only 2.35 K and = = tors, fK, of 1.3, 1.3, 2.5 and 9.1 for CS(J 2–1), N H+(J 1–0), a comparison of the two emission lines to retrieve a rotational tem- = 2 = CS(J 1–0) and NH3 lines, respectively. There is a 50 per cent perature would likely be dominated by uncertain systematics since systematic= uncertainty associated with our calculated∼ radius that the two measurements were taken with different spectrometers and propagates into LTE mass (M ), density (n ), virial mass (M ) were separated by 2 yr. As we expect the J 1andJ 2 states of CS LTE H2 vir = = and virial abundance (χ vir). We do not account for this systematic to be roughly equally populated, the optical depths and upper-state in Table 3, but discuss it in Section A2. column densities were averaged to minimize instrumental systematic uncertainties (deemed to be larger than errors introduced by the equal-population assumption). 5.1.2 Mass and molecular abundances Of course, all analyses thus far have assumed LTE, which may not be valid, as suggested by CS J 1–0 and J 2–1 intensities. The adoption of molecular abundance ratios is probably the dom- We investigate how the calculated gas= parameters= may differ from a inant source of systematic uncertainty. It is not uncommon for more accurate non-LTE statistical equilibrium treatment using the molecular abundances to vary by an order of magnitude between freely available software RADEX (van der Tak et al. 2007). Through different Galactic regions, but given the order-of-magnitude agree- RADEX modelling, we conclude that for a CS column density of ment between the calculated LTE masses (40–80 M ), the assumed 1 1014 cm 2, the molecular hydrogen density may not exceed abundances are probably valid. Under the assumption⊙ that turbulent − 6× 104 cm 3 at a temperature of 10 K, and may be smaller for energy balances gravitational energy within Core C (which may not − ∼increasing× temperature. This solution would have implications for be valid in a core that is shock disrupted), virial masses (30–70 M ) the calculated mass and abundance, being 75 per cent smaller and for these three molecular species allowed abundances with respect⊙ 3 10 9, respectively. We note that in∼ order to correctly simu- to molecular hydrogen to be calculated. We saw no significant de- − ∼late× the observed 13CS intensity using the gas parameters outlined viationinCS,N H and NH abundance ( 1 , 1 and 2.5 , 2 + 3 above (which were consistent with CS and C34S emission), the as- respectively). ∼ × ∼ × ∼ × sumed value of [CS]/[13CS] must be adjusted to 110. Although a Systematic uncertainties in beam efficiency, beam dilution and limited investigation of CS isotopologue abundance∼ is presented in beam shape corrections are difficult to account for, but propagating Section A4, we leave a more detailed examination of this for later published systematic error estimates leads to greater than 30 per cent work. systematic error in N H and CS LTE mass and density estimates, 2 + We note that our measurements seem to trace less mass than but has only a 5 per cent effect on NH -derived mass and density 3 CO(J 1–0) observations by Moriguchi et al. (2005), who calculate estimates, since∼ many such effects cancel-out in the analysis. a Core= C mass of 400 M . This suggests that CS(J 1–0), NH In our CS analysis of Core C, several assumptions were made. 3 and N H are tracing∼ different⊙ regions of the molecular= cloud to CO, The use of an NH -derived temperature introduces some uncer- 2 + 3 most likely a denser, inner component. The Core C radial density tainty, as NH emission may trace a region of different temperature 3 profile is discussed further in Section A3. to that of CS emission. Tafalla et al. (2004) examined the starless cores L1498 and L1517B in detail and found significant variation in CS and NH3 molecular abundances with radius. NH3 (para-NH3) 8 5.2 Cores A and D abundance peaked at 1.4 and 1.7 10− towards the core cen- ∼ 9 × 34 tres and dropped to 5 10− at 0.05 pc, while CS (and C S) Table 4 shows gas parameters derived for Cores A and D. We abundances decreased∼ towards× the centre,∼ with models assuming a estimate the Core A radius to be 0.3 pc (60 arcsec at 1 kpc) via the central 0.05 pc hole, likely due to CS depletion on to dust grains, method described in Section 5.1.1.∼ Core A, being more extended providing∼ a better fit to observations than constant-abundance mod- than Core C, and having an infrared source possibly offset from the els. It follows that it is feasible that the region emitting in CS(J CS(J 1–0) peak emission (see Section 3.1), may be composed = =

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Table 4. CS(J 1–0) parameters for Cores A and D assuming a kinetic temperature of 10 K. No emission from a rarer isotopologue of = 34 CS is detected for these cores, so the maximum optical depth is calculated from the 1 TRMS noise in the C S(J 1–0) band. We display = derived values for both optically thin and thick assumptions for parameters that depend on optical depth, giving a range of solutions. Optical depth, molecular column density, H2 column density, LTE mass, LTE density, virial mass and molecular abundance are denoted by τ, NCS,

NH2 , MLTE , nH, Mvir and χ vir.

a,b a,b,c a,b,c a,b,c Core τ NCS NH2 MLTE nH Mvir χ vir 12 2 21 2 3 3 ( 10 cm− )(10 cm− )(M)(10 cm− )(M) [CS]/[H2] × × ⊙ × ⊙ Core A 0–0.44 3–4 3–4 12–15 3–4 60 2–3 10 10 × − Core D 0–4.1 40–170 40–170 30–120 100–500 100 3–10 10 10 × − aAssumed rotational temperature of 10 K. bCorrected for beam dilution assuming a source of radius of 60 arcsec ( 0.30 pc) for Core A and 25 arcsec ( 0.12 pc) for Core D. ∼ ∼ cAssuming abundance ratios stated in Section 4.4. of two smaller clumps including one emitting in infrared. These of CR protons of energy, EP, from the outer shock of the SNR, to- inhomogeneities may even be the result of an outflow originating wards the centre of this molecular core, applying time limits based from IRAS 17082 3955, but this scenario remains as speculation. on assumptions concerning the age of RX J1713.7 3946, and the As our maps do− not encompass Core D, we cannot estimate its escape time of CRs from the SNR outer shock. − radius and assume a radius of 0.12 pc for Core D (see Section A2 for alternate radius assumptions). The molecular core. We modelled a core with radius set equal to 3 Given our assumptions, LTE and viral mass solutions for Core 0.62 pc and a density of 300 cm− , consistent with volume-averaged A and D range from 12 to 120 M . We calculate CS abundances density estimates from CO(J 2–1) measurements by Sano et al. a factor of 0.2 to 1 of that assumed,⊙ and, like in Core C, we note (2010) for Core C. The diffusion= of protons is dependent on the that CS(J 1–0) seems to trace less of the total mass than CO(J strength of magnetic turbulence within the region. These magnetic = = 1–0). Core A and D CO-derived masses are 700 and 300 M , fields are generally assumed to be frozen-in to the gas, such that ∼ ∼ ⊙ respectively (Moriguchi et al. 2005). Similar to Core C, CS likely denser gas implies larger magnetic field strengths, B(nH2 ). If we traces the denser, inner components of Cores A and D. assume the relation stated in Crutcher (1999): n B(n ) 100 H2 [µG], (3) H2 ∼ 104 cm 3 6 HIGH-ENERGY PARTICLE PROPAGATION − the average magnetic field strength inside the core is B 17 µG. INTO DENSE CORES ∼ In the context of understanding the nature of the TeV gamma- ray emission from SNRs, of considerable interest is the energy- 6.1 Cosmic ray proton transport dependent propagation of high-energy protons (CRs) and electrons In the hadronic scenario for gamma-ray production, CR protons into dense cores, which may lead to characteristic gamma-ray spec- diffuse from acceleration sites and collide with matter to create tra from GeV to TeV energies. This effect could offer a new way TeV emission. The rate of diffusion of CRs is governed by magnetic to identify the parent particles (hadronic versus leptonic) responsi- turbulence, the characteristics of which are somewhat uncertain. ble for gamma-ray emission, provided such cores can be spatially If we assume that RX J1713.7 3946 is 1600 yr old (Wang et al. resolved in gamma-rays. Gabici et al. (2007) investigated the prop- 1997), we have a limit on the amount− of time∼ CR protons have had to agation of CR protons into molecular clouds and found that in be accelerated in the SNR shock and diffuse into the core. Our goal some models, suppressed diffusion of low-energy CRs resulted in was to examine how far CR protons of different energies penetrated a gamma-ray spectrum towards the cloud centre that is harder than into the core. In Fig. 10, we have visualized the results (a slice view that towards the cloud edges. This effect became more pronounced of the core) of the following equation, which gives the average radial for more centrally condensed gas distributions. Similar phenomena penetration distance of a CR proton within our modelled molecular may in fact be occurring towards the dense cores associated with core: RX J1713.7 3946. − R 0.62 6D(E ,B)[1600 t ][pc], (4) We therefore investigated CR diffusion into a molecular core = − P − 0 located adjacent to a CR accelerator. Our model is a simplistic ap- where D(EP, B) is the diffusion coefficient that depends on CR proach that only aims to show in principle the effects that dense energy, EP, and magnetic field strength, B. Equation (4) returns gas could have on the spatial distribution of CR protons of different the average distance a CR of energy, EP, will penetrate into the energies, which will have knock-on effects on the gamma-ray and modelled molecular core given 1600 yr. X-ray spectra from various parts of the core. The model configura- The start time, t0, was set equal to the minimum of the average tion is based on the Core C molecular core, and its apparent location time taken for the CR proton to escape the SNR shock, tesc, and the with respect to RX J1713.7 3946 as an assumed CR accelerator. time taken for the SNR shock to reach the boundary of the core tcore: CR transport in this region is− expected to be in the diffusion regime, t min(t ,t )[yr]. (5) since CR (proton) gyro radii at TeV energies are expected to be 0 = esc core 4 <10− pc for typical magnetic field strengths of 10 µG or more. The value for tcore 600 yr was based on the Sedov solution for Our model core is placed 5 pc from the centre of a core-collapse supernova∼ explosion into a wind-driven bubble, 7/8 RX J1713.7 3946, which has an outer shock radius growing with where the shock radius evolution is proportional to t− (Ptuskin & time to eventually− reach the core, as in the situation assumed for Zirakashvili 2005). The time-dependent shock radius and energy- Core C. We then calculated the propagation distance (via diffusion) dependent escape time mean that some CRs will escape the shock

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS Dense gas towards SNR RX J1713.7 3946 2239 − before it contacts the core. After the shock has passed the core ( 600 yr), it is assumed that CRs of all energies can reach the core boundary.∼ For the moment we ignore this CR diffusion time from the shock to the core, which is at most 100 yr for the highest energy CRs since it is assumed to take place∼ in a relatively low 3 magnetic (B few µG) and density (n 1cm− ) environment. ∼ Escape time. With the assumption that within a SNR the highest energy particles ( 1 TeV) are accelerated in the transition from the free-expansion phase≫ to the Sedov phase (Ptuskin & Zirakashvili 2005) within a short time-scale (Uchiyama et al. 2007), we used the following parametrization for the CR proton escape time (Gabici, Aharonian & Casanova 2009): 1/δ EP − tesc(EP) tSedov [yr], (6) = EP,max

where EP,max is the maximum possible CR proton energy, set equal to 5 1014 eV following Caprioli, Blasi & Amato E (2009) and × Casanova et al. (2010), tSedov is the time for the onset of the Sedov phase, set equal to 100 yr and δ is a phenomenological parameter that describes the energy-dependent release of CRs. δ is set equal to 2.48 assuming that 1015 eV CRs are accelerated near the start of the Sedov phase reducing∼ to 109 eV near the end (see Gabici et al. 2009). ∼

Diffusion. Gabici et al. (2007) considered the time-scales involved in different CR transport processes within a dense 20-pc-diameter molecular cloud. They demonstrated that the dynamical (free-fall) and advective (turbulent) time-scales involved were likely an order of magnitude larger than the time-scale for inelastic proton–proton interactions and a varying amount larger than diffusion time-scales. For our model core, we calculated dynamical and advective time- scales of >104 yr, so we too ignore these mechanisms and only consider proton–proton interactions (see later) and diffusion, using a diffusion coefﬁcient parametrized as

0.5 EP/GeV 2 1 D(E ,B(r)) χD [cm s− ], (7) P = 0 B/3 µG 

where D0 is the Galactic diffusion coefficient, assumed to be 3 27 2 1 10 cm s− to fit CR observations (Berezinskii et al. 1990), and× χ is the diffusion suppression coefficient (assumed to be <1 inside the core, 1 outside), a parameter invoked to account for possible deviations of the average Galactic diffusion coefficient inside molecular clouds (Berezinskii et al. 1990; Gabici et al. 2007) which is largely unknown.

Interactions. For energies above 300 MeV proton–proton interactions dominate over ionization interactions∼ (Gabici et al. 2007), so we consider the rate of hadronic CR interactions with molecular gas protons and ignore ionization losses. Assuming an inelasticity of 0.45 (two interactions give 79 per cent energy loss) and a proton–proton cross-section of 40 mb,∼ appropriate for TeV energies, the lifetime of this proton–proton interaction process is

1 5 nH(r) − Figure 10. The logarithm of the minimum energy CR proton able to pen- τpp 6 10 [yr]. (8) = × 100 cm 3 etrate into different radii of our simulated core. The results, presented as − 2D slices, from three different diffusion suppression coefﬁcients χ are dis- Thus, CRs in the core have a large proton–proton interaction lifetime played. Note that the arcsec scale for penetration distance assumes a distance of 105 yr, so we do not model this process. of 1 kpc. Hatching indicates a lack of CR inhabitance of CRs. ∼ Diffusion suppression and results. Diffusion-suppression coefﬁ- 3 4 5 cients χ 0.1, 0.01, 10− ,10− and 10− were trialled for proton =

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS 2240 N. I. Maxted et al. energies 1010,1010.5,upto1014 eV. This wide range of χ values these quantities vary with radius. Compared to the case for a vary- were chosen to investigate the level of CR penetration with results ing diffusion coefficient resulting from a radially dependent density from the smaller χ values displayed in Fig. 10. (see equations 3 and 7), our homogenous core model may underes- For χ 0.1 and 0.01, all CR energies were able (on average) to timate the CR penetration depth in the outer region of the core, and = 3 reach the inner core within the age of the system. For χ 10− , some overestimate the penetration depth towards the inner region of the energy-dependent penetration could be seen, as CRs= of energies core. In future work we will consider CR propagation into a core 1010 and 1010.5 eV did not reach the inner core. Energy separation with a radially varying diffusion coefficient based on the measured became more prominent with smaller values of χ, as illustrated in power-law radial density profile from CO measurements n(r) 4 5 12.5 14 5 2.2 3 ∼ Fig. 10. For χ 10− and 10− , CRs of energy 10 to >10 10 /(1 (r/0.1 pc) )cm− (Sano et al. 2010). This model should are now excluded= from the central regions of the core. This effect be three-dimensional+ and predict a line-of-sight view of gamma/ would have implications for the spectrum of gamma-ray emission, X-ray emission morphology towards the core. with the TeV gamma-ray spectrum becoming progressively harder Another limitation concerns the implications of the extremely low 5 towards the core’s centre. values of diffusion suppression we have used down to χ 10− . It is unclear whether such extreme cases of diffusion suppres- For such cases, which represent highly turbulent magnetic fields,= the 5 sion down to χ 10− required to produce these energy-dependent possibility of second-order Fermi reacceleration of the CRs might penetration effects= on such small scales are plausible. Radio con- apply as discussed by Dogiel & Sharov (1990). Uchiyama et al. tinuum measurements by Protheroe et al. (2008) when compared (2010) have in fact considered this effect in accounting for the GeV to the GeV gamma-ray emission have suggested upper limits for χ to TeV gamma-ray spectra towards several evolved SNRs (W51C, < 0.02 to <0.1 (dependent of the assumed magnetic field) inside W44 and IC 443) by considering the reacceleration of diffuse CRs the Sgr B2 molecular cloud (see also Jones et al. 2011). Suppressed inside clouds disturbed by a supernova shock. Such effects may CR diffusion (χ 0.01–0.1) is also indicated when explaining the occur in molecular cores associated with RX J1713.7 3946, par- GeV to TeV gamma-ray∼ spectral variation seen in the vicinity of ticularly those contacted by the SNR shock but at this− stage we several evolved SNRs (e.g. Gabici et al. 2010). Moreover it has leave this as an open question. Finally, there may be a regular (or been recognized that suppressed diffusion could be expected in ordered) magnetic field component, which if present may either turbulent magnetic fields likely to be found in and around shock- assist or hamper the penetration of CRs depending on the strength disrupted regions (e.g. Ormes, Ozel & Morris 1988). Overall, we and orientation of this field component. Such modelling is beyond regard these uncertainties in particle transport properties as mo- the scope of this investigation, but should be considered in more tivation for investigating the effects of a wide range of diffusion detailed models. suppression coefficients, as applied to our model core which may also be similarly shocked and turbulent. 6.2 Gamma-rays from Core C From a more theoretical standpoint, the level of CR diffusion suppression that may be expected is still somewhat unclear. Yan, We can expect broad-band GeV to TeV gamma-ray emission from Lazarian & Schlickeiser (2012) recently investigated the effect of CRs penetrating the core as they interact with core protons. The CR-induced streaming instabilities, distortions of magnetic field level of the gamma-ray emission will reflect the energy and spa- lines caused by the flow of CRs, on CR acceleration within SNRs. tial distribution of CRs within the core coupled to the mass of The authors expressed interest in solving for a diffusion coefficient protons they interact with (see e.g. Aharonian 1991; Gabici et al. in the region surrounding SNRs by incorporating both streaming in- 2007). Variationsin the gamma-ray spectrum will reflect the energy- stabilities and background turbulence. Their future work will help to dependent penetration depth of CRs, and would be a feature only constrain the level of CR diffusion suppression that can be plausibly resolvable in gamma-rays with an angular resolution of 1 arcmin expected inside gas associated with SNRs. or better according to the size of the cores. The 6 arcmin angular We also note that an additional CR component from the Galactic resolution offered by HESS is at present not sufficient∼ to probe for diffuse background ‘sea’ of CRs will be incident on the core. Given such spectral variations. 5 this is an ever-present component, the penetration of these diffuse For a wide range of diffusion suppression factors χ 10− to 3 = CRs will not be limited by SNR age, but by the age of the core, 10− , our simple model of Core C suggests that lower energy CRs and possibly by the energy loss time-scale τ pp due to proton–proton can be prevented from reaching its centre. For the more severe 4 5 collisions (equation 8). For our model core with average density values of χ 10− and 10− , the CR penetration to the core centre 3 = n 300 cm− , τ will not be the dominant loss mechanism, but can be limited to CRs of TeV or greater energies, which could lead = pp will become more significant in the central region (τ pp 600 yr to considerable differences in the gamma-ray spectra seen towards 5 3 ∼ for n 10 cm− ). The dynamical age of Core C is estimated at the centre and edge of the core. 105 yr= (Moriguchi et al. 2005) which is similar to the energy The overall gamma-ray flux expected from dense cores towards ∼loss time-scale for our averaged-density model core. For most of RX J1713.7 3946 has been discussed by Zirakashvili & Aharonian the χ values we consider, these time-scales are significantly larger (2010) (see their− fig. 14). They suggested an enhanced TeV hadronic than the time taken for CRs to diffuse into the core centre. For component towards molecular cloud cores (with combined mass 5 10 12 2 1 an example extreme case, it takes 5 10 yr for a 10 eV CR 1000 M ) may be found at a level of 6 10− erg cm− s− ∼ 5 × ∼ ∼ × to reach the core centre for χ 10− , so diffuse CRs will likely for energies⊙ above 10 TeV, which would result from CRs of penetrate the core. However, the= energy density of diffuse CRs, energy above 100∼ TeV entering the core, which could be the assumed to be approximately similar to the Earth-like level of CRs, case for most levels∼ of diffusion suppression. For these gamma- 4 would be considerably smaller (a factor of 10− ) than the local ray energies the dense-core hadronic component may reach or CR component due to an adjacent SNR (e.g.∼ Aharonian & Atoyan even exceed the SNR-wide leptonic inverse-Compton component. 1996), so we can therefore neglect it here. The >10 TeV gamma-ray flux from the central regions of Core C, Our core model reflects only average values of density and mag- which is 40–80 M based on our measurements, may therefore 13⊙ 2 1 netic field as so will have limitations in comparison to a core where reach a few 10− erg cm− s− , possibly making it detectable by ×

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS Dense gas towards SNR RX J1713.7 3946 2241 − future more sensitive gamma-ray telescopes such as the Cherenkov 7 SUMMARY AND CONCLUSION Telescope Array (CTA; The CTA Consortium 2010). With its ex- We used the Mopra 22-m telescope to map in 7-mm lines a re- pected 1 arcmin or better angular resolution, CTA could also poten- gion of gas towards the western rim of the gamma-ray-emitting tially probe for energy-dependent penetration of the parent CRs, by SNR RX J1713.7 3946, encompassing the molecular cores A, B examining the flux and spectra from the inner to outer regions of and C (labelled by− Moriguchi et al. 2005). Deep 7- and 12-mm the core. pointed observations were also taken towards several of these regions (including Core D in the eastern rim) and we analysed 6.3 Electron transport and X-ray emission towards Core C archival 3-mm data towards Core C. Our goals were to investi- As discussed in Section 1, two synchrotron X-ray emission peaks gate the extent and properties of the dense gas components towards RX J1713.7 3946 and to complement previous CO studies of the can be observed towards the boundary of Core C (Fig. 1b). These − peaks are perhaps due to increased shock interaction with the dense low to moderately dense gas (Fukui et al. 2003; Moriguchi et al. gas (see Sano et al. 2010; Inoue et al. 2012) giving rise to a region of 2005; Fukui et al. 2008; Sano et al. 2010). The major conclusions enhanced magnetic field and/or electron acceleration. The observed from our observations are summarized as follows. synchrotron X-ray emission can be produced either by electrons accelerated directly by the SNR shocks outside of Core C or, by the secondary electrons from CR proton interactions with ambient gas. (1) Detection of CS(J 1–0) emission towards three of the four In the latter case, the X-ray emission spectrum could be influenced cores sampled (Cores A,= C and D which have coincident infrared 4 3 by the energy-dependent penetration of CRs into the core and for emission) confirming the presence of high-density (>10 cm− )gas. 4 strong CR diffusion suppression (χ 10− ), one might expect an (2) Detection of moderately broad CS(J 1–0) emission to- X-ray spectral hardening towards the≤ core centre, in the same way wards a position in between Cores A, B and C (labelled= Point ABm) as for gamma-rays discussed in Section 6.2. which is towards the X-ray outer shock. This broad gas may result The dense gas and high column density from Core C will also sup- from the SNR shock passing through, although no shock-tracing press the X-ray flux for energies less than 5 keV via photoelectric SiO emission was observed at this position. absorption. Thus some X-ray emission may∼ actually originate from (3) The LTE mass for the brightest core, Core C, was estimated within or behind Core C. The X-ray flux decrease seen in going using three different molecular species, with results ranging from from the boundary of Core C to its centre is 95 per cent. As- 40 M from CS observations to 80 M from NH3 and N2H+ suming the cross-section for photoelectric absorption∼ by hydrogen, ∼observations.⊙ The range of masses is most⊙ likely attributed to un- 23 2 σ ν 10− cm (at 1 keV), a flux decrease of 95 per cent cor- certainty in molecular abundances with respect to molecular hydro- ∼ ∼ 23 2 responds to a traversed column density of NH 3 10 cm− , gen. Virial assumptions allowed molecular abundances with respect ∼ × 8 10 similar to the column density towards Core C from our CS, to molecular hydrogen of 5 10− , 5 10− and 0.7 to 9 ∼ × ∼ × ∼ N2H+ and NH3 observations which pertain to the core centre 1 10− for NH ,N H+ and CS, respectively, to be calculated for × 3 2 (see Table 3). Therefore it is possible that keV X-ray emission, Core C. Preliminary non-LTE RADEX modelling suggests a factor of either from secondary electrons produced deep within Core C from 2 lower density than our LTE results. penetrating CRs or from external electrons directly accelerated out- (4) Cores A and D were found to have LTE masses of 12–15 side and then entering Core C, is absorbed by gas within the core. and 30–120 M , respectively, as traced by CS(J 1–0) emission, A potential way to discriminate between these two scenarios although these⊙ values are subject to core–radius uncertainties.= would be to have arcmin angular resolution imaging of >10 keV (5) The inferred column density of our CS and N2H+ measure- X-rays, for which photoelectric absorption is negligible. Forthcom- ments towards Core C could lead to considerable photoelectric ab- ing hard X-ray telescopes such as Astro-H (Takahashi et al. 2010) sorption ( 95 per cent) of the <5 keV X-ray emission. The small- and NuSTAR (Harrison et al. 2010) are expected to have such scale keV∼ X-ray features on the border of Core C therefore might performance. Any >10 keV X-ray emission centred on or peaking not represent the complete X-ray emission towards this core. towards the centre of Core C may indicate the presence of pen- (6) We investigated energy-dependent diffusion of TeV cosmic etrating high-energy CRs, particularly if the energy spectrum of ray protons into Core C using a simple model for the core based the X-rays hardens towards the core. If this effect results from on average values of density and magnetic field. For the cases of 3 suppression of CR diffusion as discussed in Section 6.1 the same suppressed diffusion coefficients with factors χ 10− down 5 ∼ = suppression effect will apply to external electrons accelerated out- to 10− , lower than the Galactic average, considerable differences side the core. Strong synchrotron radiative losses on the increasing in the penetration depths between GeV and TeV CRs were found, magnetic field towards the core centre may further limit the X-ray with GeV CRs preferentially excluded. This effect could lead to component and/or alter the spectrum from these external electrons, a characteristic hardening of the TeV gamma-ray and hard X-ray to the effect that X-ray emission may appear somewhat edge- or emission spectrum peaking towards the core centre. Such features limb brightened in contrast to a more centrally peaked compo- may be detectable and resolvable with future gamma-ray and X- nent from secondary electrons inside the core. For example the ray telescopes and therefore offer a novel way to probe the level 1.5 0.5 synchrotron cooling time tsync 1.5(B/mG)− (ǫ/keV)− yr of of accelerated CRs from RX J1713.7 3946 and the strength and electrons of energy E responsible≈ for X-ray photons of energy ǫ, structure of the magnetic field within− the core. A more detailed where E 62.5√(ǫ/keV)/(B/mG) TeV, can be compared with diffusion model assuming a variable density and magnetic field ≈ 1 2 the diffusion time t 16χ − (R/1pc) √(B/3 µG)/(E/GeV) yr is left for later work. We would also finally note that mapping d ≈ into the core with radius R 0.62 pc. For hard X-ray photons in tracers of cosmic ray ionization such as DCO+ and HCO+ = 3 ǫ 10 keV and suppressed diffusion χ<10− ,wefindthatt (Indriolo et al. 2010; Montmerle 2010) could be a highly valuable ∼ sync can become similar to or considerably less than td as B increases link between RX J1713.7 3946 and the observed gas and provide beyond 80 µG towards the centre of the core. For smaller values complementary information− on the level of low-energy MeV to GeV of χ, tsync becomes less than td forevensmallervaluesofB. CRs impacting the molecular cores.

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS 2242 N. I. Maxted et al.

ACKNOWLEDGMENTS MacLaren I., Richardson K., Wolfendale A., 1988, ApJ, 333, 821 Martin S., Martin-Pintado J., Mauersberger R., Henkel C., Garcia-Burillo We would like to thank Stefano Gabici and Felix Aharonian for use- S., 2005, ApJ, 620, 210 ful discussions about the diffusion of CRs, and Malcolm Walmsley Martin S., Requena-Torres M., Martin-Pintado J., Mauersberger R., 2008, for his insightful comments. This work was supported by an Aus- ApJ, 678, 245 tralian Research Council grant (DP0662810). The Mopra Telescope Martin-Pintado J., de Vincente P., Rodriguez-Fernandez N. J., Fuente A., is part of the Australia Telescope and is funded by the Common- Planesas P., 2000, A&A, 356, L5 wealth of Australia for operation as a National Facility managed Montmerle T., 2010, in Marti J., Lugue-Escamilla P., Combi J., eds, ASP by the CSIRO. The University of New South Wales Mopra Spec- Conf. Ser. Vol. 422, High Energy Phenomena in Massive Stars. Astron. trometer Digital Filter Bank used for these Mopra observations Soc. Pac., San Francisco, p. 85 was provided with support from the Australian Research Council, Moriguchi Y., Tamura K., Tawara Y., Sasago H., Yamaoka T., Onishi T., Fukui Y., 2005, ApJ, 631, 947 together with the University of New South Wales, University of Nicholas B., Rowell G., Burton M., Walsh A., Fukui Y., Kawamura A., Sydney, Monash University and the CSIRO. Maxted N., 2012, MNRAS, 419, 251 Ormes J., Ozel M., Morris D., 1988, ApJ, 334, 722 REFERENCES Pfeffermann E., Aschenbach B., 1996, MPE Rep., 263, 267 Abdo A. 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Vol. 1085, High Energy Gamma-Ray van der Tak F., Black J., Schoier F., Jansen D., van Dishoeck E., 2007, A&A, Astronomy Am. Inst. Phys., New York, p. 104 468, 627 Fukui Y., et al., 2003, PASJ, 55, L61 van Dishoeck E., Blake G., 1998, ARA&A, 36, 317 Fukui Y., et al., 2012, ApJ, 746, 82 Walsh A., Lo N., Burton M., White G., Purcell C., Longmore S., Phillips Gabici S., Aharonian F., Blasi P., 2007, Ap&SS, 309, 365 C., Brooks K., 2008, Publ. Astron. Soc. Australia, 25, 105 Gabici S., Aharonian F., Casanova S., 2009, MNRAS, 396, 1629 Wang Z., Qu Q., Chen Y., 1997, A&A, 318, L59 Gabici S., Casanova S., Aharonian F., Rowell G., 2010, in Boissier S., Wardle M., 1999, ApJ, 525, L101 Heydari-Malayeri M., Samadi R., Valls-Gaband D., eds, Proc. French Womack M., Ziurys L., Wychoff S., 1992, ApJ, 387, 417 Soc. Astron. Astrophys., preprint (arXiv:1009:5291) Yan H., Lazarian A., Schlickeiser R., 2012, ApJ, 745, 140 Goldsmith P., Langer W., 1999, ApJ, 517, 209 Zirakashvili V., Aharonian F., 2010, ApJ, 708, 965 Gusdorf A., Cabrit S., Flower D., Pineau Des Forets G., 2008a, A&A, 482, 809 Gusdorf A., Pineau des Forets G., Cabrit S., Flower D., 2008b, A&A, 490, APPENDIX A: THE MOLECULAR CORES IN 695 FURTHER DETAIL Harrison F. et al., 2010, Proc. SPIE, 7732, 21 Ho P., Townes C., 1983, A&A, 21, 239 34 Hotzel S., Harjul J., Walmsley C., 2004, A&A, 415, 1065 A1 C SandHC3N emission Indriolo N., Blake G., Goto M., Usuda T., Oka T., Geballe T., Fields B., C34S(J 1–0) emission can be viewed towards Core C (Fig. A1, McCall B., 2010, ApJ, 724, 1357 top). This= is further evidence of the existence of a dense molecular Inoue T., Yamazaki R., Inutsuka S., Fukui Y., 2012, ApJ, 744, 71 Jones D., Crocker R., Ott J., Protheroe R., Ekers R., 2011, AJ, 141, 82 core and, with the CS(J 1–0) spectral line, allows the calculation of the optical depth and= column density. HC N(J 5–4) emission Koyama K., Kinugasa K., Matsuzaki K., Mamiko N., Sugizaki M., Torii K., 3 = Yamauchi S., Aschenbach B., 1997, PASJ, 49, L7 from Cores A and C (Fig. A1, middle and bottom) are also indicative Ladd N., Purcell C., Wong T., Robertson S., 2005, Publ. Astron. Soc. Aus- of dense cores. tralia, 22, 62 Lazendic J., Slane P., Gaensler M., Plucinsky P., Hughes J., Galloway D., Crawford F., 2003, ApJ, 593, L27 A2 Scaling factors Le Bourlot J., 1991, A&A, 242, 235 McClure-Grifﬁths N., Dickey J., Gaensler B., Green A., Haverkorn M., In this investigation, the Core C radius of 0.12 pc, as calculated from Strasser S., 2005, ApJS, 158, 178 CS(J 1–0) emission, has an uncertainty of 50 per cent and may = ∼ C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS Dense gas towards SNR RX J1713.7 3946 2243 −

Table A1. Mass, M, density, nH, and abundance, χ vir, scaling factors versus assumed Core C radius. Gas parameters derived from an assumed radius of 0.12 pc can be readily converted to be for other assumed core radii by multiplying the value by the appropriate correction.

