A Dissertation Entitled Lighting the Dark Molecular Gas and a Bok

Home , Bok globule, NGC 1266, NGC 1291, NGC 2623, NGC 695, NGC 7130

A Dissertation entitled

Lighting the dark molecular gas and a Bok globule

by Aditya G. Togi

Submitted to the Graduate Faculty as partial fulﬁllment of the requirements for the Doctor of Philosophy Degree in Physics

Dr. John-David T. Smith, Committee Chair

Dr. Adolf Witt, Committee Member

Dr. Lee Armus, Committee Member

Dr. Rupali Chandar, Committee Member

Dr. Sanjay Khare, Committee Member

Dr. Patricia R. Komuniecki, Dean College of Graduate Studies

This document is copyrighted material. Under copyright law, no parts of this document may be reproduced without the expressed permission of the author. An Abstract of Lighting the dark molecular gas and a Bok globule by Aditya G. Togi

Submitted to the Graduate Faculty as partial fulﬁllment of the requirements for the Doctor of Philosophy Degree in Physics The University of Toledo May 2016

Stars are the building blocks of galaxies. The gas present in galaxies is the primary fuel for star formation. Galaxy evolution depends on the amount of gas present in the interstellar medium (ISM). Stars are born mainly from molecular gas in the

GMCs. Robust knowledge of the molecular hydrogen (H2) gas distribution is necessary to understand star formation in galaxies. Since H2 is not readily observable in the cold interstellar medium (ISM), the molecular gas content has traditionally been inferred using indirect tracers like carbon-monoxide (CO), dust emission, gamma ray interactions, and star formation eﬃciency. Physical processes resulting in enhance- ment and reduction of these indirect tracers can result in misleading estimates of molecular gas masses. My dissertation work is based on devising a new temperature power law distribution model for H2, a direct tracer, to calculate the total molecular gas mass in galaxies. The model parameters are estimated using mid infrared (MIR)

H2 rotational line ﬂuxes obtained from IRS-Spitzer (Infrared Spectrograph- Spitzer) instrument and the model is extrapolated to a suitable lower temperature to recover the total molecular gas mass. The power law model is able to recover the dark molecular gas, undetected by CO, in galaxies at metallicity as low as one-tenth of our Milky

Way value. I have applied the power law model in U/LIRGs and shocks of Stephan’s

Quintet to understand molecular gas properties, where shocks play an important role in exciting H2. Comparing the molecular gas content derived through our power law iii model can be useful in studying the application of our model in mergers. The pa-

rameters derived by our model is useful in understanding variation in molecular gas

properties in shock regions of Stephan’s Quintet.

Low mass stars are formed in small isolated dense cores known as Bok globules. Multiple star formation events are seen in a Bok globule. In my thesis I also studied a Bok globule, B207, and determined the physical properties and future evolutionary stage of the cloud. My thesis spans studying ISM properties in galaxies from kpc to sub-pc scales. Using the power law model in the coming era of James Webb Space

Telescope (JWST) with the high sensitivity MIR Instrument (MIRI) spectrograph we will be able to understand the properties of molecular gas at low and high redshifts.

iv This work is dedicated to my determination to pursue astronomy from past 25 years Acknowledgments

There are number of people that deserve special thanks as they have played a spe-

cial role in successful completion of this thesis. Foremost, I would like to thank my

advisor, Dr. J. D. Smith for oﬀering me to join his group and continue in pursuing

my research on galaxy ISM. His knowledge, insight, patience, encouragement, and

desire to help have been valuable stimulation for my scientiﬁc development. I want to express my gratitude to Dr. Adolf Witt who has imparted the scientiﬁc wisdom and

amazed me with his scientiﬁc working style. I am very much thankful for their advise

on writing papers and my scientiﬁc afternoon talks with Dr. Witt on astronomy to

politics to philosophy will long be cherished. I want to express my thanks to Dr.

Lee Armus, who has been an inexhaustible source of scientiﬁc and technical wisdom

and is a wonderful person to work with. I am thankful to him for all the support he provided during my IPAC Visiting Graduate Student Fellowship program at Caltech.

I am thankful to my other committee members Dr. Rupali Chandar and Dr. Sanjay

Khare for accepting to be in my Ph.D. committee.

I am grateful to to Dr. Rick Irving for all the help and took out time in resolving my computer issues. Finally, I would like to thank all graduate students at the Uni- versity of Toledo. Whether talking fundamental physics, helping with code, or editing my writing, their help was fundamental to both my work and especially tolerating my insanity throughout.

vi I have always cherished the company of my friends Amogh, Hemant, Nikhil, Prab- hakar, Rajesh, Santosh Kumar, Shaiju, Sushilkumar, Venkatesh, Vidhi Mishra, Vish- wanath, and an endless list of people who always heard and supported me during times of distress. Finally, I would like to thank my family members for their constant support and motivation throughout my academic journey.

Thank you all for having been with me in this wonderful journey.

vii Contents

Abstract iii

Acknowledgments vi

Contents viii

List of Tables xiii

List of Figures xv

List of Abbreviations xviii

1 The Interstellar Medium (ISM) 1

1.1 Introduction...... 1

1.2 ConstituentsoftheISM ...... 2

1.2.1 TheISMGas ...... 3 1.3 EvolutionofISMdust ...... 6

1.3.1 Dust composition and size distribution ...... 6

1.3.2 DustprocessingintheISM ...... 8

1.4 Thecosmiclifecycle ...... 9

1.5 ISMmoleculargas ...... 11

1.5.1 Importance of H2 ...... 11 1.5.2 Detection techniques of molecular gas ...... 11

1.5.3 DarkMolecularGas ...... 13

viii 1.6 Thesisoutline ...... 15

2 Lighting the dark molecular gas: H2 as a direct tracer 17 2.1 Introduction...... 17

2.2 Sample...... 20

2.2.1 MIR H2 rotationallineﬂuxes ...... 21 2.2.2 Cold molecular gas mass from CO line intensities ...... 21

2.3 Model ...... 23

2.4 Method&Calibration ...... 28

2.4.1 Warm H2 ...... 28

2.4.1.1 Upper temperature, Tu ...... 29 2.4.1.2 Powerlawindex,n ...... 29

2.4.2 Total H2 ...... 31

2.4.2.1 Model Sensitivity Temperature, Ts ...... 32

2.4.2.2 Model extrapolated lower temperature, Tℓ ...... 38 2.4.2.3 Mass distribution function ...... 40

2.5 Results, Discussions, & Applications ...... 41

2.5.1 What are the typical molecular gas temperatures in galaxies? 41

2.5.2 Estimating total MH2 ...... 43 2.5.3 Model derived molecular gas mass in ULIRGs, LIRGs and radio

galaxies ...... 45

2.5.4 Eﬀect of dust temperature on the warm H2 fraction ...... 47 2.5.5 Molecular gas in low metallicity galaxies ...... 51

2.5.5.1 Metallicity estimation ...... 52

2.5.5.2 Cold molecular gas from CO line emission ...... 52

2.5.5.3 Molecular gas from dust emission ...... 53

2.5.5.4 Molecular gas mass using our model ...... 53

ix 2.5.6 Futureprospects ...... 57

2.6 Summary ...... 57

3 Molecular gas properties in ISM of U/LIRGs of GOALS 75

3.1 Introduction...... 75

3.2 Sample...... 77

3.2.0.1 AncillarydataCO(J=1–0)...... 77

3.2.1 DatareductionandSpectralﬁtting ...... 78 3.3 Analysis ...... 78

3.3.1 Disktemplate...... 80

3.3.2 Scaling and adding the template spectrum ...... 80

3.3.3 PAHFIT- to recover H2 lineﬂux...... 82

3.3.4 H2 gasmassfrompowerlawmodel ...... 82 3.4 Results...... 84 3.4.1 LIRG’sdisktemplate...... 84

3.4.2 Powerlawindex...... 85

3.4.3 H2 mass- extrapolating power law model to 49 K ...... 86 3.5 Discussions ...... 87

3.5.1 Low power law index in U/LIRGs ...... 87

3.5.2 Relation between LIR, PAHs and power law index ...... 88

3.5.3 Low αCO orhightemperature ...... 92

3.5.4 Tℓ fromgas-to-dustmassratioGDR ...... 92

3.5.5 Variation in the L850 ...... 95 MISM 3.5.6 Caveats ...... 97

3.6 Summary&Conclusions ...... 98

4 Molecular gas properties in shocks of Stephan’s Quintet 106

4.1 Introduction...... 106

x 4.2 H2 inshocksofStephan’sQuintet ...... 108 4.3 Observations, Data reduction and Analysis ...... 109

4.3.1 MIR H2 emissionandspectra ...... 110 4.4 ExcitationdiagramFits ...... 111

4.4.1 Discretetemperatureﬁt ...... 111 4.4.2 Powerlawmodelﬁt...... 129

4.5 Result ...... 130

4.5.1 Twotemperatureﬁts ...... 130

4.5.2 H2 lineratios ...... 132 4.5.3 Powerlawindex...... 133

4.5.4 Total and Warm H2 gasmass ...... 137

4.5.4.1 Total H2 gasmass ...... 137

4.5.4.2 Warm H2 fraction ...... 140 4.6 Summary ...... 141

5 Physical properties of the cometary globule: the case of B207 143

5.1 Introduction...... 143

5.2 Observations&ArchivalData ...... 144

5.2.1 Discovery Channel Telescope (DCT) observations ...... 145

5.2.2 Archival WISE and Herschel data ...... 147

5.3 Analysis ...... 147 5.3.1 Surfacebrightnessproﬁles ...... 148

5.3.2 Dustcharacteristics...... 152

5.3.2.1 Scattered light intensities ...... 152

5.3.2.2 Coreshine eﬀect in NIR band ...... 155

5.3.3 Temperature Analysis using SED ﬁtting ...... 157

5.3.4 MassDistribution...... 160

xi 5.3.4.1 Starcounttechnique ...... 160

5.3.4.2 Reddening of background stars ...... 162

5.3.4.3 Farinfrared(FIR)emission ...... 163

5.3.5 Temperature and density-Abel Inversion method ...... 164

5.3.6 Coreenergetics ...... 169 5.4 Discussion ...... 173

5.4.1 Surfacebrightnessincoreandrim...... 173

5.4.2 Graingrowthandagedetermination ...... 173

5.4.3 Corephysicalproperties ...... 174

5.4.4 Corecollapse ...... 175

5.5 Conclusions ...... 176

6 Summary and Future Work 178

6.1 Whatdidwelearn?...... 178

6.1.1 H2 powerlawmodel ...... 178 6.1.2 Molecular gas properties in GOALS galaxies ...... 179

6.1.3 Stephan’sQuintetwork ...... 180

6.1.4 StudyofBokglobule,B207 ...... 181

6.2 Futurework ...... 181

6.2.1 Studyofmoleculargasathighz...... 181

6.2.2 StudyonBokglobules ...... 183

References 188

xii List of Tables

1.1 Description of the phase components of the ISMa...... 5

2.1 Observed properties of our sample galaxies ...... 60

2.1 Observed properties of our sample galaxies ...... 61

2.1 Observed properties of our sample galaxies ...... 62

2.2 Observed molecular hydrogen rotational line ﬂux ...... 63 2.2 Observed molecular hydrogen rotational line ﬂux ...... 64

2.2 Observed molecular hydrogen rotational line ﬂux ...... 65

2.2 Observed molecular hydrogen rotational line ﬂux ...... 66

2.2 Observed molecular hydrogen rotational line ﬂux ...... 68

2.3 Observed molecular hydrogen lines ...... 69

2.4 Model derived parameters for SINGS galaxies ...... 70 2.4 Model derived parameters for SINGS galaxies ...... 71

2.5 Model derived parameters for radio, U/LIRGs galaxies ...... 72

2.5 Model derived parameters for radio, U/LIRGs galaxies ...... 73

2.6 Observed molecular hydrogen line ﬂuxes and mass in low metallicity dwarfs 74

3.1 H2 lineﬂuxesforGOALS ...... 100

3.1 H2 lineﬂuxesforGOALS ...... 101

3.1 H2 lineﬂuxesforGOALS ...... 103 3.2 H2lineﬂuxesforGOALS ...... 104

3.2 H2lineﬂuxesforGOALS ...... 105

xiii 4.1 MIR H2 lineﬂuxforQuintet ...... 115

4.1 MIR H2 lineﬂuxforQuintet ...... 116

4.1 MIR H2 lineﬂuxforQuintet ...... 117

4.1 MIR H2 lineﬂuxforQuintet ...... 118

4.1 MIR H2 lineﬂuxforQuintet ...... 119

4.1 MIR H2 lineﬂuxforQuintet ...... 120

4.1 MIR H2 lineﬂuxforQuintet ...... 121 4.2 Power law model results for Quintet ...... 122

4.2 Power law model results for Quintet ...... 123

4.2 Power law model results for Quintet ...... 124

4.2 Power law model results for Quintet ...... 125 4.2 Power law model results for Quintet ...... 126

4.2 Power law model results for Quintet ...... 127

4.2 Power law model results for Quintet ...... 128

4.2 Power law model results for Quintet ...... 129

5.1 Photometric calibration for 1 count/s/pixel ...... 150

5.2 DustCharacteristics ...... 154 5.3 Intensity in MJy/sr at FIR and sub-mm wavelengths ...... 158

5.4 B207core/rimtemperature ...... 166

xiv List of Figures

1-1 ISMphase...... 5

1-2 Thecosmiclifecycle...... 10

1-3 H2 energylevels...... 12

1-4 Eﬀect of metallicity on CO and H2 cloud...... 14

2-1 Power law model ﬁt for the H2 excitationdiagrams ...... 30 2-2 Histogram for the power law index, n ...... 31

2 2-3 ∆χ value in the model parameter space Tℓ andn...... 33 2-4 χ2 distribution for NGC 5033 (blue) and NGC 3627 (red) ...... 35

2-5 Histogram for the sensitivity temperature, Ts ...... 36 2-6 Average ∆χ2 contoursforSINGSsample ...... 37

2-7 Histogram for the lower cut oﬀ temperature, Tℓ ...... 39 2-8 Cold and warm molecular gas mass distribution in NGC 5033 ...... 40

2-9 Model and CO derived molecular gas mass corelation ...... 44

2-10 Histogram for the lower cut oﬀ temperature (ULIRGs and 3C galaxies), Tℓ 48 2-11 WarmgasmassinrelationtoFIRdustcolor ...... 50

2-12 Model ﬁt for the H2 excitation diagram for a low metallicity dwarf, Haro 11 54 2-13 Model predicted molecular gas mass in relation to metallicity ...... 56

3-1 IRS-Spitzer andCObeamsizediﬀerences ...... 79

3-2 LIRG’sdisktemplate...... 81

3-3 PowerlawmodelﬁttoaGOALSgalaxy ...... 83

xv 3-4 Power law indices for GOALS sample ...... 85

3-5 Molecular gas estimation from power law model in GOALS galaxies . . . 87

3-6 Power law indices for GOALS galaxies ...... 89

3-7 Relation of power law index with 6.2 mPAH...... 91

3-8 Power law model derived H2 mass comparison with the dust emission method 94

3-9 Power law model derived H2 mass comparison with the L850 ...... 96

4-1 Stephan’sQuintet...... 107

4-2 Spectralextractiongrid-SQ ...... 112

4-3 Discrete two temperature ﬁt for the H2 excitationdiagram ...... 113

4-4 Power law model ﬁt for the H2 excitationdiagram ...... 131 4-5 TwotemperatureﬁtsinshocksofSQ ...... 132

4-6 H2 lineratiosinshocksofSQ ...... 134

4-7 H2 ratiocontoursinshocksofSQ ...... 135 4-8 Variation of power law index in shocks of SQ ...... 136

4-9 χ2 variationindiﬀerentregionsofSQ...... 139

4-10 WarmgasmassfractionsinshocksofSQ ...... 142

5-1 A 3-colour stacked image of B207 consisting of V, R, and I bands . . . . 146 5-2 East-West horizontal cut across B207 for SB proﬁle ...... 149

5-3 Optical surface brightness proﬁle for B207 ...... 151

5-4 3.4micronimageofB207 ...... 156

5-5 SEDﬁtforcoreandrimofB207 ...... 159

5-6 GascolumndensityproﬁleforB207...... 162

5-7 TemperatureanddensityproﬁleforB207...... 167 5-8 EnergyratioproﬁlesforB207 ...... 172

6-1 SensitivityofJWST-MIRI ...... 183

6-2 Spectroscopic sensitivities of diﬀerent instruments ...... 184

xvi 6-3 Histogram of the globule’s projected dense core-star distance ...... 186

xvii List of Abbreviations

AGB ...... Asymptotic Giant Branch AGN ...... Active Galactic Nucleus CNM ...... Cold Neutral medium DGR ...... Dust to Gas Ratio FIR ...... Far InfraRed FWHM ...... Full Width at Half Maximum GDR ...... Gas to Dust ratio GMC ...... Giant Molecular Cloud GOALS ...... Great Observatories All Sky LIRGs Survey HIM ...... Hot Ionized medium HST ...... Hubble Space Telescope IR ...... InfraRed IGM ...... InterGalactic Medium ISM ...... InterStellar Medium ISRF ...... InterStellar Radiation Field JWST ...... James Webb Space Telescope LIRGs ...... Luminous Infrared Galaxies MIRI ...... Mid-Infrared Instrument NED ...... NASA/IPAC Extragalactic Database NIR ...... Near InfraRed OPR ...... Ortho-to-para ratio PAHs ...... Polycyclic Aromatic Hydrocarbons SED ...... Spectral Energy Distribution SFH ...... Star Formation History SFR ...... Star Formation Rate S/N ...... Signal to Noise ratio SN ...... Supernova SQ ...... Stephan’s Quintet ULIRGs ...... Ultra Luminous InfraRed Galaxies UV ...... Ultraviolet WIM ...... Warm Ionized medium WNM ...... Warm Neutral medium

xviii Chapter 1

The Interstellar Medium (ISM)

1.1 Introduction

The subject of this thesis is the most interesting component of galaxies, i.e. the

Interstellar Medium (ISM), which constitutes gas and dust. The ISM is an important constituent of galaxies, for it is the ISM that is responsible for forming stars, the building blocks of a galaxy. At the initial stage of galaxy evolution the baryonic mass in galaxies was primarily in the ISM gas and as galaxies evolve, the ISM is gradually converted to stars (Stahler & Palla, 2005). The ﬁrst generation of stars were primarily composed of basic elements, hydrogen

(H) and helium (He). As stars evolve, H and He are fused to form heavy elements like C, N, and O and very massive stars may also form Fe. After the violent death of stars these elements are ejected back in the ISM thus enriching the ISM with heavy elements. The presence of heavy elements in Sun and Earth, implies that our solar system is a descendant of the earlier generation of stars. The Ca in our teeth, Fe in our blood, O which we breath were all synthesized in star cores and hence, it is apt to say we are children of stars. Stars and ISM are well connected system, it is from the ISM gas stars are born, and as a debt to repay these stars after dying enrich the

ISM back with more heavy and complex elements.

1 In the process of a galaxy’s evolution the gas may be ejected from the galaxy in

the form of galactic winds or stripped by some major/minor merging process or can

also cause infall of hot/cold gas in the disks (Veilleux et al. 2005). At present epoch

about 10% of the baryons is in the ISM of our galaxy - Milky Way.

H2 lacks dipole moment but with the advent of Infrared Space Observatory and

Spitzer telescope astronomers were able to measure quadrupole emission of H2 in nearby and high redshift galaxies. It has been long assumed in the astronomy com- munity that the MIR H2 emission is only able to trace the warm component of molecular gas and hence, cannot be used to trace the total molecular gas content. My thesis is aimed at using the MIR H2 rotational lines as a direct tracer to detect total molecular gas in galaxies. Since our method employ direct usage of H2 molecules, it is independent of other indirect tracers like CO, dust etc, which rely on intrinsic assumptions of constant αCO, DGR and τdep, respectively. We are able to estimate molecular gas mass even in low metallicity galaxies, as low as 10% of the Milky Way, where CO fails to detect the total molecular gas mass.

1.2 Constituents of the ISM

The ISM governs the evolution of a galaxy and hence, can be determined by studying physical properties of the ISM. The constituents of the ISM are: Interstellar gas: Atoms, molecules, ions can be in the gas phase forming neutral, molecular and ionized gas, respectively. The gas is the major component of the ISM.

Interstellar dust: Small solid particles majority in the size range 0.01–0.2 m is mixed homogeneously with the ISM gas however, in cold dense molecular cloud’s core regions the dust grains can coagulate and can grow to micron size particles.

Cosmic rays: Charged particles with energies as high as 1021 eV have been detected and form the cosmic rays component of ISM.

2 Electromagnetic radiation: Stars in galaxies are major sources of electromagnetic

radiation however cosmic microwave background photons from the relics of big bang

is almost distributed homogeneously in the space. It is the radiation from AGN,

young and old stars that heat the ISM gas and dust.

Interstellar magnetic field: The electric currents in the ISM is the source of ISM magnetic field. The magnetic field guides the charged particles, cosmic rays, compo-

nent of the ISM. The magnetic ﬁeld can play a pivotal role in cloud dynamics and

hence, evolution of galaxies.

The gravitational ﬁeld: The ISM matter, stars, dust, stellar remnants, dark mat-

ter, all produce a gravitational ﬁeld.

The dark matter particles: The dark matter particles dominate the mass in galaxies, when compared to the visible baryonic mass. These particles may interact non

gravitationally with baryons, magnetic ﬁeld and other components of ISM.

1.2.1 The ISM Gas

The ISM gas can be in the molecular, atomic, or ionized form.

Molecular gas: The molecular gas in our galaxy- Milky Way is localized in GMCs.

The molecular gas phase has a small ﬁlling factor but accounts for a substantial fraction of the Galactic ISM mass. Molecular clouds can be gravitationally or pressure

bound. On average the mass and size of a GMC is 4 105 M and 40 pc, respectively. × ⊙ The dense regions of GMCs are called cores, which have densities greater than 104

cm−3 and size of the order of 1 pc. Stars are formed in the gravitationally bound

cores of GMC.

Cold and Warm Neutral Medium (CNM and WNM) The neutral atomic gas can be traced by the 21 cm spin transition line of atomic hydrogen. This neutral

atomic medium can be classiﬁed in two categories according to the temperature, cold

neutral medium (CNM) and warm neutral medium (WNM). The cold and warm

3 neutral mediums are about 100 K and 8000 K, respectively. The CNM occupies 1–

4% of the total volume and with an average density of 50 cm−3. The WNM is with

a much lower density about 0.5 cm−3 but occupies a total of 30–60% of the volume.

Warm Ionized Medium (WIM) As the name suggests the gas in this medium is warm and ionized and so are at high temperatures. This phase is most clearly associated with H II regions, where the gas is ionized by the photons from young and hot stars and emits in the Hα recombination line. The density, temperature and

the ﬁlling phase of this phase is about 0.1 cm−3, 8000 K and 0.25, respectively.The

ionization source in the mid-plane disk of galaxies is young hot stars however, at high

galactic latitudes shock heating or suprathermal particles are responsible.

Hot Ionized Medium (HIM) This phase of the ISM is hot about 106 K and density of 10−3 cm−3. The HIM occupies a large fraction of the volume of the halo but with a

small mass fraction of the ISM. The HIM is heated by strong shocks driven by violent

stellar winds from early type stars and supernova explosions. The hot gas detected at

high latitudes can be due to the superbubbles, ﬂown out of the disk mid-plane of the

galaxies. The hot gas can be detected in absorption against bright background stars

in highly ionized species like C IV, S IV, N V, O III, O VI, etc or through continuum and line emission in the far UV and X-ray wavelength range.

Table 1.1 and Figure 1-1 lists and shows the description of diﬀerent phase compo-

nents of the ISM, respectively. In the Figure 1-1 ionized medium surrounds the cold

and warm neutral mediums, which further embeds the cold molecular cloud regions.

The dark dense core regions of molecular clouds becomes gravitationally unstable to

form stars.

4 Figure 1-1 The structure of ISM phase adopted from McKee and Ostriker (1977). The cold and warm neutral mediums are embedded in the ionized medium of the ISM. The molecular clouds is further embedded in the cold neutral atomic medium. Stars, the basic building blocks of galaxies are born in the cold core dense regions of molecular clouds.

Table 1.1. Description of the phase components of the ISMa

Phase Density Temperature Volume Mass Hydrogen −3 (cm ) (K) % (M⊙)

2 6 9 Molecular cloud 10 –10 10–100 1 10 H2 CNM 1–103 50–100 1–5 1.5×109 H I WNM 0.1–10 103–104 10–20 1.5×109 H I WIM 0.01 103–104 20–50 109 H II HIM 10−4–10−2 105–107 30–70 108 H II

aThis table is a very schematic classiﬁcation, and the separation between the ISM phases is debated. The numbers are orders of magnitudes bThe masses are rough estimates of our galaxy- Milky Way cThe last column lists the main state of the hydrogen atom in diﬀerent phases

5 1.3 Evolution of ISM dust

The universe is dusty, and dust grains constitute the dominant form of solid matter in the universe. Dust is observed in a wide variety of astrophysical environments, ranging from stellar envelopes around cool red giants to SN ejecta, in diﬀuse halo regions to cool dark dense core regions, from comets to interplanetary space to nearby and high redshift galaxies and quasars. Recent studies with ALMA have traced dust in galaxies at z = 7.5, occurring within only 500 Myr of the beginning of star formation in the universe (Watson et al. 2015).

Dust grains are the main source of continuum opacity within galaxies, longward of the Lyman limit of hydrogen, resulting in absorption and scattering of starlight at

UV/visible wavelengths and thermal emission in the IR and sub-mm range. Dust play an important role in heating the ISM through photoelectric eﬀect. The surface of dust grains acts as a catalyst in the formation of H2 molecules in the galaxy ISM. Dust particles, which contributes just about 1% of the ISM mass, play a crucial role in the galaxy evolution and hence can be termed as the spice in the curry of galaxy. “What is it about a casserole that makes it taste so wonderful? It’s not the potatoes, the meat, the vegetables- no it’s the spice. In the universe, dust is but a minor constituent, but it gives it all the ﬂavor. Dust truly is the spice of the universe——”- Adolf Witt (ca.

2010)

1.3.1 Dust composition and size distribution

The composition of dust is characterized by spectral features observed in the absorption and emission. The extinction, Aλ, ratio of the ﬂux I(λ) after crossing the dust cloud to the incident I0(λ) follows

I(λ)= I (λ)exp( τ ), (1.1) 0 − λ

6 where τλ = 0.921 Aλ is the optical depth. The extinction is obtained by comparing the reddened spectrum of stars to the intrinsic spectrum from a library of spectral models.

The extinction curve can be used to constrain size distribution of dust particles.

Mathis et al. (1977) demonstrated that the average ISM extinction could be produced containing graphite and silicate grains with a power law size distribution (called as

MRN distribution) with an index of -3.5

dn a−3.5da, (1.2) ∝ where dn is the number of grains between the size range a and a+da. The distribution is truncated between sizes in the range, 0.005-0.25 m. With this distribution the large dust grains are fewer in number but however dominate the mass fraction.

However, NIR scattering in the dark dense molecular cores (coreshine phenomenon) is observed, suggesting the presence of micron size dust grains possibly formed through coagulation process (Pagani et al. 2010).

ISM dust grain models have been improved in the past three decades to ﬁt the observational constraints. Elemental abundance of heavy elements, UV visible and

IR absorption and scattering properties, IR emission, polarization properties help to constrain the composition of ISM dust. The models include silicate and carbonaceous grains with variable size distributions to reproduce the observed ISM dust properties.

After the discovery of the 2175 A˚ bump immediate studies claimed small graphite particles to be responsible for this phenomena. Other forms of carbonaceous grains (PAHs, amorphous carbons, and organic mantles on silicate grains) are being considered. The absorption feature in the MIR spectra at 9.7 and 18 m is due to interstellar silicates due to Si-O stretching and O-Si-O bending modes, respectively.

7 1.3.2 Dust processing in the ISM

In the following section we summarize the mechanism causing structural changes, disrupt or even completely destroy dust grains. Apart from photo-processing all the processes are collisional processes, interactions with the ions, molecules, and other dust grain particles.

Sputtering: This process causes atoms to be removed from the surface of dust grains resulting in erosion and returns to the gas phase. The erosion is due to grain collisions with high velocity atoms and ions in energetic environments (Jones et al.

1994). The sputtering can be classiﬁed as either non-thermal and thermal, depending on the relative motion between grain-gas and thermal motion of the gas, respectively.

Thermal sputtering occurs at high temperatures above 105 K dominated by collisions with H, He atoms and ions. In grain collisions with hydrogen, inertial sputtering happens at velocities higher than 30-40 km/s and at lower velocities dominated by collisions with heavy particles. The velocities depends on the size of dust grains and hence the eﬀect of sputtering is size dependent.

Vaporization: Grain-grain collisions with impact velocities above 20 km/s result in partial or complete vaporization of dust grains, releasing the elements present in the dust to the gas phase. Accretion: The adsorption and sticking onto grain surfaces of atoms, ions, radicals and molecules increase the grain radius and the mass. For Mg, Si, and Fe, accretion can occur at temperatures as high as 1000 K, while temperatures below 100 K are required for species leading to formation of icy mantles. In dense cores we ﬁnd CO, an eﬀective molecular gas tracer, freezing onto the grains and hence there is a reduction of CO in the ISM gas phase. Shattering: This occurs in grain-grain collisions with velocities of few km/s and cause fragmentation of dust grains resulting in redistribution of mass towards smaller

8 grains.

Coagulation: Grains colliding with each other below a critical value cause con- glomeration with a redistribution of mass towards larger grains. The critical velocity depends on the grain composition and radius, varying from 1m/s for micron sized ∼ grains to 1 km/s for 100 A˚ sized grains, and is enhanced by the icy mantles, which cause increase in the surface area and interaction time during the collision.

1.4 The cosmic life cycle

Stars are formed in the dark cold dense gravitationally unstable core regions of molecular cloud. When the temperature and density are suﬃciently high to fuse hydrogen to helium nucleus, a new star is born. Nuclear reactions form elements upto C, O, and N. The radiation pressure supports the gravitational collapse and make them stable during the long (107 - 1010 yr) lifespan of the star. After leaving the main sequence phase the star enters the AGB phase, when the outer layers are loosely bound to the core and the thermal instabilities bring the heavy elements like

C and O to be mixed and bought to the stellar surface. In the end the outer envelope is stripped away enriching the ISM with heavy elements and the core further cools down to white dwarf. However for a heavy mass star (M 8M ) they are able ⋆ ≥ ⊙ to fuse C and O into heavy elements till Fe and the core ﬁnally collapse and later reduced to a neutron star, pulsar, or a black hole.

Ionizing photons from hot stars, O and B type, create H II regions and ionize the surrounding medium and even after their death including the low mass stars ionize ISM with heavy elements with simple to complex molecules, CO, PAHs, and other acetylenic chain derivatives. After injection into the ISM the stardust and molecules can cycle many times between the intercloud and cloud phases. UV rays in the diﬀuse and reactions with ions continuously break and form molecular bonds,

9 Figure 1-2 The cosmic lifecycle. Figure adapted from Jones (2004). allowing stable species to survive. The molecular clouds consisting of dust and other molecules may become gravitationally unstable and then collapse to form second generation of stars. These stars are enriched with heavy elements, when compared to the ﬁrst generation of stars. Protoplanetary disks may form around low mass stars and likely all interstellar grains are vaporized and recondensed as solar system condensates. The circle is complete and the cycle starts again. The cosmic life cycle is schematically summarized in the Figure 1-2.

10 1.5 ISM molecular gas

1.5.1 Importance of H2

Molecular gas is a primary fuel for star formation in galaxies. Stars are formed from gravitationally unstable cores within molecular clouds. To understand the star

formation rate it is important to know the molecular gas surface density. The molec-

ular gas density is proportional to the star formation rate density (Bigiel et al. 2008,

Kennicutt 1998). In the Milky Way galaxy the atomic and molecular gas mass are

comparable however, in local mergers, ULIRGs, the atomic and molecular gas is fun-

neled at the center and in the ISM of these galaxies the molecular gas mass can dominate over the atomic gas, subsequently increasing the star formation surface density

about an order or two magnitude higher than the normal star forming galaxies.

1.5.2 Detection techniques of molecular gas

H2 is a homonuclear molecule and hence, lacks a dipole moment. The lowest

energy transitions of H2 are its purely rotational quadrupole transitions in the mid infrared spectrum. The upper energy level of this transition, S(0), occurring at λ = 28.22 m is at an energy level of 510 K, much higher than the ISM temperature. Due

to these constraints, despite H2 is the most abundant molecule in the universe it is a poor emitter and so invisible. Figure 1-3 shows rotational energy levels of the ground

vibrational state of H2. The ISM molecular gas consists other molecules which can be used as an indirect

tracers to estimate molecular gas content. Helium being monoatomic, suﬀers from similar observability problems in cold clouds. Carbon Monoxide (CO) has a weak

permanent dipole moment (0.11 D = 0.11 10−18 esu cm) and the ground rotational × transition is at an energy level of 5.5 K, which makes CO to be easily excited in cold

11 Figure 1-3 The upper energy level of the lowest rotational line transition of H2 (S(0), occurring at 28.22 m) of the ground vibrational state (ν = 0) is at a temperature equivalent of 510 K, approximately an order of magnitude higher than the average ISM gas temperature. With such high energy levels and no dipole moment H2 is classically considered a poor emitter.

dense molecular clouds. At a wavelength of 2.6 mm, J = 1–0 transition, is in the

transparent atmospheric window. Hence, CO is widely used as a tracer to detect

molecular gas in galaxies.

Solomon et al. (1987) and Scoville et al. (1987) measured velocity line width, size, virial mass, and CO luminosity for molecular clouds in the Milky Way and observed

a relationship between the cloud dynamical mass, measured by the virial theorem

with the CO luminosity. This led to the calibration of measuring molecular gas mass

using the CO luminosity measurements. To use CO as a tracer to detect molecular

gas in galaxies a conversion factor, αCO or XCO, is used to convert CO intensity into the column density of molecular gas using

N(H )= X W (CO,J =1 0), (1.3) 2 CO × −

−2 where the column density, N(H2), is in cm and the integrated line intensity, W(CO),

12 is in K km s−1. If used in mass units the equation is

Mmol = αCOLCO, (1.4)

−1 2 where Mmol is the molecular gas in solar masses and LCO is in K km s pc . Both

αCO or XCO are referred to as the “CO-H2 conversion factor”. The values of αCO, X are 4.35 M (K km s−1 pc2)−1 and 2 1020 cm−2 (K km s−1)−1, respectively. CO ⊙ ×

XCO accounts only the column density of H2 but when used αCO the correction for He and other heavy elements are considered by multiplying with a factor of 1.36.

1.5.3 Dark Molecular Gas

For almost half a century, CO is traditionally being used as the tracer to estimate molecular gas content in GMCs of Milky Way and in the ISM of extragalactic systems.

However, a substantial amount of H2 gas may lie outside the CO region, in the outer regions of the molecular cloud where the gas phase carbon can be in the form of C or

+ C . This H2 gas is termed as ”CO-dark” or ”CO-faint” gas and can be primarily due to self shielding phenomenon of H2 or shielding by dust from UV photodissociation.

6 For a standard cloud of 10 M⊙ with an incident radiation ﬁeld, G’0 = 10, the dark gas mass fraction is 0.28 and 0.31 for constant thermal pressures of 105 and 106 K

cm 3, respectively (Wolﬁre et al. 2003). Theoretical studies by Wolﬁre et al. (2003) −

indicates variation in dark gas fraction ranges from 0.25–0.33 for a range of G’0 = 3–30 and cloud mass 105–106 M . ⊙ Recent results by Herschel Space Observatory’s GOT-C+ project estimated again about 20–30% of dark gas mass fraction in the Milky Way (Pineda et al. 2013). C+

emission is majorly associated with spiral arms and traces the envelopes of clouds and

in the transition region between molecular and atomic gas. Most of the observed C+

is produced by dense PDRs, with smaller contributions from CO dark H2 gas, cold

13 Figure 1-4 Effect of metallicity on CO and H2 cloud in a uniform radiation field. Blue shading indicates the molecular gas region. Increas- ingly darker shading areas where the carbon is in C+, C, and CO. The upper sequence show the effect of decreasing metallicity and + DGR on the distribution of C , CO, and H2. The lower sequence shows the effect of changing clump size or column density at a fixed metallicity. Lower metallicity or low DGR reduces the CO emitting region and hence an increase in the conversion factor, αCO, is required (Figure from Bolatto et al. 2013)

atomic gas and ionized gas. The fraction of CO-dark H2 to total H2 increases with the Galactocentric distance, ranging from 20–80% from 4–10 kpc. Most of the C+ emission emerges from the dense PDRs with modest far-ultraviolet ﬁelds in the range

1–30. Above mentioned theoretical and observational studies indicates possibility to underestimate molecular gas content using CO as a tracer.

