XMM-Newton Observation of the Northeastern Limb of the Cygnus Loop Supernova Remnant

Norbert Nemes Graduate School of Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan

04 February 2005

Osaka University Abstract

We have observed the northeastern limb of the Cygnus Loop supernova remnant with the XMM-Newton observatory, as part of a 7-pointing campaign to map the remnant across its diameter. We performed medium sensitivity spatially resolved X-ray spectroscopy on the data in the 0.3-3.0 keV energy range, and for the first time we have detected C emission lines in our spectra. The background subtracted spectra were fitted with a single temperature absorbed non-equilibrium (VNEI) model. We created color maps and plotted the radial variation of the different parameters. We found that the heavy element abundances were depleted, but increase toward the edge of the remnant, exhibiting a jump structure near the northeastern edge of the field of view. The depletion suggests that the plasma in this region represents the shock heated ISM rather than the ejecta, while the radial increase of the elemental abundances seems to support the cavity explosion origin. The temperature decreases in the radial direction from 0.3keV to about 0.2keV , however, this ∼ ∼ decrease is not monotonic. There is a low temperature region in the part of the field of view closest to the center of the remnant, which is characterized by low abundances and high NH values. Another low temperature region characterized by low NH values but where the heavy element abundances suddenly jump to high values was found at the northeastern edge of the field of view. We theorize that these two regions could be interstellar clouds interacting with the blast wave. Contents

1 Supernovae and Supernova Remnants 1 1.1 Supernovae (SNe) ...... 1 1.1.1 Classiﬁcation of Supernovae ...... 2 1.2 Supernova Remnants (SNRs) ...... 5 1.2.1 Classiﬁcation of SNRs ...... 5 1.2.2 Shock Waves ...... 6 1.2.3 Evolution of SNRs ...... 7 1.2.4 The Interaction with Interstellar Clouds ...... 11 1.2.5 X-ray Emission from SNRs ...... 14

2 The Cygnus Loop 21 2.1 Radio Observations ...... 21 2.2 Optical Observations ...... 22 2.2.1 Depletion of Heavy Elements ...... 24 2.3 X-ray Observations ...... 24

3 XMM-Newton 28 3.1 The X-ray Telescopes ...... 28 3.1.1 X-ray Point-Spread Function ...... 30 3.1.2 X-ray Eﬀective Area ...... 30 3.1.3 European Photon Imaging Camera (EPIC) ...... 30 3.1.4 Readout Modes ...... 33 3.1.5 EPIC Filters ...... 33 3.1.6 The EPIC Background ...... 36

4 Observation and Data Preparation 39 4.1 Observation ...... 39 4.2 Data Preparation ...... 39

i CONTENTS ii

5 Analysis 42 5.1 Image analysis ...... 42 5.2 Spectral analysis ...... 42

6 Results 50 6.1 Color maps and the radial variation of things ...... 50 6.1.1 Analysis II ...... 56

7 Discussion 61

8 Conclusions 67 List of Figures

1.1 The Sedov self-similar solution. Each value is normalized by each value just behind the shock wave...... 10 1.2 The iron Kα emissivity (solid lines) and the emissivity-averaged line energy (dashed lines) as 3 −1 2 a function of Te and Tz. The unit of the emissivity are photons cm s /ne and the step is 0.2 in the log scale (Masai 1994)[29]...... 18 1.3 Fe ion fractions ...... 20 1.4 Emissivity of each Fe ion ...... 20 1.5 The center energy of Fe-K line blends ...... 20

2.1 1420 MHz radio map of the Cygnus Loop (Leahy 1995) ...... 22 2.2 ROSAT X-ray map of the Cygnus Loop (ROSAT All Sky Survey) ...... 27

3.1 Sketch of the XMM-Newton payload. The mirror modules, two of which are equipped with Reflection Grating Arrays, are visible at the lower left. At the right end of the assembly, the focal X-ray instruments are shown: The EPIC MOS cameras with their radiators (black/green ’horns’), the radiator of the EPIC pn camera (violet) and those of the (light blue) RGS detectors (pink). The OM telescope is obscured by the lower mirror module. Figure courtesy of Dornier Satellitensysteme GmbH...... 29 3.2 The light path in XMM-Newton’s open X-ray telescope with the pn camera in focus (not to scale) ...... 30 3.3 The net effective area of all XMM-Newton X-ray telescopes ...... 31 3.4 The general layout of the MOS camera ...... 32 3.5 The general layout of the pn camera ...... 32 3.6 Operating modes of the MOS camera: full frame mode (top left), large window mode (top right), small window mode (bottom left) and timing mode (bottom right) ...... 34 3.7 Operating modes of the pn camera: full frame and extended full frame mode (top left), large window mode (top right), small window mode (bottom left) and timing mode (bottom right) 35 3.8 Combined effective area of all telescopes assuming that all cameras operate with the same filters 35 3.9 The lightcurve from a MOS1 observation badly affected by soft proton flares ...... 36 3.10 Background spectrum of the MOS1 camera. The prominent features around 1.5 and 1.7 keV are Al-K and Si-K fluorescence lines ...... 37

iii LIST OF FIGURES iv

3.11 Background spectrum of the pn camera. The prominent features around 1.5 are Al-K, at 5.5 keV Cr-K, at 8 keV Ni-K, Cu-K, Zn-K and at 17.5 keV Mo-K ﬂuorescence lines. The rise of the spectrum below 0.3 keV are due to the detector noise...... 37 3.12 Background image for the MOS camera in the Si-Kα energy range ...... 38 3.13 Background images for the pn camera with spatially inhomogeneous ﬂuorescent lines: Ti+V+Cr- Kα (top-left), Nickel (7.3-7.6 keV) (top-right), Copper (7.8-8.2 keV)(bottom-left) and Molyb- denum (17.1-17.7 keV)(bottom-left) ...... 38

4.1 Lightcurves extracted from the event ﬁles before and after the GTI ﬁltering...... 40

5.1 Three-color image of the northeastern limb of the Cygnus Loop. The colors correspond to the following energy ranges: red - (0.3-0.75) keV, green - (0.75-12) keV, blue - (1.2-3.0) keV. The image has been smoothed with a 3σ gausian. North is up and west is to the right ...... 43 5.2 Source (black) and background (red) spectra of the MOS1 camera ...... 46 5.3 Source (black) and background (red) spectra of the MOS2 camera ...... 46 5.4 Source (black) and background (red) spectra of the pn camera ...... 46 5.5 Combined background subtracted spectrum of the entire FOV...... 47 5.6 The regions selected for analysis superimposed on the X-ray surface brightness map...... 47 5.7 The result of fitting the vmekal model (left) and the VNEI model (right) ...... 48 5.8 The spectra best fit (left) and worst fit (right) by our model ...... 49

6.1 The binning annuli overlayed onto the spectral selection regions...... 51

6.2 The variation of kTe ...... 52

6.3 The radial variation of kTe ...... 52 6.4 The variation of C ...... 52 6.5 The radial variation of C ...... 52 6.6 The variation of O ...... 53 6.7 The radial variation of O ...... 53 6.8 The variation of Ne ...... 53 6.9 The radial variation of Ne ...... 53 6.10 The variation of Mg ...... 54 6.11 The radial variation of Mg ...... 54 6.12 The variation of Fe ...... 54 6.13 The radial variation of Fe ...... 54

6.14 The variation of log(net) ...... 55

6.15 The radial variation of log(net) ...... 55

6.16 The variation of NH ...... 56

6.17 The radial variation of NH ...... 56 6.18 The radial variation of the EI ...... 57 6.19 The spectral extraction regions used for the second analysis ...... 57 LIST OF FIGURES v

6.20 The kTe for each region ...... 58

6.21 The log(net) for each region ...... 58 6.22 The abundance of C in each region ...... 58 6.23 The abundance of O in each region ...... 58 6.24 The abundance of Ne in each region ...... 59 6.25 The abundance of Mg in each region ...... 59 6.26 The abundance of Si in each region ...... 59 6.27 The abundance of Fe in each region ...... 59

6.28 The NH in each region ...... 60

7.1 Comparison between the spectra (MOS2) of region 2 (black) and region 6 (red) ...... 61 7.2 Comparison between the spectra (MOS2) of region 1 (black) and region 6 (red). The inset represents the same two spectra but plotted on a linear scale. The peak from the C emission is clearly visible...... 62 7.3 Comparison between the variation of the electron density obtained from the data and that predicted by the Sedov model for ω = 3 ...... 63 − 7.4 A circle with its center in the center of the Cygnus Loop and having a radius of 790 overlayed on our selection regions...... 64 7.5 Our selection regions overlayed on images of the northeastern limb of the Cygnus Loop taken in X-rays (ROSAT, top left), optical (DSS, top right), infrared (IRAS 60µ, bottom left), and radio (WENS, bottom right) ...... 65 7.6 Blowups of the radio and optical images. The optical ﬁlaments and the radio emission are indicated by arrows ...... 66 List of Tables

2.1 Summary of the abundances of heavy elements determined so far using optical or UV observations ...... 24

3.1 XMM-Newton characteristics - an overview ...... 29 3.2 The time resolution of the diﬀerent readout modes ...... 34

4.1 Details of the XMM-Newton observation of the northeastern limb of the Cygnus Loop. . . . . 39 4.2 The cange in the exposure times due to GTI ﬁltering...... 41

vi Chapter 1

Supernovae and Supernova Remnants

1.1 Supernovae (SNe)

The supernova explosions are the most energetic stellar events known. They are thought to represent the final stage in the evolution of a massive star. The study of SNe and their remnants (SNRs) is one of the most interesting topics in astrophysics. Although much has been learned in recent years, the basic nature of the explosion and the kinds of exploding stars are not well understood. At least 7 SN events in the last 2000 years have occurred in our Galaxy near enough to appear as bright new stars. Unfortunately, the last such event occurred in 1604, just a few years before the first astronomical use of the telescope by Galileo, so none of the progenitor stars of these explosions could be identified. On February 23, 1987, after 383 years since the last such event, a supernova (SN1987A) appeared in Large Magellanic Cloud (LMC). Although SN1987A was not as bright as its historical predecessors, it was near enough to identify its progenitor star, a B3 supergiant. This was the very first time that past observations were available to reveal the character of a star just before the explosion. At the exact time of the event, a burst of neutrinos was also observed. This was a remarkable confirmation of the theories about processes that occur deep inside the core of a collapsing star. Since the SN rate in galaxies largely determines the structure, kinematics, and composition of the interstellar medium, the rate of such events is important for many fields of astrophysical research. Astronomers routinely find a few dozen per year in extragalactic nebulae. Thus, the galactic SN rate is believed to be a few tens per century (e.g.,van den Bergh, Tammann 1991[1]).