Core radius (pc) 0.05 0.1 0.15 0.2 0.25 0.3

M Mass scaling factors LTE 12 mm 5.7 1.5 0.68 0.41 0.28 0.22 LTE 7 mm 5.3 1.4 0.72 0.50 0.41 0.37 LTE 3 mm 3.7 1.2 0.85 0.76 0.75 0.74 Virial 0.42 0.83 1.25 1.67 2.08 2.50

nH2 Density scaling factors LTE 12 mm 83 2.7 0.37 0.09 0.03 0.01 LTE 7 mm 77 2.6 0.39 0.11 0.05 0.03 LTE 3 mm 53 2.3 0.46 0.17 0.09 0.05

χ vir Molecular abundance scaling factors 12 mm (NH3) 14 1.8 0.56 0.25 0.14 0.09 7 mm (CS) 13 1.7 0.59 0.30 0.20 0.15 3mm(N2H+) 8.9 1.5 0.69 0.47 0.36 0.30

not necessarily be representative of core sizes traced by NH3(1,1) and N2H+(J 1–0) emission. This radius was also assumed for Core D. We therefore= provide scaling factors (Table A1) normalized to a core radius of 0.12 pc to allow parameter estimates derived from the three molecular species to be readily scaled to represent different source size assumptions. These were derived by simply calculating gas parameters for other core radius assumptions and dividing this by the result for a core radius of 0.12 pc.

A3 Core C radial density profile Sano et al. (2010) used CO measurements to derive a power-law radial density profile of index 2.2 0.4 (Fig. A2). Extrapolating the model to R < 0.12 pc yields− a number± density value of 2 4 3 5∼ ×3 10 cm− . Our LTE results indicate a density of 2–3 10 cm− 5 3 × and virial densities are 1–4 10 cm− , all an order of magnitude larger than that indicated by× CO. It follows that the Core C density profile may increase beyond the CO-derived power law at smaller radii, but this discrepancy could be due to abundance uncertainties discussed in Section 5.1.2. This would not account for the discrepancy in virial-derived densities, which may simply be due to the virial assumption being invalid for Core C. If the apparent core radius varies between different molecular transitions, densities derived from different emission lines could be scaled independently (see Table A1), potentially changing estimates by an order of magnitude.

Figure A2. Average density within radius, as traced by CO (Sano et al. 34 1 Figure A1. Top: C S(J 1–0) vLSR 13.5 to 9.5 km s− . Middle: 2010) and CS (this work). A 2.2 power-law function is also displayed for = =− 1 − − HC3N(J 5–4) vLSR 13.5 to 9.5 km s− . Bottom: HC3N(J 5–4) comparison (not ﬁtted). Uncertainties are not displayed and are discussed in = =− 1 − = vLSR 11.0 to 9.0 km s . the text. =− − −

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS 2244 N. I. Maxted et al.

TA∗(2, 2,m) τ(1,1,m) τ(2, 2,m) ln 1 1 e− . (B3) =− − T (1, 1,m) − A∗

B1.2 Rotational and kinetic temperature

tot 1 9 τ2,2 − Trot 41 ln tot [K], (B4) =− 20 τ1,1 

This work Trot Tkin [K]. (B5) = Trot 16 1 42 ln 1 1.1exp T − + − rot 

B1.3 Column density

2 tot 8kπν a τ1,1 2 N T dv [cm− ], (B6) 1,1 3 τ rot mb Figure A3. 13CS/C34S integrated intensity ratios for the J 1–0, J 2–1 = Auhc s 1 e− 1,1 = = and J 3–2 transitions. Data taken from Frerking et al. (1980), Martin et − = N al. (2008), Martin et al. (2005) and Nicholas et al. (2011). Typical statistical 1,1 E1,1/kT 2 NNH3 e Q(T )[cm− ], (B7) error in data values is 25 per cent. = g1,1

Ei /kT Q(T ) i gi e− . (B8) A4 CS isotopologues = A key assumption in the optical depth calculations is that of the sulphur and carbon isotope ratio values, [CS]/[C34S] [32S]/[34S] B2 N2H+ analysis 22.5 and [CS]/[13CS] [12C]/[13C] 75, respectively.∼ These assumptions∼ can be investigated∼ by comparing∼ the emission of 13CS B2.1 Optical depth and C34S. The 13CS(J 1–0)/C34S(J 1–0) peak intensity ratio = = from Core C is 0.26 0.06, which would appear to be consistent T 1 e τmain ± main − , (B9) with the adopted abundance ratios (22.5/75 0.3). On the other − ατ = Thf = 1 e main hand, the integrated intensity ratio is 0.16 0.05, somewhat in- − − ± consistent with our abundance assumptions. This is of concern as τ τ main . (B10) integrated intensity is more relevant than peak intensity when calcu- tot = f lating molecular abundances. We reviewed 13CS(J 1–0)/C34S(J 1–0) integrated intensity ratios in published literature= towards a va-= riety of cores. B2.2 Excitation temperature Fig. A3 presents a histogram of the ratio of integrated intensities of 13CS and C34S emission from this sample. The graph suffers Tmb s from low number statistics, but it can be seen that there is a large Tex Tb. (B11) range of recorded [13CS]/[C34S] values, and although the Core C = a (1 e τ ) + a s − RX J1713.7 3946 data point is at the low end of the distribution, it − represents only− a 1σ deviation from the average value of 0.55 (ex- cluding the Sickle∼ sources). Noteworthy in Fig. A3 are two Galactic B2.3 Column density centre sources that recorded [13CS]/[C34S] values of over 4σ from the mean. More data would be useful to compare the [13CS]/[C34S] hν/kTex ratio of Core C to that of other cores. 3√πhǫ0 e NN H 2 + = 2π2√ln 2μ2 ehν/kTex 1 N2H+ − kTex 1 (B12) APPENDIX B: THE LTE ANALYSES IN DETAIL V τ. × hν + 6 fwhm B1 Ammonia analysis

B1.1 Optical depth B3 CS B3.1 Optical depth T (J,K,m) 1 e τ(J,K,m) A∗ − , (B1) − ατ(J,K,m) τCS T ∗(J,K,s) = 1 e TCS 1 e− A − − − , (B13) T = 1 e ατCS CS iso − − τ(J,K,m) where α is the ratio of the rarer CS isotopologue abundance and CS τ tot , (B2) J,K = f (J,K) abundance.

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS Dense gas towards SNR RX J1713.7 3946 2245 − B3.2 Column density B4 LTE mass, density and virial abundance

2 2 8kπνul a τ 2πr mHNMol NCS(J u) Tmb dv , (B14) M , (B17) = = A hc3 1 e τ = χ ul s − −

N NMol CS(J 1) ECS(J 1)/kT 2 NCS = e = Q(Trot)[cm− ]. (B15) nH2 , (B18) = gCS(J 1) = χr = 2πr2m N χ H Mol . (B19) vir = M B3.3 Rotational temperature vir

1 3 NCS(J 2) − Trot 4.7 ln = [K]. (B16) This paper has been typeset from a TEX/LATEX ﬁle prepared by the author. =− 5 NCS(J 1) =

C 2012 The Authors, MNRAS 422, 2230–2245 C Monthly Notices of the Royal Astronomical Society 2012 RAS 4.2 Dense Gas Towards the RX J1713.7−3946 Supernova Remnant (1)

The following conference proceedings paper was published by the American Institute of Physics (AIP).

89 29/1/13

90 Dense gas towards the RXJ1713.7–3946 supernova remnant Nigel I. Maxted, Gavin P. Rowell, Bruce R. Dawson, Michael G. Burton, Yasuo Fukui et al.

Citation: AIP Conf. Proc. 1505, 253 (2012); doi: 10.1063/1.4772245 View online: http://dx.doi.org/10.1063/1.4772245 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1505&Issue=1 Published by the American Institute of Physics.

Additional information on AIP Conf. Proc. Journal Homepage: http://proceedings.aip.org/ Journal Information: http://proceedings.aip.org/about/about_the_proceedings Top downloads: http://proceedings.aip.org/dbt/most_downloaded.jsp?KEY=APCPCS Information for Authors: http://proceedings.aip.org/authors/information_for_authors

Downloaded 19 Dec 2012 to 192.43.227.18. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions Dense Gas Towards the RX J1713.7−3946 Supernova Remnant Nigel I. Maxted1∗, Gavin P. Rowell∗, Bruce R. Dawson∗, Michael G. Burton†, Yasuo Fukui∗∗, Andrew J. Walsh‡,AkikoKawamura∗∗, Hidetoshi Sano∗∗ and Jasmina Lazendic§

∗School of Chemistry & Physics, University of Adelaide, Adelaide, 5005, Australia †School of Physics, University of New South Wales, Sydney, 2052, Australia ∗∗Department of Astrophysics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi, 464-8602, Japan ‡Centre for Astronomy, School of Engineering and Physical Sciences, James Cook University, Townsville, 4811, Australia §School of Physics, Monash University, Melbourne, 3800, Australia

Abstract. A summary of results from a 7 mm-wavelength survey towards the young X-ray and γ-ray-bright supernova remnant, RX J1713.7−3946 (SNR G 347.3−0.5) is presented. Using the Mopra telescope, the high critical density tracer CS(1−0) was targeted, complementing previous Nanten2 molecular gas studies of CO transitions. In hadronic γ-ray emission scenarios (p-p interactions), the mass of cosmic ray target material available is an important factor, so we estimate the mass of dense gas towards RX J1713.7−3946. Also of interest was the shock-tracing molecule, SiO. Although there was no evidence of SiO emission physically excited by the RX J1713.7−3946 shock, a chance-discovery of vibrationally- excited SiO(1-0) emission is likely to be a maser that is associated with an evolved star.

Keywords: Molecular clouds, H2 clouds; Interstellar masers; Supernova remnants; γ-ray sources; Cosmic rays PACS: 98.38.Dq, 98.38.Er, 98.38.Mz, 98.70.Rz 98.70.Sa

INTRODUCTION

The young X-ray and γ-ray-bright supernova remnant, RX J1713.7−3946 (SNR G 347.3−0.5) is one of the biggest and brightest sources in the TeV sky [1, 2], ideal for investigating the possibility of cosmic ray (CR) diffusive shock acceleration in the shocks of supernova remnants (SNRs). The origin of the RX J1713.7−3946 γ-ray emission (hadronic, leptonic or both) is still unclear due to our lack of knowledge of the properties of the local high energy particle population. A key step towards constraining this and the nature of the RX J1713.7−3946 γ-ray emission is an investigation of the distribution of associated gas, which has an impact on SNR evolution, hadron/electron acceleration and resultant radiation. In considering a hadronic scenario for γ-ray emission, potential hadron target material (gas) must be identiﬁed, one of the motivations of previous CO and HI studies towards RX J1713.7−3946 (eg. [3, 4, 5, 6, 7]).

1 Email: [email protected]

Downloaded 19 Dec 2012 to 192.43.227.18. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions This work presents an extension to a previous CS(1-0) survey [8] that targeted dense gas (critical density ∼105 cm−3) towards RX J1713.7−3946, probing a component possibly missed by other tracers, so adding to the total known potential CR-target mass available in a hadronic scenario of γ-ray emission. Such a component may also be important in γ-ray emission models that consider energy-dependent cosmic ray diffusion (eg. [8, 9]), affecting the resultant high energy spectrum.

OBSERVATIONS AND ANALYSIS

In addition to our previous measurements [8], in April 2011, Mopra performed 6 scans of the northern region of RX J1713.7−3946 (centre [l,b]∼[347.36,−0.09], size ∼19.5′×19.5′) and 5 scans of the north-western region (centre [l,b]∼[347.99,−0.41], size ∼18′×18′). We use the same 7 mm spectrometer conﬁguration as that summarised −1 in Maxted et al. [8] and the achieved noise in the CS(1-0) band was TRMS∼0.13 K ch . We assume CS(1-0) emission from gas in Local Thermodynamic Equilibrium (LTE) with a temperature of 10 K (unless otherwise stated) and apply our earlier methodology [8] to estimate mass and column density of dense gas towards RX J1713.7−3946. Where signiﬁcant CS(1-0) emission extended beyond an approximate beam-area (Mopra CS(1- 0) beam FWHM ∼1′), sources were divided into segments (east and west in this study) for parameter calculations, and an additional large-scale region was used for an over-all mass-estimation of the full extent of the cloud.

PRELIMINARY RESULTS AND DISCUSSION

Figure 1 is an image of CS(1-0) emission between −12.5 and −7.5 km s−1, gas at ∼1 kpc that is believed to be associated with RX J1713.7−3946 [3, 5, 10]. Cores A, B and C were scanned by Maxted et al. [8], revealing multiple detections of 6 species (and several isotopologues) that are not re-summarised in this paper. New detections towards Cores G and L are discussed instead. Table 1 is a summary of calculated gas parameters from CS(1-0) emission detected in this survey. Cores G and L were only weakly detected in CS(1-0), with peak intensities of ∼1.5 TRMS, leading to very poorly-constrained optical depths, column densities and masses. Despite this, given such low intensities relative to those of Cores A, C and D (which have LTE masses in the range 12 - 120 M⊙), an optically thin solution yielding masses of ∼1M⊙ is probable. It follows that the densest (CS(1-0)-traced) components of Cores G and L do not represent a significant proportion of mass in the RX J1713.7−3946 −1 field at line-of-sight velocity, vLSR∼−10 km s (<0.1%) and may not play an important role in the dynamics of the SNR-shock or the production of γ-ray emission. Also displayed in Figure 1 are key 7 mm SiO spectra towards a location coincident with the surveyed field, [l,b]∼[347.05,−0.012]. SiO(1-0,v=2) emission (and tentative SiO(1-0,v=1) emission) highlights a population-inversion consistent with SiO maser emission at a line of sight velocity of ∼−6kms−1. SiO masers of this type are commonly associated with evolved stars, or in very rare cases, star-forming molecular cores. Although this source appears coincident with infrared emission (Spitzer 24, 8 and

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Downloaded 19 Dec 2012 to 192.43.227.18. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions TABLE 1. Line-of-sight velocity, line-width (full-width-half-maximum) and gas parameters derived from CS(1-0) emission for CO clumps with detected CS(1-0) emission. Statistical uncertainties are generally ∼20% unless otherwise stated, while systematic uncertainties are estimated to be ∼20%.

∗ † ∗∗ Name vLSR ∆vFWHM Optical H2 Column density Mass −1 −1 ‡ 21 −2 (km s )(kms) Depth (×10 cm )(M⊙) Core A[8] −9.82 ± 0.02 1.25 ± 0.06 0 - 0.44 3 - 4 12 - 15 Core C[8] −11.76 ± 0.01 2.08 ± 0.03 2.71 ± 0.29 55 ± 440± 3 Core D[8] −9.1 ± 0.1 2.5 ± 0.3 0 - 4.1 40 - 170 30 - 120 Core G −11.2 ± 1.1 0.9 ± 0.3 0 - 33 0.7 - 400 1 - 200 Core L −10.8 ± 0.4 1.6 ± 1.4 0 - 20 0.1 - 600 0.3 - 300 Clump N1-west −70.1 ± 0.2 4.6 ± 0.5 0 - 4.7 130 - 610 (2 - 10)×103 Clump N1-east −69.4 ± 0.4 8.0 ± 1.3 0 - 7.5 150 - 1 100 (3 - 20)×103 N1 region (5 - 30)×103 Clump N2 −70.9 ± 0.2 2.4 ± 0.5 0 - 8.8 39 - 340 (7 - 60)×102 Clump T1-east −120.0 ± 0.2 2.2 ± 0.3 0 - 4.4 64 - 280 (1 - 6)×103 Clump T1-west −119.5 ± 0.1 1.6 ± 0.3 0 - 4.6 45 - 210 (9 - 40)×102 T1 region (3 - 12)×103

∗ Name convention from Moriguchi et al. [5] and this work. † Local Thermal Equilibrium (LTE) assumption at a temperature of 10 K. Averaged over beam size. ∗∗ Assuming distances of 1, 6 and 6.5 kpc for Cores A-L, Clumps N1 and N2, and Clump T1, respectively. ‡ 34 34 Assuming [CS]/[C S]=22.5 and using the C S(1-0)-band TRMS∼0.13 K/channel to estimate upper limits where no C34S(1-0) emission is detected.

Mopra 7mm mapping regions Galactic Latitude (deg) Integrated Intensity (Kkm/s)

Galactic Longitude (deg) 0.25

0.5 Galactic Latitude (deg) Integrated Intensity (Kkm/s) 0 0.5

0 Brightness Temperature (K)

-60 -50 -40 -30 -20 -10 0 10 20 30 40 Velocity (km/s) Galactic Longitude (deg)

FIGURE 1. Nanten2 CO(2-1) emission image with overlaid HESS γ-ray emission (>1.4 TeV) contours towards RX J1713.7−3946 (top-left). Mopra CS(1-0) intensity image with overlaid Nanten2 CO(2-1) emission contours (5 - 40 K km s−1, in increments of 5 K km s−1) towards the north-western region of RX J1713.7−3946 (right). Circles represent the beam FWHM of the telescopes employed. Also displayed are spectra from 3 SiO transitions towards an SiO(1-0,v=2) maser discovered in this investigation (bottom- left).

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Downloaded 19 Dec 2012 to 192.43.227.18. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions 0-6 ms km K 60 - 10 S10 pcrmtwrsN-at Ocnorlvl r 2Kk s km K 12 - 2 are levels contour CO N1-east. towards spectrum CS(1-0) h emFH ftetlsoe mlyd ne saCH a is Inset employed. telescopes the of FWHM beam the 0 .Ioe .Ymzk,S ntua&Y uu,21,AJ 4,71. 744, ApJ, 2012, Fukui, Y. 365-371. & 309, Inutsuka SS, S. 251-266. Ap& Yamazaki, 2007, 419, R. Blasi, MNRAS, Inoue, P. 2012, T. & , Aharonian al. 10. F. et Gabici, 357-367. Dawson S. 525, B. ApJ, Rowell, 1999, 59-68. 9. G. al. 724, Maxted, et ApJ, N. Dame 2010, T. , Gaensler, 8. al. B. et 947-963. Slane, Yamamoto P. 631, H. ApJ, Sato, 2005, J. 7. 82. , Sano, 746, al. ApJ, H. et 2012, Tawara Y. , Tamura, 6. al. K. et L61-L64. Moriguchi, Y. Sato 55, PASJ, J. 2003, Sano, 5. , H. al. Fukui, Y. et Tamura 235-243. K. 464, 4. Moriguchi, A&A, Y. 2007, Fukui, Y. Collab.) (HESS 223-242. al. 449, 3. et A&A, Aharonian 2006, F. Collab.) (HESS al. 2. et Aharonian F. 1. formation. star with associated activity the investigating in interest 5.8 S10 msini onietC(-)eiso ek n rcsams fdense ﬁeld. of surveyed mass the a of traces 10 border and northern order peaks the the emission on CO(2-1) of lie coincident gas 2), Figure is (see emission displa N2 CS(1-0) are and arm N1 Norma Clumps the and arm expanding ot-etr eino XJ1713.7 RX of region north-western 2. FIGURE lm 1es seFgr ) niaigalclsdwr,dneenvironment. dense warm, localised a indicating 2), Figure (see T1-east Clump h i msinorigin. emission SiO the fC(-)eiso.Cmlmnaysuiso i n CH and SiO of studies Complementary G emission. Cores towards CS(1-0) gas of dense of presence the lm 1faue xeddC(-)emi 3-12 CS(1-0) contains and intensity, extended featured T1 Clump Downloaded 19 Dec 2012 to192.43.227.18. Redistribution subject to AIP license or copyright; see http://proceedings.aip.org/about/rights_permissions nsmay eetn u or msre fR J1713.7 RX of survey mm 7 Mopra our extend we summary, In rmnn S10 eetoscorre detections CS(1-0) Prominent Galactic Latitude (deg) µ ) h ae rge ssiluceran unclear still is trigger maser the m), − or S10 nest iae n atn O21 msin(otus oad the towards (contours) emission CO(2-1) Nanten2 and (image) intensity CS(1-0) Mopra 1 Galactic Longitude(deg) iceet f1 ms km K 10 of (increments 3 -10 CH OH(7−6) 3 4 M × ⊙ 10 − 96 w eoiyrne idctd r hw.Crlsrepresent Circles shown. are (indicated) ranges velocity Two 3946. 3 seTbe1.Smlry nte3kcepnigarm, kpc-expanding 3 the in Similarly, 1). Table (see M REFERENCES − ⊙ 1 o etadrgtiae,respectively. images, right and left for ) fdnegs CH gas. dense of pnigt akrudgsi h kpc- 3 the in gas background to sponding

256 Integrated Intensity (Kkm/s) so onietwt eko CO(2-1) of peak a with coincident ssion n adbcgon a)valwlevels low via gas) background (and L and

ute td srqie odetermine to required is study further d Galactic Latitude (deg) e nFgr .DneNraamgas, Norma-arm Dense 2. Figure in yed 3 H76 pcrmtwrsT-atada and T1-east towards spectrum OH(7-6) 3 H76 msini eetdin detected is emission OH(7-6) Galactic Longitude(deg) − 1 iceet f2Kk s km K 2 of (increments 3 Heiso a eof be may emission OH CS(1−0) − 96adconﬁrm and 3946 − 1 )and Integrated Intensity (Kkm/s) 4.3 Dense Gas Towards the RX J1713.7−3946 Supernova Remnant (2)

The following manuscript will be submitted to the peer-reviewed journal, Publications of the As- tronomical Society of Australia (PASA). I note that the most recent version of this manuscript at the time of submission is included.

96 29/1/13

Dense Gas Towards the RX J1713.7−3946 Supernova Remnant

Nigel I. MaxtedA, Gavin P. RowellA, Bruce R. DawsonA, Michael G. BurtonB, Yasuo FukuiC, Jasmina LazendicD, Akiko KawamuraC, Hirotaka HorachiC, Hidetoshi SanoC, Andrew J. WalshE, Satoshi YoshiikeC and Tatsuya FukudaC

A School of Chemistry & Physics, University of Adelaide, Adelaide, 5005, Australia B School of Physics, University of New South Wales, Sydney, 2052, Australia C Department of Astrophysics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi, 464-8602, Japan D School of Physics, Monash University, Melbourne, 3800, Australia E International Centre for Radio Astronomy Research, Curtin University, GPO Box U1987, Perth, Australia

Abstract: We present results from a Mopra 7 mm-wavelength survey that targeted the dense gas- tracing CS(1-0) transition towards the young γ-ray-bright supernova remnant, RX J1713.7 3946 (SNR G 347.3 0.5). In a hadronic γ-ray emission scenario, where cosmic ray protons interact− with gas to produce− the observed γ-ray emission, the mass of potential cosmic ray target material is an important factor. We summarise newly-discovered dense gas components, towards Cores G and L, and Clumps 4 N1, N2, N3 and T1, which have masses of 1 - 10 M⊙. We argue that these components are not likely to contribute significantly to γ-ray emission in a hadronic γ-ray emission scenario. This would be the case if RX J1713.7 3946 were at either the currently favoured distance of 1 kpc or an alternate distance (as suggested− in some previous studies) of 6 kpc. ∼ This survey also targeted the shock-tracing∼ SiO molecule. Although no SiO emission corresponding to the RX J1713.7 3946 shock was observed, vibrationally-excited SiO(1-0) maser emission was discovered towards what may− be an evolved star. Observations taken one year apart confirm a transient nature, with the intensity, line-width and central velocity of SiO(J=1-0,v=1,2) emission significantly varying. Keywords: molecular data - supernovae: individual: RX J1713.7 3946 - ISM: clouds - cosmic rays - gamma rays: ISM −

1 Introduction scale γ-ray emission features caused by energy dependent CR diffusion into dense gas (e.g. Gabici et al., RX J1713.7 3946 (G 347.3 0.5) is a supernova rem- 2009; Casanova et al., 2010; Fukui et al., 2012; Maxted nant (SNR)− that is bright− in X-ray emission (Pfeffer- et al., 2012a). mann et al. 1996; Cassam-Chenai et al. 2004; Acero The latest Fermi-LAT observations (Abdo et al. et al. 2009) and is one of the brightest sources in the 2011) towards RX J1713.7 3946 exhibit a low but hard- TeV γ-ray sky (Aharonian et al. 2006, 2007). This spectrum flux of 1-10 GeV−γ-ray emission uncharacter- remnant is therefore ideal for investigating the possibil- istic of previous hadronic models (Porter et al. 2006; ity of acceleration of cosmic rays (CRS) in the shocks Aharonian et al. 2007; Berezhko & Volk 2010; Ellison of SNRs. et al. 2010; Zirakashvili & Aharonian 2010). But, if Knowledge of the distribution of matter towards one considers an inhomogeneous ISM into which the RX J1713.7 3946 is important to help distinguish be- SNR shock has expanded, the existence of a hadronic tween models− of γ-ray emission which are dominated component may still be plausible (Zirakashvili & Aha- by high energy electrons (inverse-Compton scattering ronian 2010; Inoue et al. 2012). There is also sup- of photons) and models dominated by CR hadrons (p-p port for such a scenario when considering the existence interactions). The latter scenario requires target ma- of additional atomic gas together with the molecular terial for CRs. CR target material may be in any (Fukui et al. 2012). chemical form, including molecular and atomic gas, RX J1713.7 3946 exhibits a shell-like structure at which have been studied with CO (Fukui et al. 2003; both keV X-ray− and TeV γ-ray energies (see Figures 1 Moriguchi et al. 2005; Fukui 2008) and HI+CO (Fukui and 2), with the keV X-ray emission best correspond- et al. 2012), respectively. ing to a void in molecular gas, bordering molecular −1 We take particular interest in the study of dense cores at a kinematic distance of 1kpc (vLSR 10 km s ) molecular gas, which is well-traced by CS(1-0) emis- (Fukui et al. 2003; Moriguchi et∼ al. 2005).∼ This − dis- sion (critical density 105 cm−3). This transition high- tance is consistent with X-ray absorption modeling lights gas mass possibly∼ missed by other tracers (such by Pfeffermann et al. (1996) for a plausible SNR-age as CO) and aids in the prediction of possible small- ( 1600 years old) that corresponds to a progenitor event ∼

1 2 Publications of the Astronomical Society of Australia

observed by Chinese astronomers in 393 AD (Wang et al. 1997). Fessen et al. (2012) argue that if a SN 393 AD connection to RX J1713.7 3946 is assumed, the initial RX J1713.7 3946 SN− explosion must have been optically subluminous− for the 1 kpc distance to hold. Irrespective of this, recent work∼ still favours a 1kpc distance (eg. Inoue et al., 2012, Fukui et al.,∼ 2012), and an examination of keV X-ray emission (Figure 2) suggests some degree of anticorrelation with CO(2-1) −1 peaks at vLSR 10 km s (a kinematic distance of 1 kpc). Sano∼ et − al. (2010) note that synchrotron in-