Dust and gas are homogeneously mixed in the galaxy ISM and DGR is almost constant in the galaxy ISM. Israel et al. (1997) using dust emission determined the molecular gas mass in low metallicity galaxies, where CO is unable to trace the dark molecular gas component. Assuming a constant DGR and estimating the dust and atomic gas mass from IR and 21 cm line observation, respectively, can be used in

14 determining molecular gas mass using the equation

M GDR = M(HI)+ M(H ) (1.5) dust × 2

Molecular gas is the fuel for the star formation in galaxies. Assuming a constant

molecular gas depletion time (τdep) to form stars and estimating the star formation rate (SFR) using observation tracers, Hα and IR continuum, the molecular gas content can be estimated using,

M = SF R τ (1.6) mol × dep

(Schruba et al. (2012)).

Estimating molecular gas content using dust or SFR assume a constant DGR

or τdep, respectively, and are subjected to their own internal biases. Recent studies have indicated at lower metallicities, 12+log[O/H] 8, the dependence of DGR is ≤ steeper, implying relatively less dust (more gas) at lower abundances (Remy-Ruyer et al. 2014). Physical processes in the galaxy ISM can alter these constants and the molecular gas mass estimated from these indirect tracers can be under/over estimated.

A model employing the direct tracer of molecular gas, H2, free from such internal bias is required for estimating molecular gas mass in galaxies, and

this holds the motivation for the thesis.

1.6 Thesis outline

The thesis outline is as follows

Chapter 2: I discuss here our method in using MIR H2 rotational lines to detect total molecular gas mass in galaxies and apply our model in low metallicity galaxies

to estimate the molecular gas content.

Chapter 3: In this chapter I apply our power law model, discussed in the previ-

15 ous chapter, in local mergers, ultra/luminous infrared galaxies (U/LIRGs) of GOALS

sample. The ISM in mergers of GOALS are subjected to excess shock excitations, high turbulence, increasing the dust and gas temperatures, when compared to normal

star forming galaxies. Using the power law model we study the ISM properties in

GOALS and compare the results with normal star forming galaxies.

Chapter 4: Stephan’s Quintet is a compact galaxy group undergoing violent collisions. Radio observations in the early 1970’s revealed a mysterious ﬁlament of emission in the IGM of these galaxies. The Spitzer telescope discovered powerful

MIR H2 rotational lines in the IGM of Stephan’s Quintet, powered by shocks. I use our method in detecting molecular gas content and in understanding the ISM physics of Stephan’s Quintet.

Chapter 5: Star formation in galaxies majorly occurs in GMCs, however there are small isolated dark nebulae containing dense dust and molecular gas, known as Bok globules, forming low mass stars. The cause of cometary structure of Bok globules is still a mystery and hence, a subject of intense research. Here, I studied the properties of an isolated small molecular cloud, B207, harboring a Class I protostar,

IRAS04016+2610, in the Taurus-Auriga molecular cloud region. Using optical to sub-mm observational data we study physical properties and the evolutionary fate of

B207.

Chapter 6: Here we state our future plans and how in the coming era of James Webb Space Telescope (JWST) and other major coming up and existing telescopes, with much better sensitive instruments, will revolutionize the study of ISM physics.

The Mid Infrared Instrument (MIRI) spectrograph, onboard JWST, with sensitivities

100 better than the previous IRS-Spitzer is capable of detecting H lines in high × 2 redshift galaxies. Using these ﬂuxes of H2 rotational lines in our power law model it will be possible to understand molecular ISM properties in galaxies across diﬀerent redshifts and hence, star formation history that shaped our universe.

16 Chapter 2

Lighting the dark molecular gas:

H2 as a direct tracer

2.1 Introduction

4 By a factor of more than 10 , H2 is the most abundant molecule in the universe, found in diverse environments ranging from planet atmospheres to quasars hosts

(Hanel et al. 1979, 1981, Walter et al. 2003, Genzel et al. 2014). It was the ﬁrst neutral molecule to form in the Universe and hence dominated the cooling of

pristine gas at early times (Lepp et al. 2002). Stars form principally from molecular

clouds, and most physical prescriptions for stellar formation rate (SFR) are therefore

directly linked to the surface density of H2 gas (Kennicutt 1998, Bigiel et al. 2008). To understand the star formation processes and how it varies and has evolved over

the star-forming history of the Universe, it is necessary to accurately measure the

mass and distribution of H2.

Despite its high abundance, H2 can be diﬃcult to study directly. It possess no permanent dipole moment, which makes it a weak rotational emitter. In addition,

the upper energy level for the lowest permitted rotational (quadrupole) transition is

E/k = 510 K above ground (Dabrowski 1984; van Dishoeck & Black 1986). Hence,

17 the H2 gas that comprises the bulk of the molecular interstellar medium (ISM) is commonly believed to be too cold to be visible. And yet, despite these observational disadvantages, the advent of the Infrared Space Observatory (ISO) and in particular

Spitzer’s Infrared Spectrograph (IRS, Houck et al. 2004) revealed pure rotational

H2 emission from a rich variety of extragalactic sources, including normal star forming galaxies (Roussel et al. 2007), ultraluminous and luminous infrared galaxies

(U/LIRGs Lutz et al. 2003, Pereira-Santaella 2010; Veilleux et al. 2009; Stierwalt et al. 2014), galaxy mergers (Appleton et al. 2006), radio-loud AGN (Ocana Flaquer et al. 2010), UV-selected galaxies (O’Dowd et al. 2009), quasar hosts (Evans et al.

2001), cooling-ﬂow cluster systems (Egami et al. 2006), sources with extreme shock- dominated energetics (Ogle et al. 2010), and even star-forming sources at redshifts

& 3 (Walter et al. 2003; Solomon $ Vanden Bout 2005).

In the absence of direct measurements of H2, the lower rotational line transitions of CO (the next most abundant molecule) are generally used as a molecular gas

12 tracer. To convert the measured integrated intensities of CO to H2 column density a conversion factor, αCO, is needed, typically calibrated against virial mass estimates in presumed self-gravitating clouds (Solomon et al. 1987; Scoville et al. 1987; Strong

& Mattox 1996; Abdo et al. 2010). However recent evidence indicates that the value of αCO varies substantially, both within galaxies and at diﬀerent epochs (Genzel et al. 2012; Sandstrom et al. 2013). In molecular clouds in our Galaxy, the observed γ-ray ﬂux arising from the cosmic ray interactions with H2 can be used to recover H2 gas mass accurately (Bhat et al. 1985; Bloeman et al. 1984,1986), but this method requires information on the cosmic ray distribution not available in other galaxies. Another method to assess H2 content is to use dust as a tracer, with a presumed or recovered dust-to-gas (DGR) ratio (e.g. Sandstrom et al. 2013; Remy Ruyer et al. 2014). Among other biases, both the CO and dust-based methods lose reliability at low metallicity. Due to

18 declining dust opacity and less eﬀective self-shielding than H2, the CO abundance drops rapidly with decreasing metallicity (Wolﬁre et al. 2010; Bolatto et al. 2013).

Variations in the radiation ﬁeld can also lead to selective CO destruction (Hudson

1971; Bolatto et al. 2013). At the lowest metallicities, DGR itself begins to scale non-linearly with the metal content of the gas (Herrera-Camus et al. 2012; Fisher et al. 2014; Remy-Ruyer et al. 2014). Another method of inferring molecular gas content is to couple measured star formation rates with an assumed constant H2 depletion timescale (τdep), equivalent to a constant star formation eﬃciency (SFE) in galaxies (Schruba et al. 2012). None of these methods provide direct tracers of the

H2 reservoirs, and the relevant indirect tracers all rely on physical assumptions (e.g. constant or measurable values of αCO, DGR, or τdep) which are unlikely to be valid in all environments.

Here we challenge the long-stated assumption that H2 rotational emission is a poor tracer of the total molecular content in galaxies. Our understanding of the structure of the molecular material in galaxies is undergoing signiﬁcant revision. While CO traces the coldest component of the molecular ISM, half or more (and sometimes much more) of the molecular gas in galaxies is in a warmer, CO-dark state, where H2 persists (Field et al. 1966; Tielens 2005; Draine 2011; Wolﬁre et al. 2010; Pineda et al. 2013; Velusamy & Langer 2014). What this means is that the common wisdom that all molecular gas is found at temperatures T = 10 20 K is incorrect. With − molecular material existing in quantity at excitation temperatures 50 - 100K, it becomes possible to use the rotational emission spectrum of the Universe’s dominant molecule to directly assess a substantial portion of the total molecular content in galaxies.

We introduce here a simple continuous temperature model which enables direct use of the H2 rotational emission from galaxies to recover their total molecular gas content. While several assumptions are required to make such a model possible, the

19 resulting biases are expected to be completely distinct from those of the indirect gas

tracers. The paper is laid out as follows. We describe the archival sample in 2. A § rotational temperature distribution model is presented in 3, and in 4 we describe § § the method and its calibration procedure. Section 5 presents results, discussions,

applications and future prospects of our model. We summarize our conclusions in 6. §

2.2 Sample

We have selected a large sample of galaxies spanning a wide range of diﬀerent

physical properties with reliable H2 rotational emission detections. Our sample includes 14 Low Ionization Nuclear Emission Regions (LINERs), 18 galaxies with nuclei

Ultra Luminous Infrared galaxies (ULIRGs), 9 Luminous Infrared galaxies (LIRGs),

and 1 Quasi Stellar Object (QSO) host galaxy. The galaxies were chosen to have

at least three well-detected H2 pure-rotational lines with Spitzer/IRS (Houck et al. 2004), including either S(0) or S(1), occurring at 28.22 and 17.04 m, respectively.

We also required an available measurements of CO line emission (either J = 1–0 or

2–1) for an alternative estimate of the total molecular gas mass. See Table 2.1 for a

complete sample list with relevant physical parameters and the references from which

each galaxy was drawn.

The ﬂux ratios S70 are calculated using 70 and 160m intensities obtained from the S160 Herschel-PACS instrument (Poglitsch et al. 2010). We convolved PACS 70 m maps to the lower resolution of PACS 160 m to calculate ﬂux ratios for mapped regions,

for which we have the H line ﬂux. For ULIRGs and other unresolved galaxies, S70 2 S160 represents the global ﬂux ratio. The PACS70/PACS160 ratios are listed in Table 2.1

for each galaxy.

20 2.2.1 MIR H2 rotational line ﬂuxes

All MIR H2 rotational line ﬂuxes were obtained from Spitzer-IRS observations at low (R 60 – 120) and high (R 600) resolution between 5 – 38 m. The Spitzer ∼ ∼ Infrared Nearby Galaxies Survey (SINGS, Kennicutt et al. 2003) is a diverse sample of nearby galaxies spanning a wide range of properties. The SINGS sample consists of

LINERs, Seyferts, dwarfs, and galaxies dominated by star formation in their nuclei.

We adopted the H2 rotational line ﬂuxes for four lowest rotational lines (S(0) to S(3)) in SINGS galaxies from Roussel et al. 2007. The targets were observed in spectral

mapping mode and the details of the observing strategy is described in Kennicutt et

al. 2003 and Smith et al. 2004.

H2 rotational line ﬂuxes for 10 3C radio galaxies are from Ogle et al. 2010. This

sample includes from S(0) to S(7). For the radio galaxy 3C 236, the ﬂuxes of H2 rotational lines are obtained from Guillard et al. 2012.

The H2 rotational line ﬂuxes for QSO PG1440+356 were taken from the Spitzer Quasar and ULIRG Evolution Study (QUEST) sample of Veilleux et al. 2009, and

those for the 19 ULIRGs were obtained from Higdon et al. 2006. The ﬂuxes of H2 rotational lines for the NGC 6240 and other LIRGs in the sample are from Armus et

al. 2006 and Pereira-Santaella et al. 2010, respectively. H2 rotational lines are also observed in the molecular outﬂow region of NGC 1266 (Alatalo et al. 2011). Table

2.2 lists the ﬂux of MIR H2 rotational lines for all our selected galaxies.

2.2.2 Cold molecular gas mass from CO line intensities

To test and calibrate a model which measures total molecular mass from the ro-

tational lines of H2, an estimate of the “true” cold H2 gas mass in a subset of galaxies

is required. For this purpose, we utilize the cold H2 gas masses for the SINGS sample compiled by Roussel et al. 2007, which are derived from aperture-matched CO

21 velocity integrated intensities. The observed line intensities of the 2.6 mm 12CO(1–0) line within the measured CO beam size was chosen to match the aperture of the

Spitzer-IRS spectroscopic observations. Roussel et al. 2007 assumed a CO intensity

−1 2 −1 to molecular gas conversion factor (αCO) of 5.0 M⊙(K km s pc ) (equivalent to X =2.3 1020 cm−2(K km s−1)−1). They applied aperture corrections by project- CO × ing the IRS beam and CO beam on the 8 m Spitzer-IRAC map. The underlying assumption is that the spatial distribution of the PAH bands and CO(1–0) line emis- sions are similar at large spatial scales. PAH emission emerges from photo dissociation regions, the outer regions of molecular clouds, where UV photons are able to excite these molecules and hence the distribution are mostly co-related.

For the radio galaxies, molecular gas masses were compiled by Ogle et al. 2010, and the molecular gas mass was estimated from the CO ﬂux density corrected and scaled to the standard Galactic CO conversion factor. For the radio galaxy 3C 236 Oca˜na,

Flaquer et al. (2010) estimated an upper limit to the cold H2 gas mass. The cold

H2 gas masses for the LIRGs in our sample were obtained from Sanders et al. 1991. They used α = 6.5 M (K km s−1 pc2)−1 (equivalent to X =3.0 1020 cm−2(K CO ⊙ CO × km s−1)−1). We derived aperture corrections to the CO intensities by projecting IRS and CO beam on the 8 m IRAC map, since the CO beam size (55 arcsec aperture) is much larger than the IRS mapped region (13.4 13.4arcsec2). Required aperture × corrections are typically less than a factor of 2. For the LIRGs NGC 7591, NGC

7130, and NGC 3256, the value of molecular gas mass was obtained from Lavezzi & Dickey (1998); Curran et al. (2000); Sakamoto et al. (2006), respectively. The global molecular gas masses for ULIRGs are from Rigopoulou et al. (1996); Sanders et al.

(1991); Mirabel et al. (1989); Evans et al. (2002). For the quasar QSO PG1440+356,

Evans et al. (2001) derived the molecular gas mass.

Diﬀerent studies have utilized substantially diﬀerent αCO values to calculate molecular gas masses. In the Milky Way disk, a modern value of α =4.35 1.3M (K CO,Gal ± ⊙ 22 km s−1 pc2)−1 (equivalent to X =2.0 1020 cm−2(K km s−1)−1) has been found to CO × be consistent with a wide variety of constraints (Bolatto et al. 2013). In this work,

we scale all molecular gas mass estimates to correspond to αCO = αCO,Gal. Since we

require only the H2 gas masses in our analysis, the resulting molecular mass values were further reduced by a factor of 1.36 to remove the mass contribution of Helium

and other heavy elements. Recent dust-based studies of a subset of the SINGS sample

have revealed variations in αCO both between and within these galaxies Sandstrom et al. (2013).

Table 2.2 lists the CO-based H2 gas mass estimated for each galaxy in the sam-

ple, aperture matched to the region of Spitzer/IRS coverage, along with H2 masses calculated using the conversion factor for central regions derived by Sandstrom et al.

(2013) in parentheses, where available.

2.3 Model

The primary methods of measuring H2 mass all rely on a set of assumptions — that the αCO factor is known and constant, that the dust-to-gas ratio is fixed or tied directly to metallicity, or that the star formation depletion time is unchanged from environment to environment. All of these methods also rely on: the CO molecule, which is 10,000 less abundant than H , dust grains, with their complex formation × 2 and destruction histories and varying illumination conditions, or newly formed stars, which are presumed to be associated with molecular material with a consistent conversion efficiency. All of these methods suffer biases based on the physical assumptions made. We propose a direct means of assessing total molecular gas mass using the MIR quadrapole rotational line emission of H2. Interstellar or direct ultraviolet radiation

ﬁelds, shocks, and other mechanical heating processes are all potential sources of H2

23 excitation. The method we propose requires only the assumption that H2 rotational temperatures are, when averaged over the diversity of emitting environments and processes in galaxies, widely distributed, and smoothly varying. This is directly analogous to modeling the radiation ﬁeld intensity which heats dust grain populations in galaxies with a smooth distribution (e.g. Draine et al. 2007; Galliano et al. 2003).

We model the H2 temperature distribution as a smooth, truncated power law with

ﬁxed cut-oﬀ temperatures. Indeed, the H2 molecule is radiatively cooled by a cooling function which can be well approximated as a power law with slope 3.8 (Hollenbach

& McKee 1979; Draine et al. 1993). A similar analysis by Burton (1987) derived a cooling function with a power law index, n = 4.66, for H2 molecules in the temperature range 10–2000 K.

The temperature equivalents of H2 rotational levels are high, starting at T = 510 K (see Table 2.3). The Boltzmann distribution of energy levels, however, leads to substantial excitation even at more modest peak temperatures. The lowest upper energy levels at J = 2–4 are well populated at excitation temperatures of 50 to 150

K, whereas the higher-J levels are excited by temperatures from a few hundred to several hundred K. Typically, a small number of discrete temperature components are ﬁtted to low-J rotational line ﬂuxes, recovering warm H2 temperatures in this range (Spitzer et al. 1973; Spitzer & Cochran 1973; Spitzer et al. 1974; Spitzer $

Zweibel 1974; Savage et al. 1977; Valentijn & van der Werf 1999; Rachford et al.

2002; Browning et al. 2003; Snow & McCall 2006; Ingalls et al. 2011).

Other studies have also adopted continuous temperature distributions for H2. Za- kamska et al. (2010) in her study of H2 emission in ULIRGs used a power law model dM T −ndT to calculate the expected H rotational line ratios, where dM is the ∝ 2 mass of H2 gas with excitation temperatures between T and T + dT . In her sample, power law indices 2.5

24 in H2 to model H2 rotational emission in six local infrared bright Seyfert galaxies, with power law indexes ranging from 4–5. In the shocked environment of supernova

remnant IC 443, Neufeld et al. (2008) found a power law temperature distribution for

H2 column density with power law index varying over the range 3–6 with an average value of 4.5.

The present practice for measuring warm (T & 150K) H2 gas mass is to use

two or three distinct temperature components to model the H2 rotational line ﬂuxes.

Yet even on the scales of individual molecular clouds, H2 is present at a wide range of temperatures, calling into question whether discrete temperature components are

physical. When used purely for assessing warm gas mass (T & 100K), the power law method provides a more robust, unique and reproducible measure than discrete temperature ﬁts, which are sensitive to the arbitrary choice of starting line pair. A

continuous distribution also makes possible extrapolation to a suitable lower temper-

ature to recover the total cold molecular gas mass (see 2.4). §

We ﬁt the ﬂux of H2 rotational lines using a continuous power law temperature distribution by assuming

dN = mT −ndT, (2.1)

where dN is the column density of H2 gas between excitation temperature T and T + dT , n is the power law index, and m is a constant. Integrating this distribution to recover the total column density, the scaling co-eﬃcient m is found to be

N (n 1) m = tot − , (2.2) T 1−n T 1−n ℓ − u

where Tℓ and Tu are the lower and upper temperatures of the distribution, respectively,

and Nobs is the column density of H2 in the observed line of sight and temperature is presumed equal to the rotational temperature. For a continuous distribution of molecules with respect to temperature, the column density of molecules at upper

25 energy level j responsible for the transition line S(j) is

Tu −E gj j −n Nj = e kT mT dT, (2.3) ZTℓ Z(T ) ×

where gj is the degeneracy value for the corresponding energy level Ej. The degeneracy value for even and odd values of j corresponding to para and ortho H2 is

gj =2j +1, (2.4) and

gj = 3(2j + 1), (2.5) respectively. The factor of 3 for odd values of j is for ortho-hydrogen, which have parallel proton and electron spins, forming a triplet state. Z(T ) is the partition function at temperature T . The model assumes local thermodynamic equilibrium

(LTE) between ortho and para H2 and the abundance ratio of ortho to para H2 at any temperature, T , in LTE is given by Burton et al. (1992). The partition functions for para and ortho H2 are

∞ −Ej Z(T )= Zp(T )= (2j + 1)e kT (2.6) j=Xeven

and ∞ −Ej Z(T )= Zo(T )= 3(2j + 1)e kT , (2.7) jX=odd respectively.

Table 2.3 list the wavelength of each H2 rotational line transition, the upper energy level of the corresponding transition in temperature units, and their radiative rate coeﬃcients A (Huber 1979; Black & Dalgarno 1976).

26 Assuming H2 emission to be optically thin, the ﬂux observed in a given transition j is hνAN Ω F = j+2 , (2.8) j 4π where Ω is the solid angle of the observation. Substituting the value of Nj from equation 2.3 into Eq. 4.3 and then using equation 2.2, we obtain the total column density 4πF λ(T 1−n T 1−n) N = j ℓ u (2.9) tot − −Ej+2 Tu gj+2 AhcΩ(n 1) e kT T −ndT − Tℓ Z(T ) R From Eq. 4.3, we conclude that the column density is proportional to the ﬂux F

and the corresponding transition wavelength λ, and inversely proportional to the

spontaneous emission probability A,

F λ N j (2.10) j+2 ∝ A

To perform the ﬁt, we develop an excitation diagram from the ratio of column den-

sities,

N F λ A j+2 = j j 1 , (2.11) N3 F1λ1Aj

where N3 is the column density of the upper energy level of the transition S(1). We

select N3, corresponding to the S(1) transition, since it is the brightest and most frequently detected line. Using equation 2.3, we ﬁnd this column density ratio from the continuous temperature model to be

−Ej+2 Tu gj+2 −n N e kT T dT j+2 Tℓ Z(T ) × = −E . (2.12) R Tu g 1 N3 3 e kT T −ndT Tℓ Z(T ) × R We determined the parameters of our model by comparing the observed and the modeled column density ratios from equation 4.5 and 2.12, by varying the upper and

27 lower temperature T and power law index n (see 2.4). Knowing these parameters, ℓ § we substitute their values in equation 2.9, to obtain the total column density. The total number of molecules is calculated using

2 ntot = NtotΩd , (2.13)

where ntot is the total number of hydrogen molecules and d is the distance to the object. We then calculate the total H2 gas mass,

M = n m , (2.14) H2,tot tot × H2

where mH2 is the mass of a hydrogen molecule.

2.4 Method & Calibration

Applying the model developed in 2.3 permits direct assessment of the warm H § 2 column. Extrapolating the model to lower temperatures to recover the full molecular content requires a calibration procedure using a trusted independent estimate of H2 content. Here we describe both applications.

2.4.1 Warm H2

The power law temperature distribution of H2 molecules in Eq. 2.1 has three primary parameters: upper temperature Tu, power law index n, and lower temperature

Tℓ. An excitation diagram formed from the H2 line ﬂux ratios is the distribution of normalized level populations and constrains our model parameters. Excitation diagrams relate the column density of the upper level (Nu) of a particular transition, normalized by its statistical weight, gu, as a function of its energy level Eu. In the following sections we describe how the model can be used to estimate the warm H2

28 gas mass. In practice, except in a few cases, the lower temperature cutoﬀ Tℓ is not directly constrained (see 2.4.2.1). The model ﬁt results themselves are given in Table § 2.4.

2.4.1.1 Upper temperature, Tu

The bond dissociation energy for H is 4.5 eV, corresponding to E/k 5 2 ∼ × 4 10 K, hence H2 is not typically bound above this temperature. H2 present in photo- dissociation regions (PDRs) in the outer layers of the molecular cloud can reach temperatures of a few 100 K (Hollenbach et al. 1997, Hollenbach et al. 1999). For the SINGS galaxies, Roussel et al. (2007) concluded that the mass of H2 greater than 100 K contributes 1–30% of the total H2 gas mass. In the MOlecular Hydrogen

Emission Galaxies (MOHEGs) of Ogle et al. (2010), M(H2) > 1500 K contributes only 0.01% of the total H2. M(H2) > 300 K contributes less than 1% in ULIRGs (Higdon et al. 2006).

In our model, when Tu is allowed to vary above 1000 K, we found negligible impact on the recovered total gas mass or the quality of the ﬁt to the excitation diagram. We therefore ﬁxed the upper temperature of the power law model distribution at

Tu = 2000 K. H2’s ro-vibrational excitation spectrum (including the 1-0 S(1) line at λ =2.12n) would provide sensitivity to even hotter gas, but the mass contribution of this very hot gas in the context of our model is insubstantial.

2.4.1.2 Power law index, n

Keeping a ﬁxed value of Tu = 2000 K, the other two model parameters, Tℓ and n, are varied using a Levenberg-Marquardt optimization (Markwardt et. al. 2009) to match the observed line ﬂux ratios (suitably converted to column density ratios using Eq. 4.5). Figure 2-1 is an example excitation diagram for galaxy NGC5033.˜

The model ﬁt converges to Tℓ = 51K, n = 4.65, with a ﬁxed value of Tu = 2000K.

29 Figure 2-1 Excitation Diagram for NGC 5033 and 3c293. The Nu/gu ratios are normalized with respect to the S(1) transition. The solid red line indicates our model fit to the observed normalized columns, denoted by black points. The error bars on the black points are comparable to the symbol sizes. The resulting model parameters Tu, and n are indicated. The two solid lines demonstrate the two discrete temperature fit adopted by Roussel et al. (2007). The blue diamonds show model-predicted ratio values for the (unobserved) S(4)–S(7) H2 rotational lines. The below panel for 3c293 shows our model fit to all the MIR rotational lines S(0)– S(7) detected with the IRS-Spitzer

Model predicted ratio values for the unobserved lines S(4)–S(7) are indicated, as are the two discrete temperature ﬁts chosen by Roussel et al. (2007).

The power law index n in our sample ranges from 3.79–6.39, with an average

valuen ¯ = 4.84 0.61. Figure 2-2 is a frequency distribution of power law index ±

required to fit the MIR H2 rotational line fluxes in the SINGS galaxies. The power law index range derived in our model is comparable to the indices required to fit the

H2 rotational line ﬂuxes for ULIRGs (2.5 < n < 5.0) and Seyfert galaxies (3.4–4.9) (Zakamska et al. 2010, Pereira-Santaella et al. 2014). 30 Figure 2-2 The frequency distribution of the power law index, n, required to ﬁt the MIR H rotational lines. The average valuen ¯ =4.84 0.61 2 ± for the SINGS galaxy sample.

Galaxies with a steep power law index have low warm gas mass fractions, since a larger quantity of H2 in these systems are at lower temperatures. Molecular gas heated by shocks and other turbulent energetic phenomena have higher temperatures and hence, higher warm gas mass fractions than gas in photo-dissociation regions (PDRs)

(Appleton et al. 2015 in prep). The power law index therefore gives information on the relative importance of gas heating by shocks, photoelectric heating, UV pumping, etc.

2.4.2 Total H2

With a continuous power law model well reproducing the rotational emission lines from warm H2, it is natural to consider whether the total molecular gas reservoir could be probed by suitable extrapolation of our model to lower temperatures. Typically,

31 the entire reservoir of H2 cannot be probed through rotational emission, since the model loses sensitivity at temperatures far below the ﬁrst rotational energy state.

Recovering the total molecular content from rotational H2 emission therefore typically requires an additional free parameter — an extrapolated model lower temperature,

Tℓ — which must be calibrated against known molecular mass estimates. We ﬁrst explore the models sensitivity to low temperatures, and then describe the calibration

procedure we adopt.

2.4.2.1 Model Sensitivity Temperature, Ts

The upper energy level of the lowest rotational transition of H2 is 510 K — sub- stantiallly higher than typical kinetic temperatures in molecular regions. Yet, even

at temperatures well below this value, molecules in the high temperature tail of the

energy distribution can yield detectable levels of rotational emission. Below some

limiting temperature, however, increasing the number of cold H2 molecules will increase the implied molecular gas mass, but result in no measureable changes to the

H2 rotational line ﬂuxes.

We deﬁne the sensitivity temperature, Ts, as that temperature below which the H2 reservoir is too cold for changes in the amount of gas to lead to measurable changes in

the excitation diagram. To evaluate this in the context of our model, we calculated the

diﬀerence between the model-derived and observed column density ratios, Nu/gu . (Nu/gu)S(1) Note that with the adopted normalization to the S(1) line, a unique excitation curve exists for any given pair n, T ( T T ). We varied these model parameters and ℓ ∀ ℓ ≤ s evaluated the quality of the model ﬁt using

m R R 2 χ2 = i,mod − i,obs , (2.15) σ Xi=1 Ri,obs

Nu/gu where R = ln (N /g ) , Ri,mod and Ri,obs are, respectively, the modeled and ob- u u S(1) 32 2 Figure 2-3 The ∆χ value in the model parameter space Tℓ and n for NGC 5033. At temperatures lower than 88 K (the maximum Tℓ value for 1σ contour plot), the model yields similar ﬂux ratios. Molecules with temperature less than 88 K have negligible contribution to H2 rotational line ﬂux in the galaxy NGC 5033.

th served ﬂux ratios for the i transition, with uncertainty σRi,obs , and the summation is

2 over all independent line ﬂux ratios. We map the χ space in Tℓ and with σ values, following (Avni 1976), via ∆χ2 = χ2 χ2 (where χ2 is the minimum χ2 value). − min min 2 Figure 2-3 shows example ∆χ contours for the galaxy NGC 5033. The value of Ts is determined at the maximum value of lower cutoﬀ temperature Tℓ along the 1σ contour. For the galaxy NGC 5033, T 88K. s ∼ The near-horizontal orientation of the contours indicates little correlation between

n and Tℓ. Since for most of the sample, the contours do not close as you go towards

lower temperatures Tℓ < Ts, any chosen lower cutoﬀ of the power law distribution of

temperatures below Ts remains consistent with the data.

Generally, diﬀerences between the model and observed ﬂux ratios decrease as Tℓ

33 decreases, and do not signiﬁcantly change below 80 K. However, in some LINER ∼ and Seyferts systems (e.g. NGC 2798, NGC 3627, and NGC 4579), the contours close,

and χ2 has a deﬁned minimum. Figure 2-4 illustrates this phenomenon in the galaxy

2 NGC 3627, evaluating χ along the ridge line of best-fitting indices n for each Tℓ, and contrasting this galaxy with the more typical case of an indefinite minimum. Evident in the fits to NGC 3627 is a single best-fitting lower cutoff temperature of T 120K. ℓ ∼ In such cases, a continuation of the power-law distribution to temperatures below this

best-ﬁtting value is counter-indicated, as it degrades the ﬁt. This indicates that in

these cases, the bulk of H2 is directly detected via rotational emission in a warm gas component excess.

To identify galaxies with warm molecular gas excess, we imposed the constraint ∆χ2 = χ2 χ2 > 2.3, where χ2 is the χ2 value at 20 K. Figures 2-5 and 2- 20K − min 20K

6 show the distribution of sensitivity temperature Ts and the corresponding average conﬁdence contour plot for all SINGS galaxies (excluding in total 8 galaxies, identiﬁed

as having a warm gas excess (NGC 2798, NGC 3627, and NGC 4579) and few other

galaxies (e.g. NGC 1266, NGC 1291, NGC 1316, NGC 4125, and NGC 5195) with

low signal-to-noise (S/N) ratio in their S(0) line ﬂux). The excluded galaxies are all LINERs or Seyferts with low S(0)/S(1) ratios (in the range 0.04–0.2, vs. median

0.33 in the SINGS sample, Roussel et al. (2007)). They exhibit evidence for shocks,

unusually high dust temperatures, and merger morphologies — all processes that

could result in substantial quantities of warm molecular gas (Alatalo et. al. 2011,

Skibba et. al. 2011, Pellegrini et. al. 2013, Horellou et. al. 2001, Wilson et. al.

2013, Kohno et.al. 2002, Mentuch et. al. 2012).

The average value of Ts is 81 K. This implies that, with the quality of H2 rotational

spectroscopy provided by the Spitzer/IRS instrument, H2 gas down to rotational temperatures of 80 K can be reliably detected. ∼

34 Figure 2-4 The χ2 distribution for a normal galaxy NGC 5033 (blue) and an excess warm molecular gas galaxy NGC 3627 (red). The minimum χ2 occurs at a cutoﬀ temperature of 120 K for NGC 3627 however, for the galaxy NGC 5033 the χ2 curve decreases throughout as the lower temperature is decreased. For temperatures less than 50 K the model show no change in the ﬂux ratios since temperatures are too cold to occupy rotational energy levels and hence, a constant χ2 curve.

35 Figure 2-5 The distribution of sensitivity temperatures Ts (the temperature above which H2 can be directly traced via rotational emission) for the SINGS sample, omitting warm excess sources. On average, the sensitivity temperature is 81 K.

36 Figure 2-6 The average ∆χ2 contours of the SINGS sample, excluding warm excess galaxies. The average value is Ts = 81K with an average power law index of n = 4.8. Using these parameters,

MH2 (> 81K)/MH2,total = 15% of the H2 mass is probed directly via rotational emission ( 2.4.2.3). §

37 2.4.2.2 Model extrapolated lower temperature, Tℓ

Given our model sensitivity to H columns down to rotational temperatures 80K, 2 ∼ we evaluate the potential for extrapolating the power law distribution to lower temperatures to attempt to recover the the total molecular gas mass.

To calibrate an extrapolated lower temperature cutoﬀ – Tℓ — we require a set of

galaxies with well-established molecular gas masses obtained from LCO. We began constructing a training sample using SINGS galaxies, omitting galaxies with a central warm excess (see 2.4.2.1). The ULIRGs and radio galaxies are avoided due to §

ambiguity in their αCO values. Recent studies have also shown αCO in low metallicity galaxies is higher than the Galactic value (Bolatto et al. 2013, Schruba et al. 2012,

Leroy et. al. 2011) and hence we restricted our sample to galaxies with an oxygen

abundance value of 12 + log[O/H] 8.4. We used the average of their characteristic ≥ metallicities derived from a theoretical calibration (KK04 values) and an empirical calibration (PT05 values).

To perform this calibration, a given model ﬁtted to the rotational excitation dia-

gram is extrapolated to the particular temperature where the model mass equals the

cold molecular gas mass, estimated from CO emission (LCO), using αCO,Gal (column 10 of Table 2.2).

Figure 2-7 shows the frequency distribution of extrapolated model lower temper-

ature, Tℓ, required to ﬁt the molecular gas mass in the SINGS sample (with and without warm excess sources). The full sample is described by an average extrapola-

tion temperature of T ⋆ = 49 9 K. Excluding galaxies with warm gas excess narrows ℓ ±

the distribution, but does not signiﬁcantly change the average value of Tℓ. Table 2.4

lists the value of Tℓ, with the value in parentheses calculated when the conversion factor derived by Sandstrom et. al. (2013) through dust emission is assumed.

38 Figure 2-7 The frequency distribution of model lower temperature, Tℓ, required to ﬁt the molecular gas mass using the Galactic αCO,Gal. On average the value for Tℓ is 49 K for our SINGS training sample. The below histogram (in blue) is plotted excluding warm galaxies with high Ts. However, no change in the average value of Tℓ is found including or excluding galaxies with warm gas excess.

39 Figure 2-8 The distribution dM/dT vs molecular temperature for galaxy NGC 5033. The darker and lighter shades in the plot show two diﬀerent regions, below and above the sensitivity temperature, Ts = 88 K. The fraction of H2 gas mass below Ts = 88K for the galaxy NGC 5033 is about 86%.

2.4.2.3 Mass distribution function

Since dM/dT is a strong negative power law, the number of molecules decreases rapidly with increasing temperature — most of the H2 gas mass resides at the lowest temperatures. We can evaluate the fraction of the total molecular mass our model is sensitive to by comparing M(T = T T ) and M(T = T T ) ℓ → s s → u Figure 2-8 shows an example mass-temperature distribution dM/dT for NGC 5033 as a function of molecular temperature. The total molecular gas mass of 1.9 108 ×

M⊙ is distributed with an index n = 4.65 in the temperature range Tℓ = 51K to

Tu = 2000K. The fraction of cold H2 gas mass (< TS = 88K for NGC 5033) is 86%. ∼ Using the average power-law index and sensitivity temperature from the SINGS

40 training sample (see Fig. 2-6) we ﬁnd M (> T = 81K)/M 15%. Adopting H2 s H2,total ∼

instead the 2σ contour, the value of Ts becomes 97 K and the ratio MH2 (> Ts = 97K)/M is 8%. This demonstrates that, despite the many shortcoming of H2,total ∼

H2 as a rotational emitter, we can trace a substantial fraction of the H2 in galaxies directly.

Our model using the power law continuous distribution fits the H2 MIR rotational lines and estimate the warm molecular gas content. The discrete temperature fit using two or three temperature components is a less robust technique to estimate the warm molecular gas mass in galaxies. Furthermore, for the first time using the extrapolation method we could estimate the total molecular gas content in galaxies, independent of any indirect molecular gas tracers.

2.5 Results, Discussions, & Applications

2.5.1 What are the typical molecular gas temperatures in

galaxies?