1 CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 2

1.1.1 Classiﬁcation of Supernovae

Historically astronomers have recognized two types of SNe, which are distinguished by their optical spectra. The current classification scheme is also based on their optical spectra( Harkness, Wheeler 1990[2]). The basis for the classification consists of the presence (type II supernova) or the absence ( type I supernova) of hydrogen lines in the spectrum near the maximum light. This is a fundamental criterion, not only because one or two high-quality spectra suffice for the classification, but because it is of clear-cut physical importance as well. Stars that have shed their outer hydrogen layers at the end of their evolution are pre-SN I stars, while those that have retained them up to the explosion are pre-SN II stars. SN II outbursts occur in the arms of spiral galaxies, which are known to contain bright young massive stars, dense clouds of gas and dust characteristic of recent star formation. They rarely occur in elliptical galaxies where the stellar population is older. In contrast, the SN I events occur in all kinds of galaxies and show no preference for spiral arms. This suggests that the progenitor stars of SN I are billions of years old, and consequently not very massive. Subclasses of SN I and SN II also exist. In the case of SN I, they are distinguished by the presence or the absence of Si and He lines, while the subclasses of SN II are distinguished by their light curves. SNe I and II also have different light curves and luminosities at maximum light. SN I events all have similar light curves. The intensity rises quickly to the maximum, reaching a luminosity of 9 more than 10 L in about two weeks. An initial rapid decay is followed by a long slow decline in brightness. The luminosity falls exponentially with a characteristic time of about 55 days until the SN fades to the level of invisibility. The lightcurves of SN II events can be divided into at least two distinct classes. One class of these lightcurves exhibits a ’plateau’ in the post-maximum phase (SN II-P), having a nearly constant luminosity for about 50 days, while the other subclass exhibits little or no plateau, having a linear decline after the maximum (SN II-L). The progenitors of SN I, especially SN Ia (a subclass of SN I), are believed to be white dwarfs in binary systems in which there is mass transfer from the companion onto the white dwarf, while those of SN II are believed to be massive stars with masses of more than 10M . The gravitational collapse of the core of such stars leads to the SN II explosion.

Type Ia Supernovae (SNe Ia)

Hoyle, Fowler (1960)[3] pointed out that SN I was the result of an explosion following the ignition of nuclear fuel under conditions of extreme degeneracy in an evolved star. Arnett (1969)[4] presented CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 3 the hydrostatic and hydrodynamic calculations of the evolution of the ignited core. An explosive instability due to the ignition of C+C develops at a center density 2 109 g cm−3 and leads ∼ × to a supersonic burning (“detonation wave”) and shock wave toward the surface of the star; final velocity up to 20000 km s−1. The star is totally disrupted; no condensed remnant is left. The ∼ relevant nuclear reactions produce large amounts of 56Ni, most of the material of the star. Finally, significant amount of iron is produced by the following nuclear decays, 56Ni 56Co 56Fe. → → However, the amounts of the iron produced predicted by the the model, are several times larger than those derived from observations. To solve this problem, Nomoto et al. (1984)[5] proposed “deflagration” instead of “detonation”. They proposed the carbon deflagration models in accreting C+O white dwarfs as a plausible model for the SN I explosion. According to the model, the relatively rapid accretion onto the surface of white dwarf leads to the initiation of the core. Subsequent propagation of the convective carbon burning front (“deflagration wave”) and associated explosive nucleosynthesis were calculated for several cases of mixing length in the convection theory. The deflagration wave synthesizes 56Ni of

0.5 0.6M in the inner layer of the star; this amount is sufficient to power the light curve of SN I − by the radioactive decays 56Ni and 60Co. In the outer layers, substantial amounts of intermediate mass elements, Ca, Ar, S, Si, Mg, and O are synthesized in the decaying deflagration wave; this is consistent with the spectra of SN I near the maximum light. As the result of a large amount of energy release, the star is completely disrupted, leaving no compact remnant behind. This carbon deflagration model is the standard SN I model.

Type Ib Supernovae (SNe Ib)

Another subclass of the SN I is SN Ib which is fainter than the SN Ia. SN Ib events occur in spiral galaxies and star forming regions. The clearest diﬀerence is in the spectra in the late phase of the explosion, 250 days. Iron lines dominate the spectra of SN Ia, while oxygen lines dominate the ≥ spectra of SN Ib. The progenitors of SN Ib are thought to be massive stars that have lost their hydrogen envelope. Wolf-Rayet stars, for example, are such possible progenitors, since they shed their outer hydrogen envelope in their strong stellar winds. There is also a subclass of SN Ib, called SN Ic, which exhibit weak helium lines in their spectra.

TypeII Supernovae (SNe II)

The evolution of a star having a mass larger 10 M is quite different from that of lighter star. It consumes its nuclear fuel very quickly, and when this fuel is exhausted, the star ends its existence in s type II supernova event. Gravity is a dominant force throughout the life of the star, and the CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 4 energy released in the final explosion is also gravitational. At the beginning of the evolution of such massive stars, hydrogen in the core is fused into helium. When this is exhausted, the star contracts. During the contraction, the temperature of the core goes up. This contraction lasts until the core temperature is sufficiently high to start fusing helium into carbon and oxygen. At the same time, the temperature also increases in the hydrogen layer surrounding the core. This results in initiation of nuclear burning in this outer layer, which creates a shell of helium surrounding the core of heavier elements. This process continues until the elements in the core of the star are fused into iron. At this stage, the star is stratified into “onion” like layers. This iron core can no longer generate nuclear energy. It is stabilized by electron pressure and is at the Chandrasekhar limit. The mass of the core, however, is continuously increasing as the adjacent layer of silicon is fused into iron. The core is compressed more and the internal temperature increases to 1010 K. This causes the decomposition of 56Fe, '

56Fe 134He + 4n 124.4 MeV. (1.1) → −

As a result, the energy is absorbed, reducing the pressure and causing the core to shrink even further. Free protons are created which combine with electrons to make neutrons (and neutrinos). Some electrons supporting the core, thus disappear causing a further pressure drop. The process now runs away and gravity overwhelms the electron pressure. The gravitational collapse proceeds and finally leads to heavier homogeneous neutron matter which is supported by nuclear force. The energy explosively released by the infalling matter creates a shock wave. This shock propagates outward through the still-infalling outer layers until it reaches the outermost part of the star. The shock leads to an explosive nuclear fusion and ejects the fused material outwards. Therefore, the abundances of the heavy elements created by a type II supernova explosion are related to the thickness of the envelope, which in torn depends on the mass of the collapsing star. After the explosion, a rapidly-cooling hot neutron star is left at the center and, if this remnant of the core is spinning rapidly, it will be later observable as a pulsar at the center of the remnant. The total energy generated by the collapse and subsequent nuclear reactions exceeds 1053 erg. This is carried off mostly by neutrinos. These neutrinos, because of their low reaction cross section, escape easily from the collapsing star and are extremely difficult to detect. The amount of energy carried away by photons is only 1049 ergs. The kinetic energy of the expanding matter is typically 1051 erg. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 5

1.2 Supernova Remnants (SNRs)

The remnants created by the supernova explosion are called ”supernova remnants (SNRs)”. The study of SNRs can yield information about the explosion mechanism and the progenitor stars. Most SNRs have so far been discovered as spatially extended sources in radio surveys. They are distinguished from H II regions by the relatively ﬂat shape of their radio spectra. Most of these sources appear to be approximately circular in shape and are limb-brightened as if we were looking at emission from a large hollow shell which is transparent to its own radiation. The X-rays from most SNRs are produced by the matter ejected during the supernova explosion (hereafter “ejecta”) and the interstellar matter (hereafter “ISM”) which are heated up to 107 K by the shock wave ' created by the core collapse.

1.2.1 Classiﬁcation of SNRs

According to their radio morphology, SNRs can be classified into three types: shell, plerion and composite. Since the morphology of plerion type SNRs is center-filled, it is also called ”center-filled”. In the ”composite” type of SNRs, we can see both the shell and the center-filled component. This type is also called ”irregular”(e.g., Green 1988[6]).

Shell Type SNRs

Shell type SNRs have a shell-like morphology. They are limb brightened in radio, optical and X-ray wavelengths. Most SNRs are of this type. Examples os shell-like remnants are Cas A, Tycho’s SNR, the Cygnus Loop, and Kepler’s SNR. According to the classiﬁcation of Weiler et al. (1988[7]), some SNRs which have weak [OIII], [SiII] lines in their optical spectra are called “Balmer-dominated” SNRs, while those which have an intense [OIII] line are called “oxygen-rich” SNRs. We expect the X-ray spectra of these remnants to be thin thermal in origin however, Koyama et al. (1996[8]) reported that the dominant X-ray emission from the shell of the shell-type SNR, SN 1006 is non-thermal. They explained it be synchrotron emission from relativistic electrons accelerated by the shock wave. Subsequently, Koyama et al. (1997[9]) discovered that the X-ray emission from another shell-type SNR, RX J1713.7–3946 is also non-thermal in origin.

Plerion Type SNRs

Plerion type SNRs have a center-ﬁlled morphology in radio and both their X-ray and radio emissions are non-thermal synchrotron emissions. This synchrotron emission originates from a neutron star located at the center of the remnant. Such SNRs are the Crab, 3C58, CTB87, etc. Since the Crab CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 6 nebula was the ﬁrst SNR detected in X-rays, and since it belongs to this category, plerion type SNRs are sometimes referred to as ”Crab-like” as well. Roughly 5 percent of the known SNRs belong to this group.

Composite Type SNRs

The morphology of the composite type SNRs show both shell and center-ﬁlled components. Ex- amples of this class are W28, VelaXYZ, etc. Some SNRs like W49B, W44, CTB1, 3C397, have an interesting morphology in that they appear as shell-type in the radio and as center-ﬁlled in X-rays. In 1996, observations made with ASCA discovered that their X-ray emission is thin thermal in origin (e.g., Fujimoto et al. 1995[10]).

1.2.2 Shock Waves

A shock wave is a region of small thickness over which different fluid dynamical variables change rapidly. From a mathematical point of view, one can consider the shock wave as a discontinuity over which different variables jump suddenly. Let us consider a shock propagating into an undisturbed medium of density ρ0 and pressure p0. If we now move into the rest frame of the shock, the density, pressure and velocity are ρ0, p0 and v0 on one side, and ρ1, p1 and v1 on the other. Under steady conditions, the mass, momentum and energy fluxes should be conserved from one side of the discontinuity to the other. Thus we can write:

ρ0v0 = ρ1v1 (1.2)

2 2 p0 + ρ0v0 = p1 + ρ1v1 (1.3) 1 1 ρ v (w + v2) = ρ v (w + v2) (1.4) 0 0 0 2 0 1 1 1 2 1

where w0 and w1 are the enthalpy of the gas on the left and on the right side of the discontinuity respectively. In the case of an ideal gas, the enthalpy can be written as w = γp/ρ(γ 1). − Substituting this in 1.4 and by eliminating p2 and v2 with the help of two of the equations, we end up with the following equation: 2 ρ1 (γ + 1)M = 2 (1.5) ρ0 2 + (γ 1)M − where the dimensionless quantity v v M = 0 = 0 (1.6) γp0/ρ0 cS,0 is known as the Mach number. cS,0 is the soundp speed in medium 0. Note that equation (1.19) is not valid if M < 1. If we go back and eliminate ρ1 and v1 from equations (1.2-1.4), we end up with CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 7 the following relation: p 2γM2 (γ 1) 1 = − − (1.7) p0 γ + 1 From (1.5) and (1.7) by using the equation of state for a perfect gas, we can write a similar relation for the temperature:

T [2γM2 (γ 1)][2 + (γ 1)M2] 1 = (1.8) − − 2 2 − T0 (γ + 1) M Such equations that relate the ﬂuid variables before and after a shock, are called Rankine- Hugoniot relations. From these equations, we can see that as the shock advances, more and more material passes behind it and gets compressed to a higher density and pressure. The density compression has a maximum limiting value that can be found when putting M (strong → ∞ shock)in (1.5). This limiting value is: ρ γ + 1 1 (1.9) ρ → γ 1 0 − In the case of a monoatomic gas, γ = 5/3 and this limiting density compression turns out to be 4. In other words, if the shock tries to compress such a gas by a factor of 4, that will give rise to a shock moving at inﬁnite speed. As such, it is not possible to achieve a higher density compression. On the other hand, from (1.7) and (1.8) we can see that the pressure and temperature gap can be arbitrarily large. For the velocities of the gas before and after the shock we can write:

1 p1 v0 = (γ + 1) (1.10) s2 ρ0

2 1(γ 1) p1 v1 = − (1.11) s 2(γ + 1)ρ0

v0 is the velocity of the material in the pre-shocked region as seen from the co-moving frame of the shock, and thus actually the shock velocity VS. From the above formulae and making use of the equation of state, we can write out the relation between the shock velocity and the temperature behind it as: 2(γ 1) 3 kT = − µV 2 = µV 2 (1.12) 1 (γ + 1)2 S 16 S

1.2.3 Evolution of SNRs

The evolution of SNRs can be divided into 4 phases: free expansion, adiabatic expansion, radiative cooling, and disappearance. In the following we shall assume that the explosion is sperically symmetric and that it happened in a uniform medium. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 8

Free Expansion Phase

The free expansion phase is the initial phase in the evolution of a SNR. The shell of the ejecta expands rapidly and sweeps up the surrounding medium. This assumption holds as long as the mass of swept-up material is negligible when compared to the mass of the ejecta. The expansion proceeds at a uniform velocity, v = (5 10) 108 cm s−1, without deceleration (thus the name of 0 − × this phase). Therefore, the radius is simply expressed by

Rs = v0t. (1.13)

The initial velocity is expressed by 1 E = M v2, (1.14) 0 2 0 0 where E0 is the initial explosion kinetic energy and M0 is the total mass of the ejecta. This phase will last until that the swept up mass becomes equal to that of the ejecta. The radius Rs and its age t can be expressed by

1/3 3M0 Rs = (1.15) 4πµmHn0 1/3 −1/3 −1/3 M0 n0 µ 1.9 − pc (1.16) 1M 1cm 3 1.36 ∼ t = Rs/v0 (1.17) 1/3 −1/3 −1/3 −1/3 M0 n0 µ v0 190 −3 9 −1 yr (1.18) ∼ 1M 1cm 1.36 10 cm s where µ is the mean atomic weight of the cosmic material per H atom, mH is the mass of the hydrogen atom, and n0 is the hydrogen number density of the ISM. In the case of the typical ISM density and pressure, the sound velocity is about 10 km s−1. Since this is much less than the initial velocity of the ejecta, a shock wave consequently forms at the leading edge of the ejecta and travels outward into the ISM (hereafter, “blast wave”). The deceleration of the ejecta by the ISM causes another shock wave to propagate inward through the ejecta (hereafter, “reverse shock”)(McKee 1974[26]). The boundary between the swept-up ISM and the ejecta is called a “contact discontinuity”. As seen from an observer in the rest frame of the remnant, both shock waves initially travel outward. Assuming that the shocked ejecta is in approximate pressure equilibrium with the gas behind the blast wave, the velocity of the reverse shock wave in the relatively dense ejecta is also lower than the blast-wave velocity. After the swept- up mass becomes greater than the ejecta mass, the reverse shock propagates back to the center (e.g., Chevalier 1982[12]). CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 9

Adiabatic Phase

The mass of the swept up material is now large compared with the mass of the ejecta. However, the total energy radiated by the material in the shell is still negligibly small compared with its internal energy. Sedov (1959[13]; 1993[14]) and Taylor (1950)[15] independently derived the self-similar solution for the shock wave generated by a point explosion located in an uniform medium. Self-similarity means that the evolution of the blast wave is of such nature that if some initial configuration expands uniformly, a subsequent configuration must appear like an enlargement of the previous configuration. Shklovskii (1962)[16] proved that the self-similar Sedov solution was applicable to the supernova explosion phenomenon. Therefore, this phase is known as the Sedov-Taylor phase. Suppose that an energy E is suddenly released, creating a spherical blast wave, which passes through an ambient medium of density ρ0. Let λ be a scale parameter giving the size of the blast wave at time t after the explosion. The evolution of λ may depend on E and on ρ0. There is only one way of combining t, E and ρ0 to get a dimension of length

2 1/5 λ = (Et /ρ0) (1.19)

If we consider r(t) to be the radius of a gas shell, for a self-similar expansion, r(t) has to evolve in the same way as λ. Thus we can introduce a dimensionless distance parameter r ρ ξ = = r( 0 )1/5 (1.20) λ Et2 such that the value of this parameter does not change with time. Each gas shell can then be labelled by a particular value of ξ. If ξ0 corresponds to the shock front, then the radius of the spherical blast can be written as

Et2 Rs(t) = ξ0( ) (1.21) ρ0

ξ0 can be determined from the equation of energy conservation (Landau & Lifshitz 1959)[17]. For a monoatomic gas, its value is 1.17, and thus the radius and the temperature just behind the shock front can be writen as

E 1/5 n −1/5 t 2/5 R = 5.0 0 0 pc (1.22) s 1051 erg 1cm−3 1000 yr E 2/5 n −2/5 t −6/5 T = 4.5 0 0 keV. (1.23) s 1051 erg 1cm−3 1000 yr Here, we use the atomic weight of cosmic material, µ = 1.26 (Allen 1973)[18]. The velocity vs of the shock wave is R v = 0.4 s t−3/5. (1.24) s t ∝ CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 10

Figure 1.1: The Sedov self-similar solution. Each value is normalized by each value just behind the shock wave.

Figure 1.1 shows the physical quantity proﬁles calculated by the Sedov self-similar solution, where velocity, density, pressure, and temperature are normalized by each value just behind the shock wave. According to numerical calculations done by Chevalier(1974)[19], in this phase of evolution, roughly 70% of the initial energy of the ejecta has been transformed into thermal energy of the ISM.

The Radiative Cooling Phase

As the material behind the shock cools, the cooling rate actually increases. At this stage, the radiative energy loss is not negligible when compared with the internal energy. After the temperature drops to about (2 3) 105 K, some electrons have already recombined with the dominant − × heavy elements like carbon and oxygen ions, and the gas is then able to radiate by the very eﬃcient process of ultraviolet line emission. The material behind the shock cools and forms the denser shell. At this point, the outermost shell s driven by the internal hot gas. In the zero-th order approximation, the internal hot gas expands adiabatically.

P V γ = const., (1.25) CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 11 where P is the mean pressure of the internal gas and γ is the speciﬁc heat ratio (=C /C ). P v , p V ∝ s V R3. For a monoatomic gas, γ = 5/3, and ∝ s

v2R5 = const. R t2/7 (1.26) s s −→ s ∝

(McKee, Ostriker 1977[20]). This stage is called the pressure-driven snowplow (PDS) stage. As the internal gas cools, the shell expands due to the momentum conservation.

Msvs = const., (1.27) where M is the mass of the shell. Since M R3, s s ∝ s

v R3 = const. R t1/4 (1.28) s s −→ s ∝

This stage is called the momentum-conserving snowplow (MCS) stage.

Disappearance Phase

In this phase, the expanding shell coasts through interstellar space becoming fainter until its expansion velocity is comparable to the random motion of the ISM ( 106cm s−1). At this point it ∼ starts to lose its identity, becoming indistinguishable from the the surrounding ISM. Due to its low density, and to the fact that the radiative energy loss of such a plasma is very small, the interior of the shell maintains a high temperature, creating a hot cavity.

1.2.4 The Interaction with Interstellar Clouds

Since the evolution of most of the older SNRs is determined by the interaction of the blast wave with the interstellar medium, in this section we shall describe a few aspects of this interaction. When a blast wave encounters an obstacle, such as a cloud, three kinds of shocks result: a shock travelling around the cloud, a shock transmitted through the cloud (transmission shock) and a shock reflected from the cloud (reflection shock). The most important of these shocks is the reflection shock, which is responsible for providing additional heating to the material behind the incident blast wave, resulting in strong X-ray emission from these regions.

The Reﬂection Shock

Let us assume that a blast wave propagates in a medium having a pressure p0, and the gas behind this blast wave has a pressure p1. We furthermore assume that at a certain point, the blast wave encounters a spherical cloud with a high enough density to be considered an incompressible fluid. If the flow behind the incident wave is supersonic relative to the cloud, after the encounter, a reflection CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 12 shock will propagate into the opposite direction of the primary blast wave. Let the pressure behind the reflection shock is p2. Assuming that thermal conduction and radiation can be ignored, Courant

& Friedrichs (1948)[21] found the following relation between p0, p1 and p2:

p (3γ 1)p (γ 1)p 6M2 2 2 = − 1 − − 0 = − (1.29) p (γ 1)p + (γ + 1)p M2 + 3 1 − 1 0 The last term is for a monoatomic gas. Using the above relation and the Rankine-Hugoniot relations, we can ﬁnd the velocity of the velocity of the ﬂow behind the incident shock wave divided by the speed of sound in that region as (Spitzer 1982)[22]

v 3(1 1/M2) 1 = (1.30) 2− 2 1/2 cS,1 [(1 + 3/M )(5 1/M )] − We notice that this ratio is unity for M = 2.76. An incident shock wave with a Mach number less than this value, is subsonic with respect to the cloud, and as such it will dissipate as an acoustic wave. An incident shock with a Mach number larger than 2.76, a bow shock will be formed upstream of the cloud. From the Rankine-Hugoniot relations derived earlier we know that the pressure before and behind the reﬂection shock satisfy the following relation

p 5M2 1 2 = r − (1.31) p1 4

Using this relation together with eq. (1.30) we can calculate the Mach number of the reﬂection shock as 5M2 1 M2 = − (1.32) r M2 + 3

In the strong shock limit, Mr = √5 and the velocity of the reflection shock front relative to the cloud can be written as V = v v1 (1.33) r 1r − where v1r is the flow velocity relative to the reflection shock front, and v1 is the flow velocity behind the incident blast wave. For the SNRs observed so far in X-rays, the blast wave can be considered to be in the strong limit. Thus, the density and the pressure behind the reflection shock are 2.4 and 2.5 times higher than those behind the primary incident shock. We have so far analyzed the reflection shock under the assumption that the cloud from which it is reflected is an incompressible fluid. Let us now assume that density contrast between the cloud and the ISM is not high enough to treat the cloud as an incompressible fluid. As such, some of the blast energy will be released by the transmission shock propagating into the cloud. The physical properties of the transmission shock as well as those of the reflection shock depend on the density contrast ρ4/ρ0, where ρ4 is the density of the cloud. Sgro (1975)[23] studied the interaction considering the density contrast in the assumption of a strong shock limit of the blast CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 13 wave (M > 6). He solved the fluid equations of mass, momentum and energy conservation across the discontinuity between the reflection shock and the transmission shock. Across the discontinuity, the pressure is constant (p3 = p4). The density of the cloud, ρ4 is α times higher than that of the interstellar medium ρ0. When the incident shock strikes the cloud, the matter behind the transmission shock experiences an overpressure relative to the ambient medium by a factor β

2 2 ρ3v3 = βρ1v1 (1.34)