Galactic Latitude (deg) ∼ Integrated Intensity (K.km/s) tensity peaks on the boundary of the molecular clump, Core C may suggest a compression triggered by the RX J1713.7 3946 shock. Similarly, the edge of Core D is coincident− with an X-ray intensity peak, consistent with shock compression at a distance of 1 kpc. Fur- Galactic Longitude (deg) thermore, the northern and western regions∼ of RX J1713.7 3946, where cores D and C are located, corre- − Figure 1: Integrated Nanten2 CO(2-1) emission spond to peak ﬂuxes of TeV γ-ray emission. Good gas- image (Fukui 2008) of gas believed to be associated γ-ray overlap, like that seen towards RX J1713.7 3946 −1 and the 1 kpc gas, is indeed expected in a hadronic− with RXJ1713.7−3946 (vLSR= −18 to 0kms ) ∼ with overlaid HESS >1.4 TeV γ-ray photon excess scenario for γ-ray emission. In a previous study (Maxted et al. 2012a), we sur- count contours (Aharonian et al. 2007). Three ′ ′ veyed an 18 18 region centered on [l,b] = [346.99, square regions (one, the southern-most, from a 0.41] (southern-most× region indicated in Figure 1), previous investigation) indicate the extent of Mo- and− found dense gas associated with molecular cores pra 7mm mapping carried out in this study. A, C and D (see Figure 3). In this study we extend the dense gas survey with another two mapped regions, to encompass Core D and the northern peak in TeV γ- ray emission, and several bright keV X-ray emission features. CS(1-0) emission can probe the dense gas towards RX J1713.7 3946, which, as highlighted earlier, may be important− in a hadronic scenario. Fur- thermore, the Mopra radio telescope spectrometer is capable of simultaneously recording CS(1-0) emission, −2 −1 while observing the shock-tracing transition SiO(1-0). This allows us to further test the 1 kpc RX J1713.7 3946 kinematic distance solution∼ through attempting− to trace the SNR shock, while undertaking our Photons (cm .s ) survey of the dense gas. The shock-tracing molecule, Galactic Latitude (deg) SiO, has been observed towards shocked gas associated with other (albeit older) SNRs (eg. Ziurys et al., 1989 and Nicholas et al., 2012), so may possibly be present towards gas associated with RX J1713.7 3946. − We also note the usefulness of other molecular lines Galactic Longitude (deg) simultaneously observed at 7 mm with the Mopra telescope. These include emission from isotopologues of Figure 2: An XMM-Newton 0.5-4.5 keV X- CS, which are useful for probing optically-thick re- ray image (Acero et al. 2009) with overlaid in- gions, the vibrationally-excited modes of the SiO(1- tegrated Nanten2 CO(J=2-1) emission (vLSR= 0) rotational transition (v=1,2,3), which can some- −18 to 0kms−1) contours. CO(J=2-1) contours times be emitted in association with star formation span 5Kkms−1 to 40Kkms−1 in increments of or evolved stars, and the CH3OH(7(0)-6(1)) transi- 1 tion which can highlight warm regions where CH3OH 5Kkms− . The XMM-Newton image has been (methanol) is evaporated from dust grains. exposure-corrected and smoothed with a Gaussian of FWHM=30′′. Three square regions (one, the southern-most, from a previous investigation) in- 2 Observations dicate the extent of Mopra 7mm mapping carried out in this study. In April, 2011, we recorded and co-added 6 Mopra OTF (on the ﬂy) 19′ 19′ area maps centered on [l, b] =[347.36, 0.09], and× 5 Mopra OTF 16′ 16′ area maps centered− on [l, b]=[347.07, 0.11], to produce× a data − www.publish.csiro.au/journals/pasa 3

cube with 2 spatial (long/lat) and 1 spectral (veloc- estimation of H2 mass. We use no beam-filling cor- ity) dimension at 7 mm wavelengths. These maps were rection and assume spherical clumps of a size equal to ′ ′ ′′ added to our map of an 18 18 region centered on the 7 mm beam FWHM (radius 30 ). Where signif- [l, b]=[346.991, 0.408], from our× previous investigation icant CS(1-0) emission extended∼ beyond an approxi- (Maxted et al.− 2012a). mate beam-area, sources were divided into segments For all our Mopra mapping data, the cycle time is (east and west in this study) for parameter calcula- 2.0 s and the spacing between scan rows is 26′′. The tions, and an additional large-scale region was used velocity resolution of the 7 mm zoom-mode data is for an over all mass-estimation of the full extent of the − 0.2 kms 1. The beam FWHM and the pointing ac- CS emission. ′′ ′′ curacy∼ of Mopra at 7 mm are 59 2 and 6 , respectively. The Mopra spectrometer,± MOPS,∼ was employed and is capable of recording sixteen tunable, 4 Results and Discussion 4096-channel (137.5 MHz) bands simultaneously when in ‘zoom’ mode, as used here. A list of measured This investigation mapped regions indicated in Fig- frequency bands, targeted molecular transitions and ures 1 and 2 in the CS(1-0) transition towards the achieved TRMS levels are shown in Table 1. RX J1713.7 3946 SNR. Significant detections at a ve- − OTF-mapping and deep ON-OFF switched point- locity consistent with CO(1-0,2-1)-traced cores that ing data were reduced and analysed using the ATNF are believed to be associated with RX J1713.7 3946 −1 − analysis programs, Livedata, Gridzilla, Kvis, Miriad (line-of-sight velocity, vLSR 10 km s according to 1 ∼ − and ASAP . We assumed the beam efficiencies pre- Moriguchi et al., 2005; Fukui et al., 2008) were recorded. sented in Urquhart et al. (2010) to convert antenna In addition to this, we found gas consistent with the −1 intensity into main-beam intensity (0.43 and 0.53 for background Norma arm (vLSR 70 km s ) and the ∼ − −1 point source CS(1-0) and SiO(1-0) emission, respec- 3 kpc-expanding arm (vLSR 120 km s ). For the ∼ − tively). latter arm, we also note the detection of the CH3OH(7- In addition to mapping, two deep ON-OFF switched 6) transition. pointings were performed in response to a detection In addition to our CS and CH3OH detections, tran- of SiO(J=1-0, v=2) emission (see 4.2). The first of sient detections of the v=1 and 2 vibrational modes of § the SiO(1-0) rotational transition were present towards these two pointings was interrupted after achieving a −1 signal-noise ratio similar to mapping data, so a second one location (vLSR 5kms ). ∼ − pointing with a longer exposure-time was performed 12 days later. 4.1 CS(1-0) Emission The CS(1-0) transition has a critical density for emis- 3 Spectral Line Analysis sion of 105 cm−3 (at temperature 10 K) and is ideal for probing∼ the deep, inner regions of∼ molecular clouds. We use the CS(1-0) analysis outlined in Maxted et al. The dense gas traced in this study is displayed in Fig- (2012a), and we briefly summarise it here. Gaussian ures 3, 6 and 7 and are discussed in the following sec- functions were first fitted to all CS(1-0) emission lines tions. Table 2 is a compilation of spectral line fit pa- using a χ2 minimisation method. Generally one can es- rameters and gas parameters, including line-of-sight timate CS(1-0) optical depth by comparing the CS(1- velocity, line-width, optical depth, H2 column density 0) intensity to the C34S(1-0) intensity, while assum- and mass. These values are used as a basis for the ing an abundance ratio, but of the new positions that discussion of dense gas towards RX J1713.7 3946. − exhibited CS(1-0) emission, none had corresponding 34 C S(1-0) detections. We constrain optical depth by 4.1.1 CS(1-0) Emission Between placing an optically thin (optical depth, τ 0) lower- −1 vLSR∼−12.5 and −7.5kms limit and a conservative upper-limit derived→ using the 34 34 C S(1-0)-band TRMS as an upper limit on C S(1-0) Figure 3 is an image of CS(1-0) emission between vLSR= − intensity, and assuming a [CS]/[C34S] ratio of 22.5. 12.5 and 7.5 km s 1, which features detections cor- − − The calculated optical depth range is used to con- responding to cores believed to be associated with the strain the CS(J=1) column density (Equation 9, Gold- RX J1713.7 3946 SNR. − smith & Langer, 1999), and with an assumption of The dense components of cores A, B, C and D Local Thermodynamic Equilibrium (LTE) at a tem- were previously studied in detail by us (Maxted et al. perature of 10 K, we converted this to total CS col- 2012a), revealing multiple detections of 6 species (and umn density, NCS , (CS column density 3.5 CS J=1 several isotopologues), including CS(1-0) emission to- col. dens.). We note that a 50% error∼ in the× assumed wards Cores A, C and D. This allowed the mass of temperature of 10 K would result in a 20-30% system- the dense molecular gas to be estimated and these are atic uncertainty in the column density using this LTE re-stated (along with our new results) in Table 2. method (Maxted et al. 2013). In our new survey (this work), we revealed tenta- Assuming an abundance of CS with respect to molec- tive CS(1-0) emission towards Cores G and L, with −9 ular hydrogen, [CS]/[H2] 10 (Frerking et al. 1980), peak intensities of 1.5 TRMS. The CS(1-0) emission ∼ a hydrogen column density∼ is estimated, allowing the intensities in these 2 cores are very low, hence the resultant CS(1-0) optical depth estimates are poorly- 1See http://www.atnf.csiro.au/computing/software/ constrained. However, given that the CS(1-0) intensi- 4 Publications of the Astronomical Society of Australia ties of Cores G and L are relatively low compared to material for CRs accelerated in the RX J1713.7 3946 those of Cores A, C and D (which have LTE masses shock at a distance of 1 kpc (using Equation 1).− It in the range 12 - 120 M⊙), we favour the optically thin is predicted that the CR enhancement would have to solutions. It follows that dense molecular gas masses be as high as kCR 1 000 for the RX J1713.7 3946 ∼ −11 −−2 −1 of Cores G and L are on the order of 1 M⊙, and do gamma-ray flux above 1 TeV, of 6 10 cm s , not represent a significant proportion∼ of mass in the to be entirely from hadronic processes.∼ × In such a sce- −1 RX J1713.7 3946 field at vLSR 10 km s (<0.1%), nario, the dense gas components (as traced by CS(1- therefore they− probably do not∼ play − an important role 0) emission) would contribute to a gamma-ray flux − − − in the dynamics of the SNR-shock or the production of 3 10 13 cm 2 s 1. This flux may be detectable of γ-ray emission. with∼ the× current HESS sensitivity, but the HESS beam Indeed, it appears that the total CS(1-0)-derived FWHM is too large to resolve molecular cores at a scale mass of all the surveyed cores represents only a fraction of 1 ′. Future experiments such as the CTA gamma- of the total gas mass in the region. The total CO(1-0)- ray∼ telescope (The CTA Consortium 2010) may reach 4 derived mass of 1 10 M⊙ towards RX J1713.7 3946 the arcminute resolution required to do this. ∼ × − (Fukui et al. 2012) is significantly larger than the total A CR enhancement factor of kCR 1 000 towards CS(1-0)-derived mass (dense core) components of mass RX J1713.7 3946 is plausible, supported∼ by work by − 80 - 200 M⊙ in our surveyed region (a subset containing Aharonian & Atoyan (1996). Figure 1b of this paper the densest molecular gas of the CO-traced region). displays cosmic ray enhancement factors of the or- 3 Previous authors have noted a small-scale anticor- der kCR 10 at a distance of 10 pc from a SNR of 3 ∼ relation between CO emission peaks at 1kpc (vLSR age 10 yr (similar to the RX J1713.7 3946 age). The 18-0 km s−1) and X-ray emission (see∼ 1), suggest-∼ source spectral index in these simulations− was 2.2 and − ing− a SN shock interaction with gas.§ Indeed, two the CR diffusion coefficient was 1026 cm2 s 1 (slow dif- X-ray peaks lie on the outskirts of the CS(1-0) (and fusion like that seen towards, w28, e.g. Gabici et al., CO(4-3,7-6), Sano et al., 2010) emission correspond- 2010). ing to Core C (see Figure 4) and a similar X-ray peak We estimate the total cumulative energy of CRs lies coincident to Core D. The same cannot be said for above an energy of 1 TeV in the RX J1713.7 3946 re- Cores A, G and L, but, although the densest regions gion, to be, − of Cores G and A sit outside the RX J1713.7 3946 X-ray boundary, X-ray flux peaks do seem to− cor- ECR tot = EpnCR dV dE ∞ respond to regions directly adjacent to the CS(1-0) 4 3 πrSNR EP nCR dE boundaries, possibly indicating shock-compression of ∼ 3 1 TeV the Core G and A gas. However, we have previously Z59 3 −13 −3 (1.2 10 cm )(8.8 10 GeV cm )kCR noted that these features may alternatively be consis- ∼ × 44 × tent with photoelectric absorption of X-rays emitted 2kCR 10 erg (2) ∼ × behind the molecular cores (Maxted et al. 2012a). where nCR is the cosmic ray density and rSNR is the radius of a spherical region of CR enhancement, kCR Gas as CR Target Material: The gas be- −1 (assumed to be 10 pc, consistent with the RX J1713.7 tween vLSR 12.5 and 7.5 km s may be acting as ∼ − − 3946 radius). Assuming a SN blast kinetic energy of CR target material in a hadronic gamma-ray emission 10− 51 erg, a CR enhancement of 1 000 would correspond scenario for RX J1713.7 3946, so we investigate the − to 0.02% of the SN blast kinetic energy being injected effect of the mass of CS(1-0)-traced gas. into∼>1 TeV protons. Extrapolating the CR spectrum Aharonian et al. (1991) derived a relation to pre- down to 1 GeV implies that about 1% of the SN blast dict the hadronic flux of γ-rays above a given energy kinetic energy has gone into Galactic∼ CR acceleration, from the mass of CR-target material, assuming an −1.6 so energetically, a hadronic scenario is consistent. E integral power law spectrum. We can calculate Our calculated cosmic ray enhancement factor val- − the expected γ-ray flux above energy Eγ , ues, of course, assume a CR source with an E 1.6 integral power law spectrum, and that all the gas in the re- −13 −1.6 M5 −2 −1 F ( Eγ )=2.85 10 ET eV 2 kCR cm s gion is taken into account, well-traced by the latest HI, ≥ × dkpc ! CO and CS studies (Fukui et al. 2012; Maxted et al. (1) 2012b). The latter assumption may not be entirely 5 where M5 is the gas mass in units of 10 M⊙, dkpc is the valid due to a so-called ‘dark’ component of gas, where distance in units of kpc, kCR is the CR enhancement carbon is in atomic/ionic form (not in molecules such factor above that observed at Earth and Eγ >1 TeV. as CO or CS) and hydrogen is in molecular form (there- Given that in a hadronic scenario γ-ray flux is pro- fore does not emit the atomic H 21 cm line). Wolfire portional to mass, one can assume that the dense CS(1- et al. (2010) predicted that this dark component may 0)-traced component ( few percent the total mass) comprise 30% of the total mass of an average cloud may only account for ∼few percent of the total γ-ray but could∼ be even higher in regions with enhanced CR flux. In a lepton-dominated∼ scenario, a hadronic com- ionisation rates, as is likely around RX J1713.7 3946. ponent would comprise an even smaller proportion of It’s clear that in a hadronic scenario, the− atomic the total flux (eg. Zirakashvili & Aharonian, 2010). and molecular mass traced by HI and CO is signifi- Figure 5 is a graph of the predicted hadronic γ-ray cant. Even though the total flux of γ-rays from a dense flux above 1 TeV from various gas components (traced CS(1-0)-traced component may be low, tell-tale signs using HI, CO and CS) assumed to be acting as target of hadronic emission might feasibly be detected in the www.publish.csiro.au/journals/pasa 5 form of small-scale hardening of high energy spectra On the question of the RX J1713.7 3946 distance correlated with dense gas components. Such phenom- (currently thought to be 1 kpc), some− previous molec- ena would result from energy-dependent CR diffusion ular gas surveys favoured∼ an association with gas that into dense gas in turbulent regions that experience a featured broad CO emission components at a distance −1 suppressed diffusion level. This might act to hinder of 6.3 kpc (vLSR 90 km s ). It was argued that the transport of lower energy CRs more than higher an∼ enhanced CO(2-1)/CO(1-0)∼ − intensity ratio is char- energy CRs and result in a harder than average spec- acteristic of shocked gas (Slane et al. 1999; Butt et al. trum (eg. Gabici et al., 2009; Casanova et al., 2010; 2001). The optically subluminous nature of the RX Fukui et al., 2012; Maxted et al., 2012a). J1713.7 3946 progenitor event (see 1) may also be − § In a previous paper (Maxted et al. 2012a), we es- considered to support a larger distance (Fessen et al. timated the level of penetration of CRs of a range 2012). For completeness, we consider these CS(1-0) of energies (10 GeV to 102.5 TeV) into a homogenous detections in our analyses. − molecular region (average density 300 cm 3) of radius 0.62 pc (similar to Core C) within a time equal to the The Norma Arm −1 RX J1713.7 3946 age ( 1 600 yr). We found that for LSR∼ − − − ∼ (v 75 to 65 km s ): At a distance of decreasing values for the diffusion-suppression coeffi- 6 kpc, in the northernmost regions of the surveyed cient, χ (see Equation 3), the level of CR penetration field∼ (Figure 6), are CS(1-0)-traced dense gas compo- into molecular cores may plausibly be decreased, par- nents. These components, labelled here as N1, N2 and ticularly at lower energies. N3 are within the Norma arm and are coincident with For a plausible guide on the level of CR penetration peaks in CO(2-1) emission. Due to the extended na- into dense gas, we used the 3D random walk distance, ture of N1, this region had previously been scrutinised d = √6 D t, where t is time and the diffusion coeffi- in two sections N1-east and N1-west, with the calcu- 3 cient, D, was parametrised as, lated masses being of the order of a few 10 M⊙ for both sides (Maxted et al. 2012b). Further× scrutiny of 0.5 EP /GeV 2 −1 spectral data resulted in the discovery of another coin- D(EP ,B) = χD0 [cm s ], (3) B/3 µG cident dense core component, N3. Clump N3, which is „ « 3 comparable in mass to both N1-east and west ( 10 M⊙), ∼ where D0 is the galactic diffusion coefficient, assumed is apparent as one peak of the double-peaked profile 27 2 −1 to be 3 10 cm s to fit CR observations (Berezin- in the bottom-right spectra of Figure 6, (whereas the skii et al.× 1990), and χ is the diffusion suppression coef- other peak is an edge of N1) and is shown as white ficient (assumed to be <1 inside the core, 1 outside), a contours in the image. Clump N2, in the north-west parameter invoked to account for possible deviations of of the image in Figure 6 has a mass on the order of 3 the average galactic diffusion coefficient inside molecu- 10 M⊙. lar clouds (Berezinskii et al. 1990; Gabici et al. 2007). ∼ Clumps N1 and N3 are coincident with the bound- EP was the proton energy and B was the magnetic ary of the RX J1713.7 3946 HESS TeV γ-ray excess, field, calculated to be consistent with Crutcher (1999). so might feasibly be− CR target material associated − − We found that for χ =10 4 and χ =10 5, CR pro- with RX J1713.7 3946 if RX J1713.7 3946 is associ- tons with energy <10 TeV were somewhat excluded ated with the Norma− arm gas (rather than− the currently- −1 from the central 0.2 and 0.5 pc radius, respectively. favoured vLSR 10 km s /1 kpc-distance gas), and a The total level of∼ exclusion,∼ however, is difficult to hadronic scenario∼ is applicable. In contrast, clump N2 confidently constrain from such a simplistic approach, lies outside of the RX J1713.7 3946 TeV γ-ray bound- so we are currently working on diffusion models that ary, so cannot contribute to− the total hadronic γ-ray numerically solve the diffusion equation to accurately flux for any distance solution. predict the CR distribution, hence the change in CR The dense regions of Clumps N1 and N3 lie coin- enhancement inside dense gas (details to be presented cident with the northern boundary of the keV X-ray in a future paper). It is expected that diffusion-dependent emission (see Figure 4), which may be consistent with modeling will yield CR enhancement factors that are an RX J1713 3946 shock-interaction with Norma-arm functions of not only CR energy, but gas density, i.e. gas in the north,− but this correspondence may be less the CR enhancement factor, kCR, might decrease to- convincing than the north-to-east shock-correspondence −1 wards dense clumps, the effect lessening for increas- of the gas at vLSR 10 km s (see 4.1.1). ing energy. The result would be harder-than-average ∼ − § hadronic γ-ray components correlated with dense gas. The 3 kpc-Expanding Arm −1 The prediction of features in γ-ray spectra will result (vLSR∼ −122 to −118 km s ): Also coincident from future diffusion analyses. with the northern boundary of RX J1713 3946 is molecular gas in the 3 kpc-expanding arm, at− a distance of 6.5 kpc (Figure 7). The T1 cloud has a mass on the 4.1.2 CS(1-0) Emission at Other Velocities ∼ 3 order of 10 M⊙ and contains a distinctive molecular In addition to the gas believed to be in association with core in the∼ east, T1-east. A hot component in T1-east RX J1713.7 3946 (see 4.1.1), dense gas components is evidenced by our detection of CH3OH(7-6) emis- − § corresponding to background gas clouds were also de- sion, which is emitted after CH3OH is evaporated from tected. Prominent CS(1-0) emission from molecular dust-grains in hot (Temperature 100 K) conditions clouds in the Norma arm and the 3 kpc-expanding arm (van Dishoek & Blake 1998). This∼ emission is possi- are displayed in Figures 6 and 7, respectively. bly related to the coincident object, S9 of Churchwell 6 Publications of the Astronomical Society of Australia et al. (2006), which appears as an incomplete ring of an SiO population-inversion, thus the emission can be 8 µm emission (see Figure 10). The authors argue that considered as a weak SiO maser. The v=1 and v=2 such infrared ‘bubbles’ result from hot young stars in SiO(J=1-0) transitions are at consistent velocities, but massive star formation regions. Our 7 mm results are if a tentative SiO(J=1-0,v=0) detection is real, there consistent with T1-east being a hot star-forming core. is a discrepency in rest velocity (offset from the v=1 − − and 2 modes by 1.6 0.14 km s 1 and 1.4 0.1 km s 1, ± ± Background Gas as CR Target Material: respectively). This, in fact, may have been a thermal In Figure 9, we present the predicted hadronic γ-ray component, unrelated to the SiO maser, but since this components from dense gas at distances near 6kpc weak signal was only considered (and searched-for) af- (T1, N1 and N3), for the scenario where this∼ gas is ter the detection of the relatively prominent SiO(J=1- associated with RX J1713.7 3946. 0,v=2) emission, we estimate the likelihood that it − was noise. A naive post-trial analysis that considers The dense gas components in the Norma and 3 kpc- −1 the vLSR range (9 km s ) in the line-fitting process expanding arms would contribute hadronic γ-ray emis- −1 sion at a comparable level to that of the dense gas to- and the fitted line-width (1.5 km s ) leads to an esti- wards the 1 kpc region for a given CR enhancement mate of 6 trials. This decreases the significance from ∼ 1.5 TRMS to an insignificant 0.65 TRMS (1.5/√6). It factor, so expected CR enhancement estimates are not ∼ ∼ likely to help in favouring a specific distance solution. follows that although a weak thermal SiO emission line Moriguchi et al. (2005) systematically compared the may exist towards this location, we dismiss the 2011 angular correlation between the RX J1713.7 3946 X- SiO(J=1-0,v=0) detection displayed in Table 3. ray emission and CO(1-0) emission at a wide− range We do not dismiss the 2011 SiO(J=1-0,v=1) detec- of line of sight velocities, and concluded that gas in tion using a similar argument since the chance prob- the 1 kpc region had better angular correspondence ability of fitting a vLSR consistent (within 0.5 σ −1 ∼ ∼ than∼ other line-of-sight gas components (including the 0.2kms ) with the original SiO(J=1-0,v=2) detec- ± −1 tion is approximately 5% (trials in a 9 km s vLSR- Norma and 3 kpc-expanding arm gas), thus favour- ∼ ing the 1 kpc distance for RX J1713.7 3946. In a range). hadronic∼ scenario, correlation is expected− between gas and γ-ray emission, so their argument can be extended to include the hadronic production of gamma-rays, April 2012 in which case gamma-ray correspondance favours the The deep 7 mm observations of April 20th, 2012, al- the 1 kpc distance. Modelling by Inoue et al. (2012) ∼ lowed a 2.5 reduction of spectral noise, and the found that the large-scale correlation between CO(1- previously∼ tentative× (and insignificant after post-trial 0) and the HESS TeV γ-ray emission supported the analyses) SiO(1-0,v=0) line was now absent. Interest- 1 kpc gas association, a model also supported by a ∼ ingly, the peak intensities of the v=1 and v=2 SiO(J=1- small-scale gas-keV X-ray anticorrelation. 0) emission lines decreased by 35% and 75%, re- We note that the coincident dense gas components spectively, while the line-width increased∼ by ∼45% and of these galactic arms would, despite being significantly 100%, respectively. ∼ more massive than the 1 kpc gas, would produce a ∼ − − − When we consider the changes in integrated inten- similar flux of γ-rays ( 4∼10 13 cm 2 s 1 above 1 TeV) ∼ × sity (proportional to the changes in TPeak ∆vFWHM), as the dense gas believed to be associated with RX the variation may seem less dramatic and× possibly J1713.7 3946, due to the greater distance involved. − partly due to a change in the velocity distribution of We further note that CO(2-1) spectra toward N1- emitting SiO molecules. The v=1 and v=2 SiO(J=1-0) west and T1 (Figures 6 and 7, respectively) include a −1 integrated intensities decrease by 10% and 50%, re- component at vLSR 85 km s which doesn’t appear ∼ ∼ ∼ − spectively. Additionally, the rest velocity was observed to include a detectable dense gas component traced by −1 −1 to change by 1.5 km s . CS(1-0) emission (above TRMS 0.16 K ch ). This gas ∼ 2 We note that χ -minimisation gaussian-fits for the may correspond to ‘Cloud A’ (Slane∼ et al. 1999; Butt April 8th SiO(1-0) observations were divergent, so the et al. 2001) or gas traced by Moriguchi et al. (2005). full width half maximum was set manually in order to achieve a χ2-minimisation fit for the other line param- 4.2 SiO(1-0) Emission eters. A detection of vibrational modes (v=1, 2) of the SiO(1- 0) transition towards [l,b] [347.05, 0.012] in April, The SiO Maser Origin 2011, prompted follow-up observations∼ − that were carried out one year later. The position of this detection is SiO masers of this type are commonly associated with indicated in Figure 3 and spectra are displayed in Fig- evolved stars, or in very rare cases, star-forming molec- ure 8. Spectral characteristics from χ2-minimisation ular cores. As can be seen from Figure 8, no counter- fits are presented in Table 3. part is detected in CO(2-1) or CS(1-0) bands towards the SiO maser discovered in this investigation, discred- iting the molecular core scenario. April 2011 At infrared wavelengths (24, 8 and 5.8 µm, Fig- We measured SiO(J=1-0,v=2) emission that had an ure 10), a source coincident the SiO maser location is intensity greater than the intensity of the lower vibra- present, but as yet, we have been unable to locate the tional mode, v=1, indicating the possible presence of source in Spitzer catalogues. www.publish.csiro.au/journals/pasa 7

5 Summary and Conclusion Casanova S., Jones D., Aharonian F., et al.2010, PASJ, 62, 1127-1134 We carried out a 7 mm survey of the northern and western regions of RX J1713.7 3946, targeting the dense Cassam-Chenai G., Decourchelle A., Ballet J., gas-tracing CS(1-0) transition− and the shock-tracing Sauvageot j.-l., Dubner S. & Giacani E., 2004, A&A, SiO(1-0) transition. We report: 427, 199-216 1) the discovery of dense components correspond- −1 Churchwell E. et al., 2006, ApJ, 649, 759-778 ing to Cores G and L at velocity, vLSR 11 km s , ∼ − −1 as well as gas in the Norma arm at vLSR 70 km s ∼ − −1 Crutcher R., 1999, ApJ, 520, 706-713 and the 3 kpc-expanding arm at vLSR 120 km s , 2) the discovery of a transient SiO(1-0)∼ − maser, in The CTA Consortium, 2010, arXiv:1008.3703 v=1 and 2 states, outside the western shell of the SNR, possibly generated by an evolved star, Ellison D., Patnaude D., Slane P. & Raymond J., 2010, 3) the detection of dense gas and hot gas as in- ApJ, 712, 287-293 dicated by CH3OH(7-6)-emission coincident with the Fessen R., Kremer R., Patnaude D. & Milisavljevic the infrared bubble, S9 of Churchwell et al. (2006), D.., 2012, ApJ, 143, 27-33 4) and that a hadronic scenario for the RX J1713.7 3946 SNR would require a CR enhancement above Frerking M., Wilson R., Linke R. & Wannier P., 1980, − 1 TeV of 1 000, with dense CS(1-0)-traced compo- ApJ, 240, 65-73 nents only∼ contributing a gamma-ray flux above 1 TeV − − − of 3 10 13 cm 2 s 1, a few percent of the total hadronic Fukui, Y., Moriguchi, Y., Tamura, K., Yamamoto, H., − flux,∼ assuming× an E 1.6 integral power law spectrum. Tawara, Y., Mizuno, N., Onishi, T., Mizuno, A., et al., 2003, PASJ, 55, L61-L64 Acknowledgments Fukui, Y., 2008, AIP Conf Proc, 1085, 104-111 Fukui, Y., Sano, H., Sato, J., Horachi, H., Torii, K., This work was supported by an Australian Research McClure-Griffiths, N., Rowell, G., Aharonian, F., Council grant (DP0662810, DP1096533). The Mo- 2012, ApJ, 746, 82 pra Telescope is part of the Australia Telescope and is funded by the Commonwealth of Australia for oper- Gabici, S., Aharonian, F., Blasi, P., 2007, Ap& SS, ation as a National Facility managed by the CSIRO. 309, 365-371 The University of New South Wales Mopra Spectrom- eter Digital Filter Bank used for these Mopra observa- Gabici, S., Aharonian, F., Casanova S., 2009, MNRAS, tions was provided with support from the Australian 396, 1629-1639 Research Council, together with the University of New Gabici S., Casanova S., Aharonian F. & Rowell G., South Wales, University of Sydney, Monash University 2010, in Boissier S., Heydari-Malayeri M., Samadi and the CSIRO. R., Valls-Gaband D., eds, Proc. French Soc. Astron. Astrophys., SF2A, 313-317

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Table 1: The window set-up for the Mopra Spectrometer, MOPS, at 7 mm. The centre frequency, targeted molecular line, targeted frequency and total mapping noise (TRMS) are displayed. Centre Molecular Line Map TRMS − Frequency Emission Line Frequency (K ch 1) (GHz) (GHz) West North Northwest 42.310 30SiO(J=1-0,v=0) 42.373365 0.07 0.07 0.10 42.500 SiO(J=1-0,v=3) 42.519373 ∼0.07 ∼0.07 ∼0.10 42.840 SiO(J=1-0,v=2) 42.820582 ∼0.07 ∼0.08 ∼0.10 29SiO(J=1-0,v=0) 42.879922 ∼ ∼ ∼ 43.125 SiO(J=1-0,v=1) 43.122079 0.08 0.07 0.12 43.395 SiO(J=1-0,v=0) 43.423864 ∼0.08 ∼0.09 ∼0.12 ∼ ∼ ∼ 44.085 CH3OH(7(0)-6(1) A++) 44.069476 0.08 0.10 0.12 ∼ ∼ ∼ 45.125 HC7N(J=40-39) 45.119064 0.09 0.12 0.12 ∼ ∼ ∼ 45.255 HC5N(J=17-16) 45.26475 0.09 0.13 0.13 ∼ ∼ ∼ 45.465 HC3N(J=5-4,F=5-4) 45.488839 0.09 0.13 0.13 46.225 13CS(J=1-0) 46.24758 ∼0.09 ∼0.13 ∼0.13 ∼ ∼ ∼ 47.945 HC5N(J=16-15) 47.927275 0.12 0.15 0.15 48.225 C34S(J=1-0) 48.206946 ∼0.12 ∼0.15 ∼0.15 48.635 OCS(J=4-3) 48.651604 ∼0.13 ∼0.15 ∼0.15 48.975 CS(J=1-0) 48.990957 ∼0.12 ∼0.16 ∼0.17 ∼ ∼ ∼ 10 Publications of the Astronomical Society of Australia Maxted et al. d sis assumptions. 3 3 3 3 2 2 3 to estimate upper limits 3 f 10 10 10 10 10 10 10 f 10 3 ) RMS × × × × × × × ⊙ × ± M , assumed distance, line-width (M 40 12 - 15 30 - 120 1 - 200 0.3 - 300 LSR (1-6) (2-10) (3-20) (1-14) (5-30) (7-60) (9-40) (3-12) ) 2 e e − S(1-0)-band T 4 c 2 cm 34 ± - - K. Averaged over beam size. H 21 3 - 4 N 55 73 - 800 39 - 340 64 - 280 45 - 210 40 - 170 10 130 - 610 0.1 - 600 0.7 - 400 , are indicated. 150 - 1 100 × ( M b e e 0.29 ], line-of-sight velocity, v b - - , ± l 0 - 11 0 - 4.1 0 - 4.7 0 - 7.5 0 - 8.8 0 - 4.4 0 - 4.6 0 - 33 0 - 20 0 - 0.44 Depth Optical 22.5 and using the C 2.71 = S] , and mass of H, ) 2 1 34 H 0.3 0.3 1.4 0.5 1.3 0.9 0.5 0.3 0.3 0.06 0.03 − - - N ± ± ± ± ± ± ± ± ± ± ± FWHM ∆v 2.5 0.9 1.6 4.6 8.0 5.5 2.4 2.2 1.6 (km s 1.25 2.08 re likely dominated by the systematics introduced by the analy Assuming [CS]/[C - - b 1.0 1.0 1.0 1.0 1.0 6.0 6.0 6.0 6.0 6.5 6.5 3946. Galactic Coordinates, [ − Assumed Distance (kpc) ) 0.2 0.1 1.1 0.4 0.2 0.4 0.3 0.2 0.01 1 0.1 0.02 ± ± − ± ± ± ± ± ± ± ± ± - - LSR v 9.1 11.2 10.8 70.1 69.4 76.6 70.9 Thermal Equilibrium (LTE) assumption at a temperature of 10 (km s 9.82 120.0 119.5 c 11.76 − − − − − − − − − − − 4.1.1) § ◦ ◦ , optical depth, average H column density, ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ 0.09 0.07 0.03 0.01 0.067 0.133 0.32 0.40 FWHM ] ,0.01 − − − − − − − − b , , ,+0.01 , ,+0.02 , , , , , ◦ - - , ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ ◦ l [ Direction 347.31 347.21 347.14 347.18 347.24 347.24 347.00 346.94 347.08 347.033 347.433 S(1-0) emission is detected. 34 Lower values favoured (see e d d d a N1+N3 region T1 region Clump N3 Clump N2 Clump T1-east Clump T1-west Core C CoreD CoreG Core L Clump N1-west Clump N1-east Name Core A Name convention from Moriguchi et al. (2005) and this work. a Table 2: Parameters of CS(1-0) emission towards RXJ1713.7 (full-width-half-maximum), ∆v Statistical uncertainties are on the order of 20%, so errors a where no C (2012a) www.publish.csiro.au/journals/pasa 11

0.8 Core G

0.25

-0.3 2

Brightness Temperature (K) 0

-120 -100 -80 -60 -40 -20 0 20 Velocity (km/s) 0.5 Core L

0 Galactic Latitude (deg) Integrated Intensity (K.km/s) 2.5

Brightness Temperature (K) 0 -120 -100 -80 -60 -40 -20 0 20 Galactic Longitude (deg) Velocity (km/s)

−1 Figure 3: Left Panel: Colour image of integrated CS(1-0) emission (vLSR= −12.5 to −7.5kms ) from −1 Mopra overlaid with black contours of CO(2-1) emission (vLSR= −18 to 0kms ) from Nanten2 (Fukui 2008), as well as solid blue contours of HESS >1.4 TeV excess emission (same levels as for Figure 1). Core names and the position of a SiO maser are indicated. CO(2-1) emission contour-levels are 5, 10, 15, 20, 25, 30, 35 and 40Kkms−1. Right Panel: We also show spectral proﬁles of molecular emission towards locations of interest (indicated).