UV pumping sets the level populations of upper level states, J > 3, in particular at low column densities of H2 . As a result, these states may result in rotational temperatures well in excess of their kinetic temperatures. For our purposes whatever combination of collisional (including shocks) and UV pumping determines the level populations and hence average H2 excitation, we assume a single power law distribution of rotational temperature describes the ensemble of molecules. Since the mass in the power law model is dominated by gas with the lowest rotational temperatures and hence lowest excitations, it is instructive to compare the derived lower temperature cutoﬀs ( 4.2.2) with various models and measurements of temperature in molecular § gas.

41 ⋆ The average lower extrapolation cutoff, Tℓ = 49 K, is comparatively higher than what is typically assumed for molecular regions ( 10–30 K). And yet, this high lower ∼ cutoff is essential in describing the portion of molecular material following a power-law distribution of temperatures. For example, if we forced the extrapolation temperature to a lower value of 20 K while retaining the average power law index n =4.8( 4.1.2), § the estimated molecular gas mass would be on average 30 times higher than the ∼ mass measured using LCO. To calculate the total molecular gas mass, we extrapolate using a single power law index. The possibility of a broken or non-power-law temperature distribution at temperatures lower than our sensitivity temperature cannot be excluded (and indeed in warm gas excess sources, will be required to explain ongoing star formation). The ratio of warm diffuse to cold dense molecular gas in galaxies is a key step in understanding the H2 temperature distribution. Assuming an incident radiation

5 6 field G0 = 10 for a cloud with mass 10 –10 M⊙, Wolfire et al. (2010) estimated that molecules in the outer diffuse region (AV < 1) obtain temperatures in the range 50–80 K, with stronger incident radiation fields leading to even higher temperatures.

Due to the differences in self shielding from dissociating radiation, molecular clouds have an outer layer of varying thickness which contains molecular hydrogen, but little or no CO. This gas cannot be traced through CO transitions and is hence called dark molecular gas (Wolfire et al. (2010)). This dark gas can account for a significant fraction (24–55%) of the total molecular gas mass in galaxies (Pineda et. al. 2013,

Wolﬁre et. al. 2010, Smith et. al.2014, Planck Collaboration 2011).

CO-dark and diﬀuse molecular gas is heated to higher temperatures than dense CO-emitting gas in molecular cloud cores. Indeed, individual molecular cloud simula-

tions ﬁnd average mass-weighted H temperatures of 45 K for typical cloud masses 2 ∼ and radiation (Glover et al. 2012a, Glover, priv comm.). Galaxy-scale hydrodynamic simulations with a full molecular chemistry network Smith et al. 92014) also show

42 that H2 gas in the CO-emitting regions is markedly biased to the low temperature end of the full temperature distribution (Glover, priv comm.). Also, in diﬀuse and

translucent molecular clouds in the Galaxy, Ingalls et al. (2011) demonstrated that

additional sources of heating are required to explain the observed H2 and atomic cooling-line power. Our extrapolated power law model traces both warm and cold molecular gas mass in galaxies. The common assumption that the bulk of molecular gas is found at rotational temperatures of 10–30 K may be true only in the CO ∼ emitting core regions of the molecular cloud. The average mass-weighted molecular gas temperature can be much higher when the full range of emitting environments are considered. It is therefore not surprising to ﬁnd typical molecular gas temperatures of 50 K in galaxies, similar to our model derived values. ∼

2.5.2 Estimating total MH2

By fitting a continuous temperature distribution to the MIR H2 rotational lines and calibrating an extrapolating temperature, this model can be used to calculate the total molecular mass in galaxies directly from H2 rotational emission. The method is independent of any indirect tracer like CO, DGR, or assumptions about star formation depletion timescales. Any physical processes which bias these tracers will not impact results derived from fitting H2. In this section we test the model’s capability to estimate molecular gas mass in different types of galaxies.

⋆ Adopting a ﬁxed model lower extrapolation temperature Tl = 49 K the total

H2 gas mass is calculated by extrapolating the ﬁtted model. The total H2 gas mass derived by our model is shown in Figure 2-9. It compares very well with LCO along with αCO,Gal based estimates of gas mass. The scatter in our model is about 0.31 dex (factor of 2) for the SINGS sample and increases to 0.34 dex (factor of 2.2) for the complete sample, including U/LIRGs and radio galaxies. Some of this scatter no doubt arises from ignorance of the true αCO values in these systems.

43 Figure 2-9 The model extrapolated molecular gas mass, assuming a lower cutoff temperature of 49 K vs the total molecular gas mass obtained from LCO measurements using αCO,Gal. Different symbols represent different galactic systems as indicated. The solid line is one to one correspondence while the dashed and dotted lines are twice and 3 the value respectively. ×

44 Galaxies with warm gas excess and a high sensitivity temperature T ( 2.4.2.1), s § require similar values of extrapolated Tℓ as the training sample. The warm molecular gas traced by MIR rotational lines may be completely isolated from the cooler gas in these galaxies. Extrapolating to a lower temperature of 49 K yields molecular gas masses which agree with CO-derived values, assuming αCO = αCO,Gal. A possibility of enhanced CO excitation due to high molecular gas temperature with a corresponding low α in such warm galaxies cannot be ruled out (see also 2.5.3). CO §

Taken together, a correlation between H2-derived and CO-based mass estimates is found, spanning seven orders of magnitude in mass scale and across a wide range of galaxy types. The mass calculated with a continuous temperature distribution model, extrapolated to a ﬁxed cutoﬀ temperature of 49 K, can provide an independent measurement of total molecular gas mass in galaxies, good to within a factor of 2.2

(=0.34 dex). This dispersion is comparable to uncertainties in the αCO conversion factor itself (Bolatto et al. (2013)) as well as methods using DGR (Sandstrom et al. (2013)).

2.5.3 Model derived molecular gas mass in ULIRGs, LIRGs

and radio galaxies

Many local ULIRGs are recent ongoing galaxy mergers. In the merging process a large amount of gas in the spiral disk is driven to the central nuclear region, increasing the gas temperature. The increase in temperature and turbulence increases the CO linewidth, resulting in a high value of LCO for a given molecular gas mass. αCO,Gal therefore gives an overestimate of H2 gas masses in these galaxies (Downes et al. 1993,

Bryant et al. 1999). Moreover, αCO,Gal can yield molecular gas masses greater than the observed dynamical mass (Solomon et al. 1997). To avoid this, a lower value of conversion factor is suggested for ULIRGs and other merger systems — αCO = 0.8

45 M (K km s−1 pc2)−1, 5.5 lower than the standard Galactic value (Downes et al. ⊙ × (1998)). However, by considering the high-J CO ladder, some studies have suggested that even for ULIRGs αCO,Gal values are possible (Papadopoulos et al. 2012). Some

H2 emission may lie outside photo-dissociation and star forming regions in ULIRGs, powered by shocks (Zakamska et al. 2010). This H2 may reside in CO-dark gas, so that applying a low αCO value in ULIRGs may yield an underestimate H2 mass. In radio galaxies molecular gas can be predominantly heated by shocks through powerful jets. The molecular gas clouds may be aﬀected by turbulence, and not gravitationally bound, defying the use of standard αCO,Gal. Ogle et al. (2014) using DGR in NGC 4258, a low luminosity AGN (LLAGN) harboring a jet along the disk,

8 derived gas mass of about 10 M⊙, an order of magnitude lower compared to the standard method of using αCO,Gal. The molecular gas mass could be overestimated when used αCO,Gal in radio galaxies, which harbor long collimated powerful jets. In applying a power law model to the sample of ULIRGs, LIRGs and radio galaxies,

⋆ the nominal model extrapolation temperature Tℓ = 49 K is used to calculate the total

H2 gas masses, listed in column 3 of Table 2.5. The Tℓ in column 4 of Table 2.5 is the required extrapolated temperature to match the cold molecular gas mass measured from the CO line intensity.

In radio galaxies 3c424, 3c433, cen A, and 3c236 the estimated H2 gas mass using

⋆ the power law model after extrapolation to Tℓ = 49 K, is higher when compared to the CO luminosity derived values using αCO,Gal. However, when accounted for the

⋆ intrinsic variation in αCO,Gal and Tℓ the H2 gas masses are in agreement with each other except in 3c424, where the diﬀerence in masses is more than 10 . × Using α = 0.8 M (K km s−1 pc2)−1, a factor of 5.5 lower than the standard CO ⊙ × ′ Galactic value, we derive a modiﬁed extrapolation temperature Tℓ, which is required to match the lowered gas mass. Since the model mass rises rapidly to lower temper-

′ ′ atures, Tℓ > Tℓ. The Tℓ values are listed in column 7 of Table 2.5. On average for

46 ULIRGs, T ′ = 80 13K. ℓ ± ′ Figure 2-10 shows the temperature distribution of Tℓ (adopting αCO,Gal) and Tℓ

(adopting αCO,Gal/5.5) in ULIRGs. The lower temperature cutoﬀ in ULIRGs and radio galaxies (except 3c424) is very similar to the normal galaxy training sample when

αCO,Gal is adopted, but much higher with the reduced molecular mass of αCO,ULIRG.

It is of interest that when αCO,Gal is used with the nominal calibration cutoﬀ

⋆ temperature Tℓ , the ULIRG sample in Fig. 2-9 does not exhibit any particular bias.

Either αCO and Tℓ are similar to their normal Galactic values in these systems, or

they have reduced αCO and a higher H2 temperature ﬂoor. This may indicate that the

same physical processes that lead to reduced αCO in highly active system, including increased ISM pressure and radiation density, globally elevate the gas temperature.

Since ULIRGs could indeed have uniformly elevated molecular gas temperatures,

this degeneracy between αCO decrease and Tℓ increase leads to a systematic uncer-

tainty in the total H2 gas mass identical in form to that obtained directly from mass

estimates based on LCO. A suggested prescription which side-steps this ambiguity, in

applying this model to systems with non-Galactic αCO is to calculate the total gas

⋆ mass using the the nominal Tℓ = 49 K, and scale it by αCO/αCO,Gal, for the preferred

αCO. As can be seen in Fig. 2-9, which adopts a uniform αCO,Gal, the molecular mass in ULIRGs is well recovered by this procedure.

2.5.4 Eﬀect of dust temperature on the warm H2 fraction

Since typical sensitivity temperatures are T 80 K (see 2.4.2.1), we can directly s ∼ § calculate the warm H mass above 100 K without extrapoloation, and compare it 2 ∼ to the total mass as recovered by the calibrated extrapolation of 2.4.2.2. Given an §

estimate for the power law index, n, and lower cut oﬀ temperature, Tℓ, of the power law distribution, we can calculate the fraction of molecular gas mass at temperatures

47 Figure 2-10 The distribution of model extrapolated lower temperatures in ULIRG and radio galaxies when the H2 gas mass is evaluated using the Galactic conversion factor αCO,Gal (above, red), and when adopting αCO,Gal/5.5, as generally accepted for ULIRGs (below, blue). The mean lower temperature cutoﬀ is 50 K and 80,K when αCO,Gal and αCO = αCO,Gal/5.5 are used, respectively. The Tℓ distribution for the SINGS normal galaxy sample is shown above, for comparison.

48 above 100K as T M(> 100 K) u T −ndT = 100K , (2.16) Tu Mtotal R T −ndT Tℓ R where Mtotal is the total molecular gas mass estimated from the CO line intensity. Assuming 100 K T and T T we ﬁnd ≪ u ℓ ≪ u

M(> 100 K) 100K 1−n . (2.17) Mtotal ≈ Tℓ

Table 2.4 lists the calculated mass fraction M(>100 K) for each galaxy. Columns 6 Mtotal and 8 of Table 2.5 are calculated using α and 1 α as generally assumed CO,Gal 5.5 × CO,Gal for ULIRGs, respectively. At lower αCO, the warm gas mass fraction is higher. Figure 2-11 shows the fraction of warm molecular gas mass, M(>100K) , as a function Mtotal of far infrared (FIR) dust color temperature, νfν70 . The warm gas fraction obtained νfν160

using αCO,Gal ranges from 2–30%, and exhibits little correlation among diﬀerent galaxy types with dust color temperature. The ULIRGs and normal star forming galaxies

show similar warm gas fractions, though ULIRGs have warmer dust color tempera-

tures, and LINERs and Seyferts have somewhat higher warm gas mass fractions than

normal star forming galaxies on average.

In contrast, using the available dust-derived central αCO estimates of Sandstrom et. al. (2013) for normal galaxies and a reduced value 1 α for ULIRGs 5.5 × CO,Gal and QSO’s, however, leads to a strong correlation, with warmer dust implying an increasing warm H2 fraction. The average warm gas fraction for ULIRGs and QSO is then 45%, signiﬁcantly above that of normal galaxies, and on the same increasing ∼ trend with dust temperature. Depending on which prescription for total gas mass is correct, this could indicate a dependence of αCO on temperature.

49 Figure 2-11 The fraction of warm H2 gas mass (T > 100 K) versus the dust color temperature, νfν,70 , obtained from PACS. At left a con- νfν,160 sistent Galactic αCO is adopted, and little trend is seen. At right, a reduced αCO is applied to ULIRGs and QSO’s, and the dust-derived central αCO values of Sandstrom et al. (2013) are used. Galaxies with warmer dust color temperatures have high warm molecular gas mass fraction.

50 2.5.5 Molecular gas in low metallicity galaxies

As traced by their CO emission, many low metallicity dwarfs appear to have van- ishingly low molecular gas content, but retain high star formation rates. That is, they are strong outliers on the Schmidt-Kennicutt relation (Galametz et al. 2009, Schruba et al. 2012). This discrepancy implies either that in dwarf galaxies star formation eﬃciencies are higher compared to normal spirals, or they host large molecular gas reservoirs than is traced by the CO emission (Schruba et al. 2012, Glover et al.

2012b). It is possible that a signiﬁcant fraction of H2 exists outside the CO region,

+ 0 where the carbon is in C (ionized) or C (neutral) states. Since H2 can self-shield from UV photons in regions where CO is photodissociated (Wolﬁre et. al. 2010), at low metallicity, not only is the CO abundance reduced, but as dust opacity is reduced and ionized regions become hotter and more porous, αCO,Gal can severely underestimate the molecular gas mass. Considerable eﬀort has been invested in detecting and interpreting CO emission at metallicity 50 times lower than the solar metallicity,

7.0, to assess the molecular gas content (Leroy et al. 2011, Schruba et al. 2012, ∼ Cormier et al. 2014, Remy et al. 2014). Dust emission can be used to estimate the molecular gas mass in ISM, assuming a constant DGR however, it is essential to know the change in DGR with metallicity. At very low metallicities, 8, DGR appears to ≤ scale non-linearly with metallicity (Herrera et al. 2012, Remy et al. 2014).

Our direct detection of H2 gas mass through H2 rotational lines is independent of any indirect tracers, which are aﬀected by changing metallicity and local radiation eﬀects. Applying our model in low metallicity galaxies should yield an estimate of molecular gas mass without the same inherent biases introduced by these dust and

CO abundance variations. In this section we estimate the H2 gas masses through our power law model in a low metallicity galaxy sample selected to have detected

H2 rotational emission, faint CO detection, and (where available) estimates of dust

51 mass. We then compare these H2 -based estimates to models and other methods which attempt to control for the biases introduced at low metallicity.

The low metallicity galaxies were selected on availability of MIR H2 rotational lines to have atleast three rotational lines including S(0) or S(1) line ﬂuxes along

with CO derived molecular mass estimates.

2.5.5.1 Metallicity estimation

To study the variation of H2 gas mass from CO derived measurements over the metallicity range, it is essential to estimate the metallicity of galaxies. The metallicities were determined applying the direct Te method. CGCG007-025 is the lowest metallicity galaxy in our dwarf sample with the value of = 7.77 (Izotov et al. 2007).

Guseva et al. (2012) estimated the value of in the two H II regions, Haro 11B and

Haro 11C as 8.1 and 8.33, respectively hence, we adopt the average value for Haro

11. The metallicity value, , for NGC 6822 is 8.2 (Israel et al. 1997). No literature value exist for the oxygen gas phase abundance for the speciﬁc region of Hubble

V in NGC 6822, mapped by the IRS-Spitzer. Peimbert et al. (2005) estimated = 8.42 0.06 for Hubble V, which is inconsistent with the previous value of 8.2. ± For selected SINGS galaxies, the metallicity values in the circumnuclear regions, which are approximately the size of our H2 line ﬂux extracted regions, are estimated by averaging the theoretical (KK04) and an empirical metallicity calibration (PTO5) as recommended by (Moustakas et al. 2010).

2.5.5.2 Cold molecular gas from CO line emission

Although the CO abundance drops super-lineraly with decreasing metallicity, it is detected in the low metallicity sample, and as the most common molecular tracer, can be compared directly to our H2- based method. We adopted the literature values for 12CO(1–0) line intensities for CGCG007-025 and N66, while for Haro 11,

52 UM311 and Hubble V region 12CO(3–2) line intensities were scaled using the rela-

tion ICO(3−2) = 0.60 (in temperature units) due to unavailability of 12CO(1–0) line ICO(1−0)

intensities. Calculating LCO, (area integrated luminosity) the molecular gas masses

are estimated using αCO,Gal and were further scaled using the 8 m map, to account for the diﬀerence in the extracted IRS spectrum and the CO beam regions for each

galaxy. The molecular gas masses are listed in Table 2.6.

2.5.5.3 Molecular gas from dust emission

An alternative method for estimating molecular gas mass makes use of dust emission together with assumption of dust opacity and grain size distribution to calculate

a total mass, scaling dust mass to the total gas mass using a presumed or modeled

dust-to-gas ratio, and removing the measured atomic mass from the region.

Leroy et al. (2007) estimated H2 gas surface density using dust emission from

FIR map in N66 region of SMC. They derived αCO to be about 27 times the αCO,Gal. For Haro 11, UM311 and Hubble V using metallicity-DGR relation from Sandstrom et al. (2013) and with the known dust mass, we estimated the total gas mass and

after subtracting the atomic gas content subsequently calculated the molecular gas

mass. However, we ﬁnd a negative value for the molecular gas for UM311, suggesting

the ISM mass is mainly dominated by the atomic gas. The H2 gas masses calculated from the dust emission are given in Table 2.6.

2.5.5.4 Molecular gas mass using our model

The H2 line ﬂux extraction was performed for the similar region, where the CO emission was measured by Rubio et al. (1996). The cubes were prepared using

CUBISM (Smith et al. 2007b) (Jameson, K. et al. in prep) and the H2 line ﬂuxes were estimated using the PAHFIT, a MIR spectral decomposition tool (Smith et

al. 2007a). The ﬂux of H2 rotational lines for Haro 11 are from Cormier et al.

53 Figure 2-12 Excitation diagram for low metallicity galaxy Haro11. The Nu/gu ratios are normalized with respect to S(1) transition. The dashed red line indicate the model ﬁt to the observed ratios. The blue dashed line predicts the value of S(0) ﬂux ratio. The model estimated Tℓ, and n are mentioned.

(2014), while for UM 311, and CGCG 0077-025. Hunt et al. (2010) measured the H2 rotational line ﬂuxes. For Hubble V region, Roussel et al. (2007) derived the ﬂux of

H2 rotational lines. Figure 2-12 is an excitation diagram for low metallcity galaxy Haro 11, with the power law model ﬁt. Our model prediction for the unobserved S(0) line is included, and is consistent with the estimated upper limit. The H2 total gas mass for each low metallicity galaxy is measured using the power law model with lower temperature

⋆ extrapolation to Tℓ = 49 K. Table 5 lists the value of metallicity with their distance and the measured value of H2 rotational line ﬂuxes with the power law index and the

H2 gas mass derived using CO, dust, and our model.

Figure 2-13 compiles H2 gas masses derived using the various indirect tracers,

54 together with the results from our H2-only model. All values are shown relative to the H2 mass inferred using CO luminosities with αCO = αCO,Gal, and are plotted as a function of metallicity. For the SINGS sample, a variation of about 2–3 times the

LCO-derived H2 gas mass is found, likely a consequence of the intrinsic variation in

αCO at high metallicity & 8.4. At intermediate metallicity, the molecular gas content from CO line emission for the Hubble V region in NGC 6822 compares well with our model-derived gas mass, which suggests a similar Galactic conversion factor (αCO =

αCO,Gal), consistent with the results of Rijcke et al. (2006). At lower metallicity, however, our model disagrees strongly with naive CO-based estimates, yielding up to

100 the molecular gas mass inferred from CO emission. ∼ × The molecular masses we recover at low metallicity are in good agreement with other measures which attempt to account for the impact of reduced metal abundance.

These include dust-derived measurements, where available (when the strong metallicity dependence of the dust-to-gass ratio is accounted for). They also agree well with the prescription for the power-law like αCO variations with metallicity recovered from inverting star formation densities among all non-starburst galaxies in the

HERACLES sample (Schruba et al. 2012). The theoretical model of varying αCO by

22 −2 Wolﬁre et al. (2010) also agrees well, assuming an H2 column density of 10 cm in a molecular cloud, scaled accordingly to the solar metallicity value of 8.66 with

LOI log(G0/n) = -0.3 adopted from the luminosity ratio from Malhotra et al. (2001). LFIR Recent work by Shi et al. (2015) derived the conversion factor in Sextans A, with a

metallicity of 7% of the Milky Way, to be about 700 the galactic conversion factor. × This value is in good agreement with our analysis on the relation between conversion factor with metallicity (Figure 2-13). The power law model reliably recovers the total

molecular gas masses at metallicity as low as 10% of the Milky Way, where CO and

other indirect tracers suﬀer strong and non linear biases.

55 Figure 2-13 The ratio of molecular gas masses estimated using different methods to the “naive mass” obtained using LCO (and αCO = αCO,Gal), as a function of gas-phase metallicity. The black points show the molecular gas masses derived from the H2 rotational model. The blue line shows a fit to this ratio derived from inverting the star formation law for HERACLES non-starburst galaxies Schruba et al. (2012). The molecular gas masses traced by the dust emission are denoted by the red points in the plot, and are shifted slightly in their metallicity values for clarity. The black solid line is the predicted mass ratio from the theo- 22 retical model of Wolfire et al. (2010), assuming N(H2) = 10 −2 cm and log(G0/n) = -0.3. A steep increase in the ratio of model derived H2 gas mass to the LCO derived measurements is observed at metallicity values 8.4. ≤

56 2.5.6 Future prospects

At metallicities . 0.25 Z⊙, the direct power-law method recovers total molecular gas content as reliably as other tracers that account for or avoid the impact of reduced

gas-phase metal content. At even lower metallicities, the CO abundance plummets,

with essentially all of the molecular gas in a CO-dark phase. In the ﬁrst epoch of the

star formation in the universe, the extremely low abundance of heavy elements leaves

H2 as a principal coolant (Lepp et al. 2002). The Mid Infrared Instrument (MIRI) onboard JWST is sensitive enough to detect the S(1), S(2), S(3) and higher rotational lines of H2 in luminous galaxies (U/LIRGs) L till redshift 0.6, 1.3, 1.9, and higher, respectively. Assuming average H2S(1) = 10−4 LIR (Bonato et al. 2015), and L = 3 1011 L (typical for LIRGs), for S(1) at z = IR × ⊙ 0.5 to have signal to noise S/N = 5 will require 30 minutes of integration time with

JWST-MIRI. It will be possible to measure pure H2 rotational lines at high redshifts of z 6–7, almost reaching the reionization era of universe, with the SPace ≈ Infrared telescope for Cosmology and Astrophysics (SPICA) and the Cryogenic Aper- ture Large Infrared Submillimeter Telescope Observatory (CALISTO), planned for the 2020 decade (Roelfsema et al. 2012, Bradford et al. 2015).

The above mentioned future projects for the next decade provides an opportunity to observe H2 rotational lines at high redshifts. The power law model can be an useful tool in estimating molecular gas mass and study its variation and consequences at diﬀerent redshifts.

2.6 Summary

We present a new power law temperature distribution model capable of reliably estimating the total molecular gas mass in galaxies purely from as few as three mid- infrared pure-rotational H2 emission lines. Our model is independent of the biases

57 aﬀecting indirect tracers like CO, dust emission, or star formation prescriptions. It can hence be used even in environments where reliability of those indirect tracers is poor, such as at low metallicity. We calibrate the model on a sample of local star- forming galaxies with well-quantiﬁed CO-based molecular gas masses, and apply the model to local ULIRGs and low metallicity systems. Our key results are:

1. A model based on a continuous power law distribution of rotational tempera-

tures well reproduces the H2 excitation from a wide range of galaxy types, and

can directly recover the warm H2 mass (T > 100 K) more reproducibly than arbitrary discrete temperature ﬁts.

2. The power law index obtained for all SINGS galaxies ranges from 3.79 - 6.4, with an average value of 4.84.

3. With typical Spitzer detection sensitivities, the model can directly recover the

H2 gas mass down to a limiting sensitivity temperature of Ts = 81 K (when the S(0) line is available), accounting for 15% of the total molecular gas mass. ∼

4. By calibrating the model using a subset of the SINGS sample with well deter-

mined CO-based molecular masses, we ﬁnd that extrapolating the H2 tempera-

ture distribution to a single temperature of Tℓ = 49 K recovers the total H2 gas mass within a factor of 2.2 (0.34 dex).

5. When αCO,Gal is used, the fraction of warm molecular gas mass (M> 100 K)

in this training sample ranges from 0.02 to 0.30. If a reduced αCO is adopted for the ULIRGs, this fraction increases with increasing dust color temperature

νfν (70)/νfν(160).

6. In ULIRGs, the total molecular gas mass obtained by extrapolating the model

⋆ to Tℓ = 49 K is consistent with the molecular gas mass derived using αCO,Gal.

58 Alternatively, if a reduced αCO is adopted, the model extrapolation temperature required rises to 80 K. Either the warm molecular gas fraction and lower

temperature cutoﬀ in ULIRGs is higher than in normal star forming galaxies,

or αCO is closer to the Galactic value than has been presumed.

7. At low metallicity (12 + log[O/H] . 8.4), where indirect tracers of molecular mass suﬀer increasingly strong and non-linear biases, and the mass of the molec-

ular reservoirs exceed their CO-derived estimates by 100 or more, the direct × power law model recovers the total molecular gas masses reliably, as assessed

by other methods which correct for metallicity.

8. With upcoming facilities including JWST, SPICA, and CALISTO, detection

of the relevant H2 rotational lines in galaxies at intermediate to high redshifts becomes possible, opening a new window on the fueling history of star formation

in the Universe.

59 Table 2.1. Observed properties of our sample galaxies

S70 Galaxy D Type LIR S160 Ref 10 Name (Mpc) 10 L⊙ (1) (2) (3) (4) (5) (6)

N337 19.3 SF 0.568 0.807 S07 N1097 14.2 SF 2.343 0.932 S07 N1266 31.0 LIN 1.333 1.420 S07 N1291 10.4 LIN 0.039 1.382 S07 N1316 21.0 LIN 0.260 1.368 S07 N1482 22.6 SF 2.812 1.169 S07 N1566 20.4 SY 0.444 0.772 S07 N2798 25.8 SF 2.316 0.407 S07 N2976 3.6 DW 0.007 0.564 S07 N3049 19.2 SF 0.307 1.107 S07 N3184 11.4 SF 0.026 0.604 S07 N3190 19.3 LIN 0.290 0.577 S07 N3198 14.1 SF 0.147 0.813 S07 N3265 19.6 SF 0.237 1.057 S07 Mrk33 22.9 DW 1.525 N3351 9.3 SF 0.268 0.924 S07 N3521 11.2 LIN 0.266 0.572 S07 N3627 6.4 SY 0.221 1.016 S07 N3938 14.3 SF 0.105 0.436 S07 N4125 23.9 LIN 0.048 0.975 S07 N4254 14.4 SF 0.533 0.602 S07 N4321 14.3 SF 0.513 0.671 S07 N4450 16.5 LIN 0.092 1.116 S07 N4536 14.5 SF 0.905 1.172 S07 N4559 7.00 SF 0.083 0.498 S07 N4569 16.8 LIN 0.426 0.777 S07 N4579 16.4 SY 0.161 0.857 S07 N4625 7.6 DW 0.023 0.518 S07 N4631 9.3 SF 0.306 0.922 S07 N4725 20.5 SY 0.034 0.564 S07 N4736 4.7 LIN 0.115 1.708 S07

60 Table 2.1 (cont’d)

Galaxy D Type L S70 Ref IR S160 10 Name (Mpc) 10 L⊙ (1) (2) (3) (4) (5) (6)

N4826 5.3 LIN 0.116 0.782 S07 N5033 14.8 SY 0.577 0.572 S07 N5055 7.9 LIN 0.159 0.557 S07 N5194 7.6 SY 0.308 0.686 S07 N5195 7.6 LIN 0.154 1.652 S07 N5713 21.4 SF 2.998 1.001 S07 N5866 15.3 LIN 0.215 0.981 S07 N6822A 0.5 DW — 1.151 – N6946 6.8 SF 0.387 0.958 S07 N7331 14.5 LIN 0.249 0.564 S07 N7552 21.0 SF 5.052 1.244 S07 N7793 3.9 DW 0.009 0.648 S07 3c31 66.7 3C — — — 3c218 240 3C — — — 3c272.1 19.1 3C — — — 3c293 195 3C — — — 3c310 233 3C — — — 3c326n 395 3C — — — 3c424 568 3C — — — 3c433 445 3C — —- — 3c436 1016 3C —- — — CenA 11.0 3C — — — 3c236 449 3C — — — Arp220 77.6 ULI 145 1.678 H06 IRAS 00188-0856 596 ULI 256 — H06 IRAS 03521+0028 717 ULI 365 — H06 IRAS 05189-2524 186 ULI 143 2.292 H06 IRAS 06035-7102 356 ULI 166 — H06 IRAS 06206-6315 418 ULI 169 — H06 IRAS 07598+6508 700 ULI 337 — H06 IRAS 08572+3915 258 ULI 137 3.124 H06

61 Table 2.1 (cont’d)

S70 Galaxy D Type LIR S160 Ref 10 Name (Mpc) 10 L⊙ (1) (2) (3) (4) (5) (6)

IRAS 10565+2448 188 ULI 109 1.362 H06 F12112+0305 324 ULI 212 1.576 H06 IRAS 13451+1232 563 ULI 197 — H06 F14348-1447 332 ULI 224 1.550 H06 IRAS 17208-0014 188 ULI 250 1.744 H06 IRAS 19254-7245 273 ULI 121 1.468 H06 IRAS 20087-0308 483 ULI 280 — H06 IRAS 23365+3604 286 ULI 147 1.557 H06 Mrk 273 164 ULI 142 1.899 H06 UGC5101 174 ULI 100 1.053 H06 Mrk 463E 221 ULI 60 — H06 PG1440+356 347 QSO 42 1.355 E01 N6240 101 LIR 69 1.415 H06 N3110 72.5 LIR 16 0.772 P10 N3256 40.1 LIR 40 1.577 P10 N3690 44.9 LIR 63 1.663 P10 N5135 58.8 LIR 16 1.096 P10 N6701 56.2 LIR 10 0.883 P10 N7130 69.9 LIR 25 1.192 P10 N7591 70.9 LIR 10 0.821 P10 N7771 62.1 LIR 25 0.773 P10

aRef: S07 - Smith et al. 2007; K09 - Kennicutt et al. 2009; NED - NASA/IPAC Extragalactic Database; H06 - Higdon et al. 2006; P10 - Pereira Santaella et al. 2010; E01 - Evans et al. 2001 b Entries in the last column are references for the the infrared luminosity (8-1000 ), LIR. For SINGS galaxies LIR is calculated using the relation LIR = 0.94 × LTIR (D. Dale priv. comm.) and the corresponding LTIR values are from [?]. cDistance measurements are from the KINGFISH webpage for SINGS galaxies and for others through NED IPAC Extragalactic Database dThe S70 is the FIR ratio calculated from the PACS 70 and 160 ﬂuxes S160 eThe 3c radio galaxies were selected from Ogle et al. (2010).