He found the following equations for temperatures and velocities, behind the transmission and reﬂection shocks β T = T (1.35) 3 α 1 β T2 = T1 (1.36) αr β v3 = v1 (1.37) sα 3 1 15α 1/2 v = r v (1.38) 2 4 − 4 4 α 1 " − r # where αr is the density ratio of the matter behind the incident shock and behind the reﬂected shock

(ρ2/ρ1) and can be related to α as

3α (4α 1) α = r r − (1.39) [3α (4 α )]1/2 √5(α 1) 2 { r − r − r − } Cloud Evaporation

6 The time required for the transmission shock to travel through the cloud is 10 R4/v3 years, where

R4 is the radius of the cloud [pc] and v3 is the velocity of the transmission shock [km/s]. By equating the cooling time of the material behind the transmission shock to the time required for the transmission shock to travel through the cloud, we can deﬁne a critical cloud density nc. The radiative cooling time τc of the material behind the transmission shock is

3 τ = (8n )kT/(4n )2 (1.40) c 2 4 4 where is the emissivity of the thin thermal gas, which is approximately 1.33 10−16T −1[ergs/cm3/s] × in the temperature range 105 T 107 K. Thus we can write ≤ ≤ n −3 τ = 4.6 106 4 β2v 4 yr (1.41) c n 1 × 0 Using this timescale, we can write

5/7 −2/7 5/7 5/7 β R4 n0 T1 −3 nc 10 −3 7 cm (1.42) ' 3.2 1pc 0.5cm 10 K CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 14

For clouds with density greater than nc, the gas behind the transmission shock cools rapidly and clouds begin to evaporate. Note that β depends on the density ratio α = nc/n0. After the cloud is engulfed by the shock wave, it will be gradually heated up due to thermal conduction. The thermal conductivity of a fully ionized hydrogen plasma is given by (Spitzer 1962)[24]

T 5/7 ln Λ −1 κ = 1.94 1011 e ergs/s/K/cm (1.43) 107K 30 × where ln Λ is the Coulomb logarithm which is around 30 for X-rays. If the temperature diﬀerence between the cloud and the surrounding medium is ∆T , the heat ﬂux is

q = κ∆T (1.44) −

The heat ﬂux is proportional to λ/LT , where λ is the mean free path for electron energy exchange and L = T/ ∆T . λ can be written as T | | 3kT 1/2 T 2 n −1 ln Λ −1 λ = t e = 0.29 e e pc (1.45) ee m 107K 1cm−3 30 e In the case of thermal conductivity, it is usually assumed that the mean free path λ is shorter than

LT , the typical size of the evaporating cloud. However, in certain cases, this is not true. When λ becomes comparable or greater than L , the heat ﬂux is no longer equal to κ∆T . This eﬀect is T − called saturation. Cowie & McKee (1977)[25] studied the ’saturated’ thermal conduction. In the case of a spherical cloud, the timescale for complete evaporation, can be written as

n R 2 T −5/2 ln Λ t 1.8 104 4 4 1 years (1.46) ev 17 1pc 107 30 ' ×

1.2.5 X-ray Emission from SNRs

In the case of SNRs, there are two main sources of X-rays. One is the shock heated ISM/ejecta, and the other is the (central) compact object and its associated nebula. The X-rays from the first type of source are mostly thermal in origin, while those from the second type are non-thermal in origin. Here, we shall mainly treat the thermal emission from hot plasmas. As stated before, in the case of thermal emission, X-rays originate from the ISM which is heated by the blast wave and from the ejecta, which is heated by the reverse shock. These X-rays can provide us with useful information about the interaction of the shock wave and the ISM, and about the metal abundances of their regions of origin. After a shock has passed, the ions in the plasma are almost instantaneously heated to the shock temperature which is about 107 109 K. The heating mechanism for the electrons is not yet clear. − One theory (two fluid model) states that after the passing of the shock, the electrons and the ions CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 15 are not in thermal equilibrium with each other, and that the electrons are gradually heated by Coulomb collisions. In this case, the temperature of the electrons is determined by the mass ratio of the electron and ions. Another theory proposed by McKee (1974)[26] suggests that a collisionless shock with high Mach number could equilibrate the electron and the ion temperatures by means of plasma instabilities or turbulence (one fluid model). X-ray observations of Cas-A and Tycho SNR with HEAO-1 showed high energy tails up to 25 keV (Pravdo & Smith 1979)[27], corresponding to temperatures of 108K. Such high temperatures cannot be explained by taking into account only ∼ Coulomb collisions. Although these observations seem to support the one-fluid model, the high energy tails could be of non-thermal origin, as shown by Reynolds & Chevalier (1981)[28].

Ionization and Recombination

There are three processes that can change the ionization state of a plasma: electric impact ionization, photoionization, and autoionization. In general, in the case of a thin thermal plasma, the photoionization eﬀect is negligible compared to the electric impact ionization. Where there is ionization, there is also recombination. As such we can talk about three main recombination processes: three-body recombination, radiative recombination, dielectric recombination. Each is inverse process of the ionization process mentioned above. From the point of view of collisional processes, plasma conditions can be classiﬁed into the following three categories:

(1) Ionization equilibrium The ionization rate is equal to the recombination rate.

(2) Ionizing The ionization rate exceeds the recombination rate. This condition can be found in X-ray spectra of SNRs.

(3) Recombining The plasma is dominated by the recombination process.

Collisional Ionization Equilibrium

For a chemical element with atomic number, Z, the ionization rate can be written as

dfz = Sz−1fz−1 (Sz + αz)fz + αz+1fz+1 (1.47) d(net) − Z fz = 1 (1.48) zX=0 (z = 0, 1, . . . , Z), where f is the ionic fraction of the element which is ionized z 1 times. S and α are the z − z z ionization and the recombination rate coeﬃcients of the z-th ion. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 16

The characteristic timescale (tIeq) to reach ionization equilibrium can be derived from above equation. In the zero-th order approximations, this timescale can be written as (Masai 1994 [29]), Z n t (S + α )−1 e Ieq ≈ z z zX=0 [min(S + α )]−1 ≈ z z 1012cm−3s. (1.49) ≈

This value is independent of Z and Te. Assuming a density of n 1 cm−3 , then t 1012 sec 105 year. Therefore, most of SNRs e ∼ Ieq ∼ ∼ may be still in an ionizing state or non-ionization equilibrium.

Thermal Equilibrium

Here, we discuss the thermal equilibrium between electrons and ions. We assume that the electrons and ions have a Maxwellian velocity distribution and that they have temperatures T = T . Con- e 6 i sidering Coulomb collisions only, the equipartition of energy between electrons and ions is reached at a rate of can be written as dT T T = i − e (1.50) dt τeq

Here τeq is time to reach equipartition, which can be written as (Spitzer 1962)[24] 3m m k3/2 T T 3/2 τ = e i i + e . (1.51) eq 1/2 2 2 4 m m 8(2π) niZ Zi e ln Λ i e Masai (1994)[29] analytically estimated the equipartition process and found the post-shock temperature Te to be approximately

T 0.21 (ln Λ)2/5(n t)2/5T 2/5 K, (1.52) e ∼ × e s where Ts is the shock temperature (the temperature of particles heated by a shock wave with the velocity Vs) expressed as 3 kT = µm V 2, (1.53) s 16 i s where µ and mi are the mean atomic weight and the average ion mass respectively. Masai (1994)[29] showed that the electron temperature increases to 0.1T and 0.3T in 10−3t and 10−2 t , ∼ s s Eeq Eeq respectively, where tEeq is the equipartition time constant given as 3/2 3mp(kTs) tEeq = . (1.54) 1/2 1/2 4 8(2π) neme e ln Λ Another electron heating mechanism due to plasma instabilities was proposed by McKee (McKee 1974[26]; McKee, Hollenbach 1980[30]). Such plasma instabilities might force the establishment of equipartition between ions and electrons almost instantaneously at the shock front. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 17

Radiative Processes

Line Emission

In the case of hot plasmas, there are three processes reponsible for line emission: dielectric recombination, electron impact ionization, and electron impact excitation. If the plasma is in ionization equilibrium (Te = Tz), electron impact excitation and dielectric recombination are dominant. While, in the ionizing condition (Te > Tz), the dominant process is electron impact ionization (ﬁgure 1.2[29]).

Continuum Emission

There are again three processes responsible for continuum emission: thermal bremsstrahlung, radiative recombination, and two-photon radiation. Thermal bremsstrahlung is due to the accel- eration of electrons with a maxvellian velocity distribution at a temperature Te, in the Coulomb ﬁeld of the ions. The emissivity is given as (Rybicki, Lightman 1979)[31],

εff = 6.8 10−38Z2n n T −1/2e−hν/kTe g (ergs−1cm−3Hz−1) (1.55) ν × e i e ff where ne and ni are the number density of electrons and ions respectively. Z is the atomic number of the ions, and h and k are the Plank constant and Boltzmann constant respectively. Moreover, gff is a velocity averaged Gaunt factor. We can approximate gff as follows,

−4 1 5 (10 < hν/kTe < 1) gff  − ∼  1 (hν/kT 1).  e ∼  Thus, the value of gff is not importan t for the shape of the spectrum. Therefore, we can roughly estimate the spectrum shape as

ff 1 (hν/kTe < 1) εν  ∝ −hν/kTe  e (hν/kTe > 1).  Thus, the spectrum shape is uniquelydetermined by the electron temperature Te. The observed continuum ﬂux depends on the electron temperature and on n n dV n2dV called emission e i ∼ e measure. R R

Radiative recombination is dominant in the recombining state (Te < Tz) of a plasma. In this process, a free electron is captured by a nearby ion, which results in the emission of a photon. In the two-photon radiation , the energy of photons is shared with the electron transition energy. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 18

Figure 1.2: The iron Kα emissivity (solid lines) and the emissivity-averaged line energy (dashed 3 −1 2 lines) as a function of Te and Tz. The unit of the emissivity are photons cm s /ne and the step is 0.2 in the log scale (Masai 1994)[29]. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 19

Radiation from SNRs

The plasma in most SNRs is not in ionization equilibrium. Thus, we must take into account a non-equilibrium ionization (NEI) condition. In order to do this, we use the parameter τ (called “ionization timescale”) defined as tage τ = nedt (1.56) Zt0 where ne is the electron number density, t0 is the epoch when the matter is first engulfed by the shock wave, and tage is the epoch at the observation time. The plasma reaches the CIE condition when τ 1012 cm−3s. (1.57) ∼ We consider the effect of the NEI condition on the line emission. The ionic fractions, emissivity, center energy variation with respect to the electron temperature, Te and the ionization timescale τ of iron as derived from the Masai (1984)[32] code, are shown in figure 1.3, figure 1.4, and figure 1.5. In these figures, z denotes the (z-1)-th ionization stage of the element. In the case of iron, z=26 represents the hydrogen-like ion and z=25 represents the helium-like ion. Figure 1.3 shows that, as the ionization timescale becomes larger, the dominant ionic states become higher ionized . Since the ion fractions are not changed when τ 1012cm−3 sec, the plasma has reached the CIE. ≥ These figures also show that the dominant ionic states become higher ionized for a higher electron temperature. The emissivity of each ion is determined by a given Te and τ as shown in figure 1.4.