Table 3: Line parameters for SiO transitions towards the detected SiO maser at [l,b]∼[347.05,−0.012] for three observation periods (location indicated on Figure3). Background noise, TRMS, is shown. Ve- locity of peak, vLSR, peak intensity, TPeak, and FWHM, ∆vFWHM, were found by fitting Gaussians before deconvolving with the MOPS velocity resolution. Date SiO(1-0) TRMS vLSR TPeak ∆vFWHM transition (K ch−1) (km s−1) (km s−1) v=0 0.09 b−4.9 ± 0.3 b0.14 ± 0.05 b1.5 ± 0.7 23/24 v=1 0.07 −6.5 ± 0.4 0.11 ± 0.03 2.7 ± 1.0 April 2011 v=2 0.08 −6.3 ± 0.1 0.33 ± 0.05 2.6 ± 0.7 v=3 0.07 - - - v=0 0.11 - - - 8 v=1 0.08 a−4.2 ± 0.3 a0.08 ± 0.02 a3.9 ± 2.5 April 2012 v=2 0.07 a−4.7 ± 0.6 a0.10 ± 0.02 a5.2 ± 0.8 v=3 0.06 - - - v=0 0.03 - - - 20 v=1 0.03 −4.8 ± 0.3 0.07 ± 0.01 3.9 ± 0.6 April 2012 v=2 0.03 −5.0 ± 0.3 0.083 ± 0.009 5.2 ± 0.6 v=3 0.03 - - - aSpectral lines difficult to fit, so line widths were fixed to be equal to those of the the April 20, 2012 observations. bLine deemed insignificant in post-trial analysis (see §4.2) 12 Publications of the Astronomical Society of Australia Galactic Latitude (deg) Integrated Intensity (K.km/s)

Galactic Longitude (deg)

Figure 4: Colour image of integrated CS(1-0) emission, shown for three diﬀerent ranges indicated in each panel, overlaid with XMM-Newton 0.5-4.5 keV X-ray contours from Acero et al. (2009). X-ray contours span 0.003-0.015cm−2 s−1 in increments of 0.003 cm−2 s−1. Core names and the position of a SiO maser are indicated. The Mopra 7mm and XMM-Newton beam FWHM are represented by the small circles next to the text on the picture. www.publish.csiro.au/journals/pasa 13

RX J1713.7−3946 Total >1TeV flux (Aharonian et al. 2007)

, k CR

Figure 5: The predicted hadronic γ-ray flux as a function of CR-enhancement for gas components pos- −1 sibly associated with RX J1713.7−3946 (vLSR∼ −10kms ). The contributions from HI and CO-traced components towards the RX J1713.7−3946 region and CS(1-0) emission from 5 cores are included (this work). The total predicted hadronic γ-ray flux remains less than the measured RXJ1713.7−3946γ-ray flux for CR enhancement values less than 1000. A distance of 1kpc was assumed. 14 Publications of the Astronomical Society of Australia

0.8 Clump N2

0.25

-0.3

Brightness Temperature (K) 0 -120 -100 -80 -60 -40 -20 0 20 Velocity (km/s) 0.9 Clump N1−west

0.3 Galactic Latitude (deg) -0.3 Integrated Intensity (K.km/s) 10 Brightness Temperature (K) 0 -120 -100 -80 -60 -40 -20 0 20 Galactic Longitude (deg) Velocity (km/s) 0.8 0.8 Clump N1−east Clump N3 0.25 0.25 N3 component of N1

-0.3 -0.3 10 5 Brightness Temperature (K) Brightness Temperature (K) 0 0 -120 -100 -80 -60 -40 -20 0 20 -120 -100 -80 -60 -40 -20 0 20 Velocity (km/s) Velocity (km/s)

−1 Figure 6: Top Left Panel: Colour image of integrated CS(1-0) emission (vLSR= −75 to −65kms ) −1 from Mopra overlaid with black contours of CO(2-1) emission (vLSR= −75 to −65kms ) from Nanten2 (Fukui 2008), as well as solid blue contours of HESS >1.4 TeV excess emission (same levels as for Figure 1). CO(2-1) emission contour-levels are 10, 20, 30, 40, 50 and 60 Kkms−1. White contours indicate Clump N3 −1 Nanten2 integrated CS(1-0) emission (vLSR = −80 to −72.5kms ) with contour-levels of 0.8, 1.0, 1.2, 1.4 and 1.6Kkms−1. Right/Bottom Panels: We also show spectral proﬁles of molecular emission towards locations of interest (indicated). www.publish.csiro.au/journals/pasa 15

0.5 Clump T1−west

Brightness Temperature (K) 0 -120 -100 -80 -60 -40 -20 0 20 Velocity (km/s) 0.8 Clump T1−east 0.25 Galactic Latitude (deg) -0.3 Integrated Intensity (K.km/s) 5

Brightness Temperature (K) 0 0.8 Galactic Longitude (deg) 0.25

-0.3 -120 -100 -80 -60 -40 -20 0 20 Velocity (km/s)

−1 Figure 7: Top Left Panel: Colour image of integrated CS(1-0) emission (vLSR= −122 to −115kms ) −1 from Mopra overlaid with black contours of CO(2-1) emission (vLSR= −122 to −115kms ) from Nanten2 (Fukui 2008), as well as solid blue contours of HESS >1.4 TeV excess emission (same levels as for Figure 1). CO(2-1) emission contour-levels are 2, 4, 6, 8, 10 and 12Kkms−1. Right Panels: We also show spectral proﬁles of molecular emission towards locations of interest (indicated). 16 Publications of the Astronomical Society of Australia

0.25 0.25

0 0

0.5 0.25

0 0 0.5 0.25

0 0 Brightness Temperature (K) Brightness Temperature (K)

0.25 0.25

0 0

-60 -50 -40 -30 -20 -10 0 10 20 30 40 -60 -50 -40 -30 -20 -10 0 10 20 30 40 Velocity (km/s) Velocity (km/s) 0.2 23/24 April 2011 0 8 April 2012 0.2

20 April 2012 0

0.2 0.5

0 0 Brightness Temperature (K) 0.2 2

0 0 Brightness Temperature (K)

-60 -50 -40 -30 -20 -10 0 10 20 30 40 -60 -50 -40 -30 -20 -10 0 10 20 30 40 Velocity (km/s) Velocity (km/s)

Figure 8: Spectra (Mopra and Nanten2) towards the SiO maser discovered at (l,b)∼(347.05,−0.012). Data from the 23rd and 24th of April, 2011 were taken from OTF maps. Data from April, 2012 are from follow-up pointing data. www.publish.csiro.au/journals/pasa 17

RX J1713.7−3946 Total >1TeV flux (Aharonian et al. 2007)

, k CR

Figure 9: The predicted hadronic γ-ray ﬂux as a function of CR-enhancement if dense gas currently −1 believed to be background to RXJ1713.7−3946 (vLSR∼−70, −120kms ), were in fact, associated with RX J1713.7−3946. Note that we only include contributions from CS(1-0) emission. Distances of 6 kpc and 6.5 kpc were assumed for N1/3 and T1, respectively. 18 Publications of the Astronomical Society of Australia Galactic Latitude (deg)

5.8µ m

Galactic Longitude (deg) Galactic Latitude (deg)

8 µ m

Galactic Longitude (deg) Galactic Latitude (deg)

24 µ m

Galactic Longitude (deg)

Figure 10: Spitzer 5.8 µm (top), 8 µm (middle) and 24 µm (bottom) emission images. Objects of interest to this investigation (see §4.1.1) are indicated by circles and ellipses. Object S9 towards T1 (see text) is indicated in the middle picture (8 µm). Dashed squares indicate regions mapped in 7 mm wavelengths by Mopra. Chapter 5

Supernova Remnant CTB 37A

Thanks to a high exposure (80+ hours) on RX J1713.7−3946 by HESS (and the large ﬁeld of view of HESS), near-by supernova remnant, CTB 37A, was discovered to have a coincident gamma-ray signal, making CTB 37A a potential cosmic ray accelerator. CTB 37A is smaller, more distant and older than RX J1713.7−3946, but may still hold clues about the origin of galactic cosmic rays. This chapter is comprised of a paper that has been prepared for re-submission to the Monthly Notices of the Royal Astronomical Society (Interstellar gas towards CTB 37A and the TeV gamma-ray source HESS J1714−385) after the consideration of comments from an anonymous referee.

5.1 Interstellar gas towards CTB37A and the TeV gamma- ray source HESS J1714−385

The following manuscript was submitted to the peer-reviewed journal, Monthly Notices of the Royal Astronomical Society (MNRAS), and re-submitted after the consideration of comments from an anonymous referee.

117 29/1/13

118

Mon. Not. R. Astron. Soc. 000, 000–000 (0000) Printed 19 April 2013 (MN LATEX style ﬁle v2.2)

Interstellar gas towards CTB 37A and the TeV gamma-ray source HESS J1714−385

Nigel I. Maxted1⋆, Gavin P. Rowell1, Bruce R. Dawson1, Michael G. Burton2, Yasuo Fukui3, Andrew Walsh4, Akiko Kawamura3, Hirotaka Horachi3, Hidetoshi Sano3, Satoshi Yoshiike3 & Tatsuya Fukuda3 1School of Chemistry & Physics, University of Adelaide, Adelaide, 5005, Australia 2School of Physics, University of New South Wales, Sydney, 2052, Australia 3School of Physics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi, 464-8602, Japan 4International Centre for Radio Astronomy Research, Curtin University, GPO Box U1987, Perth, Australia

Accepted 2012 XXXXX. Received 2012 XXXXX; in original form 2011 May 18

ABSTRACT Observations of dense molecular gas towards the supernova remnants CTB 37A (G348.5+0.1) and G348.5−0.0 were carried out using the Mopra and Nanten2 radio telescopes. We present CO(2-1) and CS(1-0) emission maps of a region encompassing the CTB37A TeV gamma-ray emission, HESSJ1714−385, revealing regions of dense gas within associated molecular clouds. Some gas displays good overlap with gamma- ray emission, consistent with hadronic gamma-ray emission scenarios. Masses of gas towards the HESSJ1714−385 TeV gamma-ray emission region were estimated, and 3 4 were of the order of 10 -10 M⊙. In the case of a purely hadronic origin for the gamma ray emission (rather than leptonic), the cosmic ray ﬂux enhancement is ∼80-1100 times the local solar value. This enhancement factor and other considerations allow a discussion of the age of CTB37A, which is consistent with ∼104 yr. Key words: molecular data - supernovae: individual: CTB37A - ISM: clouds - cosmic rays - gamma rays: ISM.

1 INTRODUCTION The CTB 37A radio continuum emission (see Figure 1a) is suggestive of a ‘break-out’ morphology. Strong shell- Gamma ray observations may be the key to solving one the shaped emission emanates from the eastern (galactic co- of longest unsolved mysteries in astrophysics, the origin of ordinate system) section and a weaker lobe or ‘break- cosmic rays (hereafter CRs). Since gamma-rays are byprod- away’ region extends in a western direction. Reynoso ucts of cosmic ray interactions, high gamma-ray fluxes are & Mangum (2000) observed CO(1-0) emission towards expected from regions with enhanced cosmic ray densities, CTB 37A and investigated the possibility that the observed such as near cosmic ray acceleration sites. The leading the- features are caused by constraining molecular gas along the ory to explain the acceleration of these particles is first or- north, east and south boundaries. They found associated der Fermi acceleration in the shocks of supernova remnants −1 vLSR 65 km s molecular clouds around the northern (hereafter SNRs). ∼ − and eastern edges of the CTB 37A radio continuum emission, A candidate region for CR-acceleration is CTB 37, while minimal gas was seen in the location of the ‘break-out’ which is comprised of three SNRs: CTB 37A (G348.5+0.1), features to the west. In the south however, inconsistent with CTB 37B (G348.7+0.3) and G348.5 0.0. CTB 37A was − predictions, no gas (as traced by CO(1-0)) was seen to be initially discovered at radio wavelengths (Clark et al. constraining the remnant. 1975) and was recently observed to emit at TeV energies (HESS J1714 385, Aharonian et al., 2008a). GeV-energy Knowledge of gas distribution is also important when − excesses have also been detected (3EG J1714 3857, Green considering a possible hadronic (pion production via CR col- − et al., 1999; Hartman et al., 1999, 1FGL J1714.5 3830, Cas- lisions with gas) origin for the CTB 37A gamma-ray emis- − tro & Slane, 2010). sion, but the nature of the parent particle population (leptonic and/or hadronic) is not entirely clear. Non-thermal X-ray emission is absent from the CTB 37A radio rim (Frail ⋆ E-mail: [email protected] et al. 1996), which, in the presence of strong magnetic fields

c 0000 RAS 2 Nigel I. Maxted et al. Intensity (Jy/beam) Galactic Latitude

a Galactic Longitude b

Figure 1. (a) Molonglo 843 MHz radio continuum image showing CTB 37 (Clark et al. 1975). 80 and 100 gamma-ray excess count contours of HESS J1714−385 (CTB 37A) and HESS J1713−381 (CTB 37B) (black, dashed) (Aharonian et al. 2008a) and Molonglo 843 MHz radio continuum (bandwidth ∼4.4 MHz) contours (red) are overlaid. A dashed blue square represents the region observed with Mopra (this work) and large labeled black circles mark the approximate locations and extents of objects of interest, as visually approximated from the 843 MHz image. (b) Similar to (a), but zoomed on CTB 37A. Crosses represent both the ∼ −65 km s−1 (pink,+) and ∼ −25 km s−1 (cyan,×) OH maser populations (Frail et al. 1996), circles represent the position and beam FWHM of 7 mm Mopra deep ON-OFF switched pointings. would imply a lack of ongoing high energy electron accelera- Kassim et al. 1991), which can be seen in 843 MHz radio tion. Indeed, Brogan et al. (2000) measured strong magnetic continuum emission in Figure 1a. Two masers comprise a −1 fields (0.22-1.5 mG) towards shocked regions of CTB 37A, population at line-of-sight-velocity, vLSR 22 km s while ∼ − −1 and in such environments TeV leptons have limited lifetimes eight comprise a second population at vLSR 65 km s . ∼ − due to synchrotron losses (synchrotron lifetimes of .250 yr, Although it has been suggested that the 2 maser popula- very short compared to the SNR age, see 5.3). If the high tions may be attributable to each of the 2 SNRs separately, § energy lepton population is dimished towards the CTB 37A recent work by Tian & Leahy (2012) demonstrates that radio rim, which it appears to be, a hadronic scenario for CTB 37A may simply be associated with multiple varied- gamma-ray emission production would be favourable (Aha- velocity clouds. It follows that both populations of masers ronian et al. 2008a). may be attributable to CTB 37A (and neither would be associated with G348.5 0.0). Altenatively, a leptonic scenario for CTB 37A is sup- − ported by the presence of a coincident region of non-thermal Reynoso & Mangum (2000) found molecular CO(1- X-ray emission (Aharonian et al. 2008a). This could pos- 0) cloud associations towards most of the masers, but −1 sibly indicate a pulsar wind nebulae (PWN) accelerating two vLSR 65 km s OH masers (Locations 1 and 2, see ∼ − electrons within a blast wave (making CTB 37A a compos- Figure 1b) did not have clear CO emission counterparts ite SNR), but this hypothesis is complicated by the non- at corresponding velocities and locations. The formation detection of a point-like source or pulsar within the extended of 1720 MHz OH masers requires large gas densities of 4 5 −3 non-thermal emission (Aharonian et al. 2008a). Certainly, nH2 10 -10 cm (Draine et al. 1983; Frail et al. 1998), ∼ 3 −3 the non-thermal and thermal emission from the outer rim but CO(1-0) emission has a critical density of .10 cm and centre of CTB 37A, respectively, indicate that CTB 37A and quickly becomes optically thick. As Reynoso & Mangum is a mixed-morphology SNR. Recent work by Brandt et al. (2000) suggest, to probe deeper, observations of dense gas (2011) is suggestive of a significant Bremsstrahlung emis- tracers (i.e. higher critical density and lower abundance) are sion component between 1 and 100 GeV, with a hadronic required. component dominating at TeV energies and above, but the In addition to being conducive to OH maser gener- question of the nature of the emitting particle population is ation, dense gas may significantly affect the dynamics of still largely an open question. the SNR shock motion, while also providing denser targets Also present towards the CTB 37A region (Aharonian for gamma-ray-producing hadronic cosmic ray interactions. et al. 2008a), are 1720 MHz OH masers, which are indica- Knowing the location of dense gas may lead to both an ex- tors of shock-gas interactions, likely triggered by SNR shocks planation for the ‘break-out’ morphology of the radio contin- (Aharonian et al. 2008a; Frail et al. 1996). However, the in- uum emission and more detailed modeling of the CTB 37A terpretation of this data is confused by the existence of a co- TeV emission. Previous studies have noted that dense gas incident partial shell SNR, G348.5 0.0 (Milne et al. 1979; may hinder CR diffusion and change the resultant high en- − c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 3 ergy photon spectrum from hadronic interactions (Gabici Table 1. A summary of previous HI absorption analyses towards et al. 2009; Casanova 2011; Fukui et al. 2012; Maxted et al. CTB 37A. 2012). To complement existing Nanten2 CO(2-1) and Southern Gas Velocity Absorption? Relation to CTB 37A − Galactic Plane Survey (SGPS) HI data (McClure-Griffiths (km s 1) et al. 2005; Haverkorn et al. 2006; Tian & Leahy 2012), −22 X Foreground1,2 which presents a good general picture of low to moderately- −65 partial Background/Some Foreground1,2 dense gas and atomic gas, respectively, we took 7 mm ob- −85 X Foreground1,2 servations of the CTB 37A region with the Mopra radio −110 X Foreground1,2 telescope. We targeted the gas tracer CS(1-0) (critical den- −145 × Background2 − sity 8 104 cm 3) to investigate dense gas possibly linked ∼ × 1 2 to the evolution of the radio morphology, target material Caswell et al. (1975), Tian & Leahy (2012) associated with the TeV emission and the maser-conducive environment of this region. We simultaneously searched for tance of 7.9 1.6 in our analyses. HI absorption information ± the potential shock-tracers SiO(1-0) and CH3OH (moti- is summarised in Table 1. vated by results towards the SNR W28, Nicholas et al., 2012) to search for shocked gas related to SNR activity. The gas-phase SiO abundance is enhanced in post-shock re- 2 OBSERVATIONS gions (Schilke et al. 1997; Martin-Pintado et al. 2000; Gus- dorf et al. 2008a,b), where Si is sputtered from dust grains, In April of 2010, we observed and co-added 5 Mopra OTF ′ ′ hence SiO(1-0) can sometimes be employed as an indica- (on the fly) 19 19 area maps at 7 mm wavelength, cen- × tor of a shocked-environment like that expected towards a tered on [l, b]=[348.43, 0.16], to produce a data cube with 2 SNR, whereas in irradiated regions, CH3OH may be evap- spatial and 1 spectral (velocity) dimension. The scan length ′′ orated from dust grains, giving clues about the interstellar was 15.6 per cycle time (of 2.0 s) and the spacing between environment (van Dishoek & Blake 1998). scan rows was 26′′. Deep ON-OFF switched pointings were To investigate the gas distribution towards CTB 37A, also taken towards six locations (see Figure 1 and Table 3) we applied the methods presented in 3 to several clouds containing 1720 MHz OH masers and one location centered § of gas, which we consider separately in subsections of 4. on a peak of CS(1-0) emission seen in mapping data (Lo- § In 5.1 we compare column densities estimated by us to es- cation 7). One 12 mm deep ON-OFF switched pointing was § ◦ ◦ timates by previous authors. In 5.2 we use our gas mass also performed towards the location [l,b]=[348.37 ,0.14 ] to § estimates to estimate the cosmic ray density in several sce- follow up a feature discussed in A. See Walsh et al. (2008) § narios of gamma-ray emission from hadronic processes for for the 12 mm spectrometer setup. We used a sky reference CTB 37A. Finally, in 5.3, we discuss the age of CTB 37A. position of [l, b]=[346.40, 1.64]. § − The Mopra spectrometer, MOPS, was employed and is capable of recording sixteen tunable, 4096-channel 1.1 Distance (137.5 MHz) bands simultaneously when in ‘zoom’ mode, By noting that towards CTB 37A, HI absorption occurs in as used here. A list of measured frequency bands, targeted −1 gas at vLSR 110 km s , but not from gas that lies at molecular transitions and achieved TRMS levels are shown in ∼ −−1 vLSR 65 km s , Caswell et al. (1975) concluded that the Tables 2 and 3. ∼ − −1 vLSR 110 km s gas was nearer to us than CTB 37A. As- The velocity resolution of the 7 mm zoom-mode data is ∼ − −1 suming that the line-of-sight-velocities were primarily due 0.2 km s . The beam FWHM and the pointing accuracy ∼ ′′ ′′ to galactic kinematic motions, the authors recognised that of Mopra at 7 mm are 59 2 and 6 , respectively. The −1 ± ∼ the vLSR 65 km s gas must be on the ‘far-side’ (past the achieved TRMS values for the total 7 mm map and individual ∼ − tangent point) of the galaxy in order to be spatially behind pointings are stated in Tables 2 and 3, respectively. −1 the vLSR 110 km s gas. The distance of the CTB 37A OTF-mapping and deep ON-OFF switched pointing ∼ − radio emission was thus constrained to be between 6.7 and data were reduced and analysed using the ATNF anal- ◦ 13.7 kpc (assuming l 349 ) (this kinematic distance con- ysis programs, Livedata, Gridzilla, Kvis, Miriad and ∼ 1 straint relied on a value of 10 kpc for the orbital radius of ASAP . our sun with respect to the galactic centre). Livedata was used to calibrate data against a sky ref- More recent high-resolution SGPS data allowed Tian erence position measured after each scan of a row/column & Leahy (2012) to not only find partial HI absorption at was completed. A polynomial baseline-subtraction was −1 vLSR 65 km s , but also a distinct lack of HI absorption also applied. Gridzilla then combined corresponding fre- ∼ − −1 towards previously-overlooked gas at vLSR 145 km s , quency bands of multiple OTF-mapping runs into 16 three- ∼ − as traced by CO(1-0) (Reynoso & Mangum 2000). Tian dimensional data cubes, converting frequencies into line-of- −1 & Leahy (2012) suggest that since the vLSR 65 km s sight velocities. Data were then combined, weighting by the −1 ∼ − gas lies between the vLSR 110 km s (HI absorption) Mopra system temperature and smoothed in the Galactic −1 ∼ − ′ and vLSR 145 km s (no HI absorption) gas, the vLSR l b plane using a Gaussian of FWHM 1.25 . −∼1 − ∼ − 65 km s gas may plausibly be in a non-circular orbit, as Miriad was used to correct for the efficiency of the in- − would be the case if CTB 37A is within the inner 3 kpc of strument (Urquhart et al. 2010) for mapping data and create the galaxy, influenced by the gravitational potential of the Perseus arm. This implies that the CTB 37A SNR distance may be between 6.3 and 9.5 kpc, thus we assume the a dis- 1 See http://www.atnf.csiro.au/computing/software/

c 0000 RAS, MNRAS 000, 000–000 4 Nigel I. Maxted et al.

Table 2. The window set-up for the Mopra Spectrometer where A is the cross-sectional area of the region and 2mH is (MOPS) at 7 mm. The centre frequency, targeted molecular the mass of molecular hydrogen. The average density, nH2 , line, targeted frequency and total eﬃciency-corrected map noise was estimated by assuming that the thickness of the region (TRMS) are displayed. in the line of sight direction was of the same order as the height and width, √A. ∼ Centre Molecular TRMS Detected? Frequency Emission Line (K ch−1) (Map/Point) (GHz) 3.1 CO

30 42.310 SiO(J=1-0,v=0) 0.07 × × A CO(2-1) X-factor to convert CO(2-1) intensity, W2−1, into 28 42.500 SiO(J=1-0,v=3) 0.07 × × H2 column density, NH2 = X2−1W2−1, is difficult to find in 28 42.840 SiO(J=1-0,v=2) 0.07 × × literature, so we scaled our CO(2-1) emission by the ex- ′′ 29 ′′ SiO(J=1-0,v=0) × × pected CO(1-0)/CO(2-1) intensity ratio, 43.125 28SiO(J=1-0,v=1) 0.07 × × 43.255 - 0.07 W1−0 1 11.07 K 28 X exp (2) 43.395 SiO(J=1-0,v=0) 0.07 × W2−1 ≈ 4 Trot 44.085 CH3OH(7(0)-6(1) A++) 0.08 × X » – 44.535 - 0.08 where Trot is the rotational temperature, which we 45.125 HC7N(J=40-39) 0.09 × × assume to be 10 K. This allowed us to use the 45.255 HC5N(J=17-16) 0.09 × × more commonly cited/measured CO(1-0) X-factor, 20 −2 −1 −1 45.465 HC3N(J=5-4,F=5-4) 0.09 X X X1−0 3 10 cm (Kkms ) (Dame et al. 2001). 13 ∼ × 46.225 CS(1-0) 0.09 × × Note, that a 0.7-3 systematic error in column density 47.945 HC5N(J=16-15) 0.12 × × × 34 would be introduced for a 5 K error in temperature esti- 48.225 C S(1-0) 0.12 × × mation (using Equation 2). In an extreme case, such as 48.635 OCS(J=4-3) 0.13 × × T =40 K, like towards the shock of similar SNR, SNR W28 48.975 CS(1-0) 0.13 X X (Nicholas et al. 2011), we would expect the column density calculated from CO(2-1) using our method to change by a factor 0.4. line-of-sight velocity-integrated intensity images (moment 0) ∼ from data cubes. ASAP was used to analyse deep ON-OFF switched 3.2 CS pointing data. Data were time-averaged, weighted by system temperature and had fitted polynomial baselines subtracted. We calculate the CS(J=1) column density using Equation 9 Like mapping data, deep pointing spectra were corrected from Goldsmith & Langer (1999). This equation requires for the Mopra beam efficiency (Urquhart et al. 2010). The an optical depth, which would usually be estimated from beam efficiency for the CS(1-0) band for point and extended the CS(1-0)-C34S(1-0) intensity ratio, but as we do not de- sources are 0.43 and 0.56, respectively. tect C34S(1-0), for simplicity we assume that the CS(1-0) ∼ ∼ CO(2-1) data was taken with the Nanten2 4 m sub- emission is optically thin (τ 0). It follows that the col- → millimeter telescope during December of 2008. The tele- umn densities calculated from CS(1-0) may be considered ′′ scope has a beam FWHM of 90 at 230 GHz and a point- as lower limits. ′′ ∼ ing accuracy of 15 . The Acoustic Optical Spectrometer An LTE assumption at Trot 10 K implies that the to- ∼ −1 ∼ (AOS) had 2048 channels separated by 0.38 km s , pro- tal CS column density is simply a factor 3.5 times the −1 ∼ viding a bandwidth of 390 km s . The achieved TRMS was CS(J=1) column density, and the molecular abundance of − − .0.7 K ch 1. This CO(2-1) data offers superior spatial and CS with respect to hydrogen is assumed to be 10 9 (Fr- ∼ velocity resolution when compared to previously-published erking et al. 1980). The systematic error introduced into the CO(1-0) (Dame et al. 2001) data. CS(1-0) column density by our temperature assumption is likely to be even smaller than that introduced for CO(2-1), with a 50% temperature systematic corresponding to a fac- 3 GAS PARAMETER CALCULATION tor 0.7-1.2 error in column density. In the extreme case of T =40 K, column density calculated from CS(1-0) using our To address the amount of available hadronic target material method changes by 1.8 times. towards HESS J1714 385, the column density towards ab- ∼ − sorbed X-ray sources and the density towards the observed OH masers, we calculate column density, mass and density 3.3 HI from CO(2-1), CS(1-0) and HI data. As we discuss in 4, § HI data is available (McClure-Griffiths et al. 2005; the gas observed towards CTB 37A appears extended, so we Haverkorn et al. 2006), and exhibits emission and absorp- integrate our spectral line maps over a spatially wide region tion features towards CTB 37A. Where the level of radio ([α,δ]-space) to estimate average gas parameters within cho- continuum-absorption appears minor and HI emission is sen regions. We used the Miriad functions moment 0 and present, we constrain column density using an HI X-factor, mbspect to calculate integrated intensity, V Tb dvLSR dαdδ 18 −2 −1 −1 −1 2 XHI =1.823 10 cm (Kkms ) (Dickey & Lockman (Kkms deg ), and produce spectral line maps. × R 1990). The mass of gas within the region, M, is related to the For absorption lines, we first estimate an optical depth, average column density, NH2 , by τ ln (T0/Tb), where T0 is the continuum intensity ∼ M =2mH NH2 A (1) and Tb is the local minimum intensity of an absorption

c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 5 line. This allows the calculation of atomic column density, 18 NH 1.9 10 τ∆vFWHMTs, where ∆vFWHM is an approxi- ∼ × mated full-width-half-maximum and Ts is the spin temperature, assumed to be 100 K. Since the calculated column density is proportional to the spin temperature, the uncertainty in column density due to our assumed temperature is the percentage as the uncertainty in temperature.