62 Table 2.2. Observed molecular hydrogen rotational line ﬂux

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) M(H2) Name (106 M⊙) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

N03371,1 01.16(0.38) 02.10(0.49) 01.54(0.99) 00.97(0.52) 56 (228) N10971,1 21.31(4.26) 72.61(4.33) 29.36(2.94) 42.30(2.34) 1493 N126625,1 01.64(0.85) 14.85(0.66) 12.18(0.71) 18.98(1.16) 10.27(1.74) 24.19(1.99) 19.22(2.86) 1253 N12911,1 00.37(0.18) 02.98(0.48) 01.39(0.82) 03.16(1.00) 9 N13161,1 00.15(0.08) 03.60(0.61) 01.84(0.59) 08.40(0.99) 124 N14821,1 10.68(3.51) 42.40(5.34) 18.40(2.28) 20.75(2.69) 1607 N156626,1 02.40(0.22) 12.95(0.71) 05.53(0.48) 09.16(1.76) 389 N27981,1 04.32(2.53) 20.78(2.21) 09.07(0.92) 10.52(1.21) 273 1S,1 63 N2976 00.89(0.24) 01.57(0.30) 00.49(0.35) 00.52(0.42) 1.08 (0.25) N30491,1 00.64(0.22) 2.37(0.38) 01.17(0.65) 01.11(0.52) 148 N31841S,1 00.98(0.23) 02.26(0.29) 00.63(0.35) 26 (10.6) N31901,1 01.81(0.29) 07.53(0.80) 02.09(0.64) 07.16(1.26) 110 N31981,1 01.32(0.49) 03.21(0.54) 01.02(0.35) 01.87(0.85) 31 N32651,1 00.93(0.32) 03.06(0.35) 01.14(0.79) 01.53(0.74) 94 Mrk331,1 01.39(0.56) 02.93(0.37) 01.15(0.53) 04.57(0.86) 81 N33511S,1 06.28(1.05) 21.84(2.06) 08.83(1.01) 16.98(1.99) 197 (32) N35211,1 01.78(0.36) 03.12(0.69) 01.23(0.40) 02.05(0.88) 20 N36271S,1 03.12(0.39) 31.86(1.22) 14.17(0.52) 20.91(1.26) 208 (27) N39381S,1 00.80(0.12) 01.34(0.33) 00.42(0.32) 37 (30) Table 2.2 (cont’d)

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) M(H2) Name (106 M⊙) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

N41251,1 00.26(0.16) 01.76(0.47) 01.26(0.64) 01.80(0.88) 26 N42541S,1 01.76(0.13) 08.73(0.95) 04.66(0.92) 03.25(0.88) 342 (700) N43211S,1 07.82(1.17) 26.75(2.28) 13.21(2.46) 16.45(1.62) 1386 (200) N44501,1 01.03(0.16) 09.14(0.52) 03.37(0.95) 08.90(1.11) 63 N45361S,1 10.87(3.23) 41.16(4.05) 17.56(2.33) 21.68(2.07) 810 (415) N45591,1 01.36(0.21) 01.79(0.35) 00.40(0.15) 02.34(1.37) 18 N45691,1 04.16(0.69) 31.61(0.87) 15.24(0.52) 30.94(1.87) 760 N45791,1 00.89(0.23) 16.41(0.52) 10.58(1.24) 25.63(1.00) 205 N46251S,1 00.80(0.16) 00.96(0.19) 00.54(0.43) 8 (21) 1,1

64 N4631 05.82(0.64) 12.36(1.61) 06.04(0.50) 04.68(0.91) 73.4 N47251S,1 01.17(0.17) 3.71(0.51) 1.99(0.81) 3.80(0.90) <170 (<28) N47361S,1 03.32(0.68) 25.08(1.64) 10.01(1.04) 22.17(1.36) 21 (1.4) N48261,1 07.13(0.65) 34.53(1.58) 15.09(1.09) 21.06(1.03) 65 N50331,1 03.66(0.35) 18.20(1.04) 06.35(0.31) 12.69(1.91) 190 N50551S,1 04.40(0.24) 15.80(0.91) 05.20(0.67) 08.02(1.06) 87 (20) N51941,1 01.77(0.28) 13.44(0.91) 07.57(0.47) 18.73(1.77) 32 N51951,1 05.42(2.09) 31.04(1.23) 12.77(0.65) 27.50(1.72) 80 N57131S,1 02.74(0.36) 15.16(1.43) 05.09(0.79) 08.56(0.70) 329 (238) N58661,1 01.55(0.15) 09.00(0.55) 03.91(0.70) 03.72(0.65) 81 Table 2.2 (cont’d)

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) M(H2) Name (106 M⊙) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

N6822A1,1 00.81(0.43) 02.11(0.43) 01.60(0.41) 02.59(0.38) 0.03 N69461S,1 22.77(6.19) 63.69(3.35) 27.16(1.71) 28.63(2.93) 346 (32) N73311,1 01.64(0.16) 04.96(0.50) 01.38(0.19) 02.34(0.83) 120 N75521,1 25.78(10.69) 56.53(4.26) 24.59(2.25) 31.59(1.48) 1950 N77931,1 00.70(0.17) 01.50(0.32) 01.17(0.46) 00.53(0.37) 3 3c0312,8 00.64(0.11) 01.36(0.58) 00.59(0.15) 0.60(0.17) 00.76(0.27) 00.80(0.18) 695 3c2182,9 00.55(0.11) 00.41(0.22) 00.23(0.09) 00.55(0.08) 00.42(0.15) 00.23(0.05) 0.16(0.05) 1895 3c272.12,10 00.42(0.14) 00.55(0.29) 00.27(0.15) 01.40(0.20) 01.00(0.40) 01.60(0.40) 1.8 3c2932,11 01.60(0.20) 05.30(0.40) 01.94(0.07) 03.25(0.07) 01.20(0.10) 02.80(0.20) 00.31(0.11) 1.30(0.10) 14450 2

65 3c310 00.12(0.06) 00.36(0.07) 00.08(0.04) 00.48(0.04) 00.19(0.06) 00.29(0.09) 3c326n2,12 00.30(0.06) 00.69(0.06) 00.41(0.04) 01.26(0.05) 00.31(0.06) 00.46(0.22) 00.25(0.09) 00.29(0.09) 1183 3c4242,13 00.45(0.07) 01.12(0.06) 00.21(0.03) 00.43(0.04) 00.15(0.04) 00.17(0.07) 00.28(0.05) <3560 3c4332,14 02.00(0.40) 01.40(0.20) 00.58(0.17) 01.20(0.20) 01.60(0.50) 01.20(0.30) <5495 3c4362 00.48(0.16) 00.46(0.07) 00.31(0.12) 00.28(0.04) 00.22(0.10) 00.41(0.12) 00.21(0.10) CenA2,15 10.00(6.00) 57.00(9.00) 27.00(4.00) 09.30(3.70) 12.00(3.00) 27.00(4.00) <210 3c2363,10 00.20(0.03) 00.95(0.07) 00.32(0.05) 00.64(0.05) <6220 Arp2204,16 < 970 18.62(1.68) 09.80(1.30) 07.30(0.20) 12.90(3.80) 22500 IRAS 00188-08564,16 < 19 00.43(0.05) 00.20(0.04) 00.38(0.12) < 32 21300 IRAS 03521+00284,16 < 13 00.82(0.13) 00.27(0.09) 00.37(0.03) < 3.0 29400 Table 2.2 (cont’d)

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) M(H2) Name (106 M⊙) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

IRAS 05189-25244,16 < 282 03.40(0.70) 01.50(0.20) 03.60(1.30) < 341 3200 IRAS 06035-71024,17 < 61 04.17(0.04) 02.33(0.58) 03.4(1.00) < 116 19000 IRAS 06206-63154,17 < 29 01.29(0.10) 00.50(0.05) 00.59(0.19) < 18 41400 IRAS 07598+65084,16 < 30 01.38(0.70) 00.37(0.06) 00.67(0.02) < 225 36000 IRAS 08572+39154,16 < 154 01.19(0.04) 00.51(0.10) 00.46(0.13) < 430 4200 IRAS 10565+24484,16 < 109 06.57(0.05) 02.56(0.09) 04.03(0.02) < 54 17900 F12112+03054,18 1.4(0.4) 4.12(0.44) 1.73(0.31) 2.37(0.03) 4.10(0.8) 19200 IRAS 13451+12324,18 < 45 02.83(0.65) 01.29(0.05) 02.19(0.26) < 41 <46900 F14348-14474,18 < 6.1 4.47(0.15) 1.95(0.10) 2.4(0.21) < 31 20500 4,16

66 IRAS 17208-0014 < 239 08.81(0.09) 04.97(0.85) 05.7(1.1) < 85 22400 IRAS 19254-72454,17 < 85 08.81(0.57) 03.82(0.95) 03.82(0.04) < 4.00 21000 IRAS 20087-03084,16 < 21 02.29(0.14) 00.84(0.33) 01.3(0.40) < 22 51100 IRAS 23365+36044,16 < 91 03.9(0.31) 02.01(0.95) 03.1(0.5) < 30 27000 Mrk 2734,16 < 262.5 10.24(0.09) 05.6(0.70) 10.4(0.9) < 150 15870 UGC51014,19 < 100 04.96(0.47) 02.7(0.5) 02.8(0.30) < 195 7500 Mrk463E4,18 < 79 02.79(0.37) 01.31(0.08) 02.8(0.60) < 385 2180 PG1440+3565,20 0.60(0.14) 1.14(0.14) 0.51(0.06) 0.64(0.11) 6400 N62406,21 8.60(1.20) 50.40(1.50) 39.8(0.50) 70.90(1.90) 36.4(10.8) 95.2(16.6) 33.7(12.5) 14100 N31107,21 1.60(0.20) 10.00(0.90) 4.00(1.00) 5750 67 Table 2.2 (cont’d)

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) M(H2) Name (106 M⊙) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

N32567,22 9.00(3.00) 61.0(5.00) 34.0(3.00) 1400 N36907,21 3.80(0.60) 22.0(1.00) 11.0(4.00) 3700 N51357,21 1.30(0.50) 17.00(1.00) 9.30(1.40) 5500 N67017,21 1.90(0.90) 10.00(1.00) 4.60(0.80) 1200 N71307,23 1.40(0.30) 09.90(0.70) 4.20(1.70) 4130 N75917,24 1.00(0.30) 05.50(0.60) 3.00(1.00) 3270 N77717,21 3.50(1.80) 16.00(1.00) 8.70(1.20) 3280

a −1 2 −1 The cold H2 gas mass is calculated using αCO,Gal = 3.2 M⊙(K km s pc ) (not considering Helium and other heavy element mass 68 contribution) b The mass value in the parentheses is calculated using CO weighted mean αCO, suggested by Sandstrom et al. (Table 4) 2013 using a constant dust to gas ratio (DGR) marked in the reference as “S” cThe two numbers as the notemark in the first column of the table correspond to references. The first number is the reference from which we adopt the MIR rotational line flux and the second number is for the cold gas mass derived from the CO emission. Ref: (1) Roussel et al. 2007; (1S) Sandstrom et al.2013 + Roussel et al. 2007; (2) Ogle et al. 2010; (3) Guillard et al. 2012; (4) Hiqdon et al. 2006; (5) QUEST sample by S. Veilleux (2009); (6) Armus et al. 2006; (7) M. Pereira-Santaella. 2010; (8) Okuda et al. 2005; (9) Salome & Combes 2003; (10) Ocaña Flaquer et al. 2010; (11) Evans et al. 1999; (12) Nesvadba et al. 2010; (13) Saripalli & Mack 2007; (14) Evans et al. 2005; (15) Israel et al. 1990; (16) Solomon et al. 1997; (17) Mirabel et al. 1989; (18) Evans et al. 2002; (19) Rigopoulou 1996; (20) Evans et al. 2001; (21) Sanders et al. 1991; (22) Kazushi Sakamoto et al. (2006); (23) Curran et al. (2000); (24) Lavezzi & Dickey 1998; (25) Young et al. (2011); (26) Harnett et al.(1991) Table 2.3. Observed molecular hydrogen lines

Eu Transition Short notation Rest λ k A ν = 0 (m) (K) (10−11s−1) (1) (2) (3) (4) (5)

J = 2 −→ 0 S(0) 28.219 0510 2.95 J = 3 −→ 1 S(1) 17.035 1015 47.6 J = 4 −→ 2 S(2) 12.279 1681 275.0 J = 5 −→ 3 S(3) 9.665 2503 980.0 J = 6 −→ 4 S(4) 8.025 3473 2640.0 J = 7 −→ 5 S(5) 6.910 4585 5880.0 J = 8 −→ 6 S(6) 6.109 5828 11400.0 J = 9 −→ 7 S(7) 5.511 7196 20000.0

aThe rotational upper level energies were computed from the molecular constants given by Huber & Herzberg 1979 and transition probabilities are from Black & Dalgarno 1976

69 Table 2.4. Model derived parameters for SINGS galaxies

Galaxy T n M(T>100K) ℓ Mtotal Name (K) (in %) (1) (2) (3) (4)

N0337 59 (43) 5.47 9.46 (2.3) N1097 47 5.00 4.88 N1266 26 3.80 2.30 N1291 52 4.27 11.79 N1316 30 3.79 3.48 N1482 51 5.00 6.76 N1566 42 3.89 8.15 N2798 71 4.96 25.76 N2976 66 (89) 5.87 13.22 (56.6) N3049 42 5.02 3.06 N3184 57 (69) 5.57 7.67 (18.3) N3190 55 4.68 11.08 N3198 60 5.20 11.70 N3265 53 5.15 7.17 Mrk33 43 4.28 6.28 N3351 43 (70) 4.75 4.22 (26.2) N3521 63 5.42 12.97 N3627 43 (77) 4.53 5.08 (39.7) N3938 57 (55) 6.00 6.02 (5.03) N4125 50 4.16 11.18 N4254 35 (29) 4.68 2.10 (1.05) N4321 38 (62) 4.96 2.18 (15.1) N4450 53 4.28 12.46 N4536 49 (58) 5.03 5.64 (11.1) N4559 51 5.90 3.69 N4569 37 4.30 3.76 N4579 37 3.92 5.48 N4625 65 (54) 6.39 9.81 (3.61) N4631 51 5.25 5.72 N4725 > 51 4.79 <7.8

70 Table 2.4 (cont’d)

Galaxy T n M(T>100K) ℓ Mtotal Name (K) (in %) (1) (2) (3) (4)

N4736 52 (112) 4.54 9.88 (149) N4826 50 4.85 6.93 N5033 51 4.65 8.56 N5055 50 (72) 5.05 6.04 (26.4) N5194 39 3.94 6.28 N5195 50 4.51 8.78 N5713 56 (61) 4.91 10.36 (14.5) N5866 55 4.70 10.95 N6822A 39 4.20 4.91 N6946 45 (82) 4.96 4.23 (45.6) N7331 49 5.21 4.96 N7552 51 5.02 6.67 N7793 48 5.25 4.42

aThe value in the parentheses is calculated assuming central αCO from the dust emission, evaluated by Sandstrom et al. 2013

71 Table 2.5. Model derived parameters for radio, U/LIRGs galaxies

Galaxy Ref Model mass T n [M(T>100K)] T ′ [M(T>100K)] ℓ Mtotal ℓ Mtotal 6 ′ Name 10 M⊙ (K) in%,for Tℓ (K) in%for Tℓ (1) (2) (3) (4) (5) (6) (7) (8)

3c031 1 360 41 4.69 3.73 65 20.40 3c218 1 1040 41 4.47 4.53 67 24.92 3c272.1 1 1.87 50 3.41 18.8 101 102.4 3c293 1 13210 48 4.77 6.28 75 33.81 3c310 1 515 4.11 3c326n 1 2604 64 4.05 25.0 112 126.2 3c424 1 40820 >88 5.19 >58.5 >132 >320.0 3c433 1 12850 >62 4.51 >18.7 >101 >103.6 3c436 1 18820 4.40 CenA 1 379 >58 4.64 >13.8 >93 >76.79 3c236 2 14083 >61 4.86 >14.8 >95 >82.04 Arp220 3 10000 41 5.07 2.65 62 14.13 IRAS 00188-0856 3 5472 33 4.38 2.36 55 13.13 IRAS 03521+0028 3 53970 57 5.35 8.67 84 48.02 IRAS 05189-2524 3 3600 52 4.27 11.8 87 62.94 IRAS 06035-7102 3 19240 50 4.39 9.54 82 51.55 IRAS 06206-6315 3 11760 36 4.68 2.33 56 11.80 IRAS 07598+6508 3 76700 60 5.27 11.3 88 58.93 IRAS 08572+3915 3 6586 53 5.02 7.80 85 51.64 IRAS 10565+2448 3 19746 51 5.04 6.60 78 35.82 IRAS 12112+0305 3 38640 59 5.07 11.7 90 63.80 IRAS 13451+1232 3 43890 >49 4.57 >7.83 >78 >41.27 IRAS 14348-1447 3 37130 59 4.74 13.9 92 72.38 IRAS 17208-0014 3 14900 45 4.59 5.69 71 29.40 IRAS 19254-7245 3 89760 69 5.42 19.4 101 106.48 IRAS 20087-0308 3 45390 49 5.03 5.64 74 28.89 IRAS 23365+3604 3 18230 45 4.72 5.13 71 27.30 Mrk 273 3 9730 43 4.37 5.82 71 31.55 UGC5101 3 11655 56 4.96 10.1 85 53.17 Mrk 463E 3 4320 61 4.24 19.7 102 107.1

72 Table 2.5 (cont’d)

Galaxy Ref Model mass T n [M(T>100K)] T ′ [M(T>100K)] ℓ Mtotal ℓ Mtotal 6 ′ Name 10 M⊙ (K) in%,for Tℓ (K) in%for Tℓ (1) (2) (3) (4) (5) (6) (7) (8)

PG1440+356 4 11735 58 5.04 11.1 88 59.58 N6240 5 7240 40 3.73 8.20 65 30.95 N3110 5 1520 33 4.22 2.82 51 11.33 N3256 5 1360 50 3.71 15.3 NGC3690/IC694 5 1310 36 4.04 4.48 56 17.21 N5135 5 820 25 3.70 25.2 41 9.17 N6701 5 800 44 4.13 7.65 68 30.36 N7130 5 1320 35 4.18 3.55 54 14.13 N7591 5 754 32 4.18 2.67 49 10.17 N7771 5 1000 33 3.82 4.39 54 17.25

A ⋆ a. The molecular gas mass in column 3 is calculated extrapolating the power law model to Tℓ = 49 K. b. The temperature in column 4 is the model extrapolated temperature required to ﬁt the total molecular gas mass, calculated using the αCO,Gal. c. The warm gas mass fraction listed in column 6 is derived using the cold molecular gas mass by assuming αCO,Gal. d. The temperature in column 7 is the model extrapolated temperature required to ﬁt the total −1 2 −1 molecular gas mass assuming a low αCO of 0.8 M⊙(K km s pc ) . e. The warm gas mass fraction listed in column 8 is derived using the cold molecular gas mass by assuming a low αCO

73 Table 2.6. Observed molecular hydrogen line ﬂuxes and mass in low metallicity dwarfs

Galaxy 12+log[O/H] S(0) S(1) S(2) S(3) S(4) S(5) D M(CO) M(dust) M(model) n (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13)

CG007-025 7.77 5.45(0.43) 1.67(0.43) 0.72(0.21) 24.5 41.2 3935 5.24 N66 8.10 475(181) 1025(116) 1283(175) 433(207) 586(400) 482(314) 0.06 0.016 0.435 0.451 3.59 Haro 11 8.20 <2.49 1.68(0.55) 1.01(0.13) 1.21(0.18) 92 1670 4500d 6700 4.52 UM311 8.31 1.49(0.69) 0.73(0.35) 0.66(0.27) 24 95 400 4.51 HubbleV 8.42 0.81(0.43) 2.11(0.43) 1.60(0.41) 2.59(0.38) 0.5 0.27 0.28 0.16 4.20

a −17 −2 All rotational lines, masses, and ditance are in units 10 W m ,M⊙, and Mpc respectively b

74 Ref for metallicity CGCG007-025:(Izotov et al. 2007); N66:(Dufour et al. 1982,Dufour et al. 1984); Haro11:(Guseva et al. 2012); UM311:(Izotov et al. 1998) c −17 −2 For CGCG007-025 we also used the S(7) line ﬂux of H2, (0.46 ± 0.13) × 10 Wm , from (Hunt et al. 2010) d Ref for CO derived H2 mass CGCG007-025:(Hunt et al. 2015); N66:(Rubio et al. 1996); Haro11 and UM311:(Cormier et al. 2014); HubbleV: (Israel et al. 2003) e Ref for dust derived H2 mass N66:(Leroy et al. 2007); Haro11:(Cormier et al. 2014); HubbleV:(Israel et al. 1996) f 8 The molecular gas mass for Haro11 is in the range (4.5–11.5)×10 M⊙, due to uncertainty in H I mass. In the table the minimum value is mentioned Chapter 3

Molecular gas properties in ISM of

U/LIRGs of GOALS

3.1 Introduction

The Infrared Astronomical Satellite (IRAS) discovered a large population of luminous infrared galaxies (LIRGs), whose bolometric luminosities are dominated by the infrared part of their spectral energy distribution (SED; L 1011 L , Soifer et IR ≥ ⊙ al. (1987)) Galaxies with L 1012 L , known as Ultra Luminous Infrared Galaxies IR ≥ ⊙ (ULIRGs) are generally major mergers of molecular gas rich galaxies. The star formation rate in U/LIRGs are above a magnitude or two higher and also exhibit high

FIR color compared to normal star forming galaxies. The merging morphology, high

LIR, high star formation rate and high dust temperature makes U/LIRGs to stand out in their interstellar medium (ISM) properties from normal star forming galaxies. Stars form from molecular clouds, hence the knowledge of molecular gas content is essential to understand star formation in galaxies.

H2, the most abundant molecule in the universe, is diﬃcult to observe because of the lack of dipole moment and high rotational energy levels. The lower rotational transitions of carbon monoxide (CO) are used as a tracer to determine molecular gas

75 masses in galaxies. To convert the measured integrated intensities of CO luminosity to

molecular gas mass a conversion factor, αCO, is used, calibrated against the virial mass estimates in presumed self gravitating molecular clouds of the Milky Way (Solomon et al. 1987, Scoville et al. 1987). Using the standard Milky Way αCO in ULIRGs the molecular gas mass is overestimated and is about 5 times the dynamical mass of the galaxy (Solomon et al. 1997). To avoid this a low conversion factor for ULIRGs, of about 5 , is used as compared to the galactic value. The conversion factor is × proportional to √n/T , where n and T are the number density and temperature of

molecular clouds (Rachford et al. 2002). The observed high FIR color (high dust

temperatures) in ULIRGs plausibly suggest elevated gas temperatures in U/LIRGs,

which can reduce the conversion factor, αCO. The FIR color of LIRGs on average are in between the values of a normal star forming galaxy and ULIRGs, which may

suggest intermediate values of αCO. We used the power law model to estimate molecular gas content and study the molecular ISM properties in normal star forming galaxies of the Spitzer Infrared

Nearby Galaxy Survey (SINGS). The merging morphology, high dust temperature of galaxies in GOALS suggests indication of shocks. In this chapter we would like to test our power law model in galaxies, where shocks play a signiﬁcant contribution in exciting H2. The main motivation of this chapter is: 1. to test the power law model in estimating molecular gas mass

2. how molecular mass estimated from the power law model compare with the dust based and sub-mm luminosity, L850 measurements 3. how does the power law indices compare with the SED infrared slope 4. is there any change in the power law indices for AGN and star formation nucleus dominated galaxies.

The chapter is organized in the following manner. First we describe our sample

76 selection from GOALS in ,2. In ,3 we describe our analysis followed by our results § § and discussion in ,4 and ,5 , respectively. Finally we summarize our results in ,6. § § §

3.2 Sample

The IRAS Revised Bright Galaxy Sample (IRAS-RBGS; Sanders et al. (2003)) is a complete ﬂux limited sample of 629 galaxies, at Galactic latitudes b > 5◦ with S | | 60m > 5.24 Jy. The Great Observatories All-Sky LIRG Survey (GOALS; Armus et al. (2009)) includes a complete luminosity-limited sample of 180 LIRGs and 22 ULIRGs from the IRAS-RBGS. The galaxies in the GOALS sample range over distances 15–

400 Mpc, with the median redshift z = 0.0215 ( 95.2 Mpc). The spectra of these ∼ galaxies were obtained in the staring mode using the IRS Short-Low (SL: 5.5–14.5

m) and Long-Low (LL; 14–38 m) instruments. At the median galaxy distance the

nuclear spectrum covers the central 1.8 and 5.2 kpc in the SL and LL instruments. The on-source integration time range from 30–610 s, depending on the brightness of

nuclei.

3.2.0.1 Ancillary data CO(J=1–0)

We would like to compare our power law derived molecular gas with the CO derived mass values. For this research work we selected 49 galaxies from the GOALS

sample, for which the CO luminosity values were available in the literature. The CO

(J = 1–0) line intensities for our selected galaxies are from Sanders et al. (1991). We

estimated the molecular gas masses using the galactic conversion factor αCO = 4.35 M (K km s−1 pc2)−1 (equivalent to X = 2 1020 (K km s−1 cm2)−1) (Bolatto ⊙ CO × et al. 2013). The molecular gas masses were further reduced by a factor of 1.36 to remove the heavy element contribution in the ISM molecular gas mass.

77 3.2.1 Data reduction and Spectral ﬁtting

The IRS-Spitzer spectroscopic nuclear data were reduced using the S17 and S18.7

IRS pipeline from the Spitzer Science Center. The pipeline software removes the bad pixels, subtracts the background, corrects for non-linearity and performs wavelength and ﬂux calibration. The background is subtracted using a dedicated background when available. The standard extraction aperture and the point source calibration modes were used to extract the one-dimensional spectra using the Spitzer IRS Custom

Extraction software (SPICE). The data reduction is described in detail and all the reduced GOALS spectra are presented in Stierwalt et al. (2013). For systems observed in the mapping mode, spectra were extracted using the CUBISM (Smith et al. 2007b).

3.3 Analysis

The main aim of this research work is to calculate the total H2 gas mass and test whether MIR H2 rotational lines can be used as a tracer for estimating molecular gas content in U/LIRGs. We would like to compare the estimated molecular gas mass with the CO derived masses. However, only the central nucleus region is observed in the staring mode with the IRS spectrograph in most of the GOALS galaxies. The CO beamsize is about 1 arcmin wide covering sometimes the entire or may be signiﬁcant regions of galaxies. There is a discrepancy between the observed regions of galaxies by the IRS-Spitzer and CO beam. Figure 3-1 shows the IRS-Spitzer (blue rectangle) and CO beam (blue circle) on one of our sample galaxy NGC 5135. The IRS-Spitzer observes the central nuclear sub-region of the galaxy when compared to the large CO beam. Several galaxies are unresolved in the IRS-Spitzer beam and hence the IRS and CO beam observe complete galaxy region.

78 Figure 3-1 The observed IRS-Spitzer and CO beam regions on NGC 5135. The blue circular region is about 1 arcmin wide in diameter. The IRS-Spitzer slit and CO beam observe diﬀerent regions of the galaxy.

79 3.3.1 Disk template

To compare our power law derived H2 gas masses with the CO derived masses we require H2 line ﬂuxes from similar observed regions. As discussed in the previous section, the IRS-Spitzer and the CO beam coverages are diﬀerent, hence a correction is

required to estimate the H2 line ﬂuxes and compare for the similar region as observed by the CO beam. A method to correct this mismatch between the IRS and CO beam was to derive a disk spectrum template and appropriately scale and add it to the IRS

nucleus spectrum. The derived ﬁnal spectrum is an equivalent MIR spectrum of the

CO beam observed region. The H2 rotational line ﬂuxes is then measured from the ﬁnal spectrum to evaluate the molecular gas mass in galaxies.

To prepare the disk template we used galaxies, which were observed in the mapping

mode. We selected a total of 10 galaxies for this, after excluding systems which have widely separated nucleus and a steep MIR slope. We deﬁned the boundary of the

nucleus region at 1 kpc radius from the merging center. From the spectrum of the

entire region (nucleus and disk), we subtracted the nucleus spectrum to estimate the

disk spectrum for each of our selected 10 galaxies. We calculated the median value

of the ﬂux from the disk spectra at each wavelength and prepared the disk template.

The median LIRG’s disk template is shown in Figure 3-2 (in blue). For comparison we have plotted the starburst nucleus (in red) and star forming SINGS galaxy template

(in black) from Brandl et al. (2006) and Smith et al. (2007), respectively.

3.3.2 Scaling and adding the template spectrum

We scaled the LIRG’s disk template appropriately, and added to the IRS-Spitzer

nuclear spectrum of each galaxy to construct an equivalent spectrum for the observed

wide CO beam region. For this we used the IRAC- 8 m and MIPS- 24 m ﬂuxes of the same CO beam observed region. We scaled the SL and LL (short low and long

80 Figure 3-2 The LIRG’s disk template spectrum (blue) is prepared after subtracting the nucleus from the total spectrum obtained from the mapped galaxies. For comparison we also plot the normal star forming galaxy (SINGS, (Smith et al. (2007)), in black) and the nucleus starburst template (Brandl et al. (2006)), in red). The LIRG’s disk template is similar to the spectrum of normal star forming galaxies.

81 low) template and added to the IRS nuclear spectrum to match the IRAC - 8 m and

MIPS - 24 m fluxes. Ideally with this procedure the short low and the long low MIR spectrum need to be continuous but a slight mismatch between the two was observed in the spectrum. To get a continuous spectrum the new version of the SL and LL templates were scaled accordingly to match the two parts of the spectrum, finally deriving a continuous MIR spectrum. We evaluated the percentage differences, which was less than 20%, between the IRAC - 8 m and MIPS - 24 m fluxes with the final

ﬂuxes at 8 m and 24 m MIR spectrum estimated from the scaled and added IRS spectrum.

3.3.3 PAHFIT- to recover H2 line ﬂux

By scaling and adding the template we build the continuous MIR spectrum for the CO beam observed region for each galaxy in the sample. We used the PAHFIT tool developed by Smith et al. (2007) to estimate H2 line fluxes for our region of interest. PAHFIT is a spectral decomposition tool to separate IRS low-resolution spectra into broad Polycyclic Aromatic Hydrocarbon (PAH) features, unresolved line emission, grain continuum, and the full line flux of any blended features. Several H2 rotational lines are blended with PAH features and atomic ionized lines in the IRS low-resolution spectra. The line FWHM, line equivalent width, and uncertainty in the fluxes were determined within PAHFIT. The PAHFIT tool uses Drude profiles to

ﬁt PAH features of diﬀerent width in the IRS observed wavelength range.

3.3.4 H2 gas mass from power law model

After recovering H2 line fluxes from PAHFIT, we fit the MIR rotational line fluxes using the temperature power law distribution. Using the power law model we derived the molecular gas properties in our selected GOALS galaxies.

82 Figure 3-3 Power law model ﬁt (red solid) to the observed H2 line ratios (black points) for a sample galaxy NGC23 in GOALS

We assumed the column density of H2 molecules are distributed by a power law function with respect to temperature, dN T−n dT, where dN is the number of ∝ molecules in the temperature range T—T+dT (the model is described in detail in chapter 2 of the thesis). Keeping the upper temperature, Tu, ﬁxed at 2000 K and varying Tℓ and n, we ﬁt the H2 excitation diagram for each galaxy selected from the

GOALS sample. Figure 3-3 is a model ﬁt (red solid) to the observed H2 line ratios (black points) in the excitation diagram of NGC 23, with n = 4.32 in the temperature range 50–2000 K. With a continuous power law model well reproducing the rotational emission lines from warm H2, we extrapolated our model to lower temperatures to estimate the total molecular gas reservoir. We calculated our molecular gas masses by extrapolating the model to 49 K, the average value of extrapolated lower temperature, determined by Togi & Smith, (2016, submitted) in their normal star forming SINGS galaxies to recover similar amount of molecular gas mass derived using LCO.

83 3.4 Results

3.4.1 LIRG’s disk template

We prepared the LIRG’s disk template (in blue) from the mapped GOALS galaxies and compared it with the star burst nucleus template (in red, Brandl et al. (2006) and normal star forming galaxy template from SINGS (in black, Smith et al. (2007)), all normalized at 24 m.

The LIRG’s disk template is similar to the normal star forming galaxy template but deviates signiﬁcantly from the nuclear starburst template (Figure 3-2). The MIR slope of the LIRG’s disk template is lower than the starburst nucleus. The high MIR slope is an indication of warm dust. The ﬂux ratio, F30 , a MIR slope indicator, can F15 be used to characterize a starburst or an AGN dominated nucleus (Laurent et al.

(2000)). The ratio F30 is greater than 5.9 and less than 4.8 in starburst nuclei and F15 AGN dominated environments, respectively (Brandl et al. (2006)). The MIR slope in nuclei region of GOALS galaxies are in the range 2 < F30 < 35.4 (Stierwalt et al. F15 (2013)). A majority of the LIRGs (63%) have MIR slope in the range 4 < F30 < 10. F15 When compared to the less luminous LIRGs, ULIRGs show a much steeper slope

on average F30 = 12.5 compared to 7.11, for LIRGs. Stierwalt et al. (2013) also F15 discovered the most obscured nuclei have steeper MIR slopes since most of the warm

dust emission is hidden behind a large amount of cooler dust.

The energy source in the nucleus is primarily through the compact star forming

regions or by an AGN making the environment warmer than compared to the disk region. The PAH features in the starburst nuclei regions are weak compared to the

disks of the galaxies which suggests the possibility of PAHs getting destroyed by the

harsh radiation from the nucleus.

84 Figure 3-4 The model derived power law indices for our selected GOALS galaxies. The average power law index is 4.41 0.49 ±

3.4.2 Power law index

H2 molecules in a galaxy’s ISM can be heated through various excitation mechanism including UV radiation from stars, shocks from AGN and supernova. Cooling of H2 molecules result in various diﬀerent rotational lines, which can be ﬁt using a power law temperature distribution. Using a temperature power law distribution we

ﬁt the MIR rotational line ﬂuxes in our sample galaxies of GOALS.

The power law index in our sample range from 2.83–5.53, with a mean value of

4.41 0.49. Fig 3-4 is a histogram of derived power law indices observed for GOALS ± galaxies. The power law indices observed in GOALS galaxies are found to be lower than the average power law index of 4.8, for normal SINGS star forming galaxies, an indication of warm gas in the galaxy ISM of GOALS sample.

Neufeld et al. (2008) in a shocked environment of supernova remnant IC 443

found a power law temperature distribution for H2 column density in the range 3–6,

85 with an average value of 4.50. (Zakamska et al. (2010)) in her observation of ULIRGs

used a power law model with indices in the range 2.5–5.0 to ﬁt the observed H2 line ratios. Similarly Pereira-Santaella et al. (2014) in six local infrared bright seyferts

required a power law index in the range 4–5 to reproduce the observed H2 Spectral Line Energy Distribution (SLED). Our derived power law indices are consistent with

the theoretical predicted and other observed values in the literature (Neufeld & Yuan

(2008), Hollenbach & McKee (1979)).

3.4.3 H2 mass- extrapolating power law model to 49 K

The present method of using two or three temperature components to ﬁt the MIR

H2 rotational line ﬂuxes is a simple but contrary to the distribution of molecules with continuous temperature in the ISM. We employed a temperature power law

distribution of H2 molecules to ﬁt the rotational line ﬂuxes. A continuous power law distribution model can be extrapolated to lower temperatures to recover the

total molecular gas mass. For normal star forming galaxies in the SINGS sample for calibration we estimated the average extrapolated temperature of 49 10 K to match ± the amount of molecular gas mass estimated from CO emission, when used a galactic

conversion factor, within a factor of 2. Similarly extrapolating our model to 49 K ≈ we estimated the molecular gas mass for GOALS galaxies.

Figure 3-5 show the deviation of the model derived molecular gas mass with the

CO derived luminosity values. The solid line is the one-to-one correspondence line with a factor of two deviation, shown by dotted lines. Galaxies are color coded in 4

categories according to their LIR,

1011 log LIR 1011.33, L⊙ ≤ ≤ 1011.33 log LIR 1011.66, L⊙ ≤ ≤ 1011.66 log LIR 1011.99, and L⊙ ≤ ≤ log LIR 1011.99, L⊙ ≥ 86 Figure 3-5 The model derived molecular gas mass extrapolated to 49 K correlates with the CO derived molecular gas with assuming Galac- tic conversion factor. The dotted lines are a factor of two deviation from one to one correspondent solid lines. Generally galaxies with LIR 11.66 show deviation from the solid line. This may L⊙ ≥ be due to a low αCO or high molecular gas temperatures.

in black, blue, green and red respectively. Generally galaxies with log LIR 1011.66 L⊙ ≥ show deviation from the solid line, hinting for a requirement of high αCO or a high extrapolation temperature than 49 K (Figure 3-5).

3.5 Discussions

3.5.1 Low power law index in U/LIRGs

The variation in H2 rotational line ratios can cause change in the power law index, n, required to ﬁt MIR H2 ratios. Galaxies with warm molecular ISM result in a large number of molecules at high temperatures causing a less steep temperature power law

87 distribution or a low power law index. Hence, a low power law index is an indication

of warm molecular ISM. The average power law index in GOALS is calculated to be

4.41 0.49, lower than the normal star forming SINGS galaxies, an indication of a ± warmer molecular ISM in GOALS than compared to normal star forming galaxies.

The turbulence and shocks due to merging phenomenon in addition to radiation

from newly forming stars at a rate of '100 M⊙/yr can be a plausible explanation for heating of molecular gas in GOALS. The FIR color, a proxy for dust temperature,

is higher in U/LIRGs than the normal star forming galaxies, which may possibly

suggest a warm molecular ISM (Sanders & Mirabel (1996), U et al. (2012)). The

infrared luminosity in U/LIRGs is due to high star formation rate. The high infrared

luminosity can be due to intense radiation from young forming stars capable of heating the ISM gas. Figure 3-6 show the relation between power law index, n, and the

infrared luminosity, LIR. The blue points in the plot are the galaxies which require a template addition to construct the MIR spectrum for the observed CO region.

The red points are unresolved and require no template addition. The power law

index decreases with the increase in infrared luminosity. As discussed previously low

power law index is an indication of warm molecular ISM, galaxies with high infrared luminosity also indicate a warm molecular ISM.

3.5.2 Relation between LIR, PAHs and power law index

We study the relation of the power law index, n, with the infrared luminosity

LIR and 6.2 PAH ﬂux. ULIRGs emit most of their energy in the infrared spectral region, implying that they are heavily dust obscured. To power their huge infrared

luminosities these galaxies must undergo an intense star formation rate of 100 ∼

M⊙/yr. The dust in these galaxies absorbs the radiation from young forming stars and re-radiates at long wavelengths causing high infrared luminosities. Another pos-

sible energy source can be the accretion of large quantities of gas onto a central

88 Figure 3-6 The power law index decrease with the increase in the infrared 12 luminosity for LIR 10 L⊙. A decrease in the power law index suggests warm molecular≥ ISM in ULIRGs.

89 supermassive blackhole (SMBH) in an AGN (Sanders et al. (1988)). In most cases a

combination of star formation and AGN can contribute to the emission from U/LIRGs and the relative contribution of the two processes has been extensively studied (Lutz

et al. 1998, Genzel et al. 1998, Laurent et al. 2000, Armus et al. 2007, Spoon et

al. 2007, Veilleux et al. 2009, da Cunha et al. 2010). ULIRGs are in an advanced

merging stage than compared to LIRGs, with two or more spirals that consists of a

ﬂat rotating disk containing stars, gas and dust and a central concentration of stars

in the bulge. The merging phenomenon may result in shocks and turbulence heating

H2 molecules and a high warm gas mass fraction, causing the power law index to reduce.

The MIR spectrum includes diﬀerent PAH bands along with other atomic, molecular, and ionized lines. Diﬀerent ionized and neutral PAH bands can be observed in the MIR band. PAH molecules can be destroyed in harsh environments of AGN

(Smith et al. (2007)). The mean equivalent widths (EQWs) of 6.2 m PAH feature in the LIRGs of GOALS sample is 0.55 m lower than compared to ULIRGs with 0.3

m (Stierwalt et al. 2013). Hence, this indicates a possibility of change in the 6.2 m

PAH feature with the LIR. This also suggests a variation in the 6.2 m PAH feature with the power law index, n. Figure 3-7 demonstrate the relation between power

law index, n, and the equivalent width of the 6.2m PAH band. The blue points in

the plot are the galaxies which require a template addition, while the red points are unresolved and require no template addition. A low power law index also have low 6.2

PAH EQWs, implying weak PAH emission in the warm molecular ISM environments.

This may suggest PAH molecules getting destroyed or small PDRs than compared to

normal galaxies.

90 Figure 3-7 Relation between 6.2 m PAH equivalent width as a function of power law index. Galaxies with low power law index have elevated warm molecular gas mass fraction. In such warm environments PAH molecules can be destroyed resulting in low equivalent widths

91 3.5.3 Low αCO or high temperature

The 49 K is the average extrapolation temperature required to recover the total molecular gas mass for normal star forming SINGS galaxies when using a galactic conversion factor. However, galaxies of GOALS are mergers with high infrared luminosity and far infrared color, with a plausibility of high gas temperatures. High gas temperatures and turbulence driven by merging or high star formation rate result an increase in CO linewidth, causing overestimation of molecular gas mass when used a Galactic conversion factor. The median CO FWHM linewidth is broad (average

FWHM 800 km/s) especially in sub millimeter galaxies and are often observed with ∼ double-peaked line proﬁles, indicating merging or a disk (Greve et al. 2005). The merging phenomenon and turbulence may result an increase in the linewidth. The normal galactic conversion factor yields M(H2) = 2.5 Mdyn, a clear overestimate in molecular gas mass (Solomon et al. (1997)).

In Figure 3-5 galaxies are generally on the solid line, implying an average of 49

K model extrapolated temperature is able to recover the molecular gas mass derived from CO emission. However, galaxies with high infrared luminosity, LIR 11.66 L⊙ ≥ show deviation from the solid line. The deviation in these galaxies can be minimized

using a high conversion factor or high molecular gas temperature (> 49 K) or both. Galaxies above the solid line may be dominated by the eﬀect of high gas temperatures and may require model extrapolation to temperatures above 49 K to estimate the true molecular gas mass. Galaxies to the left of the solid line are overestimated in their molecular gas masses estimated form their CO emission and may require a low αCO.