The center energy of the iron K line blends with a given Te and τ are shown in ﬁgure 1.5. The variation of the center energy is large in the range of log τ = 1010 1011.5. Detailed investigation − of the proﬁle of the iron K line-blends can reveal the plasma condition. CHAPTER 1. SUPERNOVAE AND SUPERNOVA REMNANTS 20

Figure 1.3: Fe ion fractions

Figure 1.4: Emissivity of each Fe ion

Figure 1.5: The center energy of Fe-K line blends Chapter 2

The Cygnus Loop

The Cygnus Loop is a typical shell type, middle aged SNR, located below the Galactic equator (l = 74◦, b = 8◦.6) and 440 pc away from us. It has an apparent a radius of 1.5◦. Its large − apparent size, high surface brightness and the low hydrogen column density in its direction, have made it an ideal target for the study of its features using spatially-resolved spectroscopy. It is also at a suﬃciently high galactic latitude that confusion with background emission from the plane of the galaxy is minimized. In this section, we shall try to summarize the results of the observations so far performed on this remnant, with an emphasis on those in the X-ray region of the spectrum.

2.1 Radio Observations

In the radio wavelength, the Cygnus Loop is sometimes referred to as G74.0-8.5. A 1430 MHz image of the Loop is shown in figure 2.1. We can see strong radio emission in the northeastern, western and southern regions. This radio emission is predominantly non-thermal in origin. This radiation comes from electrons gyrating around the interstellar magnetic field lines which have been compressed by the SN blast wave. Polarization of the radiation has also been detected. This polarization is up to 25% in the entire southern half of the remnant (Moffat 1971)[34]. The bright radio emission coincides with the bright optical filaments. This can be explained by the thermal instability behind the shock front compressing both the magnetic field lines and the ISM, resulting in both radio and optical emission (van der Laan 1962 citevan der Laan:1962; Duin & van der Laan 1975[36]). Uyaniker et al. (2002)[37] mapped the radio continuum of the Loop using the 100m Effelsberg radio telescope, as part of a multi-frequency continuum and polarization study. They found a fair amount of polarization (up to 30%) towards the south of the remnant. Also they found that there was a clear distinction between the distribution of polarized emission between the northern and southern part of the remnant, suggesting that the

21 CHAPTER 2. THE CYGNUS LOOP 22

Figure 2.1: 1420 MHz radio map of the Cygnus Loop (Leahy 1995)

Cygnus Loop is in fact two interacting supernova remnants.

2.2 Optical Observations

In the optical wavelength, the Cygnus Loop is referred to as the Veil Nebula or NGC 6960, 6992-5. Hubble(1937)[38] found the proper motion of the filaments to be 0”.03/yr. Minkowski (1958)[39] studied the radial velocities of 25 points distributed over the Loop and found that these velocities ranged from 46 km/s to 116 km/s. Assuming a homogeneous expansion, and combining the proper motions of 0”.03 /year, he calculated the the distance to the Loop to be 770 pc. This value was used for the calibration of the Σ D relation (Woltjer 1972)[40]. − Before X-rays were detected from it, the Cygnus Loop was believed to be an old remnant and that the energy loss due to radiation was significant ( i.e. it was in the radiative phase). This was justified by the relatively low expansion velocity of 100 km/s of the shell. Grader et al. (1970)[41] CHAPTER 2. THE CYGNUS LOOP 23 were the first to detect X-rays from the Cygnus Loop, and they fount that their spectra were well fitted by a bremsstrahlung continuum at 0.37 keV with a line that they suggested to come from O VIII. Their results indicated a shock velocity over 500 km/s. This result had a great impact on the evolutionary theories of SNRs. Many theories were proposed to explain the slow shock in optical and the fast shock in X-rays. One such theory (McKee & Cowie, 1975)[42] argues that when the SN blast wave interacts with interstellar clouds, a transmission shock is driven into the cloud. If the density of these clouds is larger than the critical density, then optical emission is expected from the regions behind the transmitted shock, while the regions behind the primary shock emit X-rays. The velocity ratio of the transmitted shock relative to the primary blast wave is proportional to the square root of the density ratio of the cloud to the ISM. Therefore we expect to see a slow shock in the optical and a fast shock in X-rays. Woodgate et al. (1974)[43] detected the [Fe XIV] λ 5303 coronal line from the Cygnus Loop and found that the temperature of the emitting gas to be 0.24 keV. This result confirmed the presence of hot plasma in the vicinity of the Cygnus Loop. In 1979, Kirshner & Taylor[44] found high velocity (up to 250 km/s) Hα filaments. Such filaments are referred to as ’non-radiative shock’ (McKee & Hollenbach 1980)[30] or ’Balmer-dominated filaments’. These filaments can be observed in the case of other SNRs as well. Such filaments are thought to be the result of a collisionless shock moving into partially neutral interstellar material, and as a result, collisional excitation, ionization and charge exchange occur (Chevalier & Raymond 1978)[45]. Important information can be obtained from the study of the Balmer-dominated filaments. Raymond et al. (1983)[46] suggested that in the post-shock region Coulomb equilibrium was favored over the more rapid equilibrium due to plasma instabilities. Smith et al. (1991)[47] showed that the observed line intensity ratios corresponded neither to Coulomb equilibrium nor to complete equilibrium. In the case of the Cygnus Loop, the Balmer-dominated filaments trace the shock front but not completely. Behind these filaments there is X-ray emitting plasma. The bright optical filaments can be found well inside this X-ray emitting region. Blair et al. (1999)[48] observed the Balmer-dominated filaments on the northeastern limb of the Cygnus Loop using the Wide Field Planetary Camera 2 of the Hubble Space Telescope. They have calculated that the proper motion of the Balmer-dominated filaments over 44 years is 3”.6 0”.5. ∼ Considering a shock velocity of 170 km/s they deduced a new distance of 440 pc to the Cygnus Loop. This fact has some important implications for the Loop’s physical properties. Thus the linear size of the remnant is 21.5 27 pc, while its age becomes 5000d/(440pc) years (in contrast × with the previously estimated age of 18000 years). ∼ CHAPTER 2. THE CYGNUS LOOP 24

Table 2.1: Summary of the abundances of heavy elements determined so far using optical or UV observations

C N O Si S Fe wavelength reference 0.4 0.25 0.2 optical Dopita et al.(1977) 0.2 far UV Benvenutti et al. (1980) 0.2 0.2 UV Raymond et al. (1980b) 0.4 0.7 0.7 0.3 UV Raymond et al. (1983) 0.5 0.25 optical/UV Raymond et al. (1988)

2.2.1 Depletion of Heavy Elements

In the case of the Cygnus Loop, there is much observational evidence of the depletion of the heavy element abundances. Benvenutti et al. (1980)[49] analyzed far-ultraviolet spectra obtained with the IUE, and found that they needed depleted metal abundances in order to satisfactorily ﬁt their spectra. C was especially depleted by a factor of 5 compared to the cosmic abundance. Raymond et al. (1980b)[50] using UV spectroscopy, found that C and Si were depleted by a factor of 5 relative to the cosmic abundance. The abundances of heavy elements in the Cygnus Loop are summarized in table 2.1.

2.3 X-ray Observations

Except for the southern region, the Cygnus Loop is almost spherically symmetric. As mentioned before, the first detection of X-rays was made by Grader et al. (1970)[41], and they found that their spectra could be fitted by a bremsstrahlung continuum and an emission line at 0.65 keV. Bleeker et al. (1972)[51] performed a rocket borne experiment and obtained a ”two-color” X-ray spectrum using thin films of different thickness together with gas proportional counters. The obtained spectra were well fitted with a thermal emission model with kT = 0.23 keV and N = 5.5 1020/cm2. e H × Broken et al. (1972)[52] performed a scanning observation in the 0.15-1 keV energy range, and found two separate emission regions, which coincide with with the optically bright filaments NGC 6960, 6992. A two-dimensional surface brightness map was first obtained by Stevens & Garmire (1973)[53]. The obtained image showed a limb-brightened feature. A more precise X-ray image was obtained by Rappaport et al. (1973[54],1974[55]) using a one-dimensional proportional counter with a spatial resolution of 30’. They constructed X-ray images in two energy bands: 0.15-0.28 keV and 0.4-0.85 CHAPTER 2. THE CYGNUS LOOP 25 keV. Strong X-ray emission was detected at the center of the remnant in the high energy band. They also reported X-ray pulsations with a period of 62 ms coming from the center, and showing a black body spectrum with a temperature of 2 106 K. The central source was not detected in the × subsequent observations done by Weisskopf et al. (1974)[57], Snyder et al. (1975)[58] and Charles et al (1975)[59]. Rapaport et al. (1979)[56] created another image of the Loop by using a Wolter type I X-ray telescope with a spatial resolution of 10’. This new image showed a limb-brightened shell with no central source. The argued that the source detected in their previous observation was an artifact of the algorithm used to construct the image.

Tuohy et al. (1982)[60] observed the northeastern region of the Loop and found that the kTe increased towards the center of the remnant. Inoue et al. (1980)[61] performed spectroscopic observations using a gas scintillation proportional counter. The energy resolution of this device was two times better than that of a gas proportional counter. They detected an emission line coming from

O VIII. The obtained spectrum was well ﬁtted by the model coded by Kato (1976)[62] with a kTe of

0.28 keV. Tsunemi (1979)[63] applied a multi-component model with different kTe. He assumed that the emission measure varied according to a power law of temperature, i.e. n(T )2dV (T ) T −γdT . ∝ Employing the Kato model, he found a good fit with N = 4.5 1020/cm2 and γ = 2.5. Sedov’s H × self similar solution for an adiabatic shock wave expanding into a uniform interstellar medium gives the kTe dependence on the emission measure as a power law with γ = 3.3. This seems to suggest that more emission measure is needed in the upper kTe region than that expected from the Sedov solution. He also investigated the evaporation of HI clouds, considering the adiabatic expansion of clouds, and found γ = 2.5. His numerical calculations show that γ was unity before the dynamical motion of the clouds became effective, while after that, γ was 2.5 for a long time. Therefore, the observed properties of the kTe and the emission measure could be explained within the framework of cloud evaporation. This model also accounted for the coincidence between Hα and the X-ray emission. A high resolution X-ray image with a spatial resolution of several arcminutes was obtained with the Einstein Observatory (Ku et al. 1984)[64]. The large-scale structure of the Loop was well modelled by a limb-brightened shell of hot gas having a temperature of 0.18 keV, created by the expansion of a blast wave into an inhomogeneous ISM. The IPC spectra indicated that the center of the remnant was hotter than the limb, with a kTe as high as 0.34 keV. Vedder et al. (1986)[65] performed a high energy resolution observation on the Loop using the Einstein FPCS. They detected emission from O VII, O VIII, and Ne IX. Based on the intensity of the O lines, they concluded that the plasma in the Cygnus Loop did not yet reach collisional ionization equilibrium (CIE). The NEI condition was later confirmed by Tsunemi et al. (1988)[66]. CHAPTER 2. THE CYGNUS LOOP 26

Ballet & Rothenﬂug (1989)[67] observed the northern and eastern region of the Loop with

EXOSAT. Their spectra were well ﬁtted by a two-kTe CIE model. Levenson et al. (1998)[68] mapped the entire Cygnus Loop using the ROSAT X-ray satellite. They found that the remnant is dominated by its interaction with an inhomogeneous environment. They measured the amount of limb brightening present in diﬀerent parts of the remnant as well, and showed that this brightening was too strong , and it could not be explained by an adiabatic blast wave propagating through a uniform medium neither by thermal evaporation. They have also found that over large scales, the blast wave is running into dense material, suggesting that the SNe that created the Cygnus Loop occurred in a preexisting cavity created by the progenitor star. This model also explains the increased limb brightening as being produced by the shock heated dense cavity walls. In 1999, Miyata et al.[69] analyzed the radial structure in the northeastern part of the Cygnus

Loop using ASCA data. They ﬁtted their data with a VNEI model and found gradients in the kTe and in the ionization timescale. A jump structure was found in all measured quantities at about

0.9RS , suggestive of the cavity walls. They also calculated the density of the bright shell to be much higher than that predicted by the blast wave expanding into a homogeneous medium model, while the density inside the shell turned out to be low and constant ( 8 10−3cm−3). Assuming ∼ × that the ejecta is conﬁned inside 0.9RS , they calculated the total mass of the progenitor star to be roughly 15M . These results represented further evidence supporting the cavity explosion theory. CHAPTER 2. THE CYGNUS LOOP 27

Figure 2.2: ROSAT X-ray map of the Cygnus Loop (ROSAT All Sky Survey) Chapter 3

XMM-Newton

XMM-Newton is the second of ESA’s four “cornerstone” missions deﬁned in the Horizon 2000 Programme and it was launched on December 10th 1999. XMM-Newton caries the following instruments:

1. European Photon Imaging Camera (EPIC) 3 CCD cameras for X-ray imaging, moderate resolution spectroscopy and X-ray photometry. The EPIC ic composed of two MOS cameras and one pn.