4 THE SPATIAL GAS DISTRIBUTION 1720 MHz OH masers CS(1-0) emission was clearly detected at line-of-sight- −1 velocities, vLSR 5, 10, 22, 60, 90 and 105 km s . ∼ − − − − − Additionally, SiO(1-0), HC3N(J=5-4) and CH3OH(7(0)- 6(1) A++) were detected towards ‘Location 3’ (Figure 5) at −1 velocity, vLSR 105 km s . Gaussian line fit parameters ∼ − to the most significant emission lines are presented in Ta- ble 3. Together, Mopra CS(1-0), Nanten CO(2-1) and SGPS HI data (McClure-Griffiths et al. 2005; Haverkorn et al. 2006) towards seven CTB 37A locations are shown in Fig-

ures 4-10. The HI data contained a strong radio continuum Velocity (km/s) component from CTB 37A, producing absorption lines in Average Intensity (K) foreground gas.

3kpc Expanding arm 4.1 Gas Morphology hot core Figure 2 is a longitude-velocity plot of CO(2-1) and CS(1- 0) data (see Figure B1 for a latitude-velocity plot). Sev- eral clouds are visible in CO(2-1) at approximate line-of- sight reference velocities, vLSR 5, 10, 20, 60 to −1 ∼ − − − 75, 90 and 105 km s . Referring to Moriguchi et al. − − − (2005), which addresses CO(1-0) emission from the nearby SNR RX J1713.7 3946, these regions of gas may corre- − −1 spond to local gas ( 5kms ), the Sagittarius arm ( 5 −1 ∼ ∼− −1 to 30 km s ), the Norma arm ( 60 to 75 km s ), − −1 ∼ − − 348.6 348.3 ‘Cloud A’ ( 80 to 95 km s , Slane et al., 1999) and the ∼ − − −1 3kpc expanding arm ( 100 to 115 km s ). Galactic Longitude (deg) ∼ − − Work by Vallee (2008) is not necessarily consistent with this scenario, with Figure 3d illustrating a model with possible gas components of the Sagittarius-Carina, Scutum-Crux Figure 2. Position-velocity image of Mopra CS(1-0) emission towards the CTB 37A region. Nanten CO(2-1) emission contours and Norma-3 kpc arms present at velocities vLSR 30 to −1 ∼ − towards the CTB 37A region are overlaid. White stars indicate 0kms towards CTB 37A (Vallee also uniﬁed the various 1720 MHz OH maser locations and the dashed lines indicate the naming conventions for diﬀerent components of single arms, extent of the 7 mm mapping campaign for CS(1-0) emission. A including the Norma and 3 kpc arms which were part of the position-velocity image for the latitudinal gas distribution is dis- −1 same structure). For velocities less than vLSR 40 km s , played in the appendix (§B1). The image has been smoothed for ∼ − the model by Vallee (2008) may predict the presence of com- clarity. ponents of the Perseus and Norma-3 kpc arms, but, as discussed by the authors, the model is less reliable towards the ◦ central 22 of the Galactic plane, so we do not attempt to in HI absorption. In Figure 3, CS(1-0) emission peaks in re- rectify it with our observations. gions displaying intense CO(2-1) emission. In contrast to the above discussion, Tian & Leahy − − (2012) make a case for the gas at 20 km s 1 and 60 km s 1 − − 4.2 G348.5 0.0 and Interstellar Gas at vLSR= 25 to both be associated with CTB 37A (ie present in the same −1 to 20kms− − arm), this gas lying within the inner 3 kpc of the galaxy − (from HI-absorption arguments, see 1.1). Figure 3a shows CS emission integrated over a velocity § All CO(2-1) emission in Figure 2 appears to have cor- containing two 1720 MHz OH masers at vLSR 23 and −1 ∼ − responding CS(1-0) emission, indicating dense gas. CS(1-0) 21 km s (Frail et al. 1996). The CS(1-0) emission is co- ∼ − −1 and CO(2-1) emission integrated around the two separate incident with both 22 km s OH masers and a CO(2-1) −1 ∼ − ′′ populations of OH masers at vLSR 22 and 65 km s emission peak and is somewhat extended, spanning 240 ∼ − − ∼ are displayed in Figures 3a and b. Figures 3c and d display ( 4 Beam FWHM) in length. Also note that the CS(1-0) ∼ × two other regions of gas along the line of sight that appear emission peak may lie on the edge of G348.5 0.0, as ap- − c 0000 RAS, MNRAS 000, 000–000 6 Nigel I. Maxted et al.

Table 3. Detected molecular transitions from deep ON-OFF switched pointings. Velocity of peak, vLSR, peak intensity, TPeak, and FWHM, ∆vFWHM, were found by ﬁtting Gaussian functions before deconvolving with MOPS velocity resolution. Displayed band noise, TRMS, and peak temperatures take into account beam eﬃciencies and contain a ∼5% systematic uncertainty (Urquhart et al. 2010), after a baseline subtraction.

Object Detected TRMS Peak vLSR TPeak ∆vFWHM Counterpart (l,b) Emission Line (K ch−1) (km s−1) (K) (km s−1)

Location 1 CS(1-0) 0.05 −73.4±0.5 0.13±0.01 18.9±1.7 −65.1 km s−1 OH maser (348.35,0.18)

Location 2 CS(1-0) 0.06 2.87±0.08 0.41±0.02 3.6±0.2 -65.2 km s−1 OH maser (348.35,0.15) HC3N(J=5-4,F=5-4) 0.05 4.7±0.2 0.12±0.03 1.9±0.6

Location 3 CS(1-0) 0.05 −105.1±0.03 0.78±0.02 2.5±0.1 −63.8 km s−1 OH masera (348.42,0.11) −88.0±0.01 0.21±0.02 1.6±0.2 −57.6±0.4 0.17±0.01 21.8±1.1 −22.4±0.5 0.10±0.07 9.2±1.4 SiO(J=1-0,v=0) 0.03 −104.6±0.3 0.06±0.01 4.4±1.2 −60.2±2.0 0.02±0.05 19.2±5.4 HC3N(J=5-4,F=5-4) 0.03 −104.8±0.1 0.20±0.01 2.7±0.3 CH3OH(7(0,7)-6(1,6) A++) 0.03 −104.4±0.1 0.13±0.01 1.9±0.2

Location 4 CS(1-0) 0.04 −61.9±0.6 0.07±0.01 12.1±1.8 −63.5 km s−1 OH maser (348.39,0.08) −21.9±0.2 0.13±0.02 1.5±0.3 8.3±0.1 0.14±0.02 1.5±0.3

Location 5 CS(1-0) 0.04 −23.0±0.1 0.18±0.02 3.1±0.4 −23.3 km s−1 OH masera (348.48,0.11)

Location 6 CS(1-0) 0.07 −63.9±0.2 0.23±0.02 7.4±0.6 −64.3 km s−1 OH maser (348.51,0.11)

Location 7 CS(1-0) 0.05 −103.9±0.1 0.26±0.02 1.7±0.2 (348.32,0.23) −89.2±0.2 0.16±0.02 3.7±0.4 −64.2±0.1 0.41±0.01 6.1±0.3

a Pointing has partial overlap with a second 1720 MHz OH maser of similar vLSR.

0.2 tinuum) data towards ‘Location 5’, which contains the −1 vLSR 22 km s population of 1720 MHz OH masers. ∼ − CS(1-0) emission corresponds to at least three of the most 0 −1 intense CO(2-1) peaks (vLSR 22, 65, 105 km s ). The ∼ − − − 5 strongest CS(1-0) emission peak towards this location is at −1 velocity vLSR 23 km s , consistent with the velocity of ∼ − the OH masers. A distinct HI absorption line also corre- −1 sponds to the dense and masing gas at vLSR 22 km s . Intensity (K) ∼ − 0 This implies that the gas is likely foreground to the radio 170 continuum emission from this region. It follows that if the radio continuum emission seen towards Location 5 is indeed 35 −1 from CTB 37A, the vLSR 22 km s gas (and associated ∼ − OH maser population) lies in front of CTB 37A. Similar −1 -100 vLSR 22 km s HI absorption features are observed to- -100 -80 -60 -40 -20 0 20 ∼ − Velocity (km/s) wards Locations 3, 4 and 6 (Figures 5, 6 and 7, respectively). These positions are, unlike Location 5, not towards regions Figure 4. Location5: This region encompasses two 1720 MHz of suspected SNR-SNR-overlap, only SNR CTB 37A. −1 OH masers. One is at velocity vLSR∼ −23.3 km s (the centre of −1 −1 The vLSR 22 km s gas is foreground to the the pointing location) and another velocity vLSR∼ −21.4 km s ∼ − (oﬀset from the centre, but within the 7 mm beam FWHM solid CTB 37A radio continuum emission and may be shocked angle). See Table 3 and Figure 1b for further details. (as indicated by OH masers) by either CTB 37A or G348.5 0.0. In the former case, the gas would not be at − its kinematic distance (possibly within the 3 kpc ring instead), while CTB 37A would be between the foreground proximately extrapolated (a priori) from the partial shell −1 observed in 843 MHz continuum data (see Figure 1). This is vLSR 22 km s gas and the background/associated − ∼ − −1 consistent with the 22 km s 1 masers being a product vLSR 65 km s gas. ∼ − ∼ − −1 of a G348.5 0.0 shock-interaction towards a region of high In the latter case (a G348.5 0.0-vLSR 22 km s − − ∼ − density. maser/gas association), the Galactic rotation model dis- −1 Figure 4 displays CO(2-1), CS(1-0) and HI (and con- tance may hold for the vLSR 22 km s gas, favouring a ∼ − c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 7

a Vlsr: −25 to −20 km/sb Vlsr: −70 to −50 km/s Galactic Latitude Galactic Latitude Integrated Intensity (Kkm/s) Integrated Intensity (Kkm/s) CTB 37A

G348.5−0.0

Galactic Longitude Galactic Longitude c Vlsr: −90 to −80 km/sd Vlsr: −110 to −100 km/s Galactic Latitude Galactic Latitude Integrated Intensity (Kkm/s) Integrated Intensity (Kkm/s)

Galactic Longitude Galactic Longitude

Figure 3. Mopra CS(1-0) emission images with overlaid Nanten2 CO(2-1) contours (black) for four different velocity ranges (panels a-d). CS(1-0) emission in all figures has been Gaussian-smoothed (FWHM∼30-90′′). All figures have overlaid HESS 80 and 100 gamma- ray excess count contours (dashed white lines) (Aharonian et al. 2008a). (a) CO contour levels are from 5 to 20 K km s−1 in steps of 5 K km s−1. The approximate location of G348.5−0.0 is indicated by a black circle (partially shown). Two blue dashed boxes represent regions used to calculate gas parameters (see § 5.1, also in c and d). Deep switched pointing locations are displayed as circles and 1720 MHz OH masers at the velocity of the CS(1-0) emission are indicated by blue crosses. (b) CO contour levels are from 24 to 48 K km s−1 in steps of 8 K km s−1. A large blue dashed box (TeV emission) represent a region used to calculate gas parameters (see §5.2). 1720 MHz OH masers at the velocity of the CS(1-0) emission are indicated by pink crosses. (c) CO contour levels are from 5 to 20 K km s−1 in steps of 5 K km s−1. (d) CO contour levels are from 10 to 30 K km s−1 in steps of 10 K km s−1. The beam FWHM for HESS, Mopra and Nanten2 observations are indicated.

− near-side distance solution of 3kpc for the 22 km s 1 OH maser generation being an interaction between SNR ∼ ∼ − masers, molecular gas and G348.5 0.0. It is unclear from CTB 37A and a second molecular gas clump of a diﬀerent − −1 current evidence which of the two scenarios is valid, but local velocity (the vLSR 22 km s gas). The work by Tian ∼ 1720 MHz OH maser emission from SNRs is relatively rare, & Leahy (2012) does seem to support the notion that the with only 10% of surveyed SNRs having detectable OH kinematic distances of these gas components are not reliable. ∼ −1 masers (Green et al. 1997). Although this survey did target An estimation of mass and density at vLSR 22 km s ∼ − (hence is biased towards) SNRs with a central thermal X- towards Location 5 can be found using Equation 1, where ray source, one might naively suggest, post-priori, that the A is set equal to the Mopra beam FWHM area (at some likelihood of G348.5 0.0 producing OH maser emission is assumed distance). For CS(1-0) emission, this yields a col- − −1 22 −2 about 10%, with the more likely cause of vLSR 22 km s umn density of NH 1 10 cm , which implies a mass ∼ − 2 ∼ × c 0000 RAS, MNRAS 000, 000–000 8 Nigel I. Maxted et al.

0.2 0.2

0 0 5 0.1

Intensity (K) 0 0.2 100

0 Intensity (K) 1 0 -100 -80 -60 -40 -20 0 20 Velocity (km/s)

Figure 6. Location4: This region encompasses one 1720 MHz −1 0 OH maser at velocity vLSR ∼ −63.5 km s . See Table 3 and Fig- ure 1b for further details. 5

0.25 0

100 0 5 0 -100 -80 -60 -40 -20 0 20 Velocity (km/s) Intensity (K) 0 170 Figure 5. Location3: This region encompasses two 1720 MHz −1 OH masers. One is at velocity vLSR∼ −63.8 km s (the centre of −1 55 the pointing location) and another velocity vLSR∼ −63.9 km s (offset from the centre, but within the 7 mm beam FWHM solid angle). See Table 3 and Figure 1b for further details. -60 -100 -80 -60 -40 -20 0 20 Velocity (km/s) 3 −3 of 400 M⊙ and density of 1 10 cm at a distance of Figure 7. Location6: This region encompasses one 1720 MHz ∼ ∼ 3× −3 −1 7.9 kpc (or 40 M⊙ and 5 10 cm at a distance of 3 kpc, OH maser at velocity vLSR ∼ −64.3 km s . See Table 3 and Fig- ∼ ∼ × −1 if G348.5 0.0 produced the vLSR 22 km s masers). This ure 1b for further details. − ∼ − 4 5 −3 density is not as high as the 10 -10 cm suspected ∼ to be required for the formation of 1720 MHz OH masers The existence of a shocked or energetic environment at (Reynoso & Mangum 2000), but our result does not rule −1 vLSR 65 km s , possibly triggered by CTB 37A, is indi- ∼ − out this density on a scale smaller than our 7 mm beam cated by the extreme broadness of the CO(2-1) and CS(1- ( 2 pc at 7.9 kpc), as expected for the maser-emission re- ∼ 0) line spectra and clear asymmetries in CO(2-1) emission gion size. Indeed, given that the CS(1-0) critical density is towards Locations 3 and 4 (Figures 5 and 6). In such en- 8 104 cm−3, its likely that the beam is only partially- ∼ × vironments, the detection of SiO emission can sometimes ‘filled’. Additionally, we have used an ‘optically-thin’ as- be expected as Si is sputtered from dust grains, but the sumption (see 3), but the region could indeed be more op- § only signal corresponding to CTB 37A from this shock- tically thick, hence have a higher column density than what tracer was tenuous. A fit to the SiO(1-0) spectrum towards we have calculated. −1 Location 3 (Figure 5, Table 3) at vLSR 60 km s (guided ∼ − by the broad CS(1-0) emission) yielded a line FWHM of − 19 5kms 1, consistent with a shocked or turbulent re- 4.3 CTB 37A and Interstellar Gas at vLSR= 70 to ∼ ± −1 − gion. This detection, albeit weak, may support the connec- 50kms −1 − tion of the vLSR 65 km s gas to the CTB 37A SNR. ∼ − Figure 3b shows CS(1-0) emission integrated over a veloc- Via CS(1-0) emission we can confirm the existence of − ity consistent with eight 1720 MHz OH masers between dense gas-associations with 65 km s 1 OH masers to- −1 ∼ − vLSR 70 and 60 km s (Frail et al. 1996). Broad wards locations 3, 4 and 6. We estimate, column densi- ∼ − ∼ − 22 −2 CS(1-0) emission is seen towards regions with intense CO(1- ties, masses and densities from CS(1-0) of 1-8 10 cm , 3 −3 ∼ × 0) emission. Some of the gas in this field is believed to be 500-2300 M⊙ and 3-10 10 cm , respectively, at these −1 ∼ ∼ × associated with the CTB 37A SNR and the 60 km s three locations (with assumptions outlined in 3). These ∼ − § masers, which are in the inner 3 kpc of the Galaxy (between densities are, similar to the previous calculation (see 4.3), 4 5 −3 § 6.3 kpc and 9.5 kpc, Tian & Leahy, 2012). but not as high as the 10 -10 cm suspected to be re- ∼ c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 9

0.5 0.2

0 0 5 5

0 Intensity (K) Intensity (K) 0

100 100

0 0 -100 -80 -60 -40 -20 0 20 -100 -80 -60 -40 -20 0 20 Velocity (km/s) Velocity (km/s)

Figure 8. Location 1: This region encompasses one 1720 MHz Figure 10. Location7: See Table 3 and Figure 1b for further −1 OH maser at velocity vLSR∼ −65.1 km s . See Table 3 and Fig- details. ure 1b for further details.

−1 vLSR 85 km s is present towards Location 3 (Figure 5). ∼ − −1 0.5 This is evidence that the vLSR 85 km s gas is foreground ∼ − to CTB 37A, but this is not especially useful in distinguishing whether this gas is associated with the CTB 37A SNR 0 (including whether this cloud is experiencing a high energy particle enhancement caused by CTB 37A). It follows that 2.5 we consider both of two scenarios: an association of this gas with the gamma-ray emission and no association of this gas with the gamma-ray emission in 5.2. This gas appears at Intensity (K) 0 § the same velocity as ‘Cloud A’ (Slane et al. 1999), which ◦ can be seen to extend over 1 in longitude (Moriguchi et al. 100 2005), suggesting a possible relation.

−1 0 4.5 Interstellar Gas at vLSR= 110 to 100 km s -100 -80 -60 -40 -20 0 20 − − Velocity (km/s) Gas from the near side of the 3 kpc-expanding-arm is ob- −1 served at vLSR 105 km s in the direction of CTB 37A, Figure 9. Location2: This region encompasses one 1720 MHz ∼ − −1 as displayed in Figure 3d. The significance of this gas OH maser at velocity vLSR∼ −65.2 km s . See Table 3 and Fig- ure 1b for further details. to the present study is a correspondence with HI absorption in the CTB 37A radio continuum (see 1.1, 4.2 § and 4.3). CO(2-1) emission highlights an abundance of quired for the formation of 1720 MHz OH masers. This does diffuse molecular gas coincident with CTB 37A. CS(1- − not rule out a density of 104-105 cm 3 on a scale smaller 0) and CO(2-1) emission peak at a position overlap- ∼ −1 than our 7 mm beam ( 2 pc at 7.9 kpc). ping Location 3 at vLSR 105 km s . CS(1-0) and ∼ ∼ − Towards locations 1 and 2, no CS(1-0) emission was con- HC3N(J=5-4) emission indicates that the gas is dense 3 −3 firmed above the noise level of 0.05 K, so like Reynoso & (CS(1-0) emission nH2 7 10 cm , see Table 6), while ∼ ⇒ ∼ × Mangum (2000), we are unable to give evidence of a dense- CH3OH(7(0)-6(1) A++) emission suggests the presence of molecular gas association towards the OH masers at these high-temperature chemistry often associated with star- two positions. Lastly, we note that towards these two posi- formation (van Dishoek & Blake 1998). SiO(1-0) emission ◦ tions, a shell-like structure of radius 0.025 centred near is also associated with this clump, implying the existence ∼ [l,b] [348.37, 0.16] appears to exist in CS(1-0) and CO(2-1) of shocked gas. Although this might be considered evidence ∼ − emission. We are unable to determine the cause of this void for a SNR shock-gas interaction, the coinciding tracers (CS, in molecular emission, but this may be a low gas density HC3N and CH3OH) can also frame a picture consistent with cavity blown out by a SNR or SNR progenitor star wind. in/outflows associated with star-formation (see Figure B2 Furthermore, we note a distict lack of molecular gas to the for SiO, HC3N and CH3OH emission maps). Indeed, this South of CTB 37A, so we are unable to add more to the narrow SiO(1-0) spectrum does not share similarities with discussion of the break-out morphology of CTB 37A. shocked gas towards the similar SNR W28, where broad SiO emission is observed at a position/velocity consistent with OH maser emission (Nicholas et al. 2012). We display the −1 4.4 Interstellar Gas at vLSR= 90 to 80kms discovered SiO, HC3N and CH3OH emission and investi- − − gate possible infrared counterparts in the appendices ( A Figure 3c is an integrated image of the CS(1-0) and CO(2-1) § −1 and B). emission around vLSR= 85 km s . Some HI-absorption at § − c 0000 RAS, MNRAS 000, 000–000 10 Nigel I. Maxted et al. ) 3 10 10 − 2 3 2 +20 − +30 − H +1 − +7 − 385. 3 20 6 n 30 − , within the 2 H 10%. ) (cm 200 1 000 3 000 2 000 n ∼ 700 ⊙ +1 000 − +1 000 − +4 000 − +2 000 − M +1 000 − y of 700 1 000 2 000 8 000 6 000 , to a different distance, 0 ) (M 2 4 2 1 2 8 d . . . . . 2 1 05 05 1 . 0 0 . 0 . . H − 0 0 − +0 +1 − − +0 N straints arise in the future. − +0 − +0 cm 0.9 1.3 383023, (see Figures 3a, c and d) 0.2 0.3 21 − , and average density, M ) (10 3 20 10 20 60 − +50 − +30 − +20 − +90 − 2 H 30 - 1.8 n 20 30 90 , mass, 2 H N ) (cm 27 000 17 000 3 000 6 000 5 000 ⊙ +23 000 − +15 000 − +3 000 − +5 000 − +30 000 − M 8 000 9 000 8 000 ng the HESS J1714-385 68% containment region defined as “TeV 47 000 30 000 uncertainty in the 68% containment radius of HESS J1714 ) (M 9 3 6 2 2 7 6 2 3 2 2 candidate source, CXOU J171419.8 ′ ...... 2 0 0 0 0 0 H − t can be rescaled from the assumed distance, − +1 − +0 − +1 − +0 − +0 e 1 N age column density, cm lculated values have an associated statistical uncertaint 21 (10 0 d for mass and density, respectively, if further distance con 1 b − ) 0 d/d ( and 100 6.3 3.0 3 000 120 1.5 1 000 60 100 6.3 1.4 3 000 50 0.8 2 000 20 100 6.3 2.1 80 7.9 2.1 3 000 80 1.1 2 000 40 80 7.9 0.5 1 000 10 0.2 700 5 50 7.9 7.1 10 000 240 1.8 3 000 60 50 7.9 3.2 9 000 80 0.8 3 000 20 50 7.9 3.9 80 7.9 1.2 20 7.9 1.7 3 000 60 0.4 700 10 20 7.920 7.9 1.5 1.8 5 000 50 0.3 900 6 2 − − − ) ) (kpc) − − − − − − − − − 1 0 Sum of the above 8.1 − d/d ( 110 to 110 to 110 to 90 to 70 to 90 to 70 to 70 to 90 to 25 to 25 to 25 to − − − − − − − − (km s − − Range− Distance, − a Gas parameters towards a rectangular region of sky containi Super/subscripts indicate uncertainty propagated from th , by multiplying by a d 383023 Distances are assumed for mass and density calculations, bu − X-ray emission CXOU J171419.8 RegionTeV emission Velocity AssumedExtended CO(2-1) CS(1-0) b selected region are shown for chosen velocity ranges. All ca Table 4. emission” (see Figure 3b), extended X-ray emission and a PWN (Aharonian et al. 2008a). CO(2-1) and CS(1-0)-derived aver

c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 11

5 DISCUSSION velocity ranges (see Tables 4 and 5), so following Aharonian et al. (1991), we can calculate the expected gamma ray flux 5.1 Previous X-ray Absorption Studies above Eγ , CTB 37A exhibits extended thermal X-ray emission, possibly from a SNR shock-gas interaction, and a more com- −13 −1.6 M5 −2 −1 F (> Eγ )=2.85 10 ET eV 2 kCR cm s (3) pact non-thermal source, CXOU J171419.8 383023 (Chan- × dkpc ! ′′ − dra beam FWHM 1 ), which may be a PWN (Aharonian ∼ 5 et al. 2008a). Aharonian et al. (2008a) used a spectral-fitting where M5 is the gas mass in units of 10 M⊙, dkpc is the analysis technique to estimate the level of X-ray-absorption, distance in units of kpc, kCR is the CR enhancement factor and hence the column density towards these two sources. We above that observed at Earth and Eγ >1 TeV. The cosmic compare column densities estimated from CO(2-1), CS(1-0) ray enhancement factor, kCR, was calculated for several ve- and HI data, which trace molecular and atomic gas, to col- locity ranges and is displayed in Table 7 (using 68% of the umn densities calculated from X-ray absorption. The column HESS J1714 385 gamma-ray flux above 1 TeV in our cal- − densities and masses of significant molecular and atomic gas culations). foreground to the CTB 37A extended X-ray emission and In a hadronic scenario for gamma-ray production, mat- CXOU J171419.8 383023 are presented in Tables 4 and 5. ter is expected to overlap with gamma-ray emission on a − The approximate X-ray emission regions are highlighted in large-scale, because the TeV gamma-ray flux is proportional Figures 3a, c and d. to the product of mass, M5, and cosmic ray enhancement, Towards the extended thermal X-ray emission region, kCR. If one assumes a uniform CR-density throughout the we calculated a lower limit for proton column density CTB 37A region, a good correlation between matter den-

(NH +2NH2 , where NH2 is the average of that derived for sity and hadronic gamma-ray emission might be expected, − CO(2-1) and CS(1-0)) of 9 1021 cm 2. Aharonian et al. which, from CO(2-1) and CS(1-0) emission (see Figure 3), ∼ × −1 (2008a) calculated an X-ray absorption proton column den- may be the case for line of sight velocity, 85 km s , − ∼ − sity of 3 1022 cm 2 for the extended thermal X-ray emis- but less likely to be so for the line of sight velocities, ∼ × −1 −1 sion region, consistent with our lower limit and work by 22 km s or 110 km s . Gamma-ray flux varia- ∼ − ∼ − Sezer et al. (2011). tion can also reflect variation in cosmic ray enhancement, Similar to towards the extended thermal X-ray emis- such that a region can have matter existing outside of the sion region, towards CXOU J171419.8 383023, we calcu- region indicated by gamma-ray emission contours (see Fig- − lated a lower limit on proton column density foreground ure 3) while still being consistent with a hadronic emis- 22 −2 to CTB 37A (NH +2NH2 1.5 10 cm ) that was consis- sion scenario. With this in mind, the line of sight ve- ∼ × −1 tent with the X-ray absorption proton column density of locity 60 km s , the suspected location of CTB 37A, − ∼ − 6 1022 cm 2. is consistent with a hadronic scenario. When we summed ∼ × −1 We note that the molecular gas fractions (H2/[H+H2]) multiple emission components, i.e. the vLSR 22 km s , −1 −1 ∼ − −1 for these two regions are fH2 0.38 and 0.47. Liszt et al. 60 km s and 85 km s gas, the vLSR 60 km s ∼ ∼ − − ∼ − (2010) investigated the atomic gas fraction from a sam- component is dominant, such that only minimal improve- ple of sources using HCO+ emission, CO emission and HI ment in molecular gas-gamma ray overlap was observed. It absorption and found that the molecular gas fraction was seems that from studies of the overlap between molecular gas fH2 0.35, i.e. 2 more atomic H atoms exist than H2 and gamma-ray emission alone, no clear conclusion about ∼ ∼ × molecules. The authors noted the results of other methods which gas clumps correspond to CTB 37A can be drawn. that put fH2 &0.25 (Bohlin et al. 1978) and fH2 ≈0.40- The proportion of gas that may be acting as target 0.45 (Liszt et al. 2002). Our calculated molecular gas frac- material towards the HESS J1714 385 region is unknown, − tions (0.38 and 0.47) are consistent with previous analyses, so CR enhancement estimates in Table 7 may be consid- adding confidence to the accuracy of our column density esti- ered as lower than plausibly expected. Conversely, a com- mations. There is, however, a factor 3-4 difference between ponent of dark gas (where carbon exists in an atomic/ionic ∼ our lower limits on column density and the X-ray absorption form and hydrogen exists in molecular form) towards the column densities. HESS J1714 385 region is not taken into account (and may − indeed exceed 30% according to Wolfire et al., 2010), making the CR enhancement estimates higher than plausibly expected. Due to these two unconstrained effects, CR en- 5.2 Towards HESS J1714 385 − hancement estimates in Table 7 should be considered with If the observed TeV emission is produced by hadronic some caution. processes (ie. CR protons or nuclei colliding with mat- CR enhancement factor estimates for the gas at vLSR −1 ∼ ter to produce neutral pions that decay into gamma-ray 22, 85 and 110 km s range between 320 and 33 000, − − − photons), constraining the mass of matter may help to whereas the CR enhancement factor esimate for the gas −1 constrain the CR density in the region. Aharonian et al. at vLSR 60 km s , the gas most likely to be associated ∼ − (1991) derived a relation to predict the flux of gamma- with CTB 37A, generally spans a smaller range of values, −1 rays above a given energy from the mass of CR-target 130 - 1 100. We assume that the gas at vLSR 60 km s −1.6 ∼ − material, assuming an E integral power law spectrum. is associated with CTB 37A, while the gas components at −1 The gamma-ray flux above 1 TeV towards CTB 37A is F (> vLSR 22 and 85 km s may or may not additionally −13 −2 −1 ∼ − − 1 TeV) 6.7 10 cm s (Aharonian et al. 2008a) and be associated, giving a range of possible CR-enhancements ∼ × the masses within the HESS best fit region (68% contain- in the CTB 37A region of 80 - 1 100 (see Table 7) that ob- ∼ × ment of the gamma-ray source) were calculated for given served in the local solar neighbourhood, assuming a hadronic

c 0000 RAS, MNRAS 000, 000–000 12 Nigel I. Maxted et al.

Table 5. Same as Table 4, but parameters are from HI absorption analyses (and emission analyse where speciﬁed) and showing atomic (in contrast to molecular) H column density.