3.5.4 Tℓ from gas-to-dust mass ratio GDR

In the previous subsection we discuss the deviation of CO derived molecular gas mass, M(H2,CO), from the H2 model derived mass, M(> 49 K). We aim to test

92 our model predicted mass with dust derived molecular gas mass estimates, another

molecular gas tracer. The dust and gas in galaxies are well mixed in the ISM and

the gas-to-dust mass ratio is usually consistent to be constant. Assuming a constant

gas-to-dust ratio and estimating the dust mass from FIR luminosity the total gas

mass in the galaxy ISM can be estimated. Subtracting the neutral atomic from the total gas mass, molecular gas mass can be calculated.

We estimated dust mass through 850 m emission using the relation

M D2 S dust = × 850 , (3.1) M B(ν, T ) κ ⊙ dust × 850,dust

M 1.25 105 D2 S dust = × × × 850 , (3.2) M T κ ⊙ dust × 850,dust

where D, S850, Tdust, κ850,dust are the distance in Mpc, 850 m ﬂux in Jy, dust temperature, and dust mass opacity in m2/kg, respectively. The dust temperature

is estimated using the ratio, S60 , 60-to-100 micron ﬂux ratio (Lisenfeld et al. 2000). S100 We assumed a value of 0.066 m2/kg for the dust mass opacity.

Two facts stand out from the analysis of Figure 3-8. The Galactic conversion factor underestimates molecular gas mass (abscissa values less than 1.0) and/or model extrapolated lower temperature of 49 K overestimate the molecular gas mass (ordinate values greater than 100). However, assuming a high conversion factor, the molecular gas mass will be over-estimated by CO emission, higher than the dynamical mass (Solomon et al. (1997)), ruling out this possibility in ULIRGs. The temperature value of 49 K was the model extrapolated temperature to recover the total molecular gas mass, estimated for the normal star forming SINGS galaxies. However galaxies in GOALS are at diﬀerent merging stages with high FIR color, all pointing to higher gas temperatures.

Few galaxies with infrared luminosities 1011.66 > L /L > 1011.33 and M(>49K) IR ⊙ Mdust

93 M(H2,CO) Figure 3-8 Galaxies with low M(>49K) , lower than 1.0 correspondingly have high M(>49K) , higher than 100. The solid line show the ratio Mdust value of M(>49K) = 100. This may be due to warm temperature Mdust in U/LIRGs resulting in Tℓ to be higher than 49 K.

94 M(H2,CO) < 100 also show M(>49K) > 1.0. The model molecular gas masses in these galaxies deviate by a factor of 2-3 from the CO derived masses. Galaxies in the lower infrared × 11 11.33 luminosity range, 10 < LIR/L⊙ < 10 , with similar physical ISM conditions of normal star forming SINGS galaxies are with the ratio M(H2,CO) 1.0, implying T M(>49K) ≈ ℓ = 49 K is the suitable model extrapolated temperature to recover the molecular gas mass in them. However, the ratio of model molecular gas to the dust mass, M(>49K) , in Mdust a few galaxies are as high as about 1000, implying model extrapolated temperature to 49 K is about a magnitude higher than the standard value of 100. Generally ≈ 11.66 galaxies with high infrared luminosities, LIR/L⊙ > 10 , require Tℓ greater than 49 K, implying warm ISM gas temperatures in these galaxies.

L850 3.5.5 Variation in the MISM

Scoville et al. (2014) empirically calibrated the ratio of 850 m luminosity to ISM

mass, α = L850 , and found to be constant in normal star forming, starburst and 850 MISM U/LIRGs galaxies. Scoville et al. (2014) had three samples for the calibration: 12 local star forming and star-burst galaxies, galactic observations from Planck and a sample of 28 SMGs at z<3 with CO(1–0) measurements and estimated α850 of 1.01, 0.79, and 1.01 1020 ergs/s/Hz/M , respectively. The ISM masses were calculated × ⊙

by assuming the atomic gas mass to be half of the molecular gas mass, hence MISM = 1.5 M(H ). We calculate the ratio of L to our model extrapolated mass estimate × 2 850 to understand the molecular gas properties in U/LIRGs.

Figure 3-9 show the relation of the ratio L850 = α with M(H2,CO) . The MISM 850 M(H2,T>49K) ISM mass in the left panel was calculated using 1.5 M(H ,T > 49K). In the left × 2 panel galaxies with ratio M(H2,CO) less than 1.0 (using galactic α ) have low α M(H2,T>49K) CO 850 (than 1020 ergs/s/Hz/M , Scoville et al. 2014, 2015), an overestimation of model ≈ ⊙ molecular gas mass. This implies the model need to be extrapolated to temperatures higher than 49 K, indicating warm molecular ISM than normal star forming galaxies. 95 L850 20 Figure 3-9 When used the galactic αCO the ratio, is 10 MISM ≈ ergs/s/Hz/M⊙, shown on the right plot. The MISM mass is calculated using the molecular gas mass, MISM = 1.5 M(H2). The molecular gas masses used on the left and right× plot are from LCO and power law model, respectively. On the left plot the ratio, L850 , increases with the molecular mass ratio derived using MISM CO luminosity and the model. Galaxies in GOALS have warm ISM gas hence, the extrapolated temperature need to be higher than 49 K. Reducing the power law model derived molecular gas mass will increase the ratio of L850 and M(H2,CO) . MISM M(>49K)

96 In the right panel of Figure 3-9 the ISM mass was estimated using molecular gas

mass derived through CO emission, M(ISM) = 1.5 M(H , CO). The α is constant × 2 850 and is ( 0.67 0.17) 1020 ergs/s/Hz/M , as estimated by Scoville et al. 2014, 2015. ± × ⊙ This suggests the model extrapolation temperature to 49 K possibly overestimates molecular gas mass and hence, a warmer ISM than compared to normal star forming galaxies.

3.5.6 Caveats

The conclusion of warm ISM in GOALS sample in the previous two subsections are subjected to many caveats due to assumptions made. The dust masses were estimated using a modiﬁed blackbody single temperature from the FIR ratio, S60 , which can S100 lead to a factor of more than 2 diﬀerence in galaxy’s dust mass (Remy-Ruyer et al. × 2015). Moreover a constant dust mass opacity values for all galaxies can add further

error in dust mass estimation. The aperture correction, discussed in section 3.3, to

match CO apertures with the IRS beam to estimate molecular gas masses can be

another possible source of error in the molecular gas to dust mass ratio. Future work

on estimating dust mass using entire IR SED can lead to true estimate of molecular

gas masses.

In the next section for estimating α850 the error arise from L850 and the molecular gas mass estimation. As discussed in chapter 2, the power law model predicted

molecular gas masses have a scatter of 0.34 dex, a factor of 2.20. Also in the ≈ analysis the ISM atomic gas is assumed to be half the molecular gas mass for all

galaxies. A future work on measuring atomic gas, dust, and molecular gas mass for

the same spatial region in galaxies can prove useful in studying and understanding variation in DGR in GOALS galaxies. This work could also lead to test any change

in DGR for a merger and a normal star forming galaxy.

97 3.6 Summary & Conclusions

We selected ten mapped LIRGs from GOALS to prepare a disk template spectrum.

We used the scaled disk template in addition to the IRS-Spitzer nucleus spectrum from the photometry ﬂux value constraint from IRAC-Spitzer 8 m and MIPS-Spitzer

24 m to get an equivalent spectrum for the galaxy region observed by the large CO beam to derive H2 line ﬂuxes. Using H2 rotational lines we derived the power law index for warm molecular gas to estimate the temperature distribution of molecules

and understand molecular gas properties in these mergers.

Our key points of this work are:

1. The disk spectrum of LIRGs are similar to normal galaxies and the eﬀects of

merging processes occur only at the nuclei region of the merger systems.

2. The power law indices (average 4.41 0.49) for our selected GOALS galaxies are ± generally found lower than the normal star forming galaxies (average 4.8 0.61). ±

3. The power law indices decrease with the infrared luminosity, LIR. High infrared luminosity sources may have high warm gas temperatures due to high star

formation rate and turbulence resulting in lower power law indices.

4. We observe an indirect relation between the power law index and 6.2 m PAH

equivalent width. Merger systems with low 6.2 m PAH width are warmer sources with high AGN fraction.

5. The model predicted molecular gas masses for high infrared luminosity galaxies

LIR > 1011.66, with extrapolation temperature to 49 K show a slight over- L⊙ estimate of molecular gas masses than compared to CO derived luminosities

using a Galactic conversion factor when compared to scatter of 2.2 in model × predicted molecular gas masses

98 6. Galaxies with an overestimation of molecular gas masses through our model

when extrapolated to 49 K show high ratio of M(H2>49K) , implying possible Mdust overestimation of model molecular gas masses than compared to normal stan-

dard assumption of molecular gas to dust mass ratio.

7. Galaxies with an overestimation of molecular gas masses through our model

when extrapolated to 49 K show low ratio of L850 than the method when used MISM a galactic conversion factor to calculate the ISM mass. This suggests warm

molecular ISM in GOALS than compared to SINGS galaxies.

99 Table 3.1. H2 line ﬂuxes for GOALS

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) (1) (2) (3) (4) (5) (6) (7) (8) (9)

NGC 23 39.7 (4.06) 239 (5.47) 118 (4.86) 209 (19.6) 79 (11.6) 106 (22.8) 23.4 (15.3) MCG-03-04-014 29.5 (7.28) 104 (7.48) 62.1 (2.11) 103 (3.15) 98.7 (5.54) NGC 695 28.4 (10.4) 154 (12.0) 91.3 (4.29) 176 (7.31) 31.5 (10.1) 106 (16.7) 16.1 (14.7) NGC 828 42.9 (9.71) 360 (13.7) 160 (10.8) 288 (25.7) 109 (35.2) 202 (37.4) 8.47 (39.2) IC 0214 22.2 (5.5) 91.4 (7.11) 51.6 (2.95) 81 (4.93) 8.38 (6.41) 72.7 (10.7) 7.51 (7.06) NGC 877-S 23.1 (2.73) 91.7 (5.02) 24.3 (2.68) 124 (38.3) 18.8 (7.07) 48.4 (22.0) 3.61 (10.8) NGC 958 46.2 (77.6) 214 (142) 74.6 (163) 146 (156) 50.9 (705) 70.0 (307) 19.3 (475) 20.1 (74.4) NGC 992 40.7 (11.7) 221 (15.1) 124 (13.7) 193 (30.8) 56.3 (48.6) 145 (48.7) 2.78 (43.2) UGC 02238 13.4 (7.11) 199 (9.72) 102 (7.92) 193 (23.4) 57 (27.6) 108 (26.8) NGC 1365 281 (86.1) 1910 (57.7) 1090 (48.7) 18 (51) 773 (224) 1190 (275) 119 (152) 203 (104)

100 NGC 1614 224 (7.98) 559 (11.1) 308 (7.01) 388 (17.2) 214 (19.2) 504 (48.7) IRAS05081+7936 7.92 (6.36) 94.5 (7.11) 55.4 (6.36) 84.2 (13.1) 81.6 (15.7) 75.5 (19.7) 8 (17.9) IRAS05189-2524 13.3 (4.64) 148 (3.7) 110 (5.36) 37.4 (7.17) 22.6 (6.33) NGC 2146 1030 (24.6) 2420 (23.3) 1410 (35.2) 2970 (83.5) 1040 (86.8) 1180 (192) 326 (145) IRAS 07251-0248 12.9 (4.42) 66.4 (9.93) 82.3 (20.7) 200 (8.52) 224 (14.2) NGC 2623 86.4 (14.7) 178 (10.4) 60.6 (6.16) 141 (16.3) 111 (17.2) 33 (19.3) 33.7 (16.4) IRAS08572+3915 284 (4.62) 533 (18.6) 62.9 (8.92) 2120 (20.8) 1110 (41.2) 1160 (28.5) UGC 4881-E 19.0 (4.04) 73.4 (5.62) 24.4 (1.84) 57.8 (44.5) 20.8 (49.7) 27.1 (5.58) 5.68 (4.41) UGC 4881-W 21.7 (4.47) 65.4 (5.03) 21 (1.8) 38.9 (3.86) 23.9 (4.72) 1.89 (4.32) UGC 5101 21.8 (6.96) 105 (5.29) 50.5 (5.95) 77.3 (15.7) 129 (15.5) 56.9 (15.4) 281 (16.8) Table 3.1 (cont’d)

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) (1) (2) (3) (4) (5) (6) (7) (8) (9)

NGC 3110 305 (12) 149 (4.48) 268 (7.9) 83.7 (14.2) 162 (27) 22.5 (15.1) NGC 3221 54.3 (6.4) 234 (8.53) 105 (5.59) 201 (25.9) 73.6 (14.4) 139 (31.7) 18.5 (58.2) NGC 3256 655 (76.7) 1530 (52.9) 844 (23.3) 1200 (33.1) 442 (93.2) 1030 (176) 93.4 (109) IRAS 10565+2448 48.9 (6.63) 114 (5.15) 52.2 (5.27) 87.7 (11.5) 76.5 (12.6) 80.6 (15.2) 26.9 (13.1) IC 2810 18.6 (6.01) 63.6 (5.55) 26 (1.57) 45.9 (2.8) 11.4 (3.98) 27.9 (4.27) 5.03 (4.15) NGC 3690E 1520 (19.7) 1900 (9.24) 582 (4.23) 2030 (8.12) 1140 (10.5) 242 (7.51) 541 (8.14) IRAS 12112+0305 3.73 (4.91) 91.6 (6.33) 20.6 (7.64) 67.7 (14.8) 52.9 (14.2) 20.6 (23.1) 46.2 (16.8) NGC 4194 324 (428) 447 (508) 220 (625) 379 (559) 228 (1550) 31.7 (213) VV250a-E 89.4 (11.2) 110 (8.19) 58.5 (5.11) 94.3 (11.5) 59.1 (14.6) VV250a-W 11.4 (3.5) 23.3 (5.05) 12.4 (5.75) 32.7 (14.4) 27.7 (19.4) UGC 08387 83.5 (11.7) 365 (12.4) 97.8 (2.2) 335 (6.44) 25.8 (5.99) 156 (12) 19 (5.52)

101 NGC 5135 75 (11.2) 350 (9.37) 165 (10.6) 282 (29.7) 81 (30.6) 345 (38.9) 27.9 (24.7) UGC 08696 9.29 (14.4) 306 (8.17) 30.4 (5.56) 403 (23.3) 258 (18.6) 96.9 (17.6) 280 (21.4) NGC 5653 54 (5.31) 311 (6.98) 123 (10.8) 267 (28.5) 71.3 (22.2) 132 (50.4) 28.6 (33.3) IRAS 14348-1447 3.69 (6.9) 140 (8.25) 26.6 (2.71) 141 (7.68) 86.4 (4.74) 14.6 (6.43) 83.7 (5.04) CGCG049-057 28 (2.95) 124 (3.85) 42 (1.89) 173 (5.39) 72.7 (5.24) 30 (7.22) 49.2 (6.29) NGC 5936 25 (11.2) 228 (12) 118 (11.4) 175 (34.1) 64.5 (31.2) 150 (41.6) Arp 220 1530 (34.2) 1100 (134) 1060 (30.5) 180 (28) 889 (38.8) NGC 6090 93.3 (2.54) 203 (3) 68.2 (6.45) 126 (9.5) 41.6 (18.9) 84.9 (35.3) 18.4 (28.6) NGC 6240 162 (19.3) 1250 (16.4) 406 (6.5) 1670 (22.3) 625 (21.2) 1220 (17.9) 105 (17.8) 542 (17.1) 102 Table 3.1 (cont’d)

Galaxy S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) S(7)(err) (1) (2) (3) (4) (5) (6) (7) (8) (9)

NGC 6701 54.6 (9.17) 275 (12.6) 122 (10.2) 335 (77) 82.1 (30.1) 65.1 (30.9) 11.6 (29.4) IRAS 19297-0406 30 (7.07) 106 (5.58) 17 (6.76) 83.6 (18.8) 53.6 (15.2) 14.2 (26.8) 38.5 (17.6) CGCCG448-020-E 57 (5.06) 199 (3.79) 22.9 (2.92) 140 (5.35) 31.8 (7.25) 47.3 (8.36) 16.7 (6.5) NGC 7130 266 (9.67) 140 (11) 162 (13.3) 125 (38.1) 118 (44.5) 51.3 (33) IC 5179 48.3 (4.63) 464 (7.76) 279 (4.8) 454 (10.4) 163 (17.7) 298 (6.8) IRAS 22491-1808 18.4 (5.46) 50.3 (7.32) 65.8 (4.81) 33.8 (4.05) 13.5 (5.42) 14.6 (5.11) NGC 7469 90.2 (35.2) 393 (25.8) 169 (7.02) 200 (8.04) 33.8 (19.7) 137 (20.5) 6.47 (16.5) NGC 7674 91.8 (6.66) 80.7 (10.3) 13.9 (5.24) 85.5 (9.91) 27.9 (10) 103 (15.4) Mrk 331 39.7 (10.3) 260 (7.60) 103 (6.07) 186 (10.6) 92.4 (16.5) 175 (19.1) 103 Table 3.2. H2 line ﬂuxes for GOALS

S60 Galaxy D n log (M(>49 K)) log (M(H2,CO) S850 S100 (Mpc) mJy (1) (2) (3) (4) (5) (6) (7)

NGC23 58.5 4.31 9.46 9.68 144 (25) 0.60 (0.10) MCG-03-04-014 79.6 4.27 9.85 10.44 0.62 (0.11) NGC695 133 4.29 9.97 10.34 136 0.60 (0.10) NGC828 71.4 4.52 9.93 10.14 0.48 (0.07) IC0214 123 4.4 9.74 10.24 0.64 (0.11) NGC877-S 50.6 4.83 9.22 9.63 0.39 (0.08) NGC958 76.5 10.14 262 0.34 (0.07) NGC992 54.1 4.35 9.38 9.63 146 0.64 (0.08) UGC02238 88.3 4.36 9.77 10.14 104 0.50 (0.09) NGC1365 21.2 4.41 9.54 10.27 0.53 (0.07) NGC1614 65.5 4.6 10.1 219 0.99 (0.06) IRAS05081+7936 229 4.05 10.1 10.69 0.58 (0.09) IRAS05189-2524 181 10.37 1.20 (0.06) NGC2146 11.9 4.61 9.26 9.6 0.71 (0.06) IRAS07251-0248 387 2.83 9.57 10.63 1.00 (0.13) NGC2623 80.5 4.51 9.72 9.77 91 0.83 (0.06) IRAS08572+3915 254 3.1 10.3 9.78 17 (7) 1.64 (0.13) UGC4881-E 169 4.77 10.1 10.46 65 (13) 0.58 (0.08) UGC4881-W 169 5 10.2 — UGC5101 168 3.31 9.37 10.32 0.57 (0.09) NGC3110 75.2 10.3 0.56 (0.11) NGC3221 61.4 4.45 9.57 9.66 0.39 (0.08) NGC3256 42.8 5 10.1 10.18 188(28) 0.77 (0.08) IRAS10565+2448 188 4.46 10.2 10.34 61(13) 0.80 (0.07) IC2810 149 4.76 9.97 10.26 106(18) 0.58 (0.13) NGC3690E 42.2 0.97 (0.08) IRAS12112+0305 324 4.34 10.5 10.62 49 (10) 0.85 (0.1) NGC4194 36.8 9.28 0.83 (0.13) VV250a-E 132 4.9 10.2 0.92 (—–) VV250a-W 132 4.83 9.46 — UGC08387 109 4.8 10.5 9.87 113 (15) 0.61 (0.11)

104 Table 3.2 (cont’d)

S60 Galaxy D n log (M(>49 K)) log (M(H2,CO) S850 S100 (Mpc) mJy (1) (2) (3) (4) (5) (6) (7)

NGC5135 60.9 4.34 9.68 10.06 0.59 (0.01) UGC08696 162 3.96 10.2 10.24 1.02 (0.06) NGC5653 51.8 4.53 9.6 9.63 205 (32) 0.53 (0.08) IRAS14348-1447 366 4.16 10.7 10.78 24 (7.2) 0.91 (0.13) CGCG049-057 56.4 4.22 9.08 9.47 200 (27) 0.71 (0.07) NGC5936 57.5 4.36 9.45 9.63 152 (28) 0.53 (0.09) Arp220 77.2 4.04 10.3 10.28 456 (47) 0.92 (0.05) NGC6090 123 5.53 10.7 10.15 91 (15) 0.75 (0.06) NGC6240 101 4.25 10.6 10.29 150 (45) 0.82 (0.06) NGC6701 53.4 4.28 9.42 9.61 0.49 (0.05) IRAS19297-0406 372 4.57 10.9 10.51 0.91 (0.13) CGCCG448-020-E 148 5.01 10.6 10.3 1.26 (0.09) NGC7130 63.6 10.16 0.64 (0.07) IC5179 43.7 4.23 9.44 9.93 0.52 (0.07) IRAS22491-1808 334 4.26 10.3 10.43 19 (5.7) 1.22 (0.11) NGC7469 62.7 4.99 10.1 9.96 192 (27) 0.74 (0.09) NGC7674 116 4.11 9.46 10.06 108 (20) 0.69 (0.11) Mrk331 72 4.62 9.86 10.11 132 (25) 0.86 (0.09) a To calculate the molecular gas from CO luminosity, L’CO values are from Sanders et al.(1991) b The 850 m luminosities, L850, are from Dunne et al. (2000) c S60 The S100 are from IRAS catalog (NED Extragalactic Database) d The molecular gas masses are in units of M⊙

105 Chapter 4

Molecular gas properties in shocks

of Stephan’s Quintet

4.1 Introduction

Stephan’s Quintet (hereafter SQ) in the constellation of Pegasus is a visual grouping of five galaxies: NGC 7317, NGC 7318a, NGC 7318b, NGC 7319 and NGC 7320, of which the first four (NGC 7320 is a foreground galaxy) form the first discovered compact galaxy group by Edouard Stephan in 1877 at Marseille Observatory. These galaxies are of interest because of their violent collisions. SQ is also one of the nearby compact groups of galaxies and hence, studied extensively at all the wavelengths of electromagnetic spectrum from X-rays (Bahcall et al. 1984, Sulentic et al. 1995,

Trinchieri et al. 2003, O Sullivan et al. 2009), UV (Xu et al. 2005), visible (Moles et al. 1998, Gallagher et al. 2001, Fedotov et al. 2011), IR (Sulentic et al. 2001; Natale et al. 2010, Cluver et al. 2010; Guillard et al. 2010; Suzuki et al. 2011; Bitsakis et al. 2014), to radio waves (Allen & Hartsuiker 1972; van der Hulst & Rots 1981;

Xu et al. 2003; Nikiel-Wroczynski et al. 2013). Previous studies have detected CO

(1–0) emission from brightest regions in NGC 7319 and in the two extragalactic star forming regions (Gao & Xu 2000, Smith & Struck 2001, Lisenfeld et al. 2002, Petitpas

106 Figure 4-1 Stephan’s Quintet in the constellation of Pegasus is a visual grouping of ﬁve galaxies: NGC 7317, NGC 7318a, NGC 7318b, NGC 7319, and NGC 7320. NGC 7320 is a foreground galaxy. Image credit: amazing-space.stsci.edu

107 & Taylor 2005). The galaxy NGC 7318b is an intruder galaxy, between NGC 7318a and NGC 7319, and the IGM between NGC 7318b and NGC 7319 is shock heated to high temperatures and glows in the X-ray wavelengths. Shocks excite H2 molecules eﬃciently and hence, IRS-Spitzer MIR spectroscopy revealed bright, broad, pure H2 rotational line emission in these regions (Appleton et al. 2006).

In this work we prepared an extensive grid of IRS spectra pertaining to the excitation of H2. We derive H2 rotational line ﬂuxes for each region in the grid and using the power law model estimated the physical properties of IGM in the shocks of SQ.

4.2 H2 in shocks of Stephan’s Quintet

The gas in the SQ group halo mainly constitutes of neutral atomic HI clouds and possibly H2 clouds embedded in hot intercloud plasma. The absence of dust features or lines of ionized gas suggests the presence of warm molecular gas with little or no star formation at all. Shocks created due to intruding galaxy and a tidal arm at a relative speed of about 1000 km/s excite H2 molecules, which result in large ﬂux of

H2 rotational line ﬂuxes. Its necessary to understand in shock regions

1. why is H2 present in postshock gas?

2. how can we account H2 excitation?

3. why H2 is the dominant coolant?

H2 formation results from the density structure of the preshock gas. The collision velocity is the shock velocity in low density regions ( 0.01 cm−3) which produces dust free X-ray emitting plasma. The pressure of the plasma drives shocks with slow speed (5–20 km/s) into dense gas in clouds. Gas with temperatures less than 106 K preserved dust and has a cooling time less than the collision age ( 5106 yr). Due to high postshock pressure the warm neutral medium is unstable the gas cools to cold neutral medium temperatures, condenses and form molecules. Guillard et al. (2009)

108 have shown for a wide range of postshock pressures, preshock cloud sizes and densities

the H2 formation timescale is lower than the collision age and the turbulent mixing timescale of the warm gas with the plasma.

Observations have shown that the non thermal kinetic energy of H2 is higher

than the thermal energy of the plasma. H2 emission is powered by the dissipation of this kinetic energy. Guillard et al. 2009 have reproduced H2 line emission ﬂuxes by appropriate combination of continuous (C-type) and jump (J-type) shock velocities with suitable preshock densities.

The thermal, Rayleigh-Taylor and Kelvin-Helmholtz instabilities produces frag- mentary postshock clouds where atomic and molecular clouds are mixed on small spatial scales and embedded in the hot plasma. The eﬃcient transfer of the kinetic energy associated with the bulk displacement of clouds to turbulent motions of low velocity within molecular gas, is essential for H2 to be a dominant coolant of the postshock gas.

There is no star formation in the shock regions of SQ, where H2 is detected suggests that the molecular fragments are short lived, not enough to collapse and become gravitationally unstable.

4.3 Observations, Data reduction and Analysis

The spectroscopy observations of SQ were made using a low resolution mode (R

= 60–127) of the IRS-Spitzer instrument. The LL module spectrally mapped an area of 2.8 3.2 arcmin2 in 21 steps of 8 arcsec (0.75 slit width), and was ∼ × × designed to cover whole radio/X-ray emitting ﬁlament. Similarly the SL module

(covering a slightly smaller area than LL) performed two partially overlapping scans perpendicular to the LL slit, in 2 23 steps of 2.8 arcsec (0.75 slit width) for each × × sub-module. All the individual frames were median combined, calibrated, corrected,

109 and assembled into 2D data cubes using the CUBISM (Smith et al. 2007) software

after processing through the Spitzer Science Center S17 pipelines. This resulted in cubes for the SL and LL mapped onto the sky with a pixel scale of 1.85 1.85 arcsec2 × and 5.1 5.1 arcsec2, respectively. Inorder to ensure that the extracted spectra of × the H2 line ﬂuxes are at a common spatial resolution, set by the S(0) line occurring at the maximum rest wavelength at 28.22 m, we convolved at each wavelength, the individual layers of the SL2 (5.2–7.7 m), SL1 (7.4–14.5 m), LL2 (14.0–21.3 m) cubes to the scale of 7 arcsec (FWHM of the 28 m line) using a Gaussian kernel. It was not necessary to smooth the LL1 (19.5–38 m) cube because the only line of interest in this paper is 28.2 m line, and so the cube was left in the native form.

This procedure has two effects that our spectral extractions were not affected by the resolution difference over the 5–28 m wavelength range, and the procedure improved

S/N ratio of the shorter wavelength data signiﬁcantly.

4.3.1 MIR H2 emission and spectra

Previous MIR spectral observations have shown strong rotational H2 emission lines, especially in the main shocked ﬁlament (Appleton et al. 2006). We aim to study spatial trends in the temperature and density of gas over the whole region that was mapped by both IRS-LL and IRS-SL instrument. Spectra were extracted from the SL2, SL1, LL2, and LL1 cubes and then stitched together to prepare the full MIR spectra. In general, no scaling was required in stitching the spectra together. A small subset of SL2 spectra required a small positive correction due to an over subtraction of the background reference spectrum.

The IRS spectral extractions were performed in CUBISM on the SL and LL cubes using the four corners of 3 3 native SL pixels to deﬁne the extraction areas over × a continuous grid. This resulted in boxes of area 5.5 5.5 arcsec2. which is about × half the width of the LL slit. Figure 4-2 shows the extraction grid of 212 spectra

110 superimposed on a B-band HST image of the Quintet. We only sample regions that are well covered in both the SL and LL cubes, and so we have been conservative about the edges of the mapped area to ensure good coverage at all wavelengths

4.4 Excitation diagram Fits

H2 being a symmetric molecule has no allowed dipole transitions, and only weak quadrupole transitions are allowed. Excitation diagrams are a convenient way of exploring molecular distribution of level populations in galaxies. We compare two approaches to ﬁt the H2 excitation diagram derived from the 2D IRS mapping of the SQ. First, we employ the traditional one, two or three discrete temperature ﬁts and the second, by assuming a single power law distribution of temperatures. Both the methods assume that the gas is in thermal equilibrium. We will discuss how each method provides insight into the system leading to self consistent conclusions.

4.4.1 Discrete temperature ﬁt

Assuming the MIR lines of H2 are optically thin, the column density of the upper energy level (Nu) of each pure rotational transition is measured observationally from the spectral line ﬂux, F, according to

4πF N = , (4.1) u hνAω where h, ν, A and ω are Planck’s constant, frequency, Einstein’s coeﬃcient of the transition and solid angle of the observed region, respectively (same equation as 2.8).

In a local thermodynamic equilibrium (LTE) the upper energy level column density is related to both T and Ntot, the excitation temperature and the total column density,

111 Figure 4-2 Spectral extraction grid used to investigate the excitation of the gas over the main H2 ﬁlament, and includes areas common to both the long-low and short-low modules. The numbered extraction boxes are 5.55 5.5 arcsec2 (2.5 2.5 kpc2, assuming × × D = 94 Mpc). The background image is using the F665 N HST image. The overall extent of the warm H2 emission is about 50 35 kpc2. ×

112 Figure 4-3 A two temperature ﬁt, T1 = 219 K and T2 = 722 K, of the excitation diagram of H2 for the square region 105 in the center of the SQ’s ﬁlament. The values for each of the seven H2 lines are shown with 1-σ uncertainties. respectively, by −Eu/kT Nu e = Ntot (4.2) gu Z(T )

The H2 excitation is usually presented as a plot of the ln[Nu/gu] versus Eu/K, where the slope of the line is proportional to 1/T.

We assumed the ortho and para H2 for the lower pure rotational H2 transitions are in equilibrium. For H densities 103 cm−3, most of the lower rotational transition 2 ≥ lines are thermalized and temperature derived from the ﬁts to the ortho and para H2 transitions should yield consistent temperatures (Roussel et al. 2007). Burton et al.

113 1992 showed that in collisional equilibrium, the ortho-to-para (OPR), increases from

about unity at T = 75 K, to a constant value of 3 at T 300 K temperatures. Since ≥

our temperatures from the rotational H2 line transitions are in the range 120 > T > 1500 K, the equilibrium values are in the range 1.8–3.0. After normalizing for this factor, signiﬁcant deviations from LTE would appear on an excitation diagram. No evidence for such deviations from equilibrium are observed in our detections.

An additional complication is that a single temperature fit is usually not able to recover all the H2 line fluxes. A two temperature fit usually fits the excitation diagram better. In the literature this is a common approach because it provides a

ﬁrst approximation to the temperatures, column densities, and the total warm H2 masses. However a unique discrete temperature ﬁt may not exist for an excitation diagram and hence a need for more robust technique is required.

Single temperature solutions were found, where there were fewer than four transitions (22% of the data) and two temperature solutions were required for the other transitions. The process for fitting a two temperature LTE model is iterative. We created an initial excitation diagram with the line fluxes (derived from Table 1) for each of the 212 extracted square regions. Initially we assumed an OPR of 3 to obtain a first approximation to the temperature minimizing the chi-squared deviations for a two temperature model. Once the chi-squared values are minimized, we assumed those temperatures as a first guess and adjust the OPR appropriate for LTE from Burton et al. (1992) and re-run and this process is repeated for several iterations until a best fit value for the T and column density are determined. Figure 4-3 show an example of such a fit for an extracted square region numbered 105 and in Table

4.2 we list the two temperature values for each 212 extracted regions.