2. Reﬂection Grating Spectrometer (RGS) 2 identical spectrometers for high resolution spectroscopy and spectro-photometry

3. Optical Monitor (OM) for optical/UV imaging and grism spectroscopy

The most important characteristics of XMM-Newton are compiled in table 3.1.

3.1 The X-ray Telescopes

XMM-Newton’s three Wolter I type telescopes are co-aligned with a relative astrometry between the three EPIC cameras calibrated to better that 1-2” across the full FOV. One telescope has the light path as shown in ﬁgure 3.2 while the two others have grating assemblies in their light paths. Approximately 44% of the incoming light focused by the multi-shell grazing incidence mirrors is directed onto the camera at the focus, while 40% of the radiation is dispersed by a grating array onto a linear strip of CCDs. The remaining light is absorbed by the support structures of the RGAs.

28 CHAPTER 3. XMM-NEWTON 29

Grating MOS

RGS pn Optical Monitor Mirror

Figure 3.1: Sketch of the XMM-Newton payload. The mirror modules, two of which are equipped with Reﬂection Grating Arrays, are visible at the lower left. At the right end of the assembly, the focal X-ray instruments are shown: The EPIC MOS cameras with their radiators (black/green ’horns’), the radiator of the EPIC pn camera (violet) and those of the (light blue) RGS detectors (pink). The OM telescope is obscured by the lower mirror module. Figure courtesy of Dornier Satellitensysteme GmbH.

Table 3.1: XMM-Newton characteristics - an overview

Instrument EPIC MOS EPIC pn RGS OM Bandpass 0.15-12 keV 0.15-15 keV 0.35-2.5 keV 180-600 nm Orbital target vis. 5-135 ks 5-135 ks 5-145 ks 5-145 ks Sensitivity 10−14 10−14 8 10−5 20.7 mag ∼ ∼ ∼ × Field of view (FOV) 30’ 30’ 50 17’ ∼ PSF (FWHM/HEW) 5”/14” 6”/15” N/A 1.4”-1.9” Pixel size 40µm(1.1”) 150µm(4.1”) 81µm(9 10−3A˚) 0.476513” × Timing resolution 1.5 ms 0.03 ms 16 ms 0.5 s Spectral resolution 70eV 80eV 0.04/0.025A˚ 350 ∼ ∼ CHAPTER 3. XMM-NEWTON 30

Figure 3.2: The light path in XMM-Newton’s open X-ray telescope with the pn camera in focus (not to scale)

3.1.1 X-ray Point-Spread Function

The point-spread function (PSF) represents the spatial distribution of light in the focal plane in response to an observed point source. The core of the on-axis PSF is narrow and varies little over a wide energy range (0.1-4 keV). Above 4 keV, the PSF becomes only slightly more energy dependent.

3.1.2 X-ray Eﬀective Area

At 1.5 keV, each telescope has an effective area of 1550cm2. The mirror effective areas folded through the response of the different focal instruments are shown in figure 3.3. From this figure we can see that the mirrors are the most effective in the 0.1 to 10 keV energy range, with a maximum at about 1.5 keV and a pronounced absorption edge near 2 keV (the Au M edge). The effective are of the MOS cameras are lower than those of the pn because only part of the incoming radiation falls onto these detectors. This is due to the fact that the MOS cameras are partially obscured by the RGAs.

3.1.3 European Photon Imaging Camera (EPIC)

The EPIC consists of 3 CCD cameras. Two of these are MOS (Metal Oxide Semiconductor) type CCD arrays and the third one is a diﬀerent CCD camera called EPIC pn. For all cameras, the sensitive area of the detector is about 30’ across. Figure 3.4 and 3.5 present the general layout of the EPIC cameras. Some of the properties of the layouts are listed below. CHAPTER 3. XMM-NEWTON 31

EPIC:PN EPIC:MOS{2modules} EPIC:MOS{single} RGS-total:-1st order 2 RGS-total:-2nd order

cm 1000 RGS1:-1st order RGS1:-2nd order Effective Area [ ]

0 5 10 15 Energy [keV]

Figure 3.3: The net eﬀective area of all XMM-Newton X-ray telescopes

1. The pn chip array is slightly oﬀset with respect to the optical axis of its X-ray telescope so that the nominal, on axis position does not fall on the central chip boundary. This ensures that 90% of the energy of an on-axis point source are collected on one pn CCD chip. ≥ 2. The MOS cameras are rotated by 90◦ with respect to each other.

3. The dead spaces between the MOS chips are not gaps, but unusable areas due to detector edges (the MOS chips physically overlap each other, the central one being located slightly behind the ones in the outer ring).

All EPIC CCDs operate in photon counting mode with a ﬁxed, mode dependent frame read-out frequency.

The MOS Camera

The MOS chip arrays consist of 7 individual identical, front-illuminated chips. The individual CCDs are not co-planar, but oﬀset with respect to each other, following closely the curvature of the focal surface of the Wolter telescopes. Each chip consists of 600 600 pixels, with each pixel × having a size of 40µm. Each pixel subtends a 1.1” solid angle on the sky. The MOS chips have a frame store region which serves as a data buﬀer for storage before they are read out through the read-out nodes, while the rest of the chip is obtaining the next exposure. CHAPTER 3. XMM-NEWTON 32

rawY rawX CCD5 CCD4 rawX rawY rawY rawX CCD6 CCD1 CCD3 rawY rawX rawX rawY rawY rawX detY CCD7 CCD2 rawX detX rawY

Figure 3.4: The general layout of the MOS camera

rawX rawY

CCD3 CCD2 CCD1 CCD4 CCD5 CCD6

CCD12 CCD11 CCD10 CCD7 CCD8 CCD9

rawY detY rawX detX

Figure 3.5: The general layout of the pn camera CHAPTER 3. XMM-NEWTON 33

The pn Camera

The pn camera consists of a single silicon wafer with 12 integrated back-illuminated chips. The size of one pn pixel is 150µm, which subtends 4.1” on the sky. The readout speed of the pn camera is much higher than that of the MOS because each pixel column has its own readout node.

3.1.4 Readout Modes

There are several modes of data acquisition available:

1. ”full frame” and ”extended full frame” (pn only) In this mode, all pixels of all CCDs are read out and thus the whole FOV is covered.

2. ”partial window” In the case of the MOS cameras, in partial window mode, the central CCDs can be operated in a diﬀerent mode of data acquisition, reading out only part of the CCD chip. In the case of the pn, in large window mode, only half of the of the area in all 12 CCDs is read out, whereas in small window mode, only a part of CCD number 4 is used to collect data.

3. Timing mode” In the timing mode, imaging is made only in one dimension, along the column (RAWX) axis. Along the RAWY axis, data from a predeﬁned area on one CCD chip are collapsed into a one-dimensional row to be read out at high speed. In the case of the pn camera there is a variation of the timing mode called ”burst” mode. This mode oﬀers a very high time resolution, but has a very low duty cycle of 3%.

The time resolution of each readout mode is tabulated in table 3.2 while ﬁgure 3.6 and 3.7 present images of the respective modes.

3.1.5 EPIC Filters

To prevent contamination of the X-ray data by non-X-ray photons, XMM-Newton is equipped with with a set of three separate filters named thick, medium and thin. The thick filter should be able to efficiently suppress the optical contamination for all point source targets op to mV of 1-4 (MOS) 3 or mV of -2-1 (pn). The medium filter is 10 less efficient than the thick filter, so it is expected that it will be useful for preventing contamination from point sources as bright as mV =6-9. The thin filter is 105 less efficient than the thick filter and it can be used to suppress contamination from point sources fainter than 14 mag. The effective area of the EPIC cameras for each of the optical filters is shown in figure 3.8. CHAPTER 3. XMM-NEWTON 34

Table 3.2: The time resolution of the diﬀerent readout modes

MOS Time Resulution Full frame (600 600) 2.6s × Small window (100 100) 0.3s × Large window (300 300) 0.9s × Full frame (600 600) 2.6s × Timing uncompressed (100 600) 1.5ms × PN Time Resulution Full frame (376 384) 73.4ms × Extended full frame (378 384) 200ms × Large window (198 384) 48ms × Small window (63 64) 6ms × Timing (64 200) 0.03ms × Burst (64 180) 7µs ×

Figure 3.6: Operating modes of the MOS camera: full frame mode (top left), large window mode (top right), small window mode (bottom left) and timing mode (bottom right) CHAPTER 3. XMM-NEWTON 35

Figure 3.7: Operating modes of the pn camera: full frame and extended full frame mode (top left), large window mode (top right), small window mode (bottom left) and timing mode (bottom right)

1000 2

100 Open position Thin filter Effective area (cm ) Medium filter Thick filter

10 10-1 100 101 Energy (keV)

Figure 3.8: Combined eﬀective area of all telescopes assuming that all cameras operate with the same ﬁlters CHAPTER 3. XMM-NEWTON 36 4 3 2 Intensity [cts / s] 1 0 2¡ 104 4¡ 104 6¡ 104 Time [s]

Figure 3.9: The lightcurve from a MOS1 observation badly aﬀected by soft proton ﬂares

3.1.6 The EPIC Background

There are three diﬀerent types of background:

1. The cosmic X-ray background

2. External “ﬂaring” background

3. Internal “quiescent” background

4. Detector noise

The Cosmic X-ray Background (CXB)

This background is dominated by thermal emission at lower energies (E¡1 keV) and a power law at higher energies. The power law background is generated by unresolved cosmological sources. The CXB varies over the sky at lower energies.