Region Velocity Assumed HI Range Distance, d0 NH M nH −1 21 −2 −3 (km s ) (kpc) (10 cm ) (M⊙) (cm )

a +0.1 +3000 +100 TeV emission − 70 to −50 7.9 5.6−0.1 9 000−6000 130−20 +0.1 5 to 8 - 0.3−0.05 - - +0.1 0 to 2 - 0.3−0.05 - - +0.9 +100 +200 −13 to −7 1.5 1.9−0.3 100−0 200−100 +1.8 +3000 +50 −24 to −18 7.9 2.8−0.2 6 000−500 50−10 +0.05 +100 +1 −74 to −71 7.9 0.1−0.05 300−100 3−1 +0.0 +200 +1 −90 to −86 7.9 0.2−0.05 400−200 4−1 +0.1 +200 +4 −107 to −103 6.3 0.2−0.0 300−100 6−1 +3.0 +3000 Absorption sum 5.8−0.4 7 000−1000 - Extended X-ray emission a − 70 to −50 7.9 4.6 5 000 100 5to8 - 0.3 - - 0to2 - 0.4 - - −13 to −7 1.5 1.0 50 100 −23 to −18 7.9 1.2 2 000 30 −79 to −76 7.9 0.2 300 4 −92 to −87 7.9 0.3 500 8 −107 to −104 6.3 0.6 500 20 Absorption sum 4.0 - -

CXOU J171419.8−383023 a − 70 to −50 7.9 5.9 4 000 200 5to8 - 0.2 - - 0to2 - 0.4 - - −13 to −7 1.5 1.3 40 200 −23 to −18 7.9 2.2 2 000 70 −79 to −76 7.9 0.3 200 10 −92 to −87 7.9 0.5 400 20 −107 to −104 6.3 0.6 300 30 Absorption sum 5.5 - -

aFrom HI emission analyses.

Table 6. Gas parameters towards locations with ON-OFF switched deep CS(1-0) observations (see Figure 1). CS(1-0)-derived average column density, NH2 , mass, M, and average density, nH2 , within selected regions are shown for signiﬁcant CS(1-0) emission lines (see Table 3). All calculated values have an associated statistical uncertainty of ∼15%.

Location Velocity Assumed CS(1-0)

Distance NH2 M nH2 −1 21 −2 −3 (km s ) (kpc) (10 cm ) (M⊙) (cm )

1 −73.4 7.9 49 1 500 7×103

3 −105.1 6.3 39 800 7×103 −88.0 7.9 6.8 200 1×103 −57.6 7.9 75 2 300 1×104 −22.4 7.9 19 600 3×103

4 −61.9 7.9 17 500 3×103 −21.9 7.9 3.9 100 600

5 −23.0 7.9 11 400 1×103

6 −63.9 7.9 34 1 100 5×103

7 −103.9 6.3 8.9 170 2×103 −89.2 7.9 1.2 370 2×103 −64.2 7.9 50 1 500 7×103

c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 13

Table 7. Atomic mass (from HI analyses), molecular mass (average of CO and CS analyses) are summed and multiplied by 1.33 to account for a 25% He component. The ranges displayed reﬂect the uncertainty in the 68% containment radius of HESS J1714-385. An estimate of CR enhancement factor above the solar system value (>1 TeV), kCR, assuming that all mass coincident the best-ﬁt region of HESS J1714-385 acts as as CR target material, is also displayed.

a Region Velocity Assumed Atomic mass Molecular mass Total mass ∼ kCR Range Distance, d0 (25% He) −1 (km s ) (kpc) (M⊙) (M⊙) (M⊙)

TeV emission −25 to −20 7.9 5 500 - 9 000 800 - 14 000 8 400 - 31 000 320 - 1 200 −70 to −50 7.9 3 000 - 12 000 4 000 - 45 000 9 300 - 76 000 130 - 1 100 −90 to −80 7.9 200 - 600 0 - 11 000 300 - 15 000 660 - 33 000 Sum of the above 8 700 - 22 000 4 800 - 70 000 18 000 - 120 000 80 - 550 −110 to −100 6.3 200 - 500 1 000 - 11 000 1 600 - 15 000 420 - 6 200

aCR enhancement factor is effectively independent of the assumed distance (as distance cancels in Equation 3 when the distance assumptions of our mass calculations are accounted for.) scenario. CR-enhancement factor estimates are expected to Certainly, the old age is consistent with the large fraction −1 be related to the age of the remnant (Aharonian et al. 1996), of energy possibly injected into the vLSR 60 km s cloud ∼ − so our CR-enhancement estimates can be used to cross- by CTB 37A (4-40%, 5.3), assuming an ejecta energy of 51 § check age estimates for consistency (assuming a hardonic 10 erg. scenario), as is done in 5.3. Finally, Aharonian et al. (1996) model the diffusion of § We note that towards the HESS J1714-385 TeV emis- CRs outwards from a continuous accelerator and plot the sion region, a calculation of the kinetic energy implied by energy-dependent CR-enhancement factor for different SNR −1 observed CS(1-0) emission at vLSR 60 km s , E ages. We assume that slow CR diffusion, like that seen to- 1 2 50 ∼ − ∼ M∆vFWHM , is 0.4 - 4 10 erg. This is a significant frac- wards the similar SNR, W28 (see eg. Aharonian et al., 2008b 2 ∼ × tion (4 - 40%) of the expected SNR ejecta kinetic energy and Gabici et al., 2010), applies to the CTB 37A region. ( 1051 erg), so may in fact be injected by CTB 37A. The On referring to Figure 2b in Aharonian et al. (1996), which ∼ −1 CS(1-0) emission at vLSR 22 km s is also broad, and corresponds to a galactic CR diffusion coefficient (param- ∼ − 49 26 2 −1 implies a kinetic energy of 0.7-3 10 erg, 0.07-3% of the eterised from a CR energy of 10 GeV) of 10 cm s and ∼ × ∼ expected ejecta energy. a source CR spectrum of spectral index γ = 2.2, a CR- − enhancement of 80-300 at TeV energies corresponds to an 4 5 ∼ age of 10 -10 yr (at a distance of 10 pc from the CR release 5.3 The Age of CTB 37A point). The range of the models considered by Aharonian The age of CTB 37A has been considered by Sezer et al. et al. (1996) does not suggest CR enhancement factors above 300. We note that the CR enhancement factor resulting (2011) using the assumption of full-ionisation equilibrium to ∼ 4 from a normal (in contrast to ‘slow’) galactic diffusion co- calculate a plasma age of 3 10 √f, where f is the plasma − ∼ × efficient of 1028 cm2s 1 is substantially lower (2-3 the lo- filling-factor within a spherical region. With the benefit of × the latest distance analyses by Tian & Leahy (2012), this cal value), inconsistent with the calculated CR enhancement estimate may be scaled upwards by 20-80%, to account range, but we favour the W28-region CR diffusion speed due ∼ for a nearer distance to CTB 37A (6.3-9.5 kpc). to the physical similarities with CTB 37A (see above). To complement the work of Sezer et al. (2011), similari- The range of age values suggested by this CR enhance- 4 5 ties of CTB 37A with other SNRs cannot be overlooked. Re- ment argument (10 -10 yr) spans larger values than those ferring to Green et al. (1997), which summarises SNRs with suggested by the previous 3 methods (the plasma age, com- detected associated OH maser emission, and cross-checking parison with similar remnants and the Sedov-Taylor scaling these with SNR catalogues (Guseinov et al. 2003, 2004a,b), relation). If a leptonic component of gamma-ray emission a short list of OH maser-associated SNRs with estimated was present, CR enhancement would be less than that cal- ages can be compiled: W28 ( 104 yr), W44 ( 104 yr), culated here. It also follows that the age would be overesti- 4 3 ∼ 5∼ W51c ( 10 yr), IC443 ( 10 yr), CTB 33 (610 yr) and mated by our CR enhancement factor argument. ∼ 3 ∼ G347+0.2 ( 10 yr). Of these, the first 4 SNRs have diame- Through this CR-enhancement factor argument, the ∼ ters of 15-35 pc, similar to CTB 37A which has dimensions simplistic shock-radius model, and the aforementioned sim- ∼◦ ◦ of 0.12 0.23 and an average diameter of 24 5pc at a ilarities to other SNRs, we find that the age of CTB 37A is ∼ × ∼ ± distance of 7.9 1.6. Based purely on these similarities, the consistent with the previous result of Sezer et al. (2011) (for ± 3 4 f 1), of the order 104 yr. CTB 37A age may be of the order of 10 -10 yr. ∼ ∼ Further support for a 103-104 yr age for CTB 37A ∼ comes from assuming a standard Sedov-Taylor time-scaling of the shock-radius (here taken from Caprioli et al. (2009), Equation 29). For an ejecta with energy 1051 erg expanding − 6 CONCLUSIONS into a medium of number density 10 cm 3, similar to towards HESS J1714-385 (although the shock radius is only Using CO(2-1), CS(1-0) and HI spectra, we conducted an − weakly dependent on density, being proportional to n 1/5), investigation of the atomic and molecular gas towards the +0.4 4 the shock radius reaches 24 5 pc after 0.6− 10 yr. CTB 37A region, which has signatures of a shock-gas inter- ∼ ± ∼ 0.3× c 0000 RAS, MNRAS 000, 000–000 14 Nigel I. Maxted et al. action (OH masers, thermal X-rays) and is a source of TeV Brandt T J., (Fermi-LAT Collab.), 2011, A view of super- gamma rays, possibly hadronic in origin. nova remnant CTB 37A with the Fermi Gamma-ray Tele- CS(1-0) observations identified new dense gas compo- scope. J. Adv. Space Res., doi:10.1016/j.asr.2011.07.021 nents towards 5 of the 6 observed locations that exhibit Brogan C., Frail D., Goss W. & Troland T., 2000, ApJ, 1720 MHz OH maser emission. 537, 875-890 CO(2-1), CS(1-0) and HI emission, and HI absorption Caprioli D., Blasi P. & Amato E, 2009, MNRAS, 396, 2065- allowed the estimation of lower limits of column density to- 2073 wards regions of interest. Column density lower limits to- Casanova S., 2011, PrPNP, 66, 681-685 wards X-ray emission regions are consistent with X-ray ab- Castro D. & Slane P., 2010, ApJ, 717, 372-378 sorption measurement-derived column densities. Caswell J., Murray J., Roger R., Cole D. & Cooke D., 1975, CO(2-1), CS(1-0) and HI-derived mass estimates for A&A, 45, 239-258 specific gas components towards the CTB 37A region al- Churchwell E. et al., 2006, ApJ, 649, 759-778 lowed an investigation of the CR hadron-target mass avail- Clark D., Green A. & Caswell J., AuJPA, 1975, 37, 75C able. 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Otrupcek R., 1996, 111, 1651-59 ∼ ′ High resolution ( 1 ), high energy (GeV-TeV) measure- Frail D. & Mitchell G., 1998, 508, 690-695 ∼ ments, such as what may be expected from future ground- Frerking M., Wilson R., Linke R. & Wannier P., 1980, ApJ, based gamma-ray telescopes (The CTA Consortium 2010), 240, 65-73 would allow a more detailed investigation of the nature of Fukui Y., Sano H., Sato J., Horachi H., Torii K., McClure- the high energy spectrum towards CTB 37A, especially in Griffiths N., Rowell G., Aharonian F. et al., 2012, ApJ, relation to the spatial correspondence of molecular gas. 746, 82 Gabici S., Aharonian F. & Casanova S., 2009, MNRAS, 396, 1629-1639 Gabici S., Casanova S., Aharonian F. & Rowell G., 2010, 7 ACKNOWLEDGMENTS in Boissier S., Heydari-Malayeri M., Samadi R., Valls- Gaband D., eds, Proc. French Soc. Astron. Astrophys., This work was supported by an Australian Research Coun- SF2A, 313-317 cil grant (DP0662810, 1096533). The Mopra Telescope is Goldsmith P. & Langer W., 1999, ApJ, 517, 209-225 part of the Australia Telescope and is funded by the Com- Green A., Frail D., Goss W. & Otrupcek R. 1997, AJ, 114, monwealth of Australia for operation as a National Facility 2058-2067 managed by the CSIRO. The University of New South Wales Green A. et al., 1999, ApJS, 122, 207 Mopra Spectrometer Digital Filter Bank used for these Mo- Gusdorf A., Cabrit S., Flower D. & Pineau Des Forets G., pra observations was provided with support from the Aus- 2008a, A&A, 482, 809-829 tralian Research Council, together with the University of Gusdorf A., Pineau des Forets G., Cabrit S. & Flower D., New South Wales, University of Sydney, Monash University 2008b, A&A, 490, 695-706 and the CSIRO. Guseinov O., Ankay A. & Tagieva S., 2003, Serb. Astron. We thank Naomi McClure-Griffiths for feedback regard- J., 167, 93-110 ing our HI analysis and our anonymous referee for his/her Guseinov O., Ankay A. & Tagieva S., 2004, Serb. 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c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 15

Fukui Y., Walsh A., Kawamura A., Horachi H. & Sano H., source. This is likely to be a wind-blown bubble surrounding 2012, MNRAS, 419, 251-266 a high-mass O or B star (object S5 from Churchwell et al., McClure-Griffiths N., Dickey J., Gaensler B., Green A., 2006), unrelated to CTB 37A and HESS J1714 385. − Haverkorn M. & Strasser S., 2005, ApJ, 158, 178-187 Emission at 24 µm surrounding (l,b) (348.37,0.14) ∼ Milne D., Goss W., Haynes R., Wellington K., Caswell J. clearly shows hot dust obscured by a infrared-dark absorber, & Skellern D., 1979, MNRAS, 188, 437-444 likely a cold foreground cloud. CO(2-1) emission at vLSR −1 ∼ Moriguchi Y, Tamura K, Tawara Y, Sasago H, Yamaoka 10 km s is observed towards this region, but the CO- − T, Onishi T & Fukui Y, 2005, ApJ, 631, 947-963 traced gas is too uniform across CTB 37A’s north-west to Nicholas B., Rowell G., Burton M., Walsh A., Fukui Y., explain the localised ‘finger’ of infrared-absorption. Obser- Kawamura A., Longmore S. & Keto E. 2011, MNRAS, vations of the cold, dense gas tracer NH3(1,1) were employed 411, 1367-1385 in an attempt to aid in constraining the absorber’s location, Nicholas B., Rowell G., Burton M., Walsh A., Fukui Y., but we found no NH3(1,1) emission towards this location in Kawamura A. & Maxted, N., 2012, MNRAS, 419, 251- the low-exposure HOPS galactic plane data (Walsh et al. −1 266 2008) and a follow-up high-exposure (TRMS 0.1 K ch ) ∼ Protheroe R., Ott J., Ekers R., Jones D. & Crocker R., deep pointing revealed no NH3(1,1) emission either. 2008, MNRAS, 390, 683-692 Reach W., Rho J., Tappe A., Pannuti T., Brogan C., et al.2006, ApJ, 131, 1479-1500 APPENDIX B: ADDITIONAL 7 MM IMAGES Reynoso E. & Mangum J., 2000, ApJ, 545, 874-884 TOWARDS CTB 37A Schilke P., Walmsley C M., Pineau Des Forets G. & Flower D., 1997, A&A, 321, 293-304 Figure B1 is a position-velocity image towards the CTB 37A Sezer A., Gok F., Hudaverdi M. & Ercan E., 2011, MNRAS, region. Similar to Figure 2, several clouds are visible in CO(2-1) at approximate line-of-sight reference velocities, 417, 1387-1391 −1 vLSR 10, 20, 60 to 75, 90 and 105 km s . Cor- Slane P., Gaensler B, Dame T., Hughes J., Plucinsky P. & ∼ − − − − − − Green A, 1999, 525, 357-367 responding CS(1-0) emission is observed towards CO(2-1)- traced clouds at approximate line-of-sight reference veloci- Tian W. & Leahy D., 2012, MNRAS, 421, 2593-2597 −1 ties, vLSR 10, 60 to 75, 90 and 105 km s , indi- Urquhart J., Hoare M., Purcell C., Brooks K., Voronkov ∼ − − − − − M., Indermuehle B., Burton M., Tothill N. & Edwards P., cating dense gas at these locations. 2010, PASA, 27, 321-330 Figure B2a/b/c are three images of emission from the Vallee J, 2005, ApJ, 130, 569-575 HC3N, CH3OH and SiO molecules. The narrow spectral Vallee J, 2008, ApJ. 135, 1301-1310 line profile and correspondence with a molecular core seen van Dishoeck E. & Blake G, 1998, ARA&A, 36, 317-368 in CO(2-1) and CS(1-0) emission, suggest possible star- Walsh A., Lo N., Burton M., White G., Purcell C., Long- formation activity. more S., Phillips C. & Brooks K., 2008, PASA, 25, 105. Wolfire M., Hollenbach D. & McKee C., 2010, 716, 1191- 1207.

APPENDIX A: INFRARED EMISSION TOWARDS CTB 37A Evidence for shock-interactions are also seen at infrared wavelengths. Reynoso & Mangum (2000) noted the presence of shocked, heated dust, IRAS 17111 3824, towards a − region of overlap between CTB 37A and G348.5 0.0. Reach − et al. (2006) later discovered several patches and ﬁlaments of 4.5 µm emission towards and around Locations 5 and 6, possibly indicating shocked H2 gas. The authors also note further evidence for shocked gas at 5.8-8 µm towards the CTB 37A-G348.5 0.0 overlap region. − Figure A1 is an image of 24, 8 and 5.8 µm infrared emission. Millimetre star-formation indicators (HC3N, CH3OH, SiO, Figure B2) are seen towards Location 3 (vLSR −1 ∼ 110 km s ), but no clear association is seen at infrared − wavelengths. Faint 8 µm emission may indicate warm dust, but this extends over a large region of the centre of CTB 37A and is most intense in the region surrounding Location 4. This characteristic, however, does not rule out the notion that warm dust may be responsible for the millimetre molecular emission towards Location 3. ◦ North of Location 3, a shell of 8 µm emission 0.02 0.03 − in diameter, can be seen surrounding a compact 24 µm

c 0000 RAS, MNRAS 000, 000–000 16 Nigel I. Maxted et al. Galactic Latitude

Galactic Longitude

Figure A1. Spitzer 24 µm, 8 µm and 5.8 µm emission are shown in red, green and blue, respectively. White contours show HESS 80 and 100 excess count gamma-ray emission, and magenta contours show Molonglo 843 MHz radio continuum emission. Crosses represent both the ∼ −65 km s−1 (pink,+) and ∼ −25 km s−1 (cyan,×) OH maser populations (Frail et al. 1996).

c 0000 RAS, MNRAS 000, 000–000 Interstellar gas towards CTB37A 17

1720 MHz OH masers Average Intensity (K) Velocity (km/s)

3kpc Expanding arm hot core

0.0 0.3 Galactic Latitude (deg)

Figure B1. Position-velocity image of Mopra CS(1-0) emission towards the CTB 37A region. Nanten CO(2-1) emission contours towards the CTB 37A region are overlaid. Black stars indicate 1720 MHz OH maser locations and the dashed lines indicate the extent of the 7 mm mapping campaign for CS(1-0) emission.

c 0000 RAS, MNRAS 000, 000–000 18 Nigel I. Maxted et al.

a HC3N(5−4)

b CH3OH(7(0)−6(1)A++) Galactic Latitude Integrated Intensity (Kkm/s)

c SiO(1−0)

Galactic Longitude

−1 Figure B2. Various spectral line emissions integrated between vLSR = −108 and −102 km s . Black contours indicate CO(2-1) integrated intensity levels of 10, 20 and 30 K km s−1 and red dashed contours indicate HESS 80 and 100 excess count gamma-ray emission. See § 4.5 for details.

c 0000 RAS, MNRAS 000, 000–000 Chapter 6

Cosmic Ray Diﬀusion

From Chapters 4 and 5, its clear that molecular gas is present towards some the RX J1713.7 3946 − and CTB 37A SNRs. If SNRs are indeed sources of CRs, an understanding of the diffusion of CRs in the immediate surroundings of SNRs may provide clues for an investigation of CR origin. In particular, we consider how CRs move in the presence of magnetic field turbulence possibly linked to molecular gas. Cosmic rays travelling through magnetic turbulence with magnetic perturbations comparable to their gyroradius (see Equation 1.4) experience random motions and may be considered to be diffusing. In understanding the motion of cosmic rays, the same mathematics that is used for low-energy particle diffusion of fluids (such as air) is employed.

6.1 Diﬀusion of Cosmic Rays into Gas

Gas can act as cosmic ray (CR) target material for gamma-ray-producing p-p interactions, but CRs may inevitably travel for some time through gas before interacting ( 5 104 yr for density 104cm−3, Equation 1.42) so we must understand how CRs move in such a∼ me×dium. One ∼ approach is to use a constant diﬀusion coeﬃcient (see § 6.1.1) with some approximations, but

more robust approaches may be needed (see § 6.1.2), particularly if one considers inhomogeneous gas.

6.1.1 The Diffusion Coefficient Consider CRs diffusing outwards from a point source. Assuming that a large number of independent variables affect the way the particles diffuse, the central limit theorem says that the spatial distribution of particles after some time, t, will be normally distributed. A Gaussian function with exponent x2/2Dt, where x is displacement and D is defined as the diffusion coefficient, describes the− CR distribution of positions in one dimension. The RMS (root-mean- squared) displacement of such a Gaussian function is, d = √2Dt (6.1) or √3Dt or √6Dt for the 2 and 3 dimensional forms of the CR distribution, respectively. The magnetic field strength of the turbulence and the energy of the CRs are key factors when considering the behaviour of the diffusion coefficient, which is parametrised as, 0.5 EP /GeV 2 −1 D(EP ,B(r)) = χD0 [cm s ], (6.2) B/3 µG 138 Molecular Core

Initial Cosmic Ray Density = 0 units

Initial Cosmic Ray Density = 1 unit

Figure 6.1: The initial state of our CR diﬀusion model at its most basic level. A homogeneous (uniform magnetic ﬁeld strength of magnetic turbulence) molecular core with null CR density lies in a CR shroud of normalised CR density.

27 2 −1 where D0 is the Galactic diffusion coefficient (for CR protons), assumed to be 3 10 cm s to fit CR observations (Berezinski et al., 1990), and χ is the diffusion suppression× coefficient (assumed to be <1 inside a molecular core, 1 outside), a parameter invoked to account for possible deviations of the average galactic diffusion coefficient inside molecular clouds (Berezinski et al., 1990; Gabici et al., 2007), which is largely unknown. A brief discussion of the validity

and magnitude of a CR diﬀusion suppression coeﬃcient was outlined in § 4.1.

Cosmic Ray Penetration of a Molecular Core

In § 4.1, we used the 3 dimensional RMS displacement (Equation 6.1, √6Dt) to estimate the level of CR penetration into a molecular core associated with RXJ1713.7 3946. Figure6.1 is an illustration of the model at its most basic level. The molecular core− was assumed to be homogeneous in density, which allowed us to assume a constant magnetic field strength for the level of magnetic turbulence within the core (Crutcher, 1999). If the magnetic turbulence, which is tied to the gas, is the dominant scattering mechanism for the CRs, it is reasonable to assume that the diffusion coefficient is constant in space. The level of displacement of CRs of a variable energy and diffusion coefficient was then estimated from the RMS displacement, given a time set to the age of RXJ1713.7 3946 (minus the time taken for CRs to escape the moving − shock, and travel to the gas). There are several problems with using Equation 6.1 to investigate the level of CR penetration into a core. The biggest issue is that the direction of travel is wrong. The equation considers a case where CRs move outwards from a point source, whereas we consider the case of CRs moving inwards towards a point. This subtle difference is of no consequence in the one dimensional case, but in 2/3D cases the difference means that the area/volume into which the CRs are diffusing

139 is decreasing rather than increasing. The problem becomes clear when considering Figure 6.1, where the source of CRs is no longer a point, but a circular/spherical cloud edge. It follows that the CR density inside the cloud increases more quickly than suggested by Equation 6.3. The problem can likely be rectified analytically for the case of a constant diffusion coefficient (as initially assumed), but a second issue (inhomogeneity) requires a more detailed approach. In Chapter 4, we approximated a molecular core as having a constant density, hence a constant magnetic field strength and diffusion coefficient. To construct a more realistic model, we must consider cores that have a more realistic density profile, such as a r−2 power-law or ∼ a Gaussian distribution. This inevitably requires us to consider a variable diffusion coefficient.

6.1.2 The Diffusion Equation In considering the diffusion of particles in an environment that has a changing diffusion coefficient, one must solve the diffusion equation, which describes the motion of particles undergoing diffusion, ∂n(r,t) = [D(r) n(r,t)] (6.3) ∂t ∇· ∇ where n(r, t) is the particle density at some location r at some time t, D is a parameter called the diffusion coefficient and is the 3-dimensional differential operator, = ∂ , ∂ , ∂ in ∇ ∇ ∂x ∂y ∂z cartesian coordinates, or = ∂ , 1 ∂ , 1 ∂ in spherical coordinates. ∇ ∂r r ∂θ rsin(θ) ∂φ The diffusion equation is derived from the differential form of the continuity equation, which states that the inflow in any part of a system is equal to the outflow (given the absence of ‘sources’ and ‘sinks’), i.e., conservation of mass,

∂n(r,t) + j(r,t)=0 (6.4) ∂t ∇· where j is the particle density flux. Fick’s first law says that the density flux is proportional to the local density gradient, j(r,t) D(n) n(r,t)=0 (6.5) − ∇ To find the distribution of any particles that are transported via diffusive processes, Equa- tion 6.3 can be solved for particle density, n, as a function of position, r, for some time t.

The solution, however, is often found by numerical methods (see §6.1.3) or by using various approximations and simpliﬁcations.

The Diffusion Coefficient in an Inhomogeneous Core Equation 6.2 is dependent on the strength of the magnetic field, which from observations of Galactic molecular clouds (Crutcher, 1999) varies as,

nH2 B(nH2 ) 100 [µG] (6.6) ∼ 104 cm−3 r where nH2 is the molecular hydrogen density. This relation is supported by theory and can be derived for the case where conductivity within molecular clouds is large, i.e. when clouds contain free ions and plasma. By combining the Maxwell-Faraday equation and the current density form of the Lorentz equation, Equation 1.2 (j = σ[E + v B], where σ is the conductivity), it can ×

140 be shown that a closed loop within the gas experiences no change in magnetic flux with time as a cloud forms (Hillas, 1972). It follows that magnetic field lines are ‘frozen-in’, or tied to the ions within molecular clouds, therefore turbulent motions of gas and magnetic field lines cannot be considered separately. The density profile of molecular cores can vary, but in the case of CoreC (towards RXJ1713.7 −2.2 3946, see §4.1), Sano et al. (2010) infer a radial power-law r distribution, so we assume a density− profile of, nc nH2 = (6.7) r 2.2 1+ r c where nc is the central (peak) number density and rc is the radius of the central core. Combining the above three equations, we get a diffusion coefficient for Core C,

1 − 4 − 1 2.2 E nc 4 r D(E, r)=3χD0 −3 1+ (6.8) GeV cm rc ! Figure 6.2 illustrates the behaviour of the derived diffusion coefficient. The effect is minimal, with a factor 3-4 increase from the centre (r = 0) to one parsec from the centre of the molecular core∼ (r = 1). With this expression, we can solve the Diffusion equation to examine the CR distribution. The following section addresses the solution.

6.1.3 Solving the Diffusion Equation If the diffusion coefficient is constant, the Diffusion Equation (Equation 6.3) reduces to a linear differential equation referred to as the ‘Heat Equation’ and can be solved using a separation of variables technique. But if the diffusion coefficient is a function of position, a numerical solution is the best approach. The following techniques were outlined by Koerber (2011).

A Linear Solution Starting with a reduced form of the diffusion equation in one spatial dimension, x, ∂n(x, t) ∂ ∂n(x, t) = D(x) (6.9) ∂t ∂x ∂x and applying the finite difference method, at time tk and position xi,

∂n(x,t) ∂n(x, t) ∆ D(x) ∂x k = k ∂t |i ∆x |i ∂n(x,t) ∂n(x,t) 1 k 1 k D(xi+ ) ∂x i+ 1 D(xi− ) ∂x i− 1 = 2 | 2 − 2 | 2 + O(∆x2) (6.10) ∆x 2 where ∆x is the distance between points x 1 and x 1 , and O(∆x ) represents higher order i− 2 i+ 2 terms, which for small ∆x become very small. We now use the ﬁnite diﬀerence method a second time (for the second partial derivative of x on the R.H.S.) and a third time (for the time derivative on the L.H.S.).

k+1 k k k k k ni ni 1 ni+1 ni ni ni−1 2 − = D(x 1 ) − D(x 1 ) − + O(∆x ) (6.11) ∆t ∆x i+ 2 ∆x − i− 2 ∆x 

141 Figure 6.2: The diﬀusion coeﬃcient, assuming χ = 1, for a CR with an energy of 1TeV in Core C, following Equation 6.8. Here, n = 5 104 cm−3, r = 0.1 pc and D = 3 1027 cm−3 c × c 0 × (see text).

142 k where ni denotes the CR density at position x = xi and time t = tk. Re-arranging,

k+1 k ∆t k k k k 2 n = n + D(x 1 ) n n D(x 1 ) n n + ∆t O(∆x ) i i ∆x2 i+ 2 i+1 − i − i− 2 i − i−1 k ∆t h k k k k i n + D(x 1 ) n n D(x 1 ) n n (6.12) ∼ i ∆x2 i+ 2 i+1 − i − i− 2 i − i−1 h i This equation forms the basis of the numerical solution to the diffusion equation, the so-called FTCS (Forward-Time Central-Space) scheme. Care must be taken to ensure that the diffusion distance per iteration, ∆tD, is at least twice as small as the spatial step, ∆x, to Nyquist sample and keep the iterative process numerically stable. The last term, O(∆x2), can be approximated as zero. The constraint for constant diffusion, D(x) D, is ∼ ∆t 1 D< (6.13) ∆x2 2 Although this model does not have a constant diffusion coefficient, the diffusion coefficient does not change rapidly in space, so this constraint is employed as an approximation. Some processing efficiency is sacrificed to make sure that the constraint is met by a wide margin.

The Spherical 3D Solution For a symmetrical (only radial variation in diffusion coefficient) 3-dimensional spherical case, like that of Core C (see Figure 6.1), the reduced form of the diffusion equation is, ∂n(r, t) 1 ∂ ∂n(r, t) = r2D(x) (6.14) ∂t r2 ∂r ∂r where r is the radius from the centre of a sphere (the core). Using the same scheme as the one-dimensional case, the solution is,

k+1 k 1 ∆t 2 k k 2 k k ni ni + r 1 D(ri+ 1 ) ni+1 ni r 1 D(ri− 1 ) ni ni−1 (6.15) 2 2 i+ 2 2 i− 2 2 ∼ ri ∆r − − − h i and now with a constraint similar to before, ∆t 1 D< (6.16) ∆r2 2 With the appropriate initial boundary conditions, a loop over Equation 6.15 can be performed k to solve for the CR density value, ni at every point, ri after some time ∆t, provided that the above condition is met.