[*]-1in

114 Table 4.1. MIR H2 line ﬂux for Quintet

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

1— — ——— —— 2 — 2.48(0.575) 3.99(0.706) — — 7.89(0.443) — 3 — 4.74(0.596) 7.14(0.991) — — — — 4 1.14(0.425) 13.2(0.612) 10.1(0.839) 30.5(1.25) — — — 5 — 12.1(0.57) 6.61(1.6) 21.3(1.25) — — — 6 — 9.12(0.633) — — — 2.92(0.441) — 7 — 10.6(0.638) 8.47(4.0) 17.7(1.25) — 21.8(3.0) — 8 — 11.1(0.494) — 21.4(1.25) — 8.61(0.546) — 9 — 9.19(0.52) 6.63(0.811) 17.5(1.33) — — — 10 2.21(0.479) 8.11(0.444) — 14.8(1.38) — 5.23(0.433) — 11 — 2.42(0.416) 2.42(0.703) 2.67(1.11) — — — 12 — 8.76(0.551) 5.23(0.767) 9.12(1.24) — — — 13 2.29(0.424) 22.9(0.602) 8.03(0.774) 18.8(1.25) — — — 14 2.62(0.426) 23.4(0.562) 15.1(0.774) 33.7(1.25) 7.38(1.63) 26.2(1.4) 16.7(1.3) 15 1.69(0.507) 16.7(0.562) 11.0(0.767) 16.7(1.24) 4.86(1.66) 16.6(1.4) 16.6(1.3) 16 1.35(0.429) 15.2(0.612) 7.53(0.839) 9.99(1.24) — — — 17 2.95(0.481) 18.1(0.594) 11.5(0.818) 23.4(1.3) 5.41(1.7) 14.0(1.3) — 18 1.12(0.567) 12.0(0.533) 7.53(0.839) 11.0(1.25) — — — 19 — 7.06(0.531) 5.62(0.832) — — — — 20 1.85(0.472) 7.23(0.546) 4.54(0.847) 5.75(1.11) — 8.76(1.4) 15.6(1.3) 21 — 3.88(0.523) 5.96(0.767) — — — — 22 — 10.6(0.551) 6.27(0.767) 5.14(1.14) — — — 23 1.97(0.557) 19.0(0.572) 11.7(0.774) 15.3(1.87) — — — 24 2.11(0.426) 23.7(0.569) 14.5(0.774) 21.1(1.79) — 15.2(1.3) — 25 2.41(0.426) 22.1(0.558) 13.0(0.832) 19.3(1.87) — 15.6(1.3) — 26 2.27(0.507) 15.4(0.585) 11.2(0.818) 13.7(1.15) — 11.3(1.3) — 27 — 11.7(0.538) — 14.5(1.77) — 13.7(1.3) — 28 — 10.7(0.57) — 6.42(1.14) — 6.56(1.3) — 29 — 7.6(0.543) 6.46(0.767) — — — — 30 — 6.04(0.551) 7.53(0.839) — — — — 31 1.14(0.424) 2.37(0.553) 2.94(0.7) — — — —

115 Table 4.1 (cont’d)

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

32 1.01(0.5) 4.57(0.512) 3.34(0.774) — — — — 33 1.9(0.479) 9.99(0.557) 5.05(0.941) 7.1(1.14) — — — 34 0.897(0.516) 20.7(0.569) 11.7(0.811) 20.1(1.25) 4.57(1.68) 12.8(0.601) — 35 2.75(0.43) 19.5(0.567) 13.2(0.839) 25.3(1.71) — 14.7(0.9) — 36 3.04(0.479) 13.7(0.553) 9.19(0.839) 13.7(2.03) — 3.73(1.38) — 37 1.66(0.8) 10.8(0.528) 8.54(0.999) 7.89(1.15) — — — 38 — 9.99(0.625) 8.32(0.818) 6.05(1.15) — — — 39 — 8.54(0.679) 4.48(0.861) 5.39(1.15) — — — 40 1.17(0.426) 7.59(0.5) 5.69(0.89) 5.18(1.15) — — — 41 — 2.95(0.479) 3.74(0.818) 7.11(1.26) — — — 42 1.49(0.42) 6.2(0.57) 6.63(0.79) 8.8(1.26) — — — 43 2.33(0.553) 16.4(0.562) 8.32(0.839) 10.5(1.28) — — — 44 1.6(0.478) 21.3(0.557) 12.2(0.839) 19.5(1.25) — 8.32(2.5) — 45 1.47(0.425) 21.1(0.554) 13.2(0.839) 29.7(1.3) 6.14(1.65) 14.0(1.5) — 46 3.09(0.426) 17.7(0.541) 7.82(0.825) 16.9(1.25) — 10.6(1.8) — 47 2.32(0.548) 10.6(0.584) 6.94(0.839) 11.2(1.28) — — — 48 1.69(0.527) 10.3(0.596) 6.69(0.818) 10.6(1.28) — — 3.9(0.679) 49 2.06(0.425) 11.4(0.623) 4.5(0.731) 10.3(1.28) — 3.29(0.437) — 50 — 9.84(0.654) — 8.25(1.28) — — — 51 — 4.23(0.612) — — — — — 52 2.35(0.47) 9.19(0.566) 6.97(0.839) 5.54(1.25) — 13.3(1.5) — 53 2.16(0.433) 16.8(0.575) 13.5(0.839) 15.9(1.31) 3.35(1.9) 8.11(0.446) — 54 3.49(0.48) 25.0(0.572) 21.2(0.847) 32.4(1.3) 5.83(1.86) 18.4(0.492) — 55 4.03(0.428) 34.8(0.575) 21.6(0.839) 41.6(1.25) 10.9(2.04) 20.4(0.648) 6.66(0.581) 56 4.05(0.426) 27.1(0.557) 17.4(0.839) 29.1(1.25) 6.02(—9.99e+21) 13.1(0.453) 8.25(0.714) 57 2.55(0.424) 18.2(0.558) 9.19(0.832) 10.1(1.26) 4.08(1.64) — — 58 2.32(0.422) 13.8(0.52) 6.77(0.825) 7.67(1.26) — 13.2(1.5) — 59 2.79(0.423) 11.9(0.613) 6.59(0.825) 5.48(1.15) — 5.08(0.624) — 60 1.71(0.47) 10.6(0.469) 5.33(0.832) 3.49(1.15) — 11.1(3.0) 3.9(0.711) 61 — 2.34(0.484) 4.58(0.745) — — — — 62 1.69(0.426) 8.39(0.509) 4.26(0.731) 4.23(1.29) — — —

116 Table 4.1 (cont’d)

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

63 2.97(0.43) 16.1(0.623) 8.54(0.839) 9.91(1.32) — 2.86(0.443) — 64 4.36(0.431) 25.2(0.639) 13.5(0.839) 18.4(1.32) — 7.82(2.0) — 65 3.93(0.504) 28.9(0.57) 17.9(0.839) 31.1(1.25) 7.67(1.87) — — 66 3.68(0.424) 33.2(0.568) 19.0(0.839) 35.2(1.7) 9.84(1.87) — — 67 3.56(0.428) 25.7(0.555) 12.9(0.839) 18.7(1.74) 5.59(1.65) — — 68 2.77(0.428) 17.0(0.6) 7.11(0.839) 10.3(1.66) — — — 69 1.99(0.523) 12.6(0.6) 5.69(0.796) 7.18(1.15) — — — 70 2.05(0.554) 10.9(0.575) 3.97(0.818) 6.79(1.15) — — — 71 — 2.18(0.575) — 3.13(1.12) — — — 72 1.22(0.429) 6.07(0.613) — 3.44(1.13) — — — 73 2.97(0.538) 12.2(0.627) 3.91(0.738) 5.88(1.33) — — — 74 3.29(0.504) 16.0(0.619) 7.53(0.839) 11.4(1.7) — — — 75 3.67(0.523) 22.8(0.585) 7.53(0.839) 14.1(1.69) — — — 76 3.73(0.427) 34.7(0.575) 15.3(0.825) 29.7(1.25) 8.39(1.71) 7.6(0.774) — 77 4.94(0.428) 36.1(0.565) 23.3(0.825) 46.3(1.3) 9.26(1.88) 24.9(0.533) 7.2(1.5) 78 4.15(0.433) 26.4(0.609) 12.2(0.839) 28.0(1.28) 4.83(1.9) 14.8(1.0) — 79 2.74(0.426) 16.9(0.575) 4.56(0.825) 11.2(1.27) — — — 80 2.32(0.429) 13.8(0.578) 4.49(0.847) 10.9(1.3) — — — 81 1.98(0.43) 13.2(0.578) 3.95(0.745) 8.54(1.25) 8.32(1.9) — — 82 1.56(0.425) 13.8(0.546) 3.63(0.731) 12.3(1.25) — — — 83 2.0(0.423) 14.1(0.479) — 11.8(1.25) — — — 84— — — — — — — 85 0.637(0.48) 3.43(0.628) — 7.6(1.3) — — — 86 2.08(0.549) 9.7(0.621) 2.97(0.839) 7.45(1.3) — — — 87 3.26(0.427) 16.0(0.604) 4.72(0.847) 11.7(1.3) — 2.86(0.8) — 88 3.39(0.429) 20.3(0.575) 6.86(0.825) 16.3(1.3) 4.74(2.11) — — 89 4.07(0.524) 31.7(0.576) 13.2(0.818) 31.1(1.3) 6.25(1.69) 9.55(0.9) — 90 4.52(0.519) 41.5(0.559) 20.6(0.825) 52.0(1.3) 13.5(2.06) 25.9(1.3) — 91 5.31(0.429) 36.1(0.567) 19.0(0.839) 48.1(1.29) 10.9(2.45) 29.7(1.2) — 92 3.93(0.426) 25.3(0.574) 9.34(0.839) 22.0(1.29) 8.32(2.02) 11.1(1.2) — 93 3.31(0.429) 18.8(0.622) 5.46(0.825) 15.0(1.3) 5.94(1.98) 2.72(0.8) —

117 Table 4.1 (cont’d)

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

94 3.63(0.562) 17.9(0.564) 7.31(0.825) 15.2(1.25) 9.7(2.0) — — 95 4.13(0.479) 18.5(0.587) 7.31(0.818) 17.8(1.26) — — — 96 2.58(0.431) 18.8(0.585) 7.6(0.811) 14.4(1.3) — — — 97 2.04(0.427) — — 6.26(—9.99e+21) — — — 98 — 2.33(0.504) — 6.8(—9.99e+21) — — — 99 0.941(0.43) 6.81(0.621) — 4.14(1.3) — — — 100 2.16(0.43) 12.0(0.634) 1.92(0.738) 7.45(1.3) — — — 101 2.71(0.432) 16.7(0.622) 4.77(0.825) 12.8(1.3) — — — 102 3.89(0.429) 29.4(0.576) 10.4(0.825) 26.8(1.3) 4.82(1.9) 12.5(1.2) — 103 3.98(0.543) 43.9(0.576) 19.5(0.839) 51.6(1.29) 11.6(1.9) 24.7(1.3) 5.64(1.3) 104 5.43(0.43) 43.3(0.578) 22.5(0.825) 59.4(1.3) 17.3(2.49) 36.3(1.4) 7.31(1.3) 105 4.43(0.426) 33.3(0.561) 15.8(0.839) 35.4(1.28) 8.76(1.79) 23.9(1.4) 4.86(1.2) 106 4.78(0.559) 27.1(0.612) 7.38(0.839) 20.6(1.3) 5.49(2.04) 7.19(0.9) — 107 4.43(0.567) 23.4(0.621) 6.83(0.818) 18.5(1.27) 8.97(2.08) — — 108 4.99(0.478) 26.1(0.561) 8.47(0.825) 22.2(1.3) 11.5(2.0) 6.85(1.2) — 109 5.21(0.554) 33.1(0.672) 11.7(0.818) 25.2(1.29) 8.47(2.18) 11.9(1.2) — 110 2.04(0.548) 3.37(0.685) — — — — — 111 — 3.44(0.688) — 7.45(1.27) — — — 112 — 3.76(0.753) — 6.78(1.3) — — — 113 1.5(0.53) 7.96(0.481) — 10.6(1.27) — — — 114 2.39(0.429) 12.0(0.625) 2.36(0.839) 12.3(1.27) — — — 115 3.37(0.432) 24.7(0.624) 7.67(0.847) 24.6(1.32) 4.52(1.85) 11.9(1.3) 3.9(0.667) 116 4.9(0.546) 43.1(0.623) 19.3(0.847) 58.6(1.29) 14.7(2.82) 33.4(1.4) 6.21(1.4) 117 4.86(0.425) 45.4(0.572) 22.4(0.825) 64.3(1.28) 18.4(1.89) 35.4(1.4) 7.06(1.4) 118 4.72(0.428) 37.1(0.567) 15.1(0.839) 44.5(1.29) 13.7(2.83) 26.2(1.2) — 119 4.8(0.558) 32.9(0.612) 10.5(0.839) 31.3(1.3) 10.2(2.01) 17.1(1.4) — 120 5.41(0.43) 35.2(0.581) 13.2(0.839) 34.6(1.25) 9.41(2.26) 14.4(1.2) — 121 5.91(0.568) 36.1(0.581) 15.1(0.839) 33.7(1.3) 8.61(1.85) 15.8(1.4) 6.12(1.4) 122 4.81(0.428) 36.9(0.539) 14.7(0.839) 30.3(1.3) 9.91(1.83) 16.6(1.2) — 123 2.16(0.474) 2.55(0.443) — — — — — 124 1.21(0.476) 3.26(0.8) — — — — —

118 Table 4.1 (cont’d)

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

125 0.223(0.479) 3.22(0.57) — 5.67(1.3) — — — 126 — 5.99(0.475) — 5.87(1.29) — — — 127 2.2(0.477) 8.11(0.631) — 6.9(1.3) — — — 128 2.45(0.473) 17.7(0.563) 4.65(0.767) 14.3(1.32) 6.76(1.72) — — 129 4.65(0.475) 35.1(0.625) 12.3(0.825) 33.1(1.3) 8.32(1.87) 17.4(1.3) 5.42(1.3) 130 4.8(0.53) 41.0(0.572) 18.0(0.825) 47.3(1.27) 13.0(1.88) 22.9(1.3) 7.11(1.3) 131 4.96(0.429) 36.5(0.562) 14.6(0.839) 38.1(1.25) 10.8(1.84) 19.0(1.4) 5.32(1.4) 132 5.55(0.43) 37.5(0.611) 13.8(0.839) 37.0(1.25) 7.96(1.82) 18.7(1.4) — 133 5.25(0.43) 35.8(0.624) 15.8(0.818) 37.6(1.25) 12.5(1.78) 14.6(1.3) 9.05(1.3) 134 6.22(0.539) 35.9(0.615) 16.6(0.818) 35.8(1.25) 15.1(1.81) 14.6(1.3) 12.6(1.3) 135 4.44(0.427) 35.6(0.478) 9.84(0.818) 20.3(1.66) 8.25(1.87) 11.9(1.4) — 136 1.32(0.478) 3.11(0.562) — — — — — 137 1.4(0.476) 4.04(0.59) — — — — — 138 1.31(0.566) 6.58(0.484) — — — — — 139 2.27(0.477) 9.84(0.628) 5.23(0.818) 6.08(1.25) — — — 140 2.57(0.564) 19.0(0.619) 5.48(0.926) 14.9(1.28) — — — 141 3.82(0.43) 31.0(0.588) 11.0(0.818) 30.5(1.3) — 11.9(1.3) — 142 6.39(0.568) 43.9(0.578) 19.4(0.839) 47.4(1.3) 9.34(1.74) 25.3(0.589) 6.3(0.58) 143 6.56(0.432) 40.4(0.567) 18.2(0.825) 47.1(1.3) 11.6(2.08) 24.5(0.524) 8.25(0.583) 144 4.99(0.431) 33.3(0.611) 8.47(0.839) 24.6(1.25) 8.54(1.7) 9.19(1.3) — 145 5.12(0.548) 31.5(0.612) 6.69(0.948) 19.6(1.25) 10.9(1.65) — — 146 4.56(0.563) 19.8(0.601) 5.06(0.811) 12.7(1.25) 6.74(1.67) 14.3(1.3) — 147 2.0(0.477) 4.07(0.56) 3.92(0.854) — — — — 148 — 3.7(0.556) — — — — — 149 — 4.83(0.476) 3.64(0.839) — — — — 150 1.6(0.428) 6.69(0.478) 5.65(0.832) 3.62(1.26) — — — 151 2.3(0.568) 12.9(0.612) 5.58(0.839) 8.47(1.25) — — — 152 3.64(0.43) 29.8(0.58) 9.41(0.847) 22.1(1.46) — — — 153 6.3(0.583) 46.5(0.579) 22.9(0.839) 47.0(1.5) 11.5(1.74) 26.4(1.4) — 154 6.91(0.432) 45.4(0.57) 20.0(0.818) 41.7(1.63) 9.7(2.0) 29.2(1.4) 8.18(1.4) 155 5.39(0.429) 33.0(0.609) 11.0(0.839) 18.8(1.75) 4.88(1.7) — —

119 Table 4.1 (cont’d)

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

156 4.13(0.43) 19.9(0.611) 6.45(0.839) 9.91(1.15) 7.11(1.61) — — 157 3.55(0.564) 14.5(0.615) 5.51(0.818) 7.09(1.27) 3.55(1.61) — — 158 1.44(0.428) 2.71(0.581) 1.8(0.861) 3.42(1.3) — — — 159 — 2.75(0.559) — — — — — 160 — 4.83(0.567) — — — — — 161 — 5.7(0.622) 2.76(0.774) — — — — 162 2.5(0.429) 10.4(0.477) 2.58(0.738) 7.6(1.24) — — — 163 3.13(0.426) 20.3(0.646) 5.91(0.796) 9.48(1.24) — — — 164 5.54(0.476) 38.0(0.581) 14.3(0.839) 28.4(1.24) 7.38(2.03) 16.5(1.3) — 165 5.7(0.428) 42.6(0.577) 18.2(0.839) 35.7(1.27) 12.4(2.04) 24.2(1.4) — 166 5.5(0.431) 29.7(0.61) 13.8(0.839) 25.3(1.3) 4.82(1.73) 17.2(1.4) — 167 4.0(0.43) 19.0(0.572) 7.67(0.839) 11.2(1.16) 4.54(1.98) 10.3(0.533) — 168 3.32(0.429) 15.0(0.622) 5.46(0.767) 8.76(1.66) 4.21(1.66) — — 169 1.61(0.426) 5.83(0.475) 1.65(0.724) — — — — 170 2.55(0.478) 5.04(0.623) 4.12(0.731) — — — — 171 1.79(0.429) 5.38(0.556) 3.07(0.825) 4.96(1.26) — — — 172 1.32(0.428) 6.18(0.582) 2.36(0.745) 4.02(1.25) — — — 173 2.71(0.43) 11.0(0.478) 1.63(0.745) 5.93(1.46) — — — 174 3.72(0.43) 18.5(0.588) 4.1(0.753) 9.34(1.3) — 4.75(1.3) — 175 6.4(0.567) 28.2(0.577) 10.4(0.818) 18.1(1.25) 3.43(1.79) 9.84(1.3) — 176 7.22(0.565) 32.3(0.577) 15.2(0.818) 25.8(1.28) 15.1(1.82) 16.8(1.4) — 177 6.04(0.432) 29.5(0.571) 11.6(0.948) 24.5(1.3) 6.06(2.08) 14.3(1.4) — 178 4.93(0.43) 23.2(0.572) 7.02(1.01) 16.0(1.41) 6.33(1.95) 16.6(1.4) — 179 4.44(0.429) 20.7(0.61) 6.2(1.16) 6.15(1.34) — 15.1(1.4) — 180 2.4(0.472) 5.98(0.473) 4.02(0.839) — — — — 181 2.63(0.425) 6.71(0.602) 4.66(0.714) — — — — 182 3.06(0.426) 11.4(0.571) 6.06(0.955) 7.6(1.29) — 6.41(1.4) — 183 4.23(0.43) 16.8(0.557) 6.36(0.825) 10.6(1.25) — 6.3(1.0) — 184 4.76(0.429) 18.6(0.622) 5.73(0.847) 7.74(1.29) — — — 185 7.38(0.569) 21.1(0.579) 5.68(0.825) 9.26(1.31) — 7.67(1.0) — 186 6.14(0.429) 24.8(0.583) 8.11(0.825) 13.5(1.25) 4.25(1.74) 9.84(1.0) —

120 Table 4.1 (cont’d)

Reg S(0)(err) S(1)(err) S(2)(err) S(3)(err) S(4)(err) S(5)(err) S(6)(err) (1) (2) (3) (4) (5) (6) (7) (8)

187 8.25(0.43) 33.7(0.58) 12.7(0.825) 20.8(1.3) 4.02(1.76) 15.5(1.3) 5.04(1.5) 188 7.53(0.431) 35.5(0.583) 10.5(0.825) 20.6(1.25) 5.71(1.78) — — 189 7.96(0.555) 29.2(0.563) 8.68(0.818) 19.8(1.25) 6.29(2.13) 14.9(1.3) — 190 5.84(0.568) 24.0(0.61) 8.9(0.839) 11.9(1.77) — 13.8(1.3) — 191 1.77(0.425) 5.2(0.612) 5.85(0.774) 3.1(1.47) — — — 192 2.94(0.43) 8.9(0.567) 7.74(0.839) 7.11(1.25) — — — 193 3.85(0.554) 16.4(0.546) 10.1(0.825) 8.97(1.25) — — — 194 6.15(0.477) 22.1(0.558) 14.2(0.839) 17.8(1.25) — 14.2(1.3) — 195 6.48(0.543) 26.3(0.622) 13.2(0.839) 17.9(1.25) 5.75(1.81) 20.8(1.3) — 196 8.11(0.428) 28.4(0.659) 11.7(0.847) 17.4(1.25) — 16.5(1.3) — 197 9.99(0.43) 37.3(0.626) 13.8(0.847) 21.0(1.32) 3.32(1.72) 7.14(1.3) 4.96(1.3) 198 12.4(0.44) 47.0(0.627) 18.7(0.839) 30.4(1.32) 5.74(1.74) 16.3(1.3) — 199 9.34(0.564) 41.2(0.619) 17.7(0.847) 31.6(1.3) 5.02(1.74) 15.6(1.3) — 200 6.94(0.562) 31.3(0.572) 14.3(0.839) 23.9(1.25) — 12.3(1.3) — 201 5.3(0.579) 24.8(0.56) 12.0(0.803) 14.4(1.69) — — — 202 1.14(0.425) 4.92(0.561) 6.59(0.774) 5.74(1.25) — — — 203 3.0(0.541) 10.7(0.624) 4.31(0.796) 12.1(1.25) — — — 204 4.68(0.558) 16.0(0.572) 5.3(0.839) 10.2(1.25) — — — 205 5.63(0.475) 23.4(0.561) 9.63(0.825) 19.0(1.25) — — — 206 6.72(0.561) 29.4(0.554) 12.9(0.825) 22.1(1.26) 14.7(1.87) — — 207 9.63(0.427) 45.6(0.606) 16.8(0.847) 29.8(1.26) 19.3(1.87) 10.7(1.3) — 208 13.0(0.564) 46.0(0.615) 16.1(0.839) 32.9(1.32) 20.8(2.18) 16.3(1.3) — 209 12.2(0.578) 49.3(0.619) 17.9(0.839) 37.9(1.3) 15.7(2.09) 22.6(1.3) — 210 11.9(0.432) 49.1(0.638) 18.5(0.839) 35.2(1.32) — — — 211 7.0(0.567) 35.0(0.61) 13.8(0.825) 19.5(1.25) — — — 212 4.33(0.43) 18.9(0.61) 9.55(0.817) 13.3(1.25) — — — aAll values in 10−19 W m−2

121 Table 4.2. Power law model results for Quintet

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

1 —– —– —– —– —–—– —– —– 2 —– —– —– —– —–—– —– —– 3 100 582.5 6.528 6.4 —– —– —– —– 4 133.4 484.4 2.496 17.41 3.44 50 10.8 11.8 5 176.1 554.5 1.728 7.232 3.84 80 4.71 31.7 6 —– —– —– —– —–—– —– —– 7 —– —– —– —– 3.78 80 3.9 32.4 8 187.7 637.5 1.216 4.416 4.19 80 6.08 27.4 9 125.1 466.6 3.776 12.10 3.65 80 2.97 34.1 10 138.7 602 5.76 3.776 4.37 50 25.6 5.22 11 —– —– —– —– —– —– —– —– 12 142.7 432 2.56 10.56 4.24 80 5.01 26.9 13 195.6 505.3 2.56 8.96 4.62 110 5.8 73 14 215.7 906 2.368 3.264 3.92 50 38.7 7.79 15 275.8 1500 0.896 0.064 3.79 50 23.2 8.66 16 170.3 381 1.28 22.4 4.58 125 2.38 100 17 179.2 619.6 2.56 6.85 4.16 50 42.5 6.29 18 100 375.8 5.12 25.66 4.30 80 7.24 26.3 19 116.4 1500 0.64 0.064 —– —– —– —– 20 207.9 816.9 5.312 6.46 3.21 50 4.15 14.4 21 100 612.1 6.4 5.12 —- —– —– —– 22 113.5 370.1 4.48 22.02 4.44 80 7.29 24.8 23 100 370.9 9.6 41.79 4.06 120 2.66 100 24 346.4 1500 0.64 0.256 4.34 135 2.59 148 25 333.9 1460.5 0.64 0.32 4.34 120 3.59 100 26 340.2 1500 0.64 0.192 4.31 50 44.3 5.54 27 194.7 847 1.6 0.128 4.13 80 6.03 28.2 28 195.2 875.7 1.28 0.64 4.74 80 9.52 21.9 29 100 475.2 8.32 11.14 —– —– —– —– 30 100 556.1 6.4 8.064 —– —– —– —–

122 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

31 100 654.5 8.32 2.368 —– —– —– —– 32 137.2 615.3 2.56 2.944 —– —– —– —– 33 147.9 441.6 3.84 8.128 4.64 50 45.2 4.13 34 348.2 1500 0.64 0.256 4.51 80 15.1 24.1 35 176.6 606.8 3.2 9.152 4.26 50 52.5 5.77 36 118.2 439.1 11.52 18.50 4.29 50 38.6 5.61 37 100 377 7.68 23.17 4.23 80 6.11 27 38 100 388.6 5.12 21.12 3.96 80 4.4 30.1 39 284.7 1500 0.64 0.192 4.67 80 7.17 22.6 40 100 397.3 7.04 14.4 4.21 50 19.1 6.02 41 100 532.7 8.32 3.712 3.11 80 0.54 42.4 42 100 439.5 8.96 10.88 3.72 50 7.74 9.22 43 117.5 355.4 7.68 35.264 4.57 100 5.7 52.1 44 349 1500 0.64 0.128 4.39 135 2.37 100 45 362.7 947.1 0.64 0.896 4.15 135 2.14 100 46 173.6 635.6 3.84 4.288 4.5 50 66.3 4.67 47 100 394 15.36 19.84 4.24 50 27.7 5.88 48 315.8 1254.6 0.64 0.384 4.06 50 21.1 6.84 49 163.6 558.5 3.2 3.904 4.94 95 6.27 39.3 50 198.3 1472.4 1.28 0.448 —– —– —– —– 51 —– —– —– —– —– —– —– —– 52 141.5 670.6 5.12 4.352 4.03 50 17.9 7.06 53 358.6 1500 0.64 0.128 4.55 135 1.98 100 54 375.1 1500 0.64 0.32 3.9 50 40.4 7.91 55 357.3 1246.5 0.64 0.576 4.43 120 5.88 100 56 347.1 1500 0.64 0.256 4.51 100 9.04 52.7 57 111.5 347.2 9.6 42.432 4.55 100 6.25 52.3 58 242.7 1035.3 0.64 0.64 4.35 50 42.3 5.32 59 147.4 559.5 5.76 5.504 4.78 50 64.5 3.66 60 265.5 1469.2 0.64 0.192 4.17 50 25.2 6.24

123 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

61 100 664.7 6.4 3.2 —– —– —– —– 62 145.7 481 3.84 6.016 4.56 50 34.1 4.43 63 151.5 470.3 5.76 11.456 4.98 95 8.78 39.5 64 147.2 435.7 8.32 23.872 4.55 75 23.9 18.9 65 100 383.7 23.04 58.56 4.22 50 73.3 5.99 66 139.8 408.1 7.04 50.048 4.18 100 8.82 56 67 132.6 378.7 8.32 43.584 4.41 80 17.1 25.1 68 149.3 405.8 5.12 17.536 4.6 80 13.4 23.3 69 152.7 406.1 3.2 12.928 4.73 85 8.86 27.6 70 165.8 545.1 3.2 3.136 4.85 85 8.42 26.5 71 123.3 892.6 4.48 0.64 —– —– —– —– 72 179.9 1500 1.28 0.256 4.93 80 6.3 20.3 73 151.6 525 5.76 3.776 5.15 80 19.3 14.6 74 130.9 394.7 8.96 21.568 4.56 50 65.3 4.42 75 161.8 440.6 5.76 13.632 4.77 100 8.95 50.3 76 212.2 533.3 2.56 12.032 4.72 120 6.72 100 77 277.2 715.3 1.28 6.272 4.37 100 11 54.1 78 182 638.8 4.48 6.656 4.5 80 19.1 24.2 79 173.5 606.9 3.84 2.944 4.81 90 10.1 33.5 80 160.3 545 3.84 4.288 4.67 85 9.24 28.2 81 204.2 1500 1.92 0.512 4.53 87 7.28 32.4 82 354.7 188.9 0.64 0.896 4.63 100 4.97 51.6 83 184.6 863 2.56 1.216 4.61 100 5.01 51.8 84 —– —– —– —– —– —– —– —– 85 187 1031.3 0.64 0.64 —– —– —– —– 86 186.1 863.7 1.92 0.832 4.81 68 16.6 11.8 87 157.8 536.5 5.76 4.736 4.92 80 16.5 20.4 88 170.8 633.3 4.48 3.712 4.65 80 16.7 22.8 89 184.3 551.3 4.48 11.392 4.65 110 8.17 72.8 90 242.8 669.6 1.92 9.216 4.32 110 8.9 74.9

124 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

91 183.6 672.6 5.12 9.856 4.24 50 94.5 5.87 92 179.4 636.8 5.12 5.184 4.71 95 11.9 41.6 93 162.5 526.2 5.76 6.272 4.79 85 13.9 27.1 94 164.7 625.3 5.12 4.352 4.49 50 66.1 4.72 95 142.6 458.9 9.6 13.184 4.55 50 74.2 4.47 96 160.6 421.9 3.84 16.512 4.6 100 6.67 51.8 97 —– —– —– —– —– —– —– —– 98 —– —– —– —– —– —– —– —– 99 205.6 1500 0.64 0.256 4.81 100 2.75 49.9 100 167.7 1092.8 3.2 0.512 4.88 85 9.49 26.2 101 171.5 593.5 3.84 3.52 4.71 85 13.4 27.9 102 189 633.5 4.48 6.016 4.64 100 10.7 51.5 103 249.6 684.4 1.92 8.128 4.95 198 2.16 100 104 216.1 701 3.84 10.048 4.2 100 11.7 55.8 105 218.5 721.5 2.56 5.568 4.4 100 10.3 53.8 106 168.4 590.9 7.68 5.696 4.91 80 27.7 20.5 107 168.2 673.7 6.4 3.648 4.68 50 111 4 108 162.3 590.4 8.32 6.656 4.67 50 123 4.01 109 185 618.5 5.76 6.464 4.78 100 13.1 50.2 110 121.6 856.1 7.68 0.96 —– —– —– —– 111 137.8 897.2 3.2 0.768 —– —– —– —– 112 143.6 932.4 2.56 0.704 —– —– —– —– 113 166.9 968.1 2.56 0.896 4.19 50 19.6 6.1 114 164.2 985.4 3.84 1.024 4.52 50 46 4.6 115 182.5 725.8 4.48 3.648 4.57 100 8.57 52.2 116 214.3 695.8 3.84 9.728 4.25 100 12.1 55.3 117 221.4 687 3.2 11.072 4.2 110 9.04 75.7 118 193.6 691.3 5.12 7.808 4.4 100 11.7 53.8 119 182.5 675.9 5.76 5.76 4.59 90 16.8 35.6 120 175.1 605.5 7.04 9.152 4.59 80 27.5 23.4

125 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

121 190.4 653 5.12 7.296 4.59 75 35.6 18.5 122 204.8 658.2 3.84 6.336 4.66 105 11.3 61.4 123 111.2 841.5 10.88 1.024 —– —– —– —– 124 135.3 873.6 3.2 0.896 —– —– —– —– 125 180 480 0 7.424 —– —– —– —– 126 182.9 1489.8 1.28 0.32 —– —– —– —– 127 177.9 814.9 1.92 0.832 4.78 50 43.9 3.66 128 189.7 861.6 3.2 1.472 4.61 100 6.31 51.8 129 195.2 689.7 4.48 5.696 4.66 107 10.4 65.7 130 224.5 683.4 3.2 8.064 4.42 105 10.9 63.4 131 185.7 655.2 5.76 7.936 4.49 100 12 52.9 132 180.5 642.6 7.04 8.064 4.55 80 28.4 23.7 133 199.4 703.7 4.48 6.336 4.45 90 16.6 37 134 220.7 824.2 3.2 3.968 4.45 50 120 5.04 135 193.5 670.9 5.12 4.16 4.86 105 12.3 59.7 136 130.1 863.7 3.84 0.96 —– —– —– —– 137 139.5 894.1 3.2 0.832 —– —– —– —– 138 178.1 1371.1 1.28 0.384 —– —– —– —– 139 130.8 416.5 6.4 11.456 4.63 50 44.1 4.15 140 183.5 609.5 3.2 3.648 4.72 95 8.77 41.9 141 188.5 605.4 4.48 7.744 4.58 105 9.09 62 142 213.4 692.9 3.84 7.936 4.55 100 15 52.4 143 185 692.4 7.04 8.192 4.5 81 27.5 25.8 144 176 615.9 7.04 5.888 4.81 100 13.4 49.9 145 175.5 990.9 7.04 1.664 4.8 90 18.8 33.5 146 155.5 832.4 8.32 1.664 4.61 50 85.9 4.25 147 100.8 566.6 14.08 4.288 4.61 50 17.7 4.24 148 —– —– —– —– —– —– —– —– 149 158.2 451.1 —– 8.448 —– —– —– —– 150 100 445.6 10.88 10.432 4.05 50 13.4 6.92

126 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

151 151.8 429.2 4.48 10.56 4.72 80 11.3 22.2 152 180.1 486.5 5.12 12.352 4.68 105 9.26 61.2 153 245.9 688 2.56 7.808 4.47 100 15.1 53.1 154 192.8 696.5 6.4 8.448 4.49 85 26.3 30.1 155 156.7 409.2 9.6 26.176 4.73 85 23.2 27.6 156 182.4 873.5 2.56 1.216 4.82 50 115 3.52 157 139.8 410.8 8.32 12.288 4.92 50 93.9 3.24 158 128.2 1024.3 4.48 0.512 4.85 50 16.1 3.44 159 —– —– —– —– —– —– —– —– 160 —– —– —– —– —– —– —– —– 161 154.3 714.1 2.56 1.664 —– —– —– —– 162 174.5 913.4 1.92 1.088 4.86 50 62.8 3.4 163 172.7 470.2 4.48 7.104 4.92 100 8.74 48.9 164 197.6 660.8 5.12 5.952 4.73 100 14.6 50.6 165 215.5 708.9 3.84 6.016 4.57 100 14.8 52.1 166 171.6 634.9 7.04 7.168 4.59 71 36.3 14.9 167 169.7 706.6 5.12 2.688 4.69 50 91.8 3.95 168 148.5 470.2 7.04 8.128 4.81 65 31.8 9.48 169 165.2 1125.8 1.28 0.448 4.99 50 41.5 3.04 170 105.3 549.1 15.36 4.928 4.79 50 27.9 3.61 171 135.1 583.7 5.12 2.368 4.68 50 25.6 3.99 172 169.8 877.7 1.92 0.704 4.78 50 33.5 3.66 173 158 1500 5.12 0.32 5.21 77 17.1 15.1 174 164.8 644.9 6.4 2.176 5.03 85 16.3 24.9 175 158.7 579.4 10.24 6.848 4.89 50 176 3.32 176 159.9 610.6 10.88 9.28 4.57 50 133 4.39 177 162.5 634.9 9.6 6.208 4.68 50 140 4 178 164.7 811.9 7.68 2.112 4.6 50 98.9 4.3 179 168.4 953.2 6.4 1.024 4.57 50 85.5 4.38 180 119.6 563.5 9.6 4.416 4.81 50 33.7 3.57

127 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

181 114.2 523.4 12.16 6.272 4.67 50 31.7 4.02 182 146.5 596.4 6.4 3.776 4.71 50 56.3 3.9 183 152.6 602 8.32 3.84 4.91 54 78 4.52 184 144.2 426.5 10.88 10.688 5.05 50 144 2.88 185 142.7 663.5 17.28 2.688 5.15 50 183 2.65 186 156 649.9 10.88 3.84 4.93 50 163 3.21 187 155.7 650.9 14.72 6.144 4.82 50 193 3.52 188 150.7 434.5 15.36 20.224 4.91 50 229 3.26 189 152.2 699.2 15.36 3.904 4.84 50 171 3.48 190 154.5 657.9 10.88 5.12 4.71 50 119 3.89 191 100 533.9 12.16 6.848 3.91 50 8.49 7.86 192 100 409.4 19.2 16 4.37 50 27.8 5.25 193 100 357.5 23.68 37.056 4.47 50 59.2 4.79 194 140.1 567.9 14.08 10.944 4.52 50 85.1 4.59 195 158.1 681.4 10.24 5.952 4.5 50 99.1 4.65 196 148.8 657.5 16.64 5.696 4.79 50 155 3.64 197 149.5 571.8 20.48 9.344 5.02 56 174 4.7 198 148.1 554.4 25.6 14.656 4.9 50 300 3.28 199 155.5 559.8 16 13.44 4.76 50 218 3.72 200 157.2 556.3 11.52 10.816 4.72 50 158 3.83 201 100 342.8 33.28 60.224 4.56 50 101 4.42 202 100 466.1 5.76 8.832 3.44 50 4.03 11.8 203 140.5 539 7.04 4.8 4.47 50 38.7 4.78 204 139.5 459 11.52 8.384 5 50 115 3.02 205 132 403.2 15.36 26.624 4.69 50 113 3.95 206 165.8 597.1 7.68 7.552 4.56 50 119 4.45 207 225.7 1069.4 3.84 1.408 4.77 50 243 3.7 208 147.6 605.2 27.52 10.688 4.83 50 266 3.51 209 155.2 634 21.76 10.112 4.76 50 260 3.73 210 131.5 386.6 33.28 60.352 4.8 50 273 3.6

128 Table 4.2 (cont’d)

Reg T1 (T2) M(> T 1) M(> T 2) n T M(> T ) [M(T>120K)] ℓ ℓ Mtotal 6 4 6 (K) (K) (10 M⊙) (10 M⊙) (K) (10 M⊙) (%) (1) (2) (3) (4) (5) (6) (7) (8) 9

211 124 344.1 21.12 69.12 4.85 80 34 21 212 100 352.8 28.16 42.88 4.64 50 85.4 4.13

4.4.2 Power law model ﬁt

Considering the diverse range of heating environments in a galaxy’s ISM, the traditional method of ﬁtting two or three discrete temperature molecule components to the excitation diagram may not be realistic. Assuming a continuous power law temperature distribution for H2, we could ﬁt the excitation diagram and calculate the total H2 gas mass in the ISM (Chapter 2). Theoretical studies have demonstrated that cooling of H2 molecules in shocks follows a power law temperature distribution (Hollenbach & Mc. Kee 1979, Burton 1987. Following this in shocked environments

of supernova IC 443 (Neufeld et al. 2008) used a power law temperature distribution

to ﬁt the mid infrared (MIR) H2 rotational line ﬂuxes. Since shocks are the dominant

excitation mechanism for H2 we used our power law model to study molecular gas properties in SQ (Guillard et al. 2009, Cluver et al. 2010, Guillard et al. 2012).

Assuming MIR H2 emission to be optically thin, the flux observed in a rotational line S(J) is hν A N Ω F = J J J+2 , (4.3) J 4π where FJ , νJ , AJ , NJ+2, Ω are the flux, frequency, spontaneous emission probability, column density of the upper energy level, solid angle of the observation, respectively, for the H2 rotational line S(J). The column density is proportional to the flux F , the corresponding transition wavelength λ, and is inversely proportional to the sponta-

129 neous emission probability A,

FJ λJ NJ+2 , (4.4) ∝ AJ hence the observed ratio of column densities are,

N N F λ A J+2 = u = J J 1 , (4.5) N3 NS(1) F1λ1AJ where N3 is the column density of H2 molecules at energy level J = 3, the upper energy level for the S(1) transition.

We assumed the column density of H2 molecules are distributed by a power law function with respect to temperature, dN T−n dT, where dN is the number of ∝ molecules in the temperature range T—T+dT. The model consists of three parameters, upper and lower temperature cut oﬀ with power law index, denoted by Tu, Tℓ, and n, respectively. Keeping the upper temperature, Tu, ﬁxed at 2000 K and varying

Tℓ and n we ﬁt the H2 excitation diagram for each square region in the grid of our mapped area of SQ. Figure 4-4 is a model ﬁt (red solid) to the observed H2 line ratios (black points) in the excitation diagram of the square region 105, with n = 4.4 in the temperature range 100–2000 K .