The External “Flaring” Background

This component is produced by by protons with energies less than a few 100 keV, which are funnelled towards the detectors by the X-ray mirrors. The spectra of these flares are highly variable and there is no clear correlation between the intensity and the spectral shape. Figure 3.9 shows the lightcurve of a MOS1 observation badly affected by such proton flares. CHAPTER 3. XMM-NEWTON 37 1 10 0.5

1 Cu 0.2 Al Zn Cu Ni cts / s keV Cr 0.1 singles/s/keV ZnAu Au 0.1 Ti Mo 0.05

0.01 0.2 0.5 1 2 5 10 1 10 Energy [keV] Energy [keV]

Figure 3.10: Background spectrum of the MOS1 Figure 3.11: Background spectrum of the pn camera. The prominent features around 1.5 and camera. The prominent features around 1.5 are 1.7 keV are Al-K and Si-K ﬂuorescence lines Al-K, at 5.5 keV Cr-K, at 8 keV Ni-K, Cu-K, Zn-K and at 17.5 keV Mo-K ﬂuorescence lines. The rise of the spectrum below 0.3 keV are due to the detector noise.

The Internal “Quiescent” Background

This component is produced by high energy particles interacting with the structures surrounding the detectors and with the detectors themselves. This component shows only small intensity variations with time. The spectra are quite flat and contain several fluorescence lines due to the detectors and the structures surrounding them. Such spectra are illustrated in figure 3.10 and 3.11.

Detector Noise

The detector noise in a CCD is mainly due to the dark current. This current is negligibly small for both types of EPIC CCD under nominal operating conditions. In the MOS camera, there are low level “flickering” of a small number of pixels at an occurrence rate of < 1%. In the pn, during high particle background periods, the offset calculation leads in some pixels to a slightly under estimate of the offset, which can result in blocks of approx. 4 4 pixels with with an enhanced low energy × signal. CHAPTER 3. XMM-NEWTON 38

Figure 3.12: Background image for the MOS camera in the Si-Kα energy range

Figure 3.13: Background images for the pn camera with spatially inhomogeneous ﬂuorescent lines: Ti+V+Cr-Kα (top-left), Nickel (7.3-7.6 keV) (top-right), Copper (7.8-8.2 keV)(bottom-left) and Molybdenum (17.1-17.7 keV)(bottom-left) Chapter 4

Observation and Data Preparation

4.1 Observation

On 25.11.2002 XMM-Newton observed the northeastern limb of the Cygnus Loop, as part of a 7- pointing campaign to image the remnant across its diameter. The ﬁeld of view (FOV) was centered on α = 20h55m23s and δ = +31◦46016”. The details of the observation are given in table 4.1.

4.2 Data Preparation

We have created the ccf file on 30.12.2004 and we processed our data using SAS 6.1.0 with the latest calibration files available to that date. We created the MOS and pn event files using the emchain and epchain tasks. We also created and out-of-time event file for the pn camera. Next we filtered our data using the evselect task. In the case of the MOS cameras, we used the #XMMEA EM flag and retained events with energies in the 300-12000 eV range and with P AT T ERN 12 (single, ≤ double, triple and quadruple pixel events. In the case of the pn, we used the #XMMEA EP flag and retained events with energies in the 200-14000 eV range, with P AT T ERN 4 (single ≤ and double pixel events). Unlike #XMMEA EM, the #XMMEA EP flag does not remove the events that lie outside the FOV, so we used the ((F LAG&0x10000) = 0) flag in order to achieve

Table 4.1: Details of the XMM-Newton observation of the northeastern limb of the Cygnus Loop.

Instrument Obsservation mode Filter Exposure Time [s] MOS1 Full Frame Medium 14511 MOS2 Full Frame Medium 14530 pn Extended Full Frame Medium 8614

39 CHAPTER 4. OBSERVATION AND DATA PREPARATION 40

MOS1 MOS1 120 120

100 100

80 80 RATE [count/s] RATE [count/s]

60 60 1.5465e+08 1.5466e+08 1.5466e+08 1.5466e+08 1.5467e+08 1.5465e+08 1.5466e+08 1.5466e+08 1.5466e+08 1.5467e+08 TIME [s] TIME [s] MOS2 MOS2 120 120

100 100

80 80 RATE [count/s] RATE [count/s]

60 60 1.5465e+08 1.5466e+08 1.5466e+08 1.5466e+08 1.5467e+08 1.5465e+08 1.5466e+08 1.5466e+08 1.5466e+08 1.5467e+08 TIME [s] TIME [s] PN PN 500 500

400 400

300 300

200 200 RATE [count/s] RATE [count/s]

100 100

0 0 1.5465e+08 1.5466e+08 1.5466e+08 1.5466e+08 1.5467e+08 1.5465e+08 1.5466e+08 1.5466e+08 1.5466e+08 1.5467e+08 TIME [s] TIME [s]

Figure 4.1: Lightcurves extracted from the event files before and after the GTI filtering. this. In this phase we have also eliminated 5 point sources. Next, we extracted lightcurves from the filtered event files, and after visually inspecting them, we applied good time interval (GTI) filtering in order to remove the flaring time periods. The lightcurves before and after the application of the GTI filter are shown in figure 4.1 while the resulting changes in the exposure times are shown in table 4.2. CHAPTER 4. OBSERVATION AND DATA PREPARATION 41

Table 4.2: The cange in the exposure times due to GTI ﬁltering.

Instrument Before [s] After [s] MOS1 14511 14112 MOS2 14530 14131 pn 8614 8432 Chapter 5

Analysis

5.1 Image analysis

From the filtered event files we created a mosaic three-color image (figure5.1). As we can see from this image, the northern and northeastern part of the FOV is dominated by low energy photons, suggesting low temperatures. In what surface brightness is concerned, there is a clear distinction between the southwestern region of the FOV and the northeastern part. The northeastern part is bright and contains filamentary structures, while the southwestern part is quite dark in comparison, and no X-ray structures are visible. The transition between the two regions is quite abrupt. We can also see dark finger-like structures on the northeastern rim of the FOV.

5.2 Spectral analysis

The analysis of extended sources with XMM-Newton is a complex procedure. Unlike the analysis of point sources, there seems to be little experience available when it comes to the creation of spectra for extended sources. This seems to be the primary reason why there are only general guidelines and not standard recipes (or threads) on this subject. Here, we shall describe the process we used to extract our spectra.

Creation of spectra

We have created our spectra using the SAS evselect task. Besides the previously mentioned ﬁlters, we also used the (FLAG==0) option. This option provides the most stringent screening of the data, removing pixels close to the edges of the CCDs and close to bad pixels, which may have incorrect energies. After extracting the spectra, in the case of the pn we performed the correction for the out-of-time events and then we binned all of them so that there are at least 20 counts per spectral bin.

42 CHAPTER 5. ANALYSIS 43

Figure 5.1: Three-color image of the northeastern limb of the Cygnus Loop. The colors correspond to the following energy ranges: red - (0.3-0.75) keV, green - (0.75-12) keV, blue - (1.2-3.0) keV. The image has been smoothed with a 3σ gausian. North is up and west is to the right CHAPTER 5. ANALYSIS 44

The response function

When we observe a source with a spectrometer, what we actually obtain is not the spectrum of the source, but rather photon counts S0 within speciﬁc instrument channels I. The relation between the actual spectrum of the source S(E) and the observed spectrum is

∞ S0(I) = S(E)R(I, E)dE (5.1) Z0 where R(I,E) is the instrumental response and it is proportional to the probability that an incoming photon of energy E will be detected in channel I. In the case of XMM-Newton, this response function is generated using the tasks arfgen and rmfgen which create an arf and an rmf ﬁle. We created the arf according to the recommendations for the case of extended sources, presented in the SAS user’s manual.

The background

When we observes an astronomical source with a spectrometer, in the ideal case that there is no instrumental background (i.e. events generated by the detector) the device will register photons coming both from the actual source and from its background. Thus, if one is interested in the spectrum of the source, then this contaminating background must be subtracted. However, as described in chapter 3, there are many kinds of background. We can classify these into two main categories: the non X-ray background (NXB) which includes the instrumental and the particle background, and the cosmic X-ray background (CXB) which includes emission from cosmological sources and the Galactic ridge X-ray emission (GRXE). However, because of the position of the Cygnus Loop relative to the Galactic plane, there is virtually no contamination from the GRXE in our data. The CXB is usually dealt with by selecting a region from a part of the detector that is not contaminated by source emission and using the spectrum from that region as the background spectrum. This method however has the disadvantage that the detector background will not be properly subtracted. Another method involves using blank-sky files. These blank-sky files are the result of the merger of several different event files from deep sky observations. Thus, the observer can select spectra from the same region of the detector, resulting in a proper instrumental background subtraction. As we can see from figure 5.1, the emission from the Cygnus Loop fills the entire FOV. Thus we decided to use the blank-sky files prepared by Read & Ponman (2003 [71]). The blank sky files contain detector coordinates only (DETX, DETY) and they have already been filtered for point sources and proton flares. Nevertheless, by visually inspecting the lightcurves of these files, we found that there were still some periods of rapid variability in the count rate left. Subsequently we removed these periods. Since we extract our spectra in sky coordinates (X,Y), CHAPTER 5. ANALYSIS 45 in order to use these blank-sky files, we had to project them on the sky at the coordinates of our FOV. After this projection, we filtered the blank-sky files for good events in the same way as our source files, removing the regions corresponding to the point sources detected in our source files as well.

Spectra

We extracted spectra for the MOS1, MOS2 and pn cameras from the entire FOV. These spectra together with the background are presented in Figs. 5.2, 5.3 and 5.4. A background subtracted spectrum in the 0.3-3.0 keV energy range is shown in ﬁgure 5.5 We can see that there are emission lines from: O VII, O VIII, Fe-L blends, Ne IX, Ne X, Mg XI, Si XIII, and, for the ﬁrs time, emission from C VI is detected in this spectrum on top of a thermal continuum.

Region selection

We wanted to examine the plasma structure on small scales, and if possible map the radial variation of different parameters. We could not use annuli because the bright X-ray structures visible in our FOV would intercept them obliquely, thus leading to a flawed analysis. We decided to divide up the part of the FOV simultaneously covered by all three instruments into 20 20 squares and analyze × their individual spectra. With this size, we have at least 4000 events/square in the case of the MOS cameras even in the low surface brightness regions. In the case of the pn camera, we have approximately three times as many events/square.We ended up with 127 such squares. The regions are shown in figure 5.6.

Model ﬁtting

We started out by fitting a single temperature collisional ionization equilibrium model (CIE) and a single temperature non-equilibrium ionization (NEI) one to the spectrum presented in figure 5.5 in the 0.3-3.0 keV energy range. The CIE model use was the vmekal and the NEI model was the VNEI version 2. To account for the interstellar absorption, we multiplied our models with the wabs model. Since there are also instrumental differences between the three cameras, we let the norm parameters (which are usually linked) of the data groups vary freely. This norm parameter is defined as 10−14 norm = n n dV (5.2) 4πD2 e H Z where ne is the electron density, nH is the hydrogen density and D is the distance to the emitting CHAPTER 5. ANALYSIS 46

Figure 5.2: Source (black) and background (red) spectra of the MOS1 camera

Figure 5.3: Source (black) and background (red) spectra of the MOS2 camera

Figure 5.4: Source (black) and background (red) spectra of the pn camera CHAPTER 5. ANALYSIS 47

Fe−L complex

C VI O VII O VIII Ne IX Ne X

Mg XI

Si XIII

Figure 5.5: Combined background subtracted spectrum of the entire FOV.