Boundary Conditions The result of the numerical solution depends heavily on the boundary conditions, i.e., the CR density at the spatial edges of the model at all times and the CR density at the beginning (t = 0) of the simulation at all locations. In this case, the latter condition is simple: begin with no CRs inside the cloud and an inﬁnite source of CRs (assumed to be a cosmic ray enhancement due to a SNR) outside the cloud,

0 ni =0, ri rcloud, 0 ≤ ni =1, ri > rcloud (6.17)

143 for all positions where rcloud is the pre-deﬁned radius of the cloud and the CR density outside the cloud is normalised to unity. Next, a spatial boundary condition for all times is,

k ni =1, ri > rcloud (6.18) i.e., the CR sea outside Core C is an infinite source (making a previous constraint redundant). This constraint obviously has its own physical limit that depends on the CR source. The last constraint to consider is the fate of CRs that reach the Core C centre (r = 0). For our model, the CRs will be retained in the core centre, and ‘fill-up’ the core, so we allow a k+1 moving constraint that changes with time. The central CR density, n0 must be calculated before Equation 6.15 is applied in each iteration, because this boundary condition depends on the previous iteration. Starting with Equation 6.15, we consider the CR diffusion to ‘reflect’ off k k r = 0, such that n = n and D(r 1 )= D(r 1 ) (while also approximating r0 = r 1 = r 1 ), −1 1 + 2 − 2 + 2 − 2

k+1 k 1 ∆t 2 k k 2 k k n0 n0 + r 1 D(r+ 1 ) n1 n0 r 1 D(r− 1 ) n0 n−1 2 2 + 2 2 − 2 2 ∼ r0 ∆r − − − h i k 1 ∆t 2 k k 2 k k n0 + r 1 D(r+ 1 ) n1 n0 r 1 D(r+ 1 ) n0 n1 2 2 + 2 2 + 2 2 ∼ r+ 1 ∆r − − − 2 h i k 2∆t k k n0 + D(r 1 ) n1 n0 (6.19) ∼ ∆r2 + 2 − h i Alternatively, a simpler condition for r = 0 can be derived from the ‘3-point forward diﬀerence formula for the ﬁrst derivative’ (Koerber, 2011),

3f(r )+4f(r ) f(r ) f ′(r )= − i i+1 − i+2 + O(∆r2) (6.20) i 2∆r where f(ri) is a value of a function at point ri. At the very centre (r = 0) of the model Core C, there is assumed to be no spatial variation in the CR ﬂux (assuming reﬂection), therefore

∂nk+1 f ′(r )= i =0 (6.21) i ∂r |i=0, ri=0 Combining Equations 6.20 and 6.21, it follows that,

3nk +4nk nk − 0 1 − 2 =0 2∆r 4nk nk ∴ nk = 1 − 2 (6.22) 0 3 By accepting a negligible lag (of ∆t) in the CR density at r = 0, we can approximate,

4nk nk nk+1 = 1 − 2 (6.23) 0 3 To summarise, with Equation 6.15, the initial conditions (Equation 6.17), the outer boundary condition of Equation 6.18 and the inner boundary condition of either Equation 6.19 or Equation 6.23, the diﬀusion of CRs into a molecular cloud can be simulated.

144 27 2 −1 χ −5 D 0 = 3*10 cm s = 10 CR Distribution within Core C CR Distribution within Core C

Time (years) 10 Time (years) 11 Cosmic rays of Energy of 10 eV Cosmic rays of Energy of 10 eV 1 0 0 250 1 250 500 500 750 750 1000 1000 0.8 0.8 CR Inhabitance CR Inhabitance

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Core Radius (pc) Core Radius (pc) CR Distribution within Core C CR Distribution within Core C

Time (years) 12 Time (years) 13 0 Cosmic rays of Energy of 10 eV 0 Cosmic rays of Energy of 10 eV 1 250 1 275 500 550 750 825 1000 1100 0.8 0.8 CR Inhabitance CR Inhabitance

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Core Radius (pc) Core Radius (pc)

Figure 6.3: The cosmic ray inhabitance as a function of radius within a core of radius 0.62 pc (similar to Core C), at intervals of 250 years. The diﬀusion coeﬃcient used for the inside of the core was 10−5 times that of the Galactic average.

6.2 Diﬀusion into an Inhomogeneous Core

Applying the above numerical solution, a simplistic model comprising a molecular core of radius 0.62 pc that contains a null CR density at t= 0, in a background sea of CRs (see Figure 6.1) with density normalised to 1, was iterated over. The resultant relevant statistics are addressed below.

6.2.1 Cosmic Ray Distribution Figure 6.3 illustrates the evolution of the spatial CR proton distribution inside a molecular cloud, for a cosmic-ray diffusion suppression of χ =10−5. In this scenario, CRs of energy 1013 eV quickly saturate the molecular cloud within hundreds of years, whereas the density of CRs of energy 1010 eV at the core is less than 10% of the background sea after 1 000 years of diffusion. This effect is less prominent for weaker diffusion suppression (larger χ values), as

illustrated in §A.4.1.

145 θ r cloud R

Figure 6.4: The 2-dimensional projection of the model molecular core. Coordinate z is directed into the page.

6.2.2 The Molecular Core in the Gamma-rays As discussed in Chapters 4 and 5, in a hadronic scenario for gamma ray emission, the gamma- ray emission is proportional to the target proton density multiplied by the CR density, npnCR. 10 Its apparent that the 10 eV CR distributions in Figure 6.3 would lead to npnCR values near core centres (r = 0-0.1 pc) that are lower than cases where diffusion effects are not taken into account. At higher CR energies (>1 TeV), magnetic turbulence perturb CR paths less and this results in a higher proportion of high energy CRs compared to low energy CRs at the core centre, hence the resultant hadronic gamma-ray spectrum may plausibly be ‘harder’ (i.e., the spectrum won’t be as steep). As part of this thesis, a preliminary investigation of this effect, whereby CR diffusion into dense gas can result in a bias towards higher energy CR interactions in core centres, was conducted. I note the similar study, carried out by Gabici et al. (2007), whereby CR diffusion into a larger, 20 pc-diameter cloud, was modelled. In this case, CRs were allowed to diffuse into the cloud indefinitely, until a steady-state distribution was found, and the CR diffusion to the cloud centre was hindered by p-p interactions. In my model, a much smaller core is considered, and an imposed time-limit (SNR age) is responsible for a decreasing population of CRs towards the core centre. The modelled molecular core is approximated as being spherical, and the diffusion simulations are spherically symmetric. Observations of molecular cores, however, present a 2- dimensional picture, so gamma-ray emission towards core centres will include components at all radii. As discussed previously, gamma-ray flux, Fγ(r, Ep, χ), is proportional to npnCRdV . To project this into 2-dimensions, an integration in cylindrical coordinates can be performed,

2π rcloud r F (r, E , χ) n (r) n (r, E , χ)RdzdRdθ γ p ∝ p CR P Z0 Z0 Z0 2 2 rcloud √rcloud−R 2π n (√z2 + R2) n (√z2 + R2,E , χ)RdzdR (6.24) ∝ p CR P Z0 Z0 where z is the axis along the line of sight, R is the radius of the circle (the projection of the

146 sphere) and θ is the angle on the plane of the sky (see Figure 6.4). Note that the substitution r = √R2 + z2 is from geometrical arguments. The molecular density (Equation 6.7) can be multiplied by 2 to retrieve a function for proton density, np, and a function for the final CR density distribution, nCR(r), can be found by fitting a function to the points from Figure 6.3 via the χ2-minimisation process. A function of the form nCR = c/ (1 + a. exp ( b.r)) consistently provided a good fit. Of course, Equation− 6.24 applies to the entire molecular core, but it may be interesting to look at radial variation of npnCR by slicing the core into segments,

2 2 Ru √rcloud−R F (r, E , χ) 2π n (√z2 + R2) n (√z2 + R2,E , χ)RdzdR (6.25) γ p ∝ p CR P ZRl Z0 where Rl and Ru are the lower and upper bounds of radius in the plane of the sky, R. For this investigation, the molecular core is split into 3 sections, 0-0.2pc, 0.2-0.4pc and 0.4-0.6pc.

6.2.3 Injected Cosmic Ray Spectrum If we assume a spectrum of CRs injected into the core that follows a power law,

−γ FCR = AEp (6.26) where A is a constant, the ﬂux of CRs between energies Ei and Ef is,

Ef −γ FCR(Ei

6.2.4 Future Work The imaging of my simulated molecular cores at gamma-ray wavelengths is left as future work. The above formulation will allow an approximation of spectral features towards a core for different levels of cosmic ray diffusion suppression, but ultimately a simulation that incorporates p-p interactions during the diffusion simulation process, changing the CR distribution (and resultant gamma-ray emission) as CRs penetrate molecular gas should be the ultimate goal. Such a simulation could be applied to different density-profile molecular clouds and to observational data towards other supernova remnants. By comparing predictions of simulated gamma-ray features towards clouds to real gamma-ray features, not only can the hadronic scenario be tested, but the CR diffusion coefficient inside distant dense gas can potentially be estimated.

147 Chapter 7

Summary and Final Remarks

This thesis comprises an investigation of the gas distribution towards two gamma-ray emitting supernova remnants, the young ( 1600yr) RXJ1713.7 3946 and the older ( 104 yr) CTB 37A. Both SNRs previously had coincident∼ gas studied through− emission from∼ the CO molecule, providing a good general picture of the diffuse molecular gas. We took this several steps further, looking at tracers possibly missed by CO emission surveys. In addition to millimetre analyses, investigations into the local cosmic ray distributions towards these two SNRs were carried out. Towards RX J1713.7 3946, we recorded 7 mm emission lines with Mopra, searching for − dense gas towards cores believed to be associated with the SNR shock wave. Using the CS(J=1- 0) transition, we estimated the molecular gas mass, density and molecular abundance towards several molecular cores, confirming the presence of dense gas. Further scrutinisation of the most chemically-rich core, Core C, was carried out through the use of archival 3 mm Mopra data and targeted 12 mm Mopra observations, recording other molecular transitions such as CS(J=2- + 1), N2H (J=1-0) and NH3(1,1)/(2,2), for further parameter estimates. Examination of the CH3OH molecule provided evidence for associations with infrared-emission regions, relevant to star-formation, while tentative broad CS(J=1-0) emission provided some evidence for the presence of a passing shock, possibly from RX J1713.7 3946. Indeed, features seen in X-ray emission were suggestive of a shock-interaction in the regi− on. Our CTB 37A 7 mm survey with Mopra targeted the CS(J=1-0) transition, to once again calculate gas parameters, this time with particular emphases on: 1) masses towards the gamma- ray emission region, as these are important in a hadronic gamma-ray emission scenario, 2) column densities towards X-ray absorption regions to compare with X-ray absorption-derived column densities, and 3) densities towards gas coincident with shock-tracing OH masers, as OH masers require dense environments to form, but some were yet to have dense gas counterparts identified. To complement this work, we targeted atomic gas using HI emission and absorption analyses of SGPS data, and analysed Nanten2 CO(2-1) data, which had high spatial and velocity resolution relative to CO data previously published towards CTB 37A. We note that in none of our surveys did we find SiO(J=1-0) emission generated by a passing SNR shock, as hoped, but a chance discovery of a vibrationally-excited SiO(J=1-0) maser near RX J1713.7 3946 may be of interest to researchers studying evolved stars. Follow-up observations towards− this location confirmed a transient nature. Also of interest, was SiO(J=1-0) emission probably associated with in/out flows in a hot star-forming core of the 3 kpc expanding arm, coincident with CTB 37A. Having calculated masses towards the RX J1713.7 3946 and CTB 37A SNRs, the cosmic −

148 ray density in a hadronic scenario for gamma-ray emission was estimated (although we didn’t strictly rule out leptonic scenarios) to be 80-1100 the local interstellar medium value for CTB 37A, and of the order 1000 the local∼ interstellar× medium value for the younger, more ∼ × energetic RX J1713.7 3946. Finally, we emphasize− the potential importance of cosmic ray diffusion on hadronic gamma- ray spectra. When considering the finite time available for cosmic rays to penetrate nearby gas, it is possible that cosmic rays of decreasing energy are less concentrated towards cloud centres, where magnetic turbulence tied to dense gas may be strongest. We found that in the case of a small homogeneous core, the spatial cosmic ray distribution will change for suppressed- diffusion scenarios, becoming harder towards the centre. This may have implications for resultant gamma-ray spectra, as higher energy cosmic rays may have access to a greater amount of target material, potentially causing gamma-ray spectra to have a GeV gamma-ray deficit, typ- ically associated more with leptonic emission scenarios. The full extent of these effects are left for future investigation. Future models should solve the diffusion coefficient inside a molecular cloud of a realistic density profile, take into account cosmic-ray energy losses and secondary particles, and yield predicted gamma-ray spectra. Such models could be used to investigate the cosmic ray population, gamma-ray emission mechanisms and diffusion properties towards Galactic supernova remnants.

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155 Appendix A

Appendices

A.1 Cosmic Rays

A.1.1 1st order Fermi Acceleration The velocity of the ejecta is related to the shock speed by the compression ratio, R, the ratio of the shocked gas density to the unshocked gas density, R = ρshocked/ρunshocked. For strong shocks, i.e. when the shock speed greatly exceeds the speed of sound in the local medium, R = 4, and the shock speed, Vshock, is related to the ejecta speed by V R shock = (A.1) V R 1 ejecta − Accounting for this, the relative change in energy of the charged particles is

∆E Vshock h i = βshock (A.2) Ei ≃ c

In the above equation (A.2), the average energy gain is proportional to βshock (1st-order acceleration), meaning that the energy gain is greater than in the case for 2nd-order acceleration (Equation1.21) for 0 <β < 1. This makes acceleration within shocks the more probable mechanism to explain the observed ﬂux of CRs within our galaxy. Of course, Equation A.2 is simply the average energy gain from one single crossing of the shock. The particle may in fact cross multiple times, each time gaining more and more energy. At this point in the derivation, where the charged particles have crossed the shock at least once, it may be more appropriate to begin referring to the charged particles as cosmic rays (CRs). To calculate the energy spectrum of CRs, the probability of a given CR escaping downstream must be calculated, Rloss Pescape = (A.3) Rcross where Rcross is the probability of a CR crossing the shock to the downstream region, and Rloss is the rate that the downstream region will carry downstream CRs away in the density ﬂow. The rate that CRs cross the shock is simply calculated by integrating RU−D (Equation 1.22)

156 over the angle corresponding to the direction forward of the shock ( 1 < cos θ < 0), − i 1 0 R = R (θ )2πd (cos θ ) cross 4π U−D i i Z−1 1 0 = ( n v cos θ )2πd (cos θ ) 4π − CR i i Z−1 1 = n v (A.4) 4 CR where nCR is the density of CRs and vCR is the CR velocity. The CR loss rate downstream depends on the downstream ﬂow speed,

V R = n shock (A.5) loss CR R 

Equation A.3 can now be evaluated and the probability of return, Preturn, can be deﬁned,

4Vshock Pescape = RvCR 4Vshock Preturn =1 (A.6) − RvCR It follows that the average probability of crossing the shock at least k times is

4V k P ( k)= 1 shock (A.7) ≥ − Rv CR after which the average expected energy would be

∆E k E ( k) = E 1+ h i (A.8) h ≥ i i E where Ei is the initial energy of the CR. Now, it is recognised that the integral energy spectrum of a population of particles that cross the shock k times is proportional to the probability of crossing the shock k times, 4V k Q ( E) 1 shock (A.9) ≥ ∝ − Rv CR where E ln E k = i (A.10) h∆Ei 1+ E from Equation A.8. It follows that

ln (Q ( k)) = ln(const.)+ kP ≥ return P = const. + return (ln(E) ln (E )) (A.11) h∆Ei − i 1+ E !

157 Now, (with some foresight) a parameter that will be shown to be the CR diﬀerential spectral index is deﬁned, ln (P ) Γ= − return h∆Ei ln 1+ E

 4Vshock ln 1 Rv = − − CR (A.12) h4 R−1 Vshocki ln 1+ 3 R c

The above equation can be simpliﬁed by noting that ln (1 + x) x, for x 1. As Vshock vCR, c, Equation A.12 can become ≃ ≪ ≪

4Vshock Γ RvCR 4 R−1 Vshock ≃ 3 R c 3 (A.13) ≃ R 1 − for v c. Now, referring back to the integral spectrum (Equation A.11) and substituting in CR → the CR spectral index, Γ,

ln (Q ( k)) = A Γ (ln (E) ln (E )) ≥ − − i = B Γln(E) (A.14) − where A and B = A +Γln(Ei) are constants.

Q ( k) = exp (B Γln(E)) ≥ − Q ( k) EΓ (A.15) ⇒ ≥ ∝ So the integral and diﬀerential CR spectra are

3 Q ( k) E R−1 (A.16) ≥ ∝ and

3 −1 Q (k) E( R−1 ) ∝ − 2+R E R−1 (A.17) ∝ respectively.

A.1.2 Hypernovae Hypernovae are a class of supernovae observed to have blast energies 5-50 larger than ordinary supernova explosions. The term ‘hypernova’ is commonly linked∼ to the× speciﬁc case of an over-luminous Ic explosion (Iwamoto et al., 1998, 2000; Mazzali et al., 2002), but may also be linked to type II events with speciﬁc H spectral features (Type IIn SN) (Smith, 2010). The former case (an over-luminous Ic SN) requires a star of mass &15 M⊙ that collapses to form a blackhole in a regular SNR explosion, but material initially released from the star’s surface falls back to the surface of the blackhole, producing an excess luminosity. In the latter

158 case (type IIn), the progenitor is more massive (>30 M⊙) and the extra luminosity may be from the SN shock interacting with dense nebular gas near to the star, eﬃciently converting shock energy into visible light. Some other models suggest that hypernovae are associated with the collapse of low metallicity stars between 140 and 260M⊙ via the pair-instability mechanism, where pair-production of gamma-rays signiﬁcantly∼ reduces the radiation pressure at the core of the star, resulting in collapse, followed by rapid fusion that releases enough energy to blow the star apart (Kasen, 2011). No compact object is left behind after this type of explosion. It has been suggested that hypernovae may be connected to some types of gamma-ray bursts (Iwamoto et al., 1998), but this is beyond the scope of this thesis.

A.2 HESS Analyses

A.2.1 Cosmic Ray Event Rejection in HESS Analyses Before any parameters are calculated, it is standard convention to clean the images (Aharonian et al., 2006). Because photomultiplier tubes may record low level detections due to the night sky background, low thresholds on the number of allowed photoelectrons are set. The shower size is deﬁned in Equation A.18, and Equation A.19 describes how a parameter, pi, is averaged, weighted by signal.

S = si (A.18) i X s p p = i i i (A.19) h i s P i i th where si is the signal (ie number of photoelectrons)P in the i photomultiplier tube pixel and th pi is a parameter associated with the i pixel. For example, the ‘centre of gravity’ parameter, th ( x , y ) can be defined from Equation A.19 using (xi, yi) as the position of the i pixel. h i h i 2 2 2 By using Equation A.19, x , y and xy can be calculated, allowing the variances, σx, 2 2 h i h i h i σy and σxy to be found. These variances allow the outer boundary of the ellipse to be defined. The mean-scaled-width of a single shower event is defined in Equation A.20 (Aharonian et al., 2006) and can be thought of simply as the average spread in the distribution of widths.

1 N w w w = i −h i (A.20) N σ i X where N is the total number of triggered Cherenkov telescopes, wi is the width of the ellipse, w is the expected width based on the shower size, distance and zenith angle (from Monte hCarloi simulations) and σ is the spread in simulated data with the same size, distance and zenith angle parameters. A similar version of Equation A.20 can be produced for the mean scale length, l. Figure A.1 shows the normalised distribution of mean reduced scaled width in both cosmic ray and gamma-ray events. By considering only the data within a certain w range, a high proportion of cosmic ray background events can be rejected. Some signal is thrown out with the background, so care must be taken in the choice of rejection method. For ‘Standard cuts’, events with 2.0 < w < 0.9 and S > 80 are kept (Aharonian et al., 2006). This will − reject most of the cosmic ray background, but so called gamma-like hadron events are retained in the dataset, as can be seen in Figure A.1. To get even stricter with cosmic ray rejection, Hard cuts can be employed. Hard cuts involve using events only with 2.0 < w < 0.7 and − 159 S > 200. This decreases the total signal and increases the minimum energy threshold. The condition of a minimum number of detectors triggered (generally 2 or 3) can also be imposed.

A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure A.1: (Aharonian et al., 2006) The percentage distribution of mean reduced scale width for Monte-Carlo-generated gamma-ray spectral index (Γ = 2.70) and cosmic ray proton (Γ = 2.59) initiated showers. Also plotted are observational background cosmic ray data.

A.2.2 Cosmic Ray Background Models After cuts are applied to reject cosmic rays, the data sample contains less than 5% of the original cosmic ray events and over 50% of the original gamma-ray events, but the cosmic ray ﬂux is considerably higher than that of gamma-rays for average gamma-ray sources. Since a signiﬁcant cosmic ray background still exists within the sample, one of several methods must be used to estimate the level of cosmic ray contamination. Most background models involve choosing ‘OFF’ regions, where no gamma-ray source is expected to be present and subtracting the OFF-region detections from the ON-region detections (which contains the signal), taking into account the relative solid angle. The excess can be described as s αb, where s is the source counts, b is the background counts and α is a normalisation factor,− which can vary from model to model. Figure A.3 (Rowell, 2003) illustrates four conventional background methods.

160 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure A.2: (Aharonian et al., 2006) This is a diagram of 2 elliptical Cherenkov images and the parameters associated with them. Length refers to the the semi-major axis length. Width refers to the semi-minor axis length. Distance refers to the distance between the Centre of Gravity and the camera centre.

ON/OFF Tracking The ON/OFF tracking method (Figure A.3, 1) uses 2 separate field of view, one containing the source (called ON), the other the OFF. By ensuring that the location in the frame of the field is constant, no corrections for the response of the telescope need to be made. The OFF source can also be restricted to the same zenith angle as the ON source further simplifying the procedure. This method is uncomplicated, with α = 1, but does have a tendency to suffer from a lack of background statistics, making it susceptible to natural variations (Aharonian et al., 2006). Also, the additional time required to apply this method could be seen as wasteful.

Discrete/Reflected Background The discrete background method (Figure A.3, 2) uses several OFF sources scattered around a constant radius in the field of view. This is only applicable for ON positions separated by sufficient angle from the tracking position, such that none of the OFF fields overlap. Ignoring the variable azimuth position of the regions, α would just be the solid angle ratio, [ON]/[OFF]. But the azimuth is not constant in this model. This can be corrected by applying a minor non-radial correction or more simply, it can be minimised by altering the tracking position at regular intervals, such that the background regions are reflected about the ON position.

161 A NOTE: This figure/table/image has been removed to comply with copyright regulations. It is included in the print copy of the thesis held by the University of Adelaide Library.

Figure A.3: (Rowell, 2003) Diagrams of four cosmic ray background rejection models.

Ring Segment Background The ring segment background method (Figure A.3, 3) is very similar to the Discrete background, except a continuous circular region (or part of one) with thickness equal to the ON source diameter is used as an OFF instead of discrete circular OFF regions. This increases the signiﬁcance of the background.

Surrounding Ring The Surrounding Ring method (Figure A.3, 4) can be used for sources lying in the centre of the ﬁeld of view. This technique lessens the azimuthal dependence on detector response, but unlike the previous 3 models, harbours a radial dependence that should be corrected for.

Template Background The Template Background Method starts with the raw mean-reduced-scaled-width data, without any Cosmic Ray Rejection methods (described in the previous subsection) applied. Cosmic ray rejection and a background estimation are applied simultaneously in mean-scaled-width- space via Equations A.21 and A.22.

s = ω ω = 1.0 ( 2 < ω < 0.6) (A.21) i i ∼ − ∼ i X

162 2 ps(ω ) b = ω ω = track,i ( 3.5 < ω < 8.0) (A.22) i i p (ω2 ) ∼ ∼ i b track,i X where ps(ωtrack,i) and pb(ωtrack,i) are 8th order polynomial radial correction terms for the signal and background and f(∆zi) is the zenith correction term. The limits placed on w define the two regimes (signal and background) are justified experimentally (Rowell, 2003) by simply fashioning the ranges such that the detections from the template model are consistent with 2 2 2 other background models. To calculate the excess, α = Ps(θ )/Pb(θ ) is used, where Ps(θ ) and 2 Pb(θ ) are total events for the signal and background regimes, respectively, where theta is the angle from the centre of the field of view (squared to insure equal solid angles). An advantage of this technique is its independence with respect to position in the sky. By eliminating the need to define an OFF position within the field of view, diffuse gamma-ray signals that may have been present within both ON and OFF regions in other methods, would not simply be subtracted away. This property could make surveys of more diffuse sources a possibility.

A.3 Erratum: Chapter 4

A.3.1 3 to 12 millimetre studies of dense gas towards the western rim of supernova remnant RX J1713.7 3946 − The following erratum was published in response to the discovery of a minor mistake in a published manuscript.

163 MNRAS 430, 2511–2512 (2013) doi:10.1093/mnras/stt061

Erratum: 3 to 12 millimetre studies of dense gas towards the western rim of supernova remnant RX J1713.7−3946 by Nigel I. Maxted,1‹ Gavin P. Rowell,1 Bruce R. Dawson,1 Michael G. Burton,2 Brent P. Nicholas,1 Yasuo Fukui,3 Andrew J. Walsh,4 Akiko Kawamura,3 Hirotaka Horachi3 and Hidetoshi Sano3 1School of Chemistry and Physics, University of Adelaide, Adelaide 5005, Australia 2School of Physics, University of New South Wales, Sydney 2052, Australia 3Department of Astrophysics, Nagoya University, Furocho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan 4Centre for Astronomy, School of Engineering and Physical Sciences, James Cook University, Townsville 4811, Australia

Key words: errata, addenda – diffusion – molecular data – supernovae: individual: RX J1713.7−3946 – ISM: clouds – cosmic Downloaded from rays – gamma rays: ISM.

Table 2. Detected molecular transitions from pointed observations. Velocity of peak, vLSR, peak intensity, TPeak and FWHM, vFWHM, were found by fitting Gaussian functions before deconvolving with the MOPS velocity resolution. Displayed values include the beam efficiencies, after a linear baseline subtraction. http://mnras.oxfordjournals.org/ Statistical uncertainties are shown, whereas systematic uncertainties are ∼7, ∼2.5 and ∼5 per cent for the 3, 7 and 12 mm calibration, respectively. Band noise, TRMS, integrated intensity, Tmb dv, possible counterparts and 12 and 100 µm IRAS flux, F12 and F100, respectively, (where applicable) are also displayed. Object Detected TRMS Peak vLSR TPeak vFWHM Tmb dv Counterparts (l,b) emission line (K/ch) (km s−1)(K)(kms−1)(Kkms−1)[F /F (Jy)] 12 100 Core A CS(J = 1–0) 0.06 −9.82 ± 0.02 0.92 ± 0.04 1.25 ± 0.06 1.22 ± 0.08 IRAS 17082−3955 ◦ ◦ (346.93,−0.30) HC3N(J = 5–4,F = 5–4) 0.04 −9.76 ± 0.04 0.29 ± 0.02 1.07 ± 0.11 0.33 ± 0.04 [5.4/138] SiO(J = 1–0) 0.03 − ––

Core B CS(J = 1–0) 0.06 – – – – at University of Adelaide on April 18, 2013 (346◦.93,−0◦.50) SiO(J = 1–0) 0.03 – – – – CS(J = 1–0) 0.05 −11.76 ± 0.01 2.12 ± 0.02 2.08 ± 0.03 4.69 ± 0.08 Core C CS(J = 2–1) 0.10 −11.62 ± 0.08 1.49 ± 0.08 2.94 ± 0.21 4.66 ± 0.42 IRAS 17089−3951 (347◦.08,−0◦.40) C34S(J = 1–0) 0.04 −11.83 ± 0.04 0.37 ± 0.02 1.40 ± 0.09 0.55 ± 0.05 [4.4/234] C34S(J = 2–1) 0.07 −11.78 ± 0.20 0.34 ± 0.06 1.89 ± 0.49 0.68 ± 0.21 13CS(J = 1–0) 0.03 −11.70 ± 0.10 0.10 ± 0.02 0.88 ± 0.22 0.09 ± 0.03 HC3N(J = 5–4,F = 5–4) 0.02 −11.65 ± 0.03 0.32 ± 0.01 1.74 ± 0.08 0.59 ± 0.03 CH3OH(7(0)–6(1) A++)0.02−10.21 ± 0.17 0.07 ± 0.01 2.13 ± 0.32 0.16 ± 0.03 CH3OH(2(−1)–1(−1) E) 0.07 −11.75 ± 0.17 0.33 ± 0.13 0.99 ± 0.90 0.35 ± 0.34 ′′ CH3OH(2(0)–1(0) A++) −11.86 ± 0.14 0.43 ± 0.08 1.44 ± 0.46 0.66 ± 0.24 SO(2,3–1,2) 0.07 −11.77 ± 0.09 0.65 ± 0.07 1.74 ± 0.25 1.20 ± 0.22 + a N2H (J = 1–0) F1 = 2–1 0.08 −11.61 ± 0.03 1.14 ± 0.03 2.18 ± 0.08 2.65 ± 0.12 ′′ ′′ F1 = 0–1 0.40 ± 0.04 1.58 ± 0.23 0.67 ± 0.12 ′′ ′′ F1 = 1–1 0.76 ± 0.03 0.87 ± 0.04 0.70 ± 0.04 a NH3((1,1)–(1,1)) F→F 0.03 −12.04 ± 0.04 0.34 ± 0.02 1.46 ± 0.09 0.53 ± 0.05 F→F−1b ′′ ′′ 0.07 ± 0.02 ′′ 0.11 ± 0.03 ′′ ′′ 0.13 ± 0.02 ′′ 0.20 ± 0.03 F→F+1c ′′ ′′ 0.13 ± 0.02 ′′ 0.20 ± 0.03 ′′ ′′ 0.12 ± 0.02 ′′ 0.19 ± 0.03 a ′′ NH3 ((2,2)–(2,2)) F→F −11.69 ± 0.10 0.16 ± 0.02 2.02 ± 0.26 0.34 ± 0.06 SiO(J = 1–0) 0.03 – – – – Core D CS(J = 1–0) 0.10 −9.06 ± 0.11 0.47 ± 0.04 2.50 ± 0.29 1.25 ± 0.18 IRAS 17078−3927 (347◦.30,0◦.00) 0.10 −71.25 ± 0.46 0.15 ± 0.04 3.38 ± 0.36 0.54 ± 0.15 [2.0/739] SiO(J = 1–0) 0.06 – – – – Point ABm CS(J = 1–0) 0.04 −8.89 ± 0.43 0.09 ± 0.02 4 ± 10.4± 0.1 (346◦.93,−0◦.38) SiO(J = 1–0) 0.06 – – – – aCentre line; bOuter satellite lines; cInner satellites lines.

⋆ E-mail: [email protected]

C 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society 2512 N. I. Maxted et al.

The paper ‘3 to 12 millimetre studies of dense gas towards the west- displayed in this erratum, are more than an order of magnitude lower ern rim of supernova remnant RX J1713.7−3946’, was published than those incorrect values presented in Maxted et al. (2012). in 2012, MNRAS, 422, 2230. Since publication, it was discovered that values for integrated intensity, Tmbdv, presented in Table 2 ACKNOWLEDGEMENTS are incorrect. The integrated intensity values in Table 2 were generated post- The authors would like to thank Fabien Voisin for alerting us to the analysis (in the editing stage of the manuscript) for the ease of presence of the error in our manuscript. the reader, and were not the integrated intensity values used to subsequently estimate gas parameters (such as mass and number REFERENCES density), so the conclusions of the publication remain the same. Maxted N. et al., 2012, MNRAS, 419, 251 To prevent any future confusion, we present a version of Table 2 with these errors corrected. The correct integrated intensity values, This paper has been typeset from a TEX/LATEX ﬁle prepared by the author. Downloaded from http://mnras.oxfordjournals.org/ at University of Adelaide on April 18, 2013 A.4 Cosmic Ray Diﬀusion

A.4.1 Cosmic Ray Distribution Inside a Molecular Core

−5 In § 6.2.1, spatial cosmic ray distributions inside a molecular core were presented for χ =10 . Figure A.4 displays the cosmic ray distributions for lower levels of cosmic ray diﬀusion-suppression, χ =10−4 and χ =10−3.