4.5 Result

4.5.1 Two temperature ﬁts

Figure 4-5 shows the distributions of T1 and T2 temperatures across the SQ. The lowest temperature map shows cooler gas in the northern part of the ﬁlament with a quite broad distributions, and peaks near the center and to the south of the main

ﬁlament reaching over 200 K. The situation is similar to the T2 component map, where there are several peaks in the hottest component, at the ends of the ﬁlament. and in the center. Note that the warmer T2 component at 650 K extends towards

130 Figure 4-4 Power law model ﬁt (red solid) to the observed H2 line ratios (black points) in an excitation diagram for the square region numbered- 105 of our mapped area.

131 Figure 4-5 Map of the temperature distribution of the warm molecular gas derived from two-temperature ﬁt to the H2 excitation diagrams at each sampled position. (a) lowest temperature (T1) map image, with contours in K, (b) same map superimposed on the HST F665N image of the Quintet, (c) The higher temperature component (T2) superimposed on the F665N HST image, and (d) T2 map as an image with contours. the direction of the Seyfert galaxy NGC 7319. The hottest regions in both the T1

and T2 maps is the south of the ﬁlament. The coolest T1 component lies near the

extragalactic star formation site called SQ-A by Xu et al. 2005. In this region the

H2 may be heated by a combination of UV radiation and shocks (Cluver et al. 2010, Appleton et al. 2013). One consequence of the large warm gas in the center of the shock is that the measured mass in warm molecules is biased towards the lower

temperature regions.

4.5.2 H2 line ratios

The molecular gas in SQ can be substantially heated by shocks. H2 molecules can be excited to their high rotational energy levels, resulting in signiﬁcant amount

132 of MIR H2 emission. An analysis of H2 line ratios can provide insights for shock energetics. In this section we study the variation of line ratios over the shock regions

of SQ.

The H2 MIR rotational line ratios S(0)/S(1), S(3)/S(1), and S(5)/S(1) for each square region through shocks are color plotted, shown in Figure 4-6. Two facts clearly emerge from this analysis. First, shock regions have low S(0)/S(1) ratios but high

S(3)/S(1) and S(5)/S(1) and second, the line ratios follow S(0)/S(1) < S(5)/S(1) <

S(3)/S(1). The contour levels of S(3)/S(1) and S(5)/S(1), shown in the Figure 4-7, map the shock areas with two central regions, where these ratios are elevated. The two center regions of contour correspond to central shock regions between galaxies,

NGC 7318b–NGC 7319 and NGC 7318b–NGC 7320. The white squares in the ratio maps correspond to regions where S(0), S(3), and S(5) lines are undetected.

H2 molecules are excited to high energy levels (J > 2) in shocks resulting a decrease in the number of molecules at energy level J = 2 hence, resulting in a low S(0) ﬂux.

This explanation is consistent with the observed increase in the ﬂux ratios of high rotational lines, S(3)/S(1) and S(5)/S(1). However, shocks are unable to excite H2 to very high rotational levels (J 5), resulting in low S(5)/S(1) when compared to ≥

S(3)/S(1). We conclude that shocks in SQ are eﬃcient in exciting H2 molecules till J 5. The regions with undetected S(3) and S(5) lines (white squares) are less warm ≤ unable to excite molecules to J = 5 and 7, respectively, resulting in low ﬂux/non-

detection of these lines.

4.5.3 Power law index

In the last sub-section, we discussed variation in the H2 rotational line ﬂux ratios caused by shocks. This variation in line ratios result in a change in the power law

index of our model. An analysis of power law index can provide insights for physical

conditions of molecular gas.

133 Figure 4-6 H2 line ratios, S(0)/S(1), S(3)/S(1) and S(5)/S(1) are estimated in shock regions of SQ, which are marked by the blue line and the center shock region is assumed to be approximately at the region numbered-91, shown in Figure–4-2. H2 line ratios, S(3)/S(1) and S(5)/S(1), are elevated in shocks of Stephan’s Quintet. However, S(0)/S(1) is constant over the shock ﬁlament of SQ, implying that molecules are excited to high energy levels (J > 2).

134 Figure 4-7 A 2D color plot for the H2 line ratios, S(0)/S(1), S(3)/S(1) and S(5)/S(1) in our mapped regions of SQ. Smooth contours are overlaid on the color plot (left) and the Hα HST image from Wide Field Camera 3 (WFC3) (right). The position of contours clearly mark the shock regions of SQ.

135 Figure 4-8 A 2D color plot for the power law index in the mapped regions of SQ. Smooth contours are overlaid on the color plot and the Hα HST image from WFC3. The position of contours clearly mark the shock regions of SQ. The shock regions have a high power law index (considering the negative sign), implying the presence of warm molecular gas.

Figure 4-8 is a 2D color plot for power law indices in the shock region of SQ.

The contour level map the main shock region of the ﬁlament very well, creating the impression of a bow-shock shaped which follows faint Hα features shown on the HST image. The power law indices estimated from our model are higher, about 4.3–4.4, at the center of the main shock and lower still to the south (4.2-4.3), considering the negative sign.

Shocks in SQ excite H2 molecules to high rotational energy levels, resulting in large ﬂux in high-J rotational lines, which in turn ﬂattens the excitation diagrams. A large number of H2 molecules are at high temperatures, leading to a less steep, less negative in warmest part of the shocks. The values of the power law index are almost all lower than the mean found for normal galaxies (4.84 0.61, chapter 2). Indeed the ± only region near SQ-A, where the value of n lies between 4.8< n <5.1.

136 4.5.4 Total and Warm H2 gas mass

4.5.4.1 Total H2 gas mass

The upper energy level of the lowest rotational transition of H2 is at 510 K, higher

than the typical ISM kinetic temperatures. As a result low temperature H2 molecules in the ISM are too cold to populate high energy levels (J = 2 and higher), and majority

of them remain in the ground state. We extrapolate our model to lower temperatures

to estimate the total molecular gas reservoir. The MIR H2 rotational lines are not

sensitive to molecules less than the temperature Ts, deﬁned in chapter 2, and as a

consequence our model show no change at lower temperatures, T < Ts.

In our analysis three diﬀerent cases emerge in determining Ts

Case1: As we decrease the lower temperature, Tℓ, the diﬀerence between the observed and the model ﬁt ratios (R) continuously decrease and below a certain

temperature (Ts) the deviation becomes insignificant, minor change in the model fit occurs. The parameter, R, is defined as,

m f f 2 R = i,mod − i,obs , (4.6) σ Xi=1 fi,obs

Nu/gu where f = ln (N /g ) , fi,mod and fi,obs are the modeled and observed ﬂux ratios u u S(1) th for the i line with uncertainty σfi,obs , and the summation is over all the independent line ﬂux ratios. The black solid curve in Figure 4-9, demonstrates this case. In such a

scenario we extrapolate our power law model to 50 K to calculate the total molecular

gas mass. The calculated molecular gas mass found by extrapolating our model to 50 K, correlates with the molecular gas mass derived using the Galactic-CO conversion

factor, αCO,Gal

Case2a: As we decrease the lower temperature, Tℓ, the value of R decreases but below a certain temperature it starts increasing and at low temperatures show no

137 signiﬁcant change. The red dotted curve in the Figure 4-9, demonstrates this case in the square region- 76. The value of R decreases untill the lower temperature of about

120 K but increase in the range 50–120 K and remains almost constant below 50 K.

In such case we adopt the corresponding temperature for Tℓ, here 120 K, where the deviation is found to be minimum. The presence of excess warm molecular gas due to shocks could be the reason for high Tℓ and the complete molecular gas in these regions are traced by the MIR H2 rotational lines. Case2b: The blue-dashed curve is a similar case but the minimum deviation occurs at very high Tℓ. In our analysis of SQ this was observed in the square region 103, the central shocked region of SQ, where the model yield the best ﬁt value of Tℓ = 198 K. The molecular gas in this central shocked region of SQ is heated to a temperature of 200 K. ∼ Case3a: In some regions the S(0) line is undetected but with detections of high

J lines of H . The S(1) and higher J lines of H , correspond to energy levels, J 2 2 ≥

3. High J levels requires high temperatures for excitation, which result in high Ts. In such cases we extrapolate our power law model to 80 K to calculate the total molecular gas mass. Several Ultra Luminous InfraRed Galaxies (ULIRGs), which are local mergers, with warm dust color temperatures have non detections of S(0) but good S/N (signal-to-noise) detection for high-J rotational lines (Higdon et al.

2006; Stierwalt et al. 2014). In these galaxies we need to extrapolate our power law model till 80 K to recover the total molecular gas mass to be consistent with their dynamical mass estimates (Togi & Smith submitted). Case3b: The ﬁnal case is when no rotational H2 lines are detected. Two interpretations can be made, no molecular gas in these regions or presence of very cold molecular gas in the ground rotational state. The latter case is highly unlikely in case of SQ, where shocks are observed leaving with a possibility of no signiﬁcant amount of molecular gas content in these regions.

Laying the criteria as discussed, we extrapolated our model to the appropriate

138 Figure 4-9 The diﬀerence between the model derived and the observed H2 line ratios (R) as a function of lower temperature to determine Tℓ. The black solid, red dotted, and blue dashed curves represent diﬀerent cases. For the black curve cases we adopt the value of Tℓ = 50 K. The red and blue curve occur in warm regions, where the temperature of all H2 molecules are high enough to be traced completely by the MIR rotational lines. In such cases we adopt the value of Tℓ at the temperature where we have the minimum deviation. For instance for the red and blue curve we adopt Tℓ = 120 and 198 K, respectively, given by our power law model.

139 Tℓ and estimated the total molecular gas mass for each square region in our mapped area of SQ. The estimated total molecular gas mass in our mapped regions is about

8.3 109 M . This molecular gas mass is consistent with the CO luminosity derived × ⊙ gas mass of 5 109 M in the bridge and the ridge regions of SQ, using the Galactic × ⊙

conversion factor αCO,Gal (Guillard et al. 2012). However, the diﬀerence in the mapped areas and the uncertainty in the conversion factor for shock regions could

lead to variation in molecular gas masses.

4.5.4.2 Warm H2 fraction

Knowing the temperature distribution from our power law model and the total molecular gas mass for each square region, we investigated the warm gas fraction in

shocks of SQ.

The H2 gas greater than 120 K, show their signatures in the MIR H2 rotational lines. We selected the molecular gas temperature above 120 K to deﬁne our warm

gas. We calculated the molecular gas mass fraction above 120 K using,

T M(> 150K) u T −ndT = 150 . (4.7) Tu Mtotal R T −ndT Tℓ R The power law index, n, is estimated from the model and the lower temperature is decided as discussed previously in the last sub-section. Calculating the warm gas

fraction for each square region in our mapped area of SQ we plotted a 2D color plot,

as shown in Figure 4-10.

The warm gas fraction is high in shock regions of SQ. On average the warm gas fraction is about 30% in shocks. The central shock region of SQ (square region- 103), the warm gas fraction is higher than 1.0, implying temperature of molecular gas is higher than 150 K (here we deﬁned our warm gas temperatures higher than 150 K).

The warm gas fraction is about 60% in the southern shock regions, between NGC

140 7318b–NGC 7320. The northern parts of our mapped regions are cold, with warm

gas fraction less than 10%. The molecular gas in the shocks of SQ are warmer when

compared to normal star forming galaxies, where the warm gas fractions is 10% ∼ (Roussel et al. 2007)

4.6 Summary

1. The discrete two temperatures ﬁts shows high temperatures in the center main shock ﬁlaments and also at the observed southern region.

2. The line ratios in shocks of SQ are observed with S(0)/S(1) < S(5)/S(1) <

S(3)/S(1).

3. The line ratio S(3)/S(1) is higher than S(5)/S(1), implying shocks are able to

excite molecules till J = 5.

4. The power law index is higher, implying high warm molecular gas fractions in shock regions of SQ.

5. The total molecular gas mass in our mapped regions of SQ is 8.3 109 M , in × ⊙ agreement with CO based estimates.

6. The warm molecular gas mass fraction is 30% in shock regions. In the ∼ central shock regions the molecular gas temperature is about 200 K. The warm gas

mass fraction in the southern shock regions are found to be as high as 60%. ∼

141 Figure 4-10 A 2D color plot for the warm gas mass fraction in the mapped regions of SQ. The top right ﬁgure show X-ray data from the Chandra Observatory in blue superposed on optical data in yel- low (APOD, Credit: X-ray: G. Trinchieri et al.). The X-rays are produced by gas heated to 106 K by shocks on cosmic scales. Smooth contours are overlaid≈ on the color plot and the Hα HST image from WFC3. The position of contours clearly mark the shock regions of SQ, where the warm gas fraction is higher. The warm gas fraction is about 30% in shocks, with an increased value of about 60% in the southern regions. In the central shocked regions the molecular gas is heated to temperatures of about 200 K.

142 Chapter 5

Physical properties of the

cometary globule: the case of B207

5.1 Introduction

Stars form inside molecular clouds, which have sizes ranging from a few tens of parsec down to small, sub-parsec cores. Isolated Bok globules (Bok & Reilly, 1947) are the simplest starless and star-forming molecular clouds (Clemens & Barvainis, 1988, Yun & Clemens 1990, Yun & Clemens 1992, Launhardt et al. 2010). Nearby

Bok globules are some of the best places to study in detail the physical and chemical processes occurring during star formation (Clemens & Barvainis, 1988, Bourke et al.

1995, Launhardt et al. 1997, Henning & Launhardt 1998, Stutz et al. 2008, Ward et al. 2007). Bok globules, being small in size and forming only one or at most a few stars, oﬀer an opportunity to study star forming processes in clouds unaﬀected by the presence of other stars. Also, the large number of Bok globules within a distance of 500 pc provides excellent spatial resolution to study star formation processes in molecular clouds.

Sometimes more than one protostars at diﬀerent evolutionary stages are seen embedded in a single Bok globule (Launhardt et al. 2010). This led Launhardt et al. 2010

143 to suggest that multiple star formation in isolated globules is non-coeval, whereby a

Class I protostar, a much younger Class 0 protostar, and a gravitationally unstable sub-mm core may all be co-existing in the same isolated, low-mass molecular cloud without requiring a causal interrelationship among them. Studying such globules will help understand time evolution and conditions required for the successive star formation process in molecular clouds.

In this paper, we study the cometary globule Barnard-207 (B207), located at a distance of 140 pc in the Taurus - Auriga molecular cloud region (Loinard et al. 2005,

Kenyon et al. 1994). B207 (LDN 1489) is a high Galactic latitude Bok globule, located at equatorial coordinates (J2000.0) RA = 61.216◦ Dec = 26.318◦ (ℓ = 168.08◦,

◦ b = -19.15 ). A 1.6 M⊙ protostellar source, IRAS 04016+2610, is currently forming at the West side of B207’s core (Yen et al. 2014). This protostar is located at a projected distance of about 10,000 AU from the center of the present-day dense core of B207. Benson et al. 1998, using high spatial and spectral line observations of

+ N2H and C3H2, show an asymmetric proﬁle for B207 (LDN 1489). They conclude that the line shapes for B207 are consistent with models of cloud cores undergoing gravitational collapse. Therefore, the globule B207 may be in a second star formation phase. Hence, studying physical properties of B207 will help in our understanding of the core collapse phenomenon and the star forming process occurring in such objects.

The goal of this paper is to perform an in-depth analysis of B207 and to determine the physical properties and evolutionary state of LDN 1489.

5.2 Observations & Archival Data

The objective of the observations is to measure both the extinction of the background stars through diﬀerent parts of B207 as well as the surface brightness of the scattered light, and to study the general properties of the cloud in diﬀerent optical

144 and infrared bands.

5.2.1 Discovery Channel Telescope (DCT) observations

B207 was imaged in several optical bands, using the Large Monolithic Imager

(LMI; Massey et al. (2013)) of the 4.3-metre Discovery Channel Telescope (DCT;

Degroff et al. (2014)), operated by Lowell Observatory, on 2013 February 5-6 and 2013 December 5. LMI exposures were taken using its e2v CCD231, having 6144 × 6160 pixels, with 2 2 binning. Imaging was performed with the Johnson UBV and × Kron-Cousins R and I filters, at effective wavelengths 366, 428, 537, 633, and 806 nm, respectively (these calculated wavelengths are the arithmetic means of the two wavelengths at which the transmission is half of the maximum1 in each filter). The

LMI ﬁeld of view was 12.3 12.3 arcmin2, large enough to cover most of the dense × parts of the globule. The plate scale was 0.24 arcsec/pixel for 2 2 binning. × The globule was observed with total exposure times of 180, 240, 105, and 75

minutes in U, B, V, and R bands, respectively, consisting of sub-exposures of 15 -

20 minutes. In the I band, two exposures were taken, each of 10 minutes duration.

The observable characteristics of the globule are represented in 5-1. It is a 3-colour

stacked image in which blue, green and red colours represent the V, R, and I bands, respectively.

The basic data reductions such as ﬂat ﬁelding, bias correction, and sky subtrac-

tion were performed using the Image Reduction and Analysis Facility (IRAF). The

eﬀects of cosmic rays in the images were removed using the L.A. Cosmic package (van

Dokkum. 2001) within IRAF.

The photometric calibration was derived using a standard star, GD71, from the list of Landolt A. U. (1992), located close to the globule’s location. Using the LMI-

1http : //www.lowell.edu/techSpecs/LMI/specs.html

145 Figure 5-1 A 3-colour stacked image of B207. The blue, green, and red colours represent the V, R, and I bands, respectively. The protostar, IRAS 04016+2610, at R.A. = 4h4m43.071s , Dec = +26◦1856.39 is forming at a distance of about 10000 AU west of the core, marked by the red arrow. A sharp boundary is seen towards the outer rim of the cloud to the East. A less dense region of material, appearing as a hole is located towards the immediate West of the protostar.

146 DCT manual, the photometric scale was ﬁxed and the zero points were determined.

The magnitudes of other stars in the ﬁeld were determined and found to be consistent,

within 10% uncertainty in the observed bands, when compared to entries in SIMBAD.

5.2.2 Archival WISE and Herschel data

We employed archival Wide-ﬁeld Infrared Survey Explorer (WISE; Wright et al.

(2010)) W1 and W2 image data at 3.4 and 4.6 m to perform star counts and to investigate the presence of coreshine in the inner regions of the B207 globule. The

WISE band images were 10 10 arcmin2 wide. The pixel scale was 1.375 arcsec/pixel × in the W1 and W2 bands. We used the WISE point source catalog (PSC) to identify

stars in the image. To determine the spectral energy distribution (SED) of the core and the rim of

the globule, we used archival Herschel Space Observatory’s Photoconducting Array

Camera and Spectrometer (PACS; Poglitsch et al. (2010)) - 160 m image with

Spectral and Photometric Imaging Receiver (SPIRE; Griﬃn et al. (2010)) - 250,

350, and 500 m maps that were about 1◦ 0.9◦ wide, observed in the Herschel- × Guaranteed-Time Key Program (KPGT) program (PI Ph. Andre). The full width half maximum (FWHM) for PACS 160, and SPIRE 250, 350, and 500 m point

spread functions (PSFs) are 12.8, 17.6, 23.9, and 35.2 arcsec, respectively.

5.3 Analysis

The mass, temperature, density distribution, along with other dust and gas properties provide hints to the past, present and future evolutionary fate of a globule. In this section, we provide a description of our methods for determining the physical properties of B207.

147 B207 shows many interesting features, as seen in Figure 5-1. First, a protostellar object (IRAS 04016+2610) is seen near the centre of the image, at a projected oﬀset of 10,000 AU from the dark core of B207. Second, a nearly transparent region ∼ of gas and dust is seen 30, 000 AU towards the West of the newly forming star. ∼ Third, a sharp edge is seen towards the eastern side of the cloud. Fourth, a small dark core in B207 is seen as a dark region to the East of IRAS 04016+2610. The

bright rim surrounding the core is typical for high-latitude globules and is interpreted

as resulting from scattering (see section 3.2.1) of the galactic radiation ﬁeld in the

optically thin outer portion of the globule (Fitzgerald et al. (1976)).

5.3.1 Surface brightness proﬁles

In contrast to many globules at lower Galactic latitudes, B207 is readily discernible through its surface brightness at optical wavelengths (Figure 5-1). In its optically thin outer portions of the globule this surface brightness is proportional to the line of sight optical depth. Mapping the optical surface brightness of globules provides, therefore, an excellent means of tracing the optical depth distribution in the outer parts of a globule like B207. With additional information on the line-of-sight interstellar radiation field (ISRF) and the intensity of the diffuse galactic light (DGL) in the sky adjacent to the globule, it is also possible to estimate the globule’s dust albedo at different wavelengths.

We obtained surface-brightness proﬁles of the globule B207 from the U, B, V,

R, and I band images. A horizontal East-West (E-W) cut, shown in Figure 5-2, was made to construct the surface brightness proﬁle. Individual surface brightness values were averaged over a box of size 5 20 arcsec2, perpendicular to the E-W cut, × oriented along the north-south (N-S) direction, yielding sky subtracted intensities in erg/cm2/s/A/sr. Table 5.1 lists the value of the conversion factor from count/s/pixel to erg/cm2/s/A/sr in U, B, V, R, and I bands, calibrated by measuring the ﬂux from

148 Figure 5-2 The position of East-West horizontal cut region across B207 on a R band image for surface brightness analysis.

a Hubble standard star GD71.

The surface brightness profiles for the five LMI bands are shown in Figure 5-3. At the eastern rim, the surface brightness rises sharply, reaching a peak almost exactly at the same spatial location for all the observed wavelengths. Given that the peak surface brightness of any given wavelength occurs at the same (wavelength-dependent) optical depth, this finding demonstrates that the line-of-sight optical depth increases sharply near the portion of the brightness peaks. This suggests that the material is compressed towards the Eastern side of the globule. At the core position, the surface brightness increases with increasing wavelength. The intensity of the core region is lower than the background sky in U and almost equal to the sky in B. The region

149 Table 5.1. Photometric calibration for 1 count/s/pixel

Band Eﬀective wavelength (λ) Intensity Name (nm) (10−7erg/s/cm2/A/sr) (1) (2) (3)

U 366 9.678 B 428 1.625 V 537 1.006 R 633 0.683 I 806 0.555

ATo calculate surface brightness, we used the conversion of 1 pixel2 = 1.354×10−12 steradian BThe wavelength listed for each band is the arithmetic mean of the two wavelengths at which transmission is half of the maximum. The transmission curves for each band can be found at www2.lowell.edu/rsch/LMI/specs.html west of the protostar, appearing as a hole in the globule, displays an intensity value greater than the clear background sky in B, V, and R bands, implying the presence of some diffuse dust. The flux of the protostar increases from undetectable at U to very bright at I, consistent with its SED peaking at 50 m (Furlan et al. 2008). ∼ The surface brightness distribution of B207 is characterized by a bright outer rim surrounding a dark core. This pattern is the consequence of a strongly forward- throwing phase function of the scattering dust, which controls the transfer of the illuminating ISRF through the object (Witt et al. 1974, Witt et al. 1990). High- latitude globules like B207 are detectable by their scattered-light surface brightness, because the diffuse Galactic light (DGL) arising in the surrounding diffuse interstellar medium has a lower surface brightness due to its much lower line-of-sight optical depth, thus providing the contrast necessary for visibility. At low Galactic latitudes, the surface brightness of the DGL and of the bright outer rim of globules are more nearly the same, thus erasing this contrast. Those globules are then recognized simply as dark core seen against a brighter background.

Given the extreme asymmetry of the scattering phase function, the globule’s sur-

150 Figure 5-3 The sky subtracted surface brightness (in ergs/cm2/s/A/sr) for B207 in U, B, V, R, and I bands of the DCT-LMI. The East - West direction is marked in the U-band plot starting from East (left) to West (right). The position of the eastern bright rim, core, protostar IRAS 04016+2610, and the transparent hole region are marked as R, C, S, and D, respectively. The East-West distance is measured from the protostar, where the zero position corresponds to R.A. = 4h4m43.5s , Dec = +26◦18′50′′

151 face brightness is determined almost exclusively by the intensity of the ISRF seen by

the far side of the globule from directions within a few degrees around the line-of-sight

direction from the observer to the globule. The surface brightness at the side facing

the observer is determined by the transfer of scattered radiation through diﬀerent

sections of the globule. The actual intensity is proportional to the product of two probabilities: the probability of scattering, measured by a(1 e−τ ), and the proba- − bility that once-scattered radiation escapes through the front surface of the globule, measured by e−τabs . Here, a is the dust albedo, τ is the line-of-sight extinction optical depth through the globule, and τabs is the typical absorption optical depth for the average once-scattered photon. A suitable approximation is τ 0.5(1 a)τ (Witt abs ≈ − et al. 2008). The bright outer rim of an externally illuminated globule occurs where the product of these two probabilities reaches a maximum. For the high dust albedos typical for globules (Witt et al. 1990), this maximum occurs at line-of-sight optical depths near τ =1.5, occurring at about -270 arcsec from the protostar in B207, as ∼ seen in Figure 5-3.

5.3.2 Dust characteristics

5.3.2.1 Scattered light intensities

The maximum surface brightness of B207 observed in the different LMI bands may be used to constrain the albedo of the dust present in this globule. Our tool is the relation between the ratio of maximum surface brightness to the intensity of the illuminating radiation field and the dust albedo, as found from Monte Carlo radiative transfer simulations by Witt et al. (1974). In order to employ this tool, we need to correct the observed maximum surface brightnesses in the five LMI bands for the background DGL intensity still present in the intensity of the sky adjacent to B207, and we also need the value of the interstellar radiation field (ISRF) at the location

152 of B207. It is this particular intensity that is crucial for determining the surface

brightness of B207 because of the strongly forward-throwing phase function of the

dust.

The sky intensity adjacent to B207 consists of foreground components stemming mainly from terrestrial airglow, scattering in the Earth’s atmosphere, and zodiacal light, and a background component consisting of DGL, arising from scattering of the ISRF by diﬀuse Galactic dust along the line of sight. The fact that the surface brightness core of B207 in U has a substantially lower surface brightness than that of the adjacent sky, suggests that most of the adjacent sky DGL arises at distances larger than that of B207. This is also supported by the recent work, which places most of the dust in the line of sight of B207 at a distance of about 250 pc and beyond (Green et al. 2015). To ﬁnd the absolute surface brightness of B207, we need to add the intensity of the adjacent DGL to the intensities displayed in Figure 3. The foreground components, contributing equally to both the sky and globule intensities, have been eliminated by the original sky subtraction and are of no further concern.

We estimate the DGL intensities in the sky adjacent to B207 by first finding the optical depth of the dust in the sky region. The all-sky map of Schlegel et al. (1998) yields a value of E(B - V) 0.197, and with the re-normalization by Schlafly et ∼ al. (2010) and Schlafly et al. (2011) yields a more probable value of E(B - V) ∼

0.169. With a value of RV = 3.1 for average diﬀuse Galactic dust, we ﬁnd AV = 0.53 mag. Scaling this value with the extinction cross sections per H nucleon (Cext/H) as

2 a function of wavelength from Draine (2003) for ISM dust (RV = 3.1), we ﬁnd the optical depth values listed in column 3 of Table 2. Noting that these optical depths are within the optically thin regime, we use the radiative transfer approach based on single scattering (Equation 4, Witt et al. (2008)) to estimate the corresponding DGL intensities. For this, we use the ISRF intensities

2http : //www.astro.princeton.edu/ draine/dust/dustmix.html

153 Table 5.2. Dust Characteristics

(DGL+SBmax) Filter ISRF τ a τabs DGL SBmax ISRF ac (1) (2) (3) (4) (5) (6) (7) (8) (9)

U 4.77 0.721 0.625 0.135 1.338 0.259 0.335 0.62±0.05 B 5.55 0.624 0.648 0.110 1.497 0.839 0.421 0.70±0.05 V 6.41 0.485 0.671 0.080 1.528 1.811 0.521 0.75±0.05 R 6.80 0.402 0.676 0.065 1.425 2.361 0.557 0.78±0.03 I 6.37 0.259 0.656 0.045 0.911 3.272 0.657 0.87±0.03

1 −8 2 The value of ISRF, DGL, and SBmax are in units of 10 erg/s/cm /A/sr. The ISRF for diﬀerent wavelengths are from Porter & Strong (2005) 2τ and a are the extinction optical depth and albedo of the dust in the sky adjacent to B207 assuming RV = 3.1. The albedo values are from Draine (2003) 3 τabs is the absorption optical depth of cloud evaluated using τabs = 0.5(1 − a)τ

4 −τ −τabs DGL is the diﬀuse galactic light adjacent to B207, derived using aIISRF (1 − e )e 4 SBmax is the peak intensity of the globule after subtracting the nearby background sky intensity 5 The (DGL+SBmax)/ISRF is the ratio of the total maximum intensity scattered by the globule to the interstellar radiation ﬁeld 6 The albedo of the cloud, ac, evaluated for the corresponding ratio (DGL+SBmax)/ISRF assuming the forward scattering asymmetry parameter, 0.6 ≤ g ≤ 0.9 from Figure 6, Witt et al. (1974) of Porter & Strong (2005) at the globule’s position, listed in column 2 of Table 2, and the dust albedos from Draine (2003) for RV = 3.1 Milky Way dust, listed in column 4 of Table 2. The resulting DGL intensities are listed in column 6 of Table 2.

In order to arrive at the background-corrected absolute surface brightness values for the maximum surface brightness, we add this DGL component to the sky- subtracted maximum surface brightness listed in column 7 of Table 2. The ratio of the corrected absolute maximum surface brightness to the ISRF listed in column 8 is the quantity to be compared directly with the model predictions in Figure 6 of Witt et al. (1974). The resulting estimates for the dust albedo, ac, in B207 are shown in the last column of Table 2 with their estimated uncertainties. The albedo values were calculated under the assumption that the phase function asymmetry, g, is close to

0.9, consistent with the results found in other dark nebulae (Gordon (2004)). Henyey

154 & Greenstein (1941) introduced the phase function asymmetry parameter, g, in the

range 1 g +1, from back scattering to isotropic scattering (g = 0) to forward − ≤ ≤ scattering. A change in the assumption of phase function asymmetry to g 0.7 ≈ causes a small reduction in the estimated albedo values Gordon (2004).

Two facts stand out from this analysis. First, the globule albedo values are generally larger than those of the dust in the adjacent diffuse dust background. Second, the albedo is increasing with wavelength, reaching its highest value of about 0.87 in the I band. These characteristics are typical for size distributions of grains that include micron-size grains, which are significantly larger than the largest grains in diffuse ISM dust, e.g. Kim & Martin (1996). The dust albedo values are comparable with those found in other studies of globules and dark nebulae. Fitzgerald et al.

(1976) evaluated the dust albedo in B-band, a = 0.70 0.08, for the Thumbprint ± nebula. The Coalsack and Libra cloud have a dust albedo of 0.6 for g 0.8 in U, ∼ ∼ B, and V bands (Mattila (1970)). However Witt et al. (1990) found the albedo value decreasing from 0.80 at 469 nm to 0.58 at 856 nm for the Bok globule CB4, which

has a much lower central optical depth compared to B207.

5.3.2.2 Coreshine eﬀect in NIR band

Coreshine is an eﬀect in which starlight in the 3–5 m wavelength range is eﬃ- ciently scattered by larger than normal ISM grains, e.g. m size grains versus the

normal size range 0.01–0.25 m. The dense cores of molecular clouds frequently ex-

hibit this behaviour (Pagani et al. 2010, Steinacker et al. 2010). The dense cores

are suﬃciently optically thick to prevent UV photons from penetrating and exciting

polycyclic aromatic hydrocarbon molecules (PAHs), thus ruling out the possibility of

3.3 m PAH emission contributing to the 3–5 m coreshine. Pagani et al. (2010) investigated a sample of 110 cores from which 95 cores were detectable in the Spitzer-

IRAC band at 3.6 m. Numerous cores, about 50, clearly had signatures of coreshine.

155 Figure 5-4 A 10 10 arcmin2 WISE W1 image of B207 at 3.4 m. The pro- × tostar IRAS 04016+2610 is at the center of the image. The blue cross sign is the core position. B207 is exhibiting the coreshine eﬀect by showing a clear excess of 3.4 m emission compared to the background. The coreshine eﬀect is due to the scattering by large grains inside the globule

The emission at 3.6 m is spatially coincident with the densest regions of the cores. The coreshine phenomenon can be explained by near-infrared (NIR) radiation

from the ISRF being scattered by micron-size grains. The dense cores of the globules

are cold and thus provide favorable physical environments for the grains to acquire

ice mantles, coagulate, and grow in size to exhibit the coreshine eﬀect (Hirashita &

Li (2013), Andersen et al. (2014)). The intensity of the coreshine depends on the

incident radiation, the extinction of the background radiation, the grain properties,

and the core properties (Steinacker et al. 2014b). We investigated the presence of coreshine in the core of B207 using the 3.4 m image of WISE. The coreshine eﬀect as a surface brightness excess in the core compared

156 to the background sky is observed in the 3.4 m WISE W1 image, shown in Figure

5-4. The observed core intensity excess above sky of B207 over an aperture of 10

arcsec radius was found to be 0.05 MJy/sr (conversion from DN to Jy units adopted

from WISE Preliminary Data Release). The surface brightness value of the B207

core at 3.4 m is comparable to the values obtained in the Taurus-Perseus sample of Lefevre et al. (2014). Theoretical modeling by Steinacker et al. (2014b) yields a

similar value of 0.06 MJy/sr for the surface brightness at 3.6 m. ∼ The core of B207 was found to be opaque, completely blocking the background starlight even at such a long NIR wavelength. The observed coreshine eﬀect further supports our idea of the presence of large grains inside B207, as already inferred from the dust albedo measurements.

5.3.3 Temperature Analysis using SED ﬁtting

The gas temperature and turbulence are major parameters in determining conditions for the core collapse, providing pressure support against the gravitational infall of the material and hence, deciding the evolutionary fate of the globule (Dickman

& Clemens (1983), Nelson & Langer (1999)). The diﬀerence between core and rim temperatures can help us estimate temperature gradients of gas and dust in the globule. The rim temperature depends on ambient ISM conditions in which the globule is located.

We used the PACS 160 m, SPIRE 250, 350, and 500 m dust emission maps from Herschel Space Observatory to model the line-of-sight average dust temperature and column density toward the core and rim of B207. We convolved 160, 250, and

350 m maps to the equivalent resolution of the 500 m map using a low-resolution kernel (Aniano et al. 2011). The core was deﬁned as a circular region of 40 arcsec diameter (> 35.2 arcsec, the PSF of SPIRE instrument at 500 m) at the position

RA = 61.2023◦, Dec = 26.314◦. Table 5.3 lists the background subtracted intensities

157 Table 5.3 Intensity in MJy/sr at FIR and sub-mm wavelengths Wavelength (m) Core Rim 160 99.5 10.0 16.4 4.0 250 155.9±12.5 24.7±5.0 ± ± 350 148.2 12.2 17.2 4.1 500 84.4± 9.2 7.1±2.7 ± ± measured in the four Herschel (PACS 160 m, SPIRE 250, 350, 500 m) bands.

Spectral energy distributions (SEDs) were constructed and single temperature modified black-body curves were used to fit the SEDs. We used a single dust temperature black body model S = ΩB(ν, T )(1 e−τ(ν)), where Ω, B(ν, T ), and τ(ν) ν d − d are solid angle of the emitting element, Planck function at dust temperature Td, optical depth at frequency ν, respectively. We used a dust opacity model, κ νβ ν ∝ with β =1.8 (Planck Collaboration 2011) to fit the SED using the MPFIT program

(Markwardt (2009)). Figure 5-5 shows single dust temperature SED model ﬁts at the core and rim.

The derived core and rim temperatures are 11.7 0.1 K and 13.3 1.4 K, respec- ± ± tively. Our derived core temperature is in agreement with the 11.7 K value predicted for B207 (LDN 1489) by Ford & Shirley (2011), who used a radiative transfer model with the ISRF as the heating source. The core and rim temperatures are consistent with literature studies for other similar Bok globules (CB244-Stutz et al. 2010,

DC000.4-19.5 Hardegree-Ullman et al. 2013, Launhardt et al. 2013, CB17- Schmalzl et al. 2014). The presence of the nearby protostar, IRAS 04016+2610, could raise the core temperature. However, Launhardt et al. (2013) showed that the presence of protostars in a globule aﬀected the temperature only to a distance of about 5000 AU.

In our case, IRAS 04016+2610 is at a projected distance of 10000 AU from the core ∼ of B207 and, therefore, is not expected to have significant effects on the core temperature. The rim temperature of the globule is affected by the external heating from the ISRF and the outside physical environment in which the globule is embedded.