27 2 −1 χ −4 D 0 = 3*10 cm s = 10 CR Distribution within Core C CR Distribution within Core C

Time (years) 10 Time (years) 11 Cosmic rays of Energy of 10 eV Cosmic rays of Energy of 10 eV 1 0 0 250 1 250 500 500 750 750 1000 1000 0.8 0.8 CR Inhabitance CR Inhabitance

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Core Radius (pc) Core Radius (pc)

27 2 −1 χ −3 D 0 = 3*10 cm s = 10 CR Distribution within Core C CR Distribution within Core C

Time (years) 10 Time (years) 11 Cosmic rays of Energy of 10 eV Cosmic rays of Energy of 10 eV 1 0 0 250 1 250 500 500 750 750 1000 1000 0.8 0.8 CR Inhabitance CR Inhabitance

0.6 0.6

0.4 0.4

0.2 0.2

0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 Core Radius (pc) Core Radius (pc)

Figure A.4: The cosmic ray inhabitance as a function of radius within a core of radius 0.62 pc (similar to Core C), at intervals of 250 years. The diﬀusion coeﬃcients used for the inside of the core were 10−4 (above) and 10−3 (below) of the Galactic average.

166 A.4.2 Cosmic Ray Diﬀusion Software // //%spherically symmetric 3d case // Nigel Maxted // // To compile: g++ Spherical_Dif_Nigeledit.cpp -o Spherical_Dif_Nigeledit ‘root-config --cflags --libs‘ // To Run: ./Spherical_Dif_Nigeledit // //% //%Log 25/9/11 -Copied from bruceftcsspherical.m //% -Changed formatting and added more comments //% 27/9/11 -Added function to save plot automatically //% -CreatedaloopoverEp //% -Changed input from iteration number to maximum time //% 3/10/11 -Added some switches to cycle outputs //% 1/03/12 -Began to translate from Matlab to C++ // 23/5/12 -Working on calculating/outputting CR spectrum at different cloud layers --sort of abandonned // 30/5/12 -Added CR distribution Logistical function fit // -Added integration of CR density* gas density // -Found error in dcoeff function (has been corrected) // 02/5/12 -Calculate nH*nCR for 3 distinct ranges-note that output spectral indices are currently incorrect // -

//----To do--- // -Convert nH*nCR to gamma-ray spectrum // -Calculate final spectral dist. correctly

#include #include #include #include #include #include #include #include

//For ROOT plotting (thanks Mat) #include "TApplication.h" //plot #include "TCanvas.h" //plot #include "TGraph.h" //plot #include "TLegend.h" //plot #include "TF1.h" //fit //#include "TText.h" //plot //#include "TAxis.h" //plot

167 //Test for double to string conversion #include //#include using namespace std;

//Functions double dcoef(double point, double dscale, double ncore) { return dscale*sqrt( 1.0/sqrt((ncore/(1.0e4))/(1.0+pow(point/0.1,2.2)) ) ); //return dscale*2.4; //%Constant diffusion coefficient //return dscale*sqrt( 1.0/sqrt(300.00));

} double density(double rxy, double z, double ncore, double r, double rc) //in cylindrical coords not speherical { return ncore/(1.0+pow(r/rc,2.2)); //Tafalla etal 2002 (in paper, not by them) } int main(int argc, char** argv) //plot {

//------//plot // This is needed to be able to draw to the screen. TApplication myApp("myApp", &argc, argv);

// Vectors containing the X & Y values (Must be the same size!!) // std::vector xValues; //std::vector yValues; //------

//%Switches int ProgressionPlots=1; //Save progression plots int MeanPenetrationOut=1; // int OutputData=0; //Output data for a future spectral analysis (not active--abandoned) int LineFit=1; //Fit to CR-distribution int Integration=1; //integrate nCR*nH wrt volume (Must have a LineFit=1) int i_f=5; //max energy iteration (including 0)

//%physical parameters of diffusion double chi=1.0e-3; // %Diffusion Suppresion coefficient doubleD0=3.14e-8; //%D0 //doubleEp=1000; //%EnergyinGeV

168 double E_exp[10]={1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5}; double Ep[10]; // %Proton energies to try //double tmax[10]={1000.0,1000.0,1000.0,1000.0,1000.0,1000.0,1100.0,1300.0, 1400.0,1500.0}; //%Maximum time allowed to diffuse (1600-tstart) double tmax[10]={1000.0,1000.0,1000.0,1000.0,1000.0,1000.0,1000.0,1000.0, 1000.0,1000.0}; //%Maximum time allowed to diffuse (1600-tstart) double tmax_sec[10];

//some inputs int xpts=100; //No of points in computational grid // double radius=0.7; //Core radius (pc) double radius=0.62; //Core radius (pc) double rc=0.1; //Inner Core parameter for density distribution double AimRcrit=0.08; //Adjusts dt //double AimRcrit=0.4; //Adjusts dt double dt; //Made this rcrit dependent //=1.0e5; // %Time step (seconds) double ncore=2.0e4; //Density inside core (cm^-3)

//CR spectrum double F0=1.0; double gamma=2.2; double FCR[10], Ei, Ef;

//Some params double pi=3.141593; double parsec=30.857e17; //parsec --> cm double c=2.99792458e8; //light speed (m/s) double mp=1.6726e-27; //proton mass (kg)

//some variables int maxIterations; double dx; double rcrit, r; double dscale; int t1, t2, t3; double y1, y2, y3, y4; double nH, nCR; double Sum, Integral, Rad_seg_i, Rad_seg_f, Rad_Av[3], Rad_prof[3], Radspec[10][4];//Radial segment double minimise, saved, x5[10]; int i, j, k; double z, rxy, theta; double dz=0.001; double drxy=0.001; // double dtheta=0.001; ofstream Radial_dist;

//graph stuff

169 /* TGraph myGraph0, myGraph1, myGraph2, myGraph3, myGraph4; TCanvas myCanvas("myCanvas", // Unique name for canvas. "Canvas Main Title", // Axis titles. 0, 0, // Window top left coordinates. 800, 600); // Window dimensions (w, h) TLegend myLegend(0.1394472,0.6829268,0.3065327,0.8954704,"Time (years)");//x1,y1, x2,y2,header */ i=0; while (i <= i_f) { tmax_sec[i]=tmax[i]*365.25*24.0*3600.0; // %now in seconds Ep[i]=1.0*pow(10.0,E_exp[i]); //Energy in GeV //cout << "\n" << i << " " << tmax_sec[i] << " " << Ep[i]; i=i+1; } //printf(num2str(length(Ep),’%4.1e’))

//%set up computational grid double* x = new double[xpts]; for(int j = 0; j < xpts; ++j) { x[j]= j*(radius/xpts); // %Declares a matrix, x, that has xpts points between 0 and ’radius’ pc //cout << "\n" << j << " " << x[j]; } dx=x[1]-x[0]; // %Calculating the space between points cout << "\n dx " << dx << "pc";

if (Integration == 1) //Open a file to record gamma distributions { //ofstream Radial_dist; Radial_dist.open ("Results/Radial_dist.out"); //Radial_dist << "Writing this to a file.\n"; } i=0; while (i <= i_f) //%Now to loop over energy { dscale=chi*D0*pow( Ep[i]/(10.0/pow(3.0,0.5)) ,0.5); //%Coefficient out the front of the variable diffusion term cout << "\n" << "dscale" << " " << dscale;

170 dt=(AimRcrit*pow(dx,2))/(2.5*dscale); r=dt/pow(dx,2); // %Refer to maths -part of the FTCS scheme cout << "\n" << "dt" << " " << dt << " seconds"; maxIterations=tmax_sec[i]/dt; // this should round to the nearest integer cout << "\n interations " << maxIterations;

//%display stability parameter, must be <0.5 for const diffusion cartesian 1d, probably similar here. rcrit=r*dscale*2.4; //%Parameter that checks that the intervals are small enough cout << "\n rcrit " << rcrit << " ... keep below 0.5\n" ; double ** n= new double*[xpts]; for(int j = 0; j <= xpts-1; ++j) { n[j] = new double[maxIterations]; } for(int j = 0; j <= xpts-1; ++j) { for(int k = 0; k <= maxIterations-1; ++k) { n[j][k]= 0.0; // %Declares a matrix, n, that is filled with zeros } }

//%initial condition 1 -Setting initial, t=0, CR density at all positions to 0 ( I admit, a bit redundant) for(int j = 0; j <= xpts-1; ++j) { n[j][0]=0.0; }

//%initial condition 2 -Boundaries for(int k = 0; k <= maxIterations-1; ++k) { n[xpts-1][k]=1.0;//1.0; // constant CR density outside the core //n(0,k)=0.0; // sink at core centre (don’t activate) }

//Declaring the half-way mark between x and x+dx double* xh= new double[xpts]; double* ds= new double[xpts]; for(int j = 0; j <= xpts-1; ++j) { xh[j]= x[j]+0.5*dx; // ds[j]=dcoef(xh[j],dscale,ncore); //Vector of diffusion coefficients between points // cout << "\n" << j << " " << ds[j];

171 } for(int k = 0; k <= maxIterations-2; ++k) { n[0][k+1]=(4.0*n[1][k]-n[2][k])/3.0; //%zero flux boundary condition from 3 point forward diff for deriv for(int j = 1; j < xpts-1; ++j) { // cout << "\n" << j << " " << k << " " << n[j,k+1] << " " << n[j,k] << " " << n[j+1,k] << " " << n[j-1,k];

//Below is Adrians original n[j][k+1]=n[j][k]+ (1.0/pow(x[j],2))*r*(pow(xh[j],2)*ds[j]*(n[j+1][k]-n[j][k]) -pow(xh[j-1],2)*ds[j-1]*(n[j][k]-n[j-1][k]));

//cout << "\n" << j << " " << k << " " << n[j][k+1]; } // cout << "\n" << "0" << " " << k << " " << n[][k+1]; }

//------if (ProgressionPlots==1) { t1=maxIterations/4.0; t2=maxIterations/2.0; t3=(3*maxIterations)/4.0; y1=(t1*dt)/(60.0*60.0*24.0*365.25); y2=(t2*dt)/(60.0*60.0*24.0*365.25); y3=(t3*dt)/(60.0*60.0*24.0*365.25); y4=(maxIterations*dt)/(60.0*60.0*24.0*365.25);

cout<<"\n"<

//Declaring vaiables for plotting double* xValues= new double[xpts]; double* xValues0= new double[xpts]; double* yValues0= new double[xpts]; double* yValues1= new double[xpts]; double* yValues2= new double[xpts]; double* yValues3= new double[xpts]; double* yValues4= new double[xpts];

for(int j = 0; j < xpts-1; ++j) { xValues[j]=x[j];

172 xValues0[j]=radius; yValues0[j]=(1.0/(double(xpts)-1.0))*double(j); yValues1[j]=n[j][t1]; yValues2[j]=n[j][t2]; yValues3[j]=n[j][t3]; yValues4[j]=n[j][maxIterations-1]; }

TGraph myGraph0, myGraph1, myGraph2, myGraph3, myGraph4; for (int k = 0; k < xpts-1; ++k) { myGraph0.SetPoint(k,xValues0[k],yValues0[k]); myGraph1.SetPoint(k,xValues[k],yValues1[k]); myGraph2.SetPoint(k,xValues[k],yValues2[k]); myGraph3.SetPoint(k,xValues[k],yValues3[k]); myGraph4.SetPoint(k,xValues[k],yValues4[k]); }

// Create a canvas to draw the graph on. TCanvas myCanvas("myCanvas", // Unique name for canvas. "Canvas Main Title", // Axis titles. 0, 0, // Window top left coordinates. 800, 600); // Window dimensions (w, h) myGraph1.SetTitle("CR Distribution within Core C;Core Radius (pc);CR Inhabitance"); myGraph1.SetMinimum(0.0); myGraph1.SetMaximum(1.1); //myGraph0.SetMinimum(); //myGraph0.SetMaximum(); myGraph0.SetLineStyle(1); myGraph1.SetLineStyle(2); myGraph2.SetLineStyle(3); myGraph3.SetLineStyle(7); myGraph4.SetLineStyle(9); myGraph0.SetLineWidth(2); myGraph1.SetLineWidth(2); myGraph2.SetLineWidth(2); myGraph3.SetLineWidth(2); myGraph4.SetLineWidth(2);

// Make the canvas the current canvas to draw to // (default is the most recently created canvas). myCanvas.cd(); myCanvas.SetFillColor(0);

173 // Draw the graph with axis "A", points "P" and curved line "C" myGraph1.Draw("APC"); //Setting up x-axis in coor myGraph0.Draw("PC"); //myGraph1.Draw("PC"); myGraph2.Draw("PC"); //For multiple points myGraph3.Draw("PC"); //For multiple points myGraph4.Draw("PC"); //For multiple points char year1[32], year2[32], year3[32], year4[32]; sprintf(year1,"%4.0f",y1); sprintf(year2,"%4.0f",y2); sprintf(year3,"%4.0f",y3); sprintf(year4,"%4.0f",y4);

TLegend myLegend(0.1394472,0.6829268,0.3065327,0.8954704,"Time (years)"); //x1,y1,x2,y2,header myLegend.SetTextSize(0.04); if (rcrit >= 0.5) { cout<< "ERROR!!!!: Rcrit >0.5"; myLegend.AddEntry(&myGraph0, "ERROR", "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph1, year1, "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph2, year2, "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph3, year3, "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph4, year4, "l"); //first arg must be pointer myLegend.AddEntry(&myGraph1, "Rcrit", "l"); //first arg must be pointer myLegend.AddEntry(&myGraph2, "Exceeds", "l"); //first arg must be pointer myLegend.AddEntry(&myGraph3, "0.5", "l"); //first arg must be pointer myLegend.AddEntry(&myGraph4, "Invalid Result", "l"); //first arg must be pointer } else { myLegend.AddEntry(&myGraph0, "0", "l"); //first arg must be pointer myLegend.AddEntry(&myGraph1, year1, "l"); //first arg must be pointer myLegend.AddEntry(&myGraph2, year2, "l"); //first arg must be pointer myLegend.AddEntry(&myGraph3, year3, "l"); //first arg must be pointer myLegend.AddEntry(&myGraph4, year4, "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph1, "y1", "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph2, "y2", "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph3, "y3", "l"); //first arg must be pointer //myLegend.AddEntry(&myGraph4, "y4", "l"); //first arg must be pointer } myLegend.Draw();

//Uncomment to manually edit graph //myApp.Run();

174 //return 0;

if (i==0) { myCanvas.SaveAs("Results/CRdist_1e10.0.eps"); } else if (i==1) { myCanvas.SaveAs("Results/CRdist_1e10.5.eps"); } else if (i==2) { myCanvas.SaveAs("Results/CRdist_1e11.0.eps"); } else if (i==3) { myCanvas.SaveAs("Results/CRdist_1e11.5.eps"); } else if (i==4) { myCanvas.SaveAs("Results/CRdist_1e12.0.eps"); } else if (i==5) { myCanvas.SaveAs("Results/CRdist_1e12.5.eps"); } else if (i==6) { myCanvas.SaveAs("Results/CRdist_1e13.0.eps"); } else if (i==7) { myCanvas.SaveAs("Results/CRdist_1e13.5.eps"); } else if (i==8) { myCanvas.SaveAs("Results/CRdist_1e14.0.eps"); } else if (i==9) { myCanvas.SaveAs("Results/CRdist_1e14.5.eps"); } delete xValues, xValues0, yValues0, yValues1; delete yValues2, yValues3, yValues4;

}

if (LineFit==1)

175 { cout << "\n" << "Fitting Logistic function to CR dist... " << "\n";

y4=(maxIterations*dt)/(60.0*60.0*24.0*365.25); //Years after explosion- -line fit

//Declaring vaiables for plotting double* xValues= new double[xpts]; double* yValues4= new double[xpts];

for(int j = 0; j < xpts-1; ++j) { xValues[j]=x[j]; yValues4[j]=n[j][maxIterations-1]; //Normalised CR densities of final year }

TGraph myGraphFit; for (int k = 0; k < xpts-1; ++k) { myGraphFit.SetPoint(k,xValues[k],yValues4[k]); }

myGraphFit.SetTitle("Fit to CR Distribution within Core C;Core Radius (pc); CR Inhabitance"); myGraphFit.SetMinimum(0.0); myGraphFit.SetMaximum(1.1); myGraphFit.SetLineStyle(9); myGraphFit.SetLineWidth(2);

// Make the canvas the current canvas to draw to // (default is the most recently created canvas). myCanvas.cd(); myCanvas.SetFillColor(0);

myGraphFit.Draw("APC");

TF1 *myfit = new TF1("myfit","[0]/(1.0 + [1]*exp(-[2]*x))", 0, 0.7);

myfit->SetParName(0,"c"); myfit->SetParName(1,"a"); myfit->SetParName(2,"b");

176 // myfit->SetParameter(0, 0.3); // myfit->SetParameter(1, 10); // myfit->SetParameter(2, 5); myfit->SetParLimits(0, 0.01, 5.0); myfit->SetParLimits(1, 0, 10000000.0); myfit->SetParLimits(2, 0, 300.0); myGraphFit.Fit("myfit","R");

TLegend myLegend(0.1394472,0.7,0.4,0.89,"c/(1.0 + a*exp(-b*x))");//x1,y1, x2,y2,header myLegend.SetTextSize(0.04); myLegend.Draw(); double a, b, c, Da, Db, Dc; c=myfit->GetParameter(0); a=myfit->GetParameter(1); b=myfit->GetParameter(2); Dc=myfit->GetParError(0); Da=myfit->GetParError(1); Db=myfit->GetParError(2); cout << "\n Fit to: c/(1.0 + a*exp(-b*x)) \n"; cout << "\n c=" << c << "+- " << Dc << " "; cout << "\n a=" << a << "+- " << Da << " "; cout << "\n b=" << b << "+- " << Db << "\n";

// myApp.Run(); // return 0; if (i==0) { myCanvas.SaveAs("Results/CRdistFit_1e10.0.eps"); } else if (i==1) { myCanvas.SaveAs("Results/CRdistFit_1e10.5.eps"); } else if (i==2) { myCanvas.SaveAs("Results/CRdistFit_1e11.0.eps"); } else if (i==3) { myCanvas.SaveAs("Results/CRdistFit_1e11.5.eps"); } else if (i==4) { myCanvas.SaveAs("Results/CRdistFit_1e12.0.eps"); }

177 else if (i==5) { myCanvas.SaveAs("Results/CRdistFit_1e12.5.eps"); } else if (i==6) { myCanvas.SaveAs("Results/CRdistFit_1e13.0.eps"); } else if (i==7) { myCanvas.SaveAs("Results/CRdistFit_1e13.5.eps"); } else if (i==8) { myCanvas.SaveAs("Results/CRdistFit_1e14.0.eps"); } else if (i==9) { myCanvas.SaveAs("Results/CRdistFit_1e14.5.eps"); } delete xValues, yValues4; if (Integration == 1) //integration of nCR*nH {

cout << "\n Calculating CR flux..."; Ei=pow(10,9.0)*pow(10.0,E_exp[i]-0.25); //Energy lower limit in eV Ef=pow(10,9.0)*pow(10.0,E_exp[i]+0.25); //Energy upper limit in eV FCR[i]=(F0/(1.0-gamma))*(pow(Ef,1.0-gamma)-pow(Ei,1.0-gamma)); cout << "Flux from " << Ei << "eV to " << Ef << "eV \n is "<< FCR[i] << "cm^-2s^-1 \n";

cout << "\n Integrating... (dz="<< dz << ",drxy="<< drxy << ")\n";

Sum=0.0; Integral=0.0; for(rxy=0.5*drxy; rxy <= radius; rxy=rxy+drxy ) { for(z=0.5*dz; z <= sqrt(pow(radius,2)-pow(rxy,2)); z=z+dz ) { nH=density(rxy,z,ncore,r,rc);//cm^-3 nCR=c/(1.0 + a*exp(-b*( sqrt(pow(rxy,2)+pow(z,2)) ))); //Dimensionless (so far)

Sum=Sum + nH*nCR*rxy;//cm^-3 * Dimensionless * (cm^-3) } }

178 Integral=Sum*dz*drxy; Integral=pow(parsec,3)*Integral; //Conversion from pc^3*cm^-3 to dimensionless Integral=2.0*Integral; //Because we only integrated half the sphere Integral=2.0*pi*Integral; //For the theta variable Integral=Integral*(FCR[i]/(c*100.00)); //Taking into account CR flux cout << "Entire Radius: Integral=" << Integral << "F0 CRs*Hs (units?) for E=" << Ep[i] << "GeV\n"; //Here we add the extra factors // cross section, energy dependence, CRs --> gammas parameterisation // Radspec[i][3]=Integral;

//Now segments Sum=0.0; Integral=0.0; for(int j = 0; j <= 2; ++j) { Rad_seg_i=double(j)*(radius/3.0) + 0.5*drxy; Rad_seg_f=double(j+1)*(radius/3.0) - 0.5*drxy; Rad_Av[j]=(Rad_seg_i+Rad_seg_f)/2.0;

for(rxy=Rad_seg_i; rxy <= Rad_seg_f; rxy=rxy+drxy ) { for(z=0.5*dz; z <= sqrt(pow(radius,2)-pow(rxy,2)); z=z+dz ) { nH=density(rxy,z,ncore,r,rc);//cm^-3 nCR=c/(1.0 + a*exp(-b*( sqrt(pow(rxy,2)+pow(z,2)) ))); //Dimensionless (so far)

Sum=Sum + nH*nCR*rxy;//cm^-3 * Dimensionless * (cm^-3) } } Integral=Sum*dz*drxy; Integral=pow(parsec,3)*Integral; //Conversion from pc^3*cm^-3 to dimensionless Integral=2.0*Integral; //Because we only integrated half the sphere Integral=2.0*pi*Integral; //For the theta variable Integral=Integral*(FCR[i]/(c*100.00)); //Taking into account CR flux Rad_prof[j]=Integral;

cout << "r=" << Rad_seg_i << "-" << Rad_seg_f << "pc, Integral= " << Integral << "F0 CRs*Hs (units?)\n"; }

179 if (i==0) { Radial_dist << "Energy (GeV) " << Rad_Av[0] << "pc " << Rad_Av[1] << "pc " << Rad_Av[2] << "pc\n"; } Radial_dist << Ep[i] << " " << Rad_prof[0] << " " << Rad_prof[1] << " " << Rad_prof[2] << "\n";

Radspec[i][0]=Rad_prof[0]; Radspec[i][1]=Rad_prof[1]; Radspec[i][2]=Rad_prof[2]; }

}

//------if (MeanPenetrationOut == 1) { saved=1.0; for(int j = 0; j <=xpts-1; ++j) {

minimise=sqrt(pow(0.5-n[j][maxIterations-1],2)); if (minimise < saved ) { saved=minimise; x5[i]=x[j]; } } cout << "saved:"<< saved << ", Mean penetration level: " << x5[i] <<"\n";

}

///------Old matlab plot stuff

/* if (MeanPenetrationOut == 1) %locate and interpolate for the position of n=0.5 as a function of time for j=1:maxIterations ind(j)=find(n(:,j)>0.5,1); z(j)=(0.5*dx+n(ind(j),j)*x(ind(j)-1)-n(ind(j)-1,j)*x(ind(j)))/(n(ind(j),j) -n(ind(j)-1,j)); end

%plot the above position %plot(dt*(k-1),z)

180 else continue end */ //------

//Now for a spectra calculation if (OutputData==1) {

// double N_save[10][7][4]; int j0,k0;

cout << "\n" << "Now to save distribution at different points"; cout << "\n" << "j (x=0.1,0.2pc..)" << " " << "k (t=0, 250yr..)" << " " << "N_save[energy][x][t]";

for(int j = 0; j <= 6; ++j) // position { j0=int((xpts-1)/7.0)*j; for(int k = 0; k <= 3; ++k) // time { k0=int((maxIterations-1)/4.0)*k;

// N_save[i][j][k]=n[j0][k0];

cout << "\n" << j << " " << k << " " << n[j0][k0]; } }

// delete N_save, //delete j0, k0;

// Writing to a file char En[10], ch[10], fileName[35]; sprintf(En,"%2.1e",Ep[i]); sprintf(ch,"%1.0e",chi);

strcat(fileName,"Results/Res_X"); strcat(fileName,ch); strcat(fileName,"_En"); strcat(fileName,En); strcat(fileName,"GeV.txt");

//cout << "\n Energy " << En <<"\n"; //cout << "\n Diff sup " << ch <<"\n";

cout << "\n Output data to: " << fileName <<"\n";

181 ofstream myfile; myfile.open (fileName);

myfile << "Writing this to a file.\n";

//continue from here!!!!

myfile.close(); }

for(int j = 0; j <= xpts-1; ++j) { delete[] n[j]; } delete[] x, n, xh, ds;

cout << "Energy " << i << " completed... "; i=i+1; } //%End energy loop

//I don’t think the below bit functions properly.. The graph output isn’t finished, but the fits are maybe okay... if (Integration == 1) { Radial_dist.close();//Closing Radial gamma distribution file

cout << "Now to look at the gamma ray spectra... \n";

double* xValues00= new double[10]; double* yValues001= new double[10]; double* yValues002= new double[10]; double* yValues003= new double[10]; double* yValues004= new double[10];

//Now some spectral analysis, i=0; while (i <= i_f) //%Now to loop over energy { // cout << "About to read data... \n"; xValues00[i]= log10(Ep[i]); yValues001[i]=log10(Radspec[i][0]); yValues002[i]=log10(Radspec[i][1]); yValues003[i]=log10(Radspec[i][2]);

182 yValues004[i]=log10(Radspec[i][3]); // cout << xValues00[i] << " "<< yValues001[i] << " "<< yValues002[i] << " "<< yValues003[i] << " "<< yValues004[i] << "\n"; i=i+1; }

// cout << "Beep beep... \n";

TGraph myGraphSpec,myGraphSpec2,myGraphSpec3,myGraphSpec4; for (int k = 0; k < i_f; ++k) { myGraphSpec.SetPoint(k,xValues00[k],yValues001[k]); myGraphSpec2.SetPoint(k,xValues00[k],yValues002[k]); myGraphSpec3.SetPoint(k,xValues00[k],yValues003[k]); myGraphSpec4.SetPoint(k,xValues00[k],yValues004[k]); } cout << "Making canvas... \n";

// Create a canvas to draw the graph on. TCanvas myCanvas("myCanvas", // Unique name for canvas. "Canvas Main Title", // Axis titles. 0, 0, // Window top left coordinates. 800, 600); // Window dimensions (w, h) myGraphSpec.SetTitle("Fit to gamma-ray spectrum for different radii\n(For some input CR spectrum);Energy (GeV);log(nCR*nH) "); // myGraphSpec.SetMinimum(); // myGraphSpec.SetMaximum(); myGraphSpec.SetLineStyle(9); myGraphSpec.SetLineWidth(2);

// Make the canvas the current canvas to draw to // (default is the most recently created canvas). myCanvas.cd(); myCanvas.SetFillColor(0); cout << "Plotting data points... \n"; myGraphSpec.Draw("AP");

TF1 *myfit = new TF1("myfit","[0]*x+[1]", 0, 6.0); myfit->SetParName(0,"d"); myfit->SetParName(1,"e"); myfit->SetParLimits(0, -3.0, 1.0); myfit->SetParLimits(1, 0, 300.0); myGraphSpec.Fit("myfit","R"); double d, e, De, Dd, alpha[4], alphaDif[4]; //Because there’s a difference

183 between int and dif spec ind. d=myfit->GetParameter(0); e=myfit->GetParameter(1); Dd=myfit->GetParError(0); De=myfit->GetParError(1); cout << "\n Fit to: d*x + e \n"; cout << "\n d=" << d << "+- " << Dd << " "; cout << "\n e=" << e << "+- " << De << "\n "; alpha[0]=d;

//2 myGraphSpec2.Draw("AP"); myfit->SetParName(0,"d"); myfit->SetParName(1,"e"); myfit->SetParLimits(0, -3.0, 1.0); myfit->SetParLimits(1, 0, 100.0); myGraphSpec2.Fit("myfit","R"); d=myfit->GetParameter(0); e=myfit->GetParameter(1); Dd=myfit->GetParError(0); De=myfit->GetParError(1); cout << "\n Fit to: d*x + e \n"; cout << "\n d=" << d << "+- " << Dd << " "; cout << "\n e=" << e << "+- " << De << "\n "; alpha[1]=d;

//3 myGraphSpec3.Draw("AP"); myfit->SetParName(0,"d"); myfit->SetParName(1,"e"); myfit->SetParLimits(0, -3.0, 1.0); myfit->SetParLimits(1, 0, 100.0); myGraphSpec3.Fit("myfit","R"); d=myfit->GetParameter(0); e=myfit->GetParameter(1); Dd=myfit->GetParError(0); De=myfit->GetParError(1); cout << "\n Fit to: d*x + e \n"; cout << "\n d=" << d << "+- " << Dd << " "; cout << "\n e=" << e << "+- " << De << "\n "; alpha[2]=d;

//4 myGraphSpec4.Draw("AP"); myfit->SetParName(0,"d"); myfit->SetParName(1,"e"); myfit->SetParLimits(0, -3.0, 1.0); myfit->SetParLimits(1, 0, 100.0);

184 myGraphSpec4.Fit("myfit","R"); d=myfit->GetParameter(0); e=myfit->GetParameter(1); Dd=myfit->GetParError(0); De=myfit->GetParError(1); cout << "\n Fit to: d*x + e \n"; cout << "\n d=" << d << "+- " << Dd << " "; cout << "\n e=" << e << "+- " << De << "\n \n"; alpha[3]=d;

cout << Rad_Av[0] << "pc, int. spectral index=" << alpha[0] << "\n"; cout << Rad_Av[1] << "pc, int. spectral index=" << alpha[1] << "\n"; cout << Rad_Av[2] << "pc, int. spectral index=" << alpha[2] << "\n"; cout << "Overall, int. spectral index=" <

alphaDif[0]=alpha[0]+1.0; alphaDif[1]=alpha[1]+1.0; alphaDif[2]=alpha[2]+1.0; alphaDif[3]=alpha[3]+1.0;

cout << Rad_Av[0] << "pc, spectral index=" << alphaDif[0] << "\n"; cout << Rad_Av[1] << "pc, spectral index=" << alphaDif[1] << "\n"; cout << Rad_Av[2] << "pc, spectral index=" << alphaDif[2] << "\n"; cout << "Overall, spectral index=" <

//These lines should be plotted on graphs and saved

myCanvas.SaveAs("Results/GammaDist.eps");

delete xValues00, yValues001, yValues002, yValues003, yValues004;

}

185