158 Figure 5-5 A modiﬁed single temperature blackbody spectrum for the dust emission at the core and rim assuming β = 1.8 to ﬁt the observed intensity values. The model yields a temperature value of 11.7 0.1 K and 13.3 1.4 K for core and rim, respectively. ± ±

159 5.3.4 Mass Distribution

Mass is one of the key physical parameters that decides a globule’s fate. The evolutionary future of the core, whether it forms a star or remains starless, depends on the likelihood of core collapse, which is directly linked to the core mass. Moreover, the type of star formed inside the core depends on the dense core mass, with a star formation eﬃciency of ǫ = M /M 30% (Motte et al. 1998, Alves densecore star densecore ≈ et al. 2007, Andre et al. 2014). Diﬀerent methods can be employed to estimate the

core mass. We derive the core mass of B207 by three diﬀerent methods: star counts,

reddening of background stars, and sub-mm 500 m emission.

5.3.4.1 Star count technique

The star count method, based on the number density of background stars (stars/arcmin2)

seen in each part of the cloud, is used to obtain the extinction, an estimate of the

column density (Dickman (1978)). The number density of stars is compared to that

on the adjacent, clear, background sky region. As the core is approached, the increase

in the column density of dust leads to higher extinction, causing the fainter stars to

disappear, below some detectability threshold. Assuming an appropriate gas to dust ratio (GDR), the total column density of gas can be estimated. Summing over the

entire globule area allows us to calculate the globule’s mass.

We used a rectilinear grid of squares, each 2 2 arcmin2 on a 3.4 m WISE W1 × map of B207. In each square, we counted the number of stars. The average num-

ber of stars in the clear background sky towards the east of B207 was found to be

2 3 1.75 stars/arcmin . Groszschedl (2012) found the slope for log(Nm) versus limiting magnitude λ for WISE W1 in an Orion A control ﬁeld of 36.7 degree2 to be 0.33, ∼ where Nm is the number of stars brighter than magnitude λ per square degree in the

3http : //othes.univie.ac.at/20156/1/2012 04 16 0408170.pdf − −

160 sky. The galactic latitude of the control ﬁeld is identical to that of B207. Comparing

the number of stars in each square region on the globule with the clear background

sky, and using the slope of 0.33 from the plot of log(Nm) versus λ we calculate the

extinction at 3.4 m (A3.4). Knowing the extinction value in each square region we calculate the mass of the globule B207, using the relation

N M =(γd)2 H Ai , (5.1) A 3.4 3.4 Xi where N(H) A N(H) = V (5.2) A3.4 A3.4 × AV N(H) = 17.63 1.87 1021 =3.3 1022cm−2mag−1. (5.3) A3.4 × × ×

Here, γ is the angular size in radians of each square in the grid, d = 140 pc is the distance to the cloud, = 1.36 the mean molecular weight corrected for helium and heavy element abundance, and i is the counting index of the square on the extinction map (Cambresy (1999)). The value of N(H) = 1.87 1021 cm−2 mag−1 is from Bohlin AV × et al. (1978). For the 3.4 m map this value needs to be scaled accordingly. From,

Draine (2003) we calculated the ratio of AV /A3.4 = 17.63 for an extinction curve with

RV = 5.5, applicable for molecular clouds. We ﬁnd the molecular gas column density at the core to be N(H ) = (4.2 2 ± 1.0) 1022 cm−2, while the corresponding mass out to 160 arcsec is (12.1 3.0)M , × ± ⊙ calculated from the star count method (our core mass includes He and other heavy element mass correction and 160 is the core radius estimated from the Bonnor-Ebert modeling, Sec 3.5). The star count method implicitly requires that all stars counted in an obscured region lie behind the cloud. This fact, along with the Poisson counting errors in the small number of stars in each square grid and the error in the distance to B207, contribute to the total error in the mass calculation of the core (Dickman

161 Figure 5-6 The variation of column density as a function of the distance from the core. The black points are the column density measurements from the WISE band colour excess (W1 - W2) of background stars in the field of view (FOV). The blue curve is a fit to the extinction profile obtained from the reddening of background stars. The red diamonds are from the FIR intensity photometry from the SPIRE-500 m map. The molecular column density of the 22 −2 core is of the order 3.6 10 cm , causing an extinction of AV 50 mag for R = 5.5.× ∼ V

(1978) Appendix).

5.3.4.2 Reddening of background stars

The change in colour of background stars seen through the globule can be used to estimate the column density of material. Assuming an appropriate value of the intrinsic colour of background stars and the GDR, we can estimate the globule’s mass.

We selected a region of 300 arcsec radius centered on the core of B207 to estimate the column density proﬁle. We determined the W1-W2 colour of background stars.

162 Galaxies in the region were removed, since they are intrinsically redder compared to

stars (Wright et al. (2010)). We chose the WISE band intrinsic colour W1 - W2

= 0.05 mag for unreddened background stars (Wright et al. 2010, Kirkpatrick et

al. 2011). Assuming the value of RV = 5.5, the relation between molecular column density and the colour excess in W1 - W2 from Draine (2003) is

N(H ) 2 =3.73 1022cm−2mag−1 (5.4) E(W 1 W 2) × −

We chose RV = 5.5 because the sizes of dust particles in the globule are greater compared to normal ISM dust. The morphological structure of our cloud is not

spherically symmetric, as the western part of the globule is more diﬀuse than the compressed eastern part. Hence, there is a considerable scatter seen in the extinction

values at a ﬁxed radial distance from the core. We averaged the extinction values

estimated from stars in 9 radial bins of 30 arcsec width and ﬁt the extinction proﬁle.

An exponential ﬁt to the column density proﬁle was marginally better than a power

law ﬁt, over the range 0–300 arcsec from the core center. Our exponential ﬁt to the

column density is 6.69 1022 exp(-0.015r), where r is the radial oﬀset from the core × in arcsec, as shown in Figure 6. The mass, measured out to 160 arcsec radius is

12.8 0.5M . ± ⊙

5.3.4.3 Far infrared (FIR) emission

We used the Herschel-SPIRE 500 m map to estimate the column density proﬁle,

as an independent check. We calculated B500(Td) (Planck function) for the core dust

temperature Td = 11.7 K (see Section 3.3). The core mass, Mcore, can be obtained from I D2 M M = 500 × H 1.36, (5.5) core κ B × M × 500 × 500 d

163 where I500 and D are the intensity at 500m and globule’s distance, respectively.

MH = 110 is the hydrogen gas-to-dust mass ratio in the solar neighborhood (Sodroski Md et al. 1997) and κ500 is the dust opacity at 500 m. We used the value for κ500 =2.9 cm2g−1 from Ossenkopf & Henning (1994) for the MRN dust distribution with thin ice mantles. We calculated the core mass of 11.7 2.9 M using 500 m emission. A large error ± ⊙ in this mass estimation is from MH /Mdust, which is uncertain by a factor of about 10– 35% (Sodroski et al. (1997)). In Figure 5-6, the red diamonds are the column density values derived from 500 m intensities. The molecular hydrogen column density,

N(H2), can be obtained from

1 1 M τ N(H )= N(H)= H 500 (5.6) 2 2 × 2 × M × κ m dust 500 × H

The masses 12.1 3.0 M , 12.8 0.5 M , 11.7 2.9 M , estimated out to the 160 ± ⊙ ± ⊙ ± ⊙ arcsec radius, derived by the three diﬀerent methods, star count technique, reddening of stars, and FIR 500 m emission, respectively, appear to be in good agreement with each other. However, assuming a constant temperature and dust opacity over the entire core region can introduce a minor error in our mass estimate values. The molecular column density at the core centre derived from the 500 m intensity map is N(H )=3.6 1022cm−2, causing an extinction of A 50 mag for R = 5.5 ( 2 × V ∼ V Draine 2003). The high column density categorizes the globule B207 as an Infrared

Dark Cloud (IRDC) (Egan et al. 1998).

5.3.5 Temperature and density-Abel Inversion method

Recently, the radial variation in dust temperature and density has been studied in a few starless cores. Roy et al. (2014), using the inverse Abel transform technique on FIR Herschel maps of B68 and L1689B, concluded that the actual core dust tem-

164 perature is about 2 K lower compared to the temperature obtained by the line of

sight averaged SED ﬁtting. Evaluating the core temperature using a SED ﬁt gives

an average temperature along the line of sight and does not take into account the

temperature gradients within the sources. We adopted the inverse Abel measurement

technique to study the variation in temperature along the radial direction towards the core of B207. We used Herschel-SPIRE FIR maps at 250 and 350 m for the

analysis.

We considered a spherically symmetric globule with radial density proﬁle, ρ(r), surrounded with a uniform background and isotropic ISRF. With an assumption of optically thin dust emission, the speciﬁc intensity, Iν(p), of the globule observed at impact parameter p, is

∞ rdr Iν(p)=2 ρ(r)B(ν, Td(r))κν + Iν,bg + Iν,N , (5.7) 2 2 Zp r p − p

where Iν,bg and Iν,N are the background and instrumental noise, respectively, B(ν, Td(r))

is the Planck function at the dust temperature value Td(r) for a given radius r from

the core centre, and κν is the frequency dependent dust opacity (Roy et al. 2014). Using the inverse Abel transform (e.g. Bracewell 1986) we obtain the integrand

of the above equation at observed frequency ν,

∞ 1 dIν dp ρ(r)B(ν, Td(r))κν = − . (5.8) 2 2 π Zr dp p r − p Evaluating the above equation at two diﬀerent frequencies and using their ratio with a

predeﬁned assumption about the dust opacity law κ νβ with β = 1.8, we calculated ν ∝ the temperature value at distance, r, from the core centre.

We used convolved 250 and 350 m Herschel-SPIRE intensity values to evaluate the temperature proﬁle of B207. The cloud was divided into 12 equal angular sector regions along with equal radial steps for each angular sector region. A radial temper-

165 Table 5.4 B207 core/rim temperature

Region TSED(K) TAbel(K) Core 11.7 0.1 9.4 0.1 Rim 13.4±1.4 13.3± 1.0 ± ±

ature proﬁle for each angular sector was computed. Figure 5-7a represents the radial

temperature proﬁle of B207, averaged over all 12 angular sector regions. The error in

the temperature values are computed using the standard deviation from 12 angular sector regions. However, because of the presence of the protostar, IRAS04016+2610,

and the transparent hole region, angular sector regions towards the western side of

the core and at a distance greater than 10,000 AU were not considered. The protostar

can heat gas and dust in its vicinity causing deviations in the temperature proﬁle of

the globule.

The temperature proﬁle, when extrapolated to the core, reaches a minimum of about 9.4 0.1 K. The temperature increases to 13.3 1.0 K in the outer regions of the ± ± cloud at a distance of about 40000 AU, where it is heated by the ISRF. The core ∼ temperature derived by the Abel inversion technique is 2.3 K less than that found from the SED ﬁtting technique. Table 5.4 lists the core and rim temperatures for

B207 derived from the SED ﬁt and Abel inversion method.

Knowing the radial temperature distribution in B207 and equation (5.8), we calculated the radial density proﬁle from the 250 m map. We used the dust mass opacity

2 −1 at 250 m, κ250 = 10.6 cm g , from Ossenkopf & Henning (1994) for the MRN dust distribution with thin ice mantles. Assuming a hydrogen gas-to-dust mass ratio of

110 in the analysis, we adopted a gas mass opacity at 250 m, κ250,gas = κ250/110 = 0.1 cm2 g−1. The density distribution was obtained again for each angular sector region. Figure 5-7b represents the density profile for B207 averaged over all angular sector regions. The density distribution flattens out towards the core center and is significantly different in slope from that in the outer regions of the cloud.

166 Figure 5-7 a. Dust temperature profile of B207 obtained by applying the Abel inversion method to circularly averaged intensity profiles observed with Herschel at 250m and 350m. The error represent the standard deviation of the mean in Td(r) values obtained from independent profile reconstruction along 12 angular directions. b. Density profile of B207 obtained by applying the Abel inversion method to circularly averaged intensity profiles observed with Herschel at 250 m.

167 We analyzed the density proﬁle using the Bonnor-Ebert (BE) model by solving

the modiﬁed Lane-Emden equation for an isothermal sphere (Bonnor 1956, Ebert 1955. Any given solution is characterized by three parameters: the temperature T , the central density ρc, and the outer radius of the cloud Rmax. Once an outer radius is speciﬁed, the model is in an unstable equilibrium if ξmax > 6.5, where

R√4πGmH ρc ξmax = 2 . (5.9) cs

cs, , and mH are the sound speed, mean atomic mass per particle in molecular clouds, and mass of hydrogen atom, respectively.

We generated a set of BE models over a 3D grid in temperature, outer radius and

central density. Our temperature grid ranged from T = 4 to 40 K in steps of 2 K.

Our radial grid varied from θmax = 80 to 240 in steps of 5 arcsec. For the central density grid, we varied the ξmax from 3.0 to 12.8 in steps of 0.2, since varying ξmax is equivalent to varying the central density, nc (or ρc). We evaluated our density profiles and calculated the best fit model by finding the minimum χ2 over the grid in temperature, θmax, and ξmax

1 N (n n )2 χ2 = i − BE,i , (5.10) N 3 σ2 − Xi=1 i

where ni, σi, and nBE,i are the density proﬁle, observed uncertainties, and BE model density proﬁles, respectively.

We found the best-ﬁt BE model with parameters T = 24 1.2 K, θ = 160 24 ± max ± arcsec and ξ = 7.0 0.9, which corresponds to central density of n = 3.4 105 max ± c × −3 cm . The value of ξmax is marginally greater than 6.5, indicating that the core may be gravitationally unstable and subject to collapse. The calculated BE mass

parameter, MBE, is 2.2 M⊙, while the actual core mass calculated with the density distribution, shown in Figure 7b, out to radius of 160 arcsec is 9.3 M⊙. 168 5.3.6 Core energetics

The observed evidence for a collapsing core for B207 is presented by Benson et al. (1998) in their survey of dense cores in dark clouds. The spectra of C3H2 (21,2 - 1 ) and the F ,F = 0,1 1,2 component of the N H+(1 - 0) transition in B207 0,1 1 → 2 show asymmetric proﬁles, consistent with the models for core collapse. Knowing the

number density and temperature distribution of the core we computed energy values due to diﬀerent processes occurring inside the core to determine whether the core is

stable or collapsing.

We calculated the gravitational potential energy, Egrav, from the density distribution 1 r1 Egrav = 4πGmH H M( r)nH (r)rdr. (5.11) −2 × Z0 ≤

Finding the density distribution proﬁle, and assuming r1 = 160 arcsec = 0.108 pc = 22,400 AU, and adopting =1.36, we calculated E = -1.78 1036J. The factor H grav × 1/2 is to compensate for the double counting of point masses.

Next, to estimate the thermal energy we determined the temperature as a function of radial distance from the core, shown in Figure 5-7,

T (r)=0.012r +9.42, (5.12)

4.5 −3 where r is in arcsec. Goldsmith (2001) showed that at densities nH > 10 cm dust and gas molecules are closely coupled, leading to identical temperatures, despite

signiﬁcant depletion of coolant molecules like CO. We assumed the dust and gas temperature in the core of B207 to be identical in our analysis since the densities are

greater than 105 cm−3. From Schmalzl et al. (2014), we ﬁnd

r1 3kB 2 Ethermal = 4π T (r)np(r)r dr, (5.13) 2 Z0

169 where kB is the Boltzmann constant, and np=nH H /p is the volume density of particles with p = 2.32 being the mean atomic mass per particle in molecular clouds (Przybilla et al. 2008). The calculated value of E = 1.03 1036J. thermal × Caselli et al. (2002), determined the ratio of rotational kinetic energy to the gravitational potential energy for the core of B207 to be about 0.74 10−3. Adopting × this value, the rotational K.E. of the core is E = 0.001 1036J. rot,K.E. × The magnetic energy for B207 was not measured. No literature value exists for the magnetic field strengths for this particular core. Thus we attempted to estimate a magnetic field value for B207. Caselli et al. (2002) adopted a typical magnetic field strength of 10 G for their sample of globules based on the OH Zeeman measurements in L1544 of Crutcher & Troland (2000). On the other hand, in a sample of 3 globules,

Wolf et al. (2003) found a magnetic strength of about 200 G on average. In addition, polarization measurements indicate an absence of a well ordered magnetic ﬁeld in

B207 (D. Clemens; priv. commn). We assumed a constant magnetic ﬁeld strength throughout the core, to calculate the magnetic energy 4πr3 E = 1 u , (5.14) mag 3 mag

2 where umag = B /20 is the magnetic energy density. We calculated Emag = (0.06– 6.0) 1036 J for the value range of B = 10–100 G. × We calculated the turbulence energy in the core of B207. The observed linewidth from Benson et al. (1998), using C3H2, provides a value of 370 m/s. The turbulent velocity dispersion, σ, is related to the line width ∆v by

8kT σ2 = ∆v2 ln(2) , (5.15) − m

where m is the mass of C3H2 molecule Myers (1983). The calculated turbulent velocity dispersion is σ = 354 m/s. The turbulence energy can then be calculated using the

170 relation 3M σ2 E = core (5.16) turb 16 ln2 × The calculated value of E = 0.62 1036J turb × The equivalent energy due to the external ISM pressure estimated from the BE

model at the outer radius, assuming T = 24 K and density of 1.91 104 cm−3 is ×

4 E = πR3p =1.03 1036J (5.17) ext 3 0 ×

(Equation 41.39 Draine (2011)). With these diﬀerent energy values we ﬁnd the net sum energy for B207,

Etot = Egrav + Ethermal + Erot,K.E. + Emag + Eturb + Eext (5.18)

E =( 1.78+1.03+0.001+0.06+0.62 1.03) 1036J (5.19) tot − − ×

E = 1.72 1036J (5.20) tot − ×

However, note the analysis is done assuming a low magnetic ﬁeld strength of 10 G.

A high magnetic field of 100 G would lead to a positive value for Etot. Figure 5-8 is a plot of energy ratio profiles for B207 as a function of distance from the core centre. We do not consider the Erot since it is less than 1% of the thermal energy and has negligible effect on the total energy. Neglecting the core rotational energy, the criterion for a core to be bound is

E + E + E therm turb mag 1. (5.21) E + E ≤ | grav| | ext|

The energy ratio in equation 5.21 reaches unity at a core distance of about 20,000

AU and decreases further out, neglecting the external ISM pressure, implying a grav-

itationally bound core and suggesting core collapse likely occurring in B207. When

171 Figure 5-8 Energy ratio proﬁles for B207. The total energy is dominated by the negative gravitational energy demonstrating a gravitationally bound core in B207. The energy ratio reaches unity at a core distance of 20,000 AU however, when the eﬀects of external ISM pressure∼ is included the ratio reaches unity at a much smaller distance of 10,000 AU. ∼

172 included the eﬀects of external ISM pressure, the energy ratio reaches unity at a

distance of about 10,000 AU from the core centre.

5.4 Discussion

5.4.1 Surface brightness in core and rim

The surface brightness proﬁles in U, B, V, R, and I bands display a bright rim surrounding a dark core with increasing core surface brightness at longer wavelengths.

The darkness of the core is due to the ineﬃciency of back scattering with a highly forward directed scattering phase function. The increase in dust albedo, in addition to an increase in the ISRF intensity at longer wavelengths, causes the core intensity to increase in redder bands. Given the forward directed phase function and the high photon escape probability in the optically thin rim, the surface brightness is greatly enhanced. Hence, the rim is brighter than the core.

The adjacent sky is darker mainly because of lower optical depths, declining with increasing wavelengths. In addition, the albedo of the dust grains in the nearby sky region to B207 are lower compared to the dust in the globule, and this diﬀerence increases with increasing wavelengths (Table 2). As a result, the contrast between the rim and the nearby sky region increases with wavelength, causing the rim intensity to increase signiﬁcantly above the sky background, while at the shortest wavelength in the U band the intensities of the rim and the sky become almost equal, making the rim nearly undetectable.

5.4.2 Grain growth and age determination

The dust albedo ac of the cloud listed in Table 5.2 increases with wavelengths from about 0.62 in the U band to around 0.87 in the I band. The increase of the

173 albedo with increasing wavelength suggests an increase in the grain size inside the

globule compared to the the dust in the diﬀuse ISM (Kim & Martin 1996, Draine

2003a), where the dust albedo is 0.65, as listed in column 4 of Table 5.2 for R = ∼ V 3.1. This suggests that the cloud possesses conditions favourable for grain growth.

The observed phenomenon of coreshine in the WISE W1 band also indicates the presence of large grains in the core of B207. With a core density of 105 cm−3 the time

required for grains to coagulate and grow to sub-micron size is about 105–106 years

(Hirashita & Li 2013, Ysard et al. 2013, Steinacker et al. 2014a). The presence of

Class I protostar, IRAS 04016+2610, also indicates an age of the globule in the range

few 105 years (Yen et al. 2014). ×

5.4.3 Core physical properties

The temperatures at the projected core position and the rim of B207 are 11.7 0.1 ± and 13.4 1.4 K, respectively, from our SED ﬁtting technique. However, the Abel ± inversion technique yields a lower value of 9.4 0.1 K at the actual core of B207. The ± number density at the core position is n =3.4 105 cm−3, decreasing to 400 cm−3 at H × the outer regions of the cloud (40000 AU). The Bonnor-Ebert model ﬁt to the density

proﬁle yields a temperature of 24 1.2 K and ξ = 7.0 0.9. The value of ξ , ± max ± max marginally greater than 6.5, suggests the core may be gravitationally unstable. The

calculated Bonnor-Ebert mass, MBE , is 2.2 M⊙, which is lower than 9.3 M⊙ estimated

using the density proﬁle. The calculated mass being greater than MBE also suggest a gravitationally unstable, collapsing core.

Lippok et al. (2013) showed an increase in CO depletion with the number density

in their sample of 6 cores. The depletions in their core sample range from 48% to 98% and at an average density of n = (1.1 0.4) 105cm−3, 50% of CO is frozen onto H ± × dust grains. The dust temperatures in the Lippok et al. (2013) core sample range from 9.8–12.9 K. The physical conditions at the core position of B207 with dust

174 temperature 9.4 K and n = 3.4 105 cm−3 are thus favourable for CO molecules to H × freeze on to the dust grains. Ford & Shirley (2011) modeled the B207’s core with

a canonical abundance of CO and found a signiﬁcant depletion by a factor of 1000 compared to the ISM value. This indicates freezing of CO and other major molecules

like H2O on dust grains, increasing the size of the dust grains.

5.4.4 Core collapse

We determined the core mass using several approaches, a) star count technique,

b) reddening of background stars, c) 500 m FIR emission, and d) Abel inversion

technique. All methods yielded consistent estimates of the core mass 12 M . Caselli ∼ ⊙ et al. (2002), measuring the velocity dispersion in B207, deduced the virial mass of the core (major and minor axes length of 1.6 and 1.1 arcmin, respectively) to be

1.47 0.06 M . Our derived core mass is substantially higher than the virial mass, ± ⊙ indicating an unstable condition and likelihood of collapse.

The total net energy, Etot, is found to be negative in the core of B207 (Equation 5.20) and Etherm+Eturb+Emag is less than unity at the scale of the core size radius, |Egrav| assuming a weak magnetic ﬁeld of 10 G. This implies the core is gravitationally bound and can be a collapsing core (Ward et al. 2007, Francesco et al. 2007, Andre et al. 1993). Our analysis of a collapsing core is consistent with the spectroscopic result of Benson et al. (1998). The ratio of E to E is about 2 in a 12 M grav th ∼ ⊙ core of B207 with a central density of 3.4 105 cm−3, making the core unstable ∼ × and subject to collapse in the context of Bok globule sample studies of Lippok et al. (2013) and Launhardt et al. (2013).

Apart from the IRAS 04016+2610 no other protostellar source is detected in B207 at FIR wavelengths as high as 500 m. The temperatures determined from the SED ﬁt and the Abel inversion technique do not show evidence of central warming, indicating an absence of a warm pre-stellar core. This leads us to conclude that the collapse of

175 B207 is in its very initial phase to form a low mass star in the future.

5.5 Conclusions

We present optical observations of B207 made with the Large Monolithic Imager

(LMI) instrument attached to the Discovery Channel Telescope (DCT) in U, B, V, R, and I bands, together with MIR and FIR data from WISE and Herschel Observatory.

We have studied the physical conditions in the globule B207. The main conclusions of our study are:

1. The dust albedo in the cloud increases with wavelength from 0.62 in the U-band

to 0.87 in the I-band, indicating grain sizes substantially in excess of those found in

the ISM.

2. The core-shine phenomenon observed in the 3.4 m WISE W1 band suggests the

presence of micron-size dust particles and the globule’s age of 106 years, required ∼ for the dust grains to coagulate and grow.

3. The radial density proﬁle can be approximated with a BE model with central den-

sity 3.4 105 cm−3 and ξ = 7.0 0.9, suggesting a gravitationally unstable core. × max ± 4. The line-of-sight averaged core and the rim temperatures are about 11.7 0.1 and ± 13.4 1.4 K, respectively, derived with the SED ﬁtting technique. However, the Abel ± inversion technique yields a lower temperature of 9.4 0.1 K at the position of the ± core center.

5. The averaged molecular column density (from the three diﬀerent methods: star

count technique, reddening of background stars, FIR 500m emission), N(H2), at the core is about (5.2 1) 1022 cm−2, causing an extinction of about A = 70 mag, ± × V assuming R = 5.5. This yields a core mass of 12 M , out to radius 160 arcsec V ∼ ⊙ with a central number density of n = 3.4 105 cm−3. H × 6. The energy values relating diﬀerent processes governing stability indicate a col-

176 + lapsing core, which is well supported by observations from line transitions of N2H and C3H2 by Benson et al. (1998). 7. The simultaneous presence of a collapsing core and a Class I protostar at a projected distance of 10000 AU indicates non-coeval star formation in B207, while the ∼ absence of a Class 0 source in the core of the globule, suggests that the collapse is in its initial phase.

177 Chapter 6

Summary and Future Work

Molecular gas is an important constituent of the ISM and a primary fuel for star formation. To understand star formation and hence galaxy evolution it is essential to understand physical properties of molecular gas in galaxies. Despite H2 being the most abundant molecule in the universe, due to lack of a dipole moment and high rotational energy levels it has never been directly used to study the bulk molecular

ISM properties in galaxies. From almost half a century CO, with an abundance of

−4 10 in number relative to H2, has been the primary tracer to estimate molecular gas content in nearby and high redshift galaxies. This thesis work is based on developing and discussing a model, using the rotational lines of H2, a direct tracer, to estimate the total molecular gas content in galaxies

6.1 What did we learn?

6.1.1 H2 power law model

The weak quadrupole pure rotational lines, detected with the ISO and IRS-Spitzer are presently employed to study warm molecular gas component in galaxies. H2 excitation diagrams are modeled using two or three discrete temperature components however, this method is not robust and does not yield unique temperature ﬁts to

178 the molecular gas emission. Physically H2 molecules in the ISM are in a continuous

temperature distribution. A need for the continuous distribution of H2 molecules with temperature, which can also model the H2 excitation diagrams was required.

We employed a temperature power law distribution for H2 and the model parameters were estimated using the rotational line ﬂuxes obtained from the IRS-Spitzer. Our

model was able to recover the H2 excitation diagram with robust and repeatable model parameters, unlike discrete temperature models. Moreover, extrapolating our

model to lower temperatures, we recover the total molecular gas mass in galaxies as

traced by CO and other indirect tracers. This resulted in a new detection method of

ISM molecular gas content in galaxies using the warm MIR H2 rotational lines. We extended our method to low metallicity dwarfs, where CO fails to recover the true molecular gas mass. Our method, which is independent of any indirect tracers

is able to recover the total molecular gas mass in low metallicity galaxies, where CO

is 50–100 under luminous and CO estimated ISM molecular gas mass are about an × order or two magnitude lower when used a Galactic conversion factor. We employed

the power law method in several low metallicity dwarfs (as low as about 10% of the

Milky Way abundance). The results yielded by the power law method was in good agreement with other indirect tracers like dust and star formation rate.

6.1.2 Molecular gas properties in GOALS galaxies

We estimate the model parameters from the emission of MIR H2 lines and with an extrapolation to lower temperature at 49 K, the molecular gas mass estimated is

comparable to the CO derived molecular masses, but subjected to the internal biases

of the CO-conversion factor and the error involved in the ﬂux of H2 lines. Applying the model in local mergers of GOALS, where turbulence and shocks result in physical

properties of the gas, which diﬀer from normal star forming galaxies and may test

179 our model for any alterations.

Using our model with an extrapolation to 49 K temperature yielded molecular gas masses consistently higher than the CO derived values. The model estimated molecular gas mass is also higher when compared to standard gas-to-dust ratio. Two possibilities arise from this result, either the dust derived molecular gas mass is lower or the model estimated molecular gas masses are higher. A solution to this problem is to increase the extrapolation temperature, higher than 49 K, which may subsequently reduce the ISM gas mass, resulting in standard dust-to-gas ratio and also a higher warm molecular mass fraction.

6.1.3 Stephan’s Quintet work

Due to collisions occurring in the galaxies of Stephan’s Quintet the molecular gas is heated to high temperatures. Shocks excite the H2 molecules and the ﬂux of rotational lines of H2 are higher than normal star forming galaxies. We used the power law model to understand the physical properties of molecular ISM/IGM gas content. Since most of the H2 gas is warm and hot, the power law model was able to estimate the molecular gas content in these shocks without any further extrapolation.

When compared to the single dish CO observations the molecular gas content was in good agreement with our power law estimates. We estimated the warm gas mass

M (>150K) fraction in Stephan’s Quintet to be about, H2 =0.3, higher than normal star Mtotal forming galaxies. However, in the central shock regions the temperature of warm gas

was estimated to be about 200 K and in the southern regions the warm gas mass

fraction was estimated to be as high as 0.6.

180 6.1.4 Study of Bok globule, B207

Stars are not only formed in core dense regions of GMCs, but also in small isolated dense core regions of molecular clouds, known as Bok globules. We study the physical properties of the Bok globule B207 located in the Taurus Auriga molecular region at a distance of 140 pc, which harbor a Class I protostar, IRAS04016+2610. The dust properties along with the temperature, volume and column number density profile is estimated using optical to sub-mm wavelength observations. The different energy profiles governing the stability of the dark dense core region and the Bonner Ebert model fit show a gravitationally unstable and collapsing core indicating that B207 is undergoing a second star formation phase.

6.2 Future work

6.2.1 Study of molecular gas at high z

The James Webb Space Telescope, successor to the Hubble and Spitzer space telescopes, is planned for launch in late 2018. The Mid Infrared Instrument (MIRI) onboard JWST has both a camera and a spectrograph covering the wavelength range from 5 to 28 microns. The detectors of the instrument are sensitive enough to detect the S(1), S(2), S(3) and higher rotational lines of H2 of nearby and low redshift objects till z = 0.6, 1.3, 1.9, and higher respectively. The wavelength dependent sensitivity limit of the MIRI instrument is shown in Figure 6-1. The sensitivities and spectral resolution are about 100 and 5 better than the previous IRS-Spitzer instrument. × × L H2S(1) −4 11 Assuming an average = 10 (Bonato et al. 2015), and LIR = 3 10 L⊙ LIR × (typical for LIRGs), the luminosity of S(1) line is 1.2 1034 W, corresponding to ﬂux × at z = 0.5 (d = 2.9 Gpc) about 1.2 10−19 Wm−2. To observe this line and a signal L × to noise ratio S/N = 5, will require 30 minutes of integration time, hence MIRI-

181 JWST is capable of detecting rotational lines of H2 at low and intermediate redshifts.

Using these H2 line ﬂuxes in our power law model, we can characterize the physical conditions of molecular gas and its role in the early universe.

The Cryogenic Aperture Large Infrared Submillimeter Telescope Observatory (CAL-

ISTO) planned for 2020 decade is a 5m space based observatory cooled to T 4 K ∼ emphasizing moderate resolution spectroscopy in the wavelength range 35–600 m band. The 5σ 1 hour line sensitivity of the telescope is less than 10−20 W m−2 (Brad- ford et al. 2015). At such high line sensitivity, it is possible to measure pure H2 rotational lines at high redshifts of z 6–7, almost reaching the reionization era of ≈ universe. Figure 6-2 shows spectroscopic sensitivities in the FIR and sub-mm wavelengths of diﬀerent telescopes. The left panel shows the spectrum of a galaxy, with

12 luminosity L = 10 L⊙ and the ﬂux dilution occurring at diﬀerent redshifts. With the

12 sensitivity of CALISTO, the MIR flux of 10 L⊙ galaxy at z = 6.0 can be observed. At this redshift the age of the universe is about 900 Myr, 7% of the universe’s present age. Shocks produced in the early universe due to rapid cold gas accretion and AGN feedback may enhance H2 line emission in many systems, when dust and metals are in their first cycle of enrichment. Using our power law model with the H2 line flux we can measure molecular gas properties at high redshifts.

The SPace Infrared telescope for Cosmology and Astrophysics (SPICA) is a joint mission between European Space Agency (ESA) and Japan Aerospace Exploration

Agency (JAXA), optimized for MIR and FIR spectroscopy with a cryogenically cooled telescope, targeted to launch in 2027-2028. SPICA will be equipped with two primary instruments: the Spica FAR infrared Instrument (SAFARI; Roelfsema et al. 2012) and the SPICA Mid-infrared Instrument (SMI). The limiting ﬂux of point sources for

5σ-1hr is few 10−19 Wm−2 for SMI and SAFARI instruments. Diﬀerent molecular, × 12 atomic, ionized, PAH line/band intensities for star forming galaxies with 10 L⊙ can be observed with the SPICA telescope even at high redshifts. The S(1) line intensity

182 Figure 6-1 Sensitivity of MIRI spectrograph onboard JWST as a function of wavelength, The sensitivity is about 10−20 Wm−2 at 10m, which is about two orders of magnitude better and with a spectral resolution of about 5 times higher than the IRS-Spitzer spectrograph.

12 of H2 can be observed till redshift, z = 1, for galaxy with 10 L⊙. The above mentioned future projects for the next decade provides an opportunity to observe H2 rotational lines at high redshifts. Our power law model can be useful tool in estimating molecular gas mass and study its variation and conditions at different redshifts.

6.2.2 Study on Bok globules

The existence of the cometary shaped morphology of Bok globule has been surprising to astronomers for many decades. Bok globules are sites of low mass star formation. Sometimes more than one protostars at diﬀerent evolutionary stages are seen embedded in a single Bok globule. A Class I protostar, a much younger Class

0 protostar, and a gravitationally unstable sub-mm core all co-exist in the same iso-

183 Figure 6-2 Spectroscopic sensitivities in the FIR and sub-mm. In the left plot the sensitivity is in Wm−2 for a single pointed observa- 12 tion. Galaxy spectra assuming L = 10 L⊙ at various redshifts are overplotted using light curves, with continuum smoothed to R=500. The magenta dashed line is the sensitivity of a quantum- limited heterodyne receiver in a bandwidth of 10 km/s The right panel shows he speed for a blind spatial spectral survey reaching a depth of 10−19 Wm−2 over a square degree, including the number of spatial beams and instantaneous bandwidth. (adapted from Bradford et al. 2015)

184 lated, low-mass molecular cloud (Bok globule) (Launhardt et al. 2010). The presence

of Class I protostar, IRAS 04016+2610, along with a collapsing core qualify B207 as a perfect case for studying sequential star formation. Many Bok globules are observed

with an embedded protostar along with a dark core in the globule sample studied

by (Launhardt et al. 2010), proving B207 is not an unique object. Figure 6-3 is a

histogram showing the projected distance between the dense core and the protostar

in a sample of 38 Bok globules. Further, these observations impose many queries on

Bok globules: 1) What is the distance between the dark core and the embedded protostar?

2) How many Bok globules show collapse features?

3) What are the physical conditions required to have core collapse?

4) Do protostars have any eﬀects on core collapse?

5) What are the age diﬀerences between newly forming stars in a Bok globule?

With the new advanced facility of Atacama Large Millimeter/submillimeter Array

(ALMA), we can now look into the deep dense core region of Bok globules. The ab-

sence of any proto stellar source in the collapsing core of B207 at submm wavelengths

observed with Herschel Space Observatory deﬁnitely suggests B207 as a potential tar- get for ALMA. We hope, in the coming decade, new ALMA observations will uncover the mystery of sequential star formation in Bok globules.

We have yet to fully grasp the physical processes that control atomic to molecular gas conversions. The fraction of molecular gas content in low density diﬀuse environments and cold dense gravitationally bound molecular clouds in a galaxy is still unknown. Future research on molecular gas fraction variation in diﬀuse environments with galaxy types can provide clue in study of star formation and hence, galaxy evolution. On a much small spatial scale, about a parsec size, low mass star formation

185 Figure 6-3 Distribution of globules according to the projected distance between the core and the protostar in a sample of 38 globules. A future study on a much bigger sample with the available FIR Her- schel data will be helpful in determining this distribution more exact.

186 occurring in isolated Bok globules may help us understand eﬀects of star formation processes on molecular clouds. In future along-with polarization maps, sensitive and good resolution IR observations can reveal the mystery of cometary shape structures of Bok globules. New avenues of research are opening with present observations of

ALMA and also in the coming era of JWST. With other large telescopes in plan def- initely promise a new age of astronomy and have potential prospect to revolutionize many areas of astrophysics.

+——————————————————————————————————+

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