Figure 5.6: The regions selected for analysis superimposed on the X-ray surface brightness map. CHAPTER 5. ANALYSIS 48

Figure 5.7: The result of ﬁtting the vmekal model (left) and the VNEI model (right) plasma. The integral in the right-hand term is called the emission measure (EM).

EM = nenhdV (5.3) Z The results of the fitting are shown in figure 5.7. The reduced Chi-squared was 21.38 (775 d.o.f.) in the case of the VNEI fit, and 35.8 (776 d.o.f.) in the case of the vmekal model. We can see from figure 5.7 that the vmekal model fails to appropriately fit the high energy part of the spectrum. As such, we decided to use the VNEI model for our analysis. The VNEI model characterizes the spectrum of an optically thin thermal plasma which has not yet reached collisional ionization equilibrium. It also assumes a constant temperature and a single ionization parameter. In the spectrum extracted from the entire FOV and shown in figure 5.5 we can see that there are emission lines from Si. However, probably due to the size of our regions and the low number of counts in the high energy region of the spectrum, these lines are not visible in most of the squares, even in the case of the pn camera. In the regions with enough counts for these lines to become visible, the best fit values for the Si abundance ranged between 0.23 and 0.38 (relative to solar abundance). For consistency reasons, we decided to fit the spectra from all regions with the Si abundance fixed to 0.3. Again, in order to account for instrumental differences between the three cameras, we let the norms of the data groups vary freely. Thus, our free parameters were: the electron temperature kTe, the heavy element abundances C, N, O, Ne, Mg, Fe=Ni, the ionization timescale net, and the norms. The hydrogen column density nH, which characterizes the interstellar absorption, was left to vary freely but we imposed a lower limit of 1 1020cm−2. · The values of the reduced Chi-squared ranged between 1.14 (286 d.o.f.) and 2.57 (271 d.o.f.). The spectra best fit and worst fit by our model are presented in figure 5.8. We must note that the CHAPTER 5. ANALYSIS 49

Figure 5.8: The spectra best fit (left) and worst fit (right) by our model plasma structure of the Cygnus Loop is complex and it is determined by its interaction with the surrounding medium. Thus there are bound to be entire ranges of temperatures in every projected patch of its surface. Thus the residuals in our fits are bound to be large when fitting such a complex plasma with a single temperature model. Chapter 6

Results

In this chapter we present the results of our analysis.

6.1 Color maps and the radial variation of things

After analyzing the spectra of 127 regions with a single temperature absorbed VNEI model in the 0.3-3.0 keV energy range, we color coded the best ﬁt values and plotted them on a two dimensional map. Furthermore, we calculated the distance of the center of each square from the center of the remnant, binned the data for clarity and plotted the radial variation of each quantity. The data was binned into 7 concentric annuli as shown in ﬁgure 6.1. Here we assumed that the Cygnus Loop has its center located at (α, δ) = (20h51m21s, +31◦01037”) (Levenson et al.[68]).

The temperature

From figure 6.2 we see that the there are two regions in which the temperature is rather low. One is in the northeastern part of the FOV, while the other is in the western part. From the Sedov solution, one would expect the temperature to decrease with radius from the center of the remnant. In this regard, the northeastern region is nothing special, however the western region is unexpected. We can see its effect on the radial variation of the temperature in figure 6.3. On average, the temperatures range from 0.2 to 0.33 keV.

The heavy element abundances

We can see that except for C, the radial variation of the abundances of all the heavy elements has more or less the same proﬁle. The abundances start out low, present a bump at about 700 from the center, and then suddenly jump to relatively high values. The relative abundance of C (ﬁgure 6.5) shows an almost monotonic increase, becoming on average larger that the solar

50 CHAPTER 6. RESULTS 51

Figure 6.1: The binning annuli overlayed onto the spectral selection regions. CHAPTER 6. RESULTS 52

0.34

0.32

0.3

0.28

0.26 (keV) e

kT 0.24

0.22

0.2

0.18 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.2: The variation of kTe Figure 6.3: The radial variation of kTe

1.2

0.8

C 0.6

0.4

0.2

0 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.4: The variation of C Figure 6.5: The radial variation of C CHAPTER 6. RESULTS 53

0.16 0.15 0.14 0.13 0.12 0.11 O 0.1 0.09 0.08 0.07 0.06 0.05 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.6: The variation of O Figure 6.7: The radial variation of O

0.3 0.28 0.26 0.24 0.22

Ne 0.2 0.18 0.16 0.14 0.12 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.8: The variation of Ne Figure 6.9: The radial variation of Ne CHAPTER 6. RESULTS 54

0.24

0.22

0.2

0.18

0.16 Mg 0.14

0.12

0.1

0.08 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.10: The variation of Mg Figure 6.11: The radial variation of Mg

0.3 0.28 0.26 0.24 0.22

Fe 0.2 0.18 0.16 0.14 0.12 0.1 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.12: The variation of Fe Figure 6.13: The radial variation of Fe CHAPTER 6. RESULTS 55

11.2

11.15

11.1 s)

-3 11.05

11 t] (cm e 10.95 log[n 10.9

10.85

10.8 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.14: The variation of log(net) Figure 6.15: The radial variation of log(net) abundance in the outer annulus. It is interesting to note that the region where there is a bump in the abundances corresponds to the position of the X-ray ﬁlament, while the outermost annulus includes the northeastern low temperature region discussed above. We also noticed that except for that of C in the outermost annulus, the abundances of all heavy elements, are depleted, in agreement with previous observations.

The ionization timescale and NH

By comparing figures 6.14 and 6.2 we see that there is a good anti-correlation between the temperature and the ionization timescale. In what the NH is concerned, from figure 6.16 we see that in the western part of the FOV, the best fit values indicate high values of absorption.

The emission integral

We gave the deﬁnition of the norm parameter in 5.2, and said the the integral nenH dV is called the emission measure. If we consider that ne = nH , we can rewrite 5.2 as R

10−14 norm = n2dAdl (6.1) 4πD2 e Z Here A is the area of the emitting plasma region, and dl is the unit distance along the line of sight. If we assume that A is constant (as is the case of our square regions), and noticing that CHAPTER 6. RESULTS 56

0.07

0.06

0.05 ) -2

cm 0.04 22 0.03 (x10 H N 0.02

0.01

0 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.16: The variation of NH Figure 6.17: The radial variation of NH

A/D2 is the solid angle θ that subtends the area A, we can rewrite 6.1 as θ10−14 norm = n2dl (6.2) 4π e Z From this equation we can write

norm4π1014 EI = n2dl = (6.3) e θ Z This quantity is called emission integral (EI) and as we notice, it does not depend on the distance to the source. In the case of our square regions, θ = 20 20 and we plotted the radial variation of the EI in × ﬁgure 6.18. The radial variation of the EI looks very similar to what one would expect from a Sedov self similar solution. We shall return to this topis in the next chapter.

6.1.1 Analysis II

In the previous section we saw that there are a few interesting regions within our FOV. In order to further investigate them, we selected six regions to extract spectra from as shown in ﬁgure 6.19. These regions are large, and as a consequence we have better statistics to constrain the values of our parameters. We again applied the one component absorbed VNEI model. Because this time, the spectra from each region contained enough high energy counts so that the Si lines were clearly visible, we CHAPTER 6. RESULTS 57

5.5e+19 5e+19 4.5e+19 4e+19

) 3.5e+19 -5 3e+19

EI (cm 2.5e+19 2e+19 1.5e+19 1e+19 5e+18 55 60 65 70 75 80 85 Radius (arcminutes)

Figure 6.18: The radial variation of the EI

Figure 6.19: The spectral extraction regions used for the second analysis CHAPTER 6. RESULTS 58

0.36 11.2

0.34 11.15

0.32 s) 11.1 3

0.3 11.05 (keV) t] (cm e e kT

0.28 log[n 11

0.26 10.95

0.24 10.9 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Region Region

Figure 6.20: The kTe for each region Figure 6.21: The log(net) for each region

1.8 0.25 1.6 1.4 0.2 1.2 1 0.15 C O 0.8 0.6 0.1 0.4 0.2 0.05 0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Region Region Figure 6.22: The abundance of C in each region Figure 6.23: The abundance of O in each region let the Si abundance vary freely. The reduced Chi-squared varied between 3.06 (467 d.o.f.) and 5.93 (556 d.o.f.). The fact that the ﬁts are so poor, is not surprising, considering the size of these regions and the fact that we are trying to ﬁt the spectra with a single temperature model. The results are as follows:

The temperature and ionization timescale

From ﬁgure 6.20 we see that the regions can be divided into two categories. One category having high temperatures (1,3,4), and one with low temperatures (2,4,6). It is interesting to note that the regions in the high temperature category, have approximately the same temperature. This is also valid for the low temperature category. In ﬁgure 6.21 we can clearly see the anti-correlation between the kTe and net CHAPTER 6. RESULTS 59

0.4 0.28 0.26 0.35 0.24 0.22 0.3 0.2 0.25 0.18 Ne Mg 0.16 0.2 0.14 0.12 0.15 0.1 0.1 0.08 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Region Region Figure 6.24: The abundance of Ne in each region Figure 6.25: The abundance of Mg in each region

0.65 0.35 0.6 0.3 0.55 0.5 0.25 0.45 Si

0.4 Fe 0.2 0.35 0.15 0.3 0.25 0.1 0.2 0.15 0.05 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Region Region Figure 6.26: The abundance of Si in each region Figure 6.27: The abundance of Fe in each region CHAPTER 6. RESULTS 60

0.1

0.08 -2 0.06 cm 22

(x10 0.04 H N

0.02

0 0 1 2 3 4 5 6 7 Region

Figure 6.28: The NH in each region

The abundance of heavy elements

By looking at these figures, we see that they confirm our previous findings. C increases monotonically toward the outside of the remnant, while the others vary in a more step-like manner. We notice that the abundances of the regions that lie inside the X-ray filament are almost constant, and then jump to high values in region 6. Si shows an interesting behavior. It is almost constant everywhere except for region 2 and 6, where it displays high values.

The hydrogen column density

Figure 6.28 shows that N is approximately constant at about 4 1020cm−2, which by the way H × is the average column density in the direction of the Cygnus Loop. The exceptions are region 2 and 6. In region 2 we see an excess of approximately 4 1020cm−2 while in region 6, the N is · H slightly lower than the average. All these results are consistent with what we found in our previous analysis. Chapter 7

Discussion

I the previous chapter, we saw that there are also two low temperature regions present in the northeastern and western region of the FOV. The heavy element abundances are depleted, but show an increase toward the edge of the remnant. Almost all the radial profiles of these elements present a bump between 650 and 800 from the center of the remnant, after which they jump to high values at the northeastern edge of the FOV. The bump region corresponds to the bright X-ray structure present in our FOV. Carbon seems to increase monotonically, and its abundance becomes larger than the solar value at the edge of the northeastern edge of the FOV. All these facts are confirmed by the second analysis. Although region 2 and region 6 seem to have the same temperature, their spectra are somewhat different, especially in the low energy region. These spectra are presented in figure 7.1. We can see that in the case of region 6 the C line is much more prominent than in the case

Figure 7.1: Comparison between the spectra (MOS2) of region 2 (black) and region 6 (red)

61 CHAPTER 7. DISCUSSION 62

Figure 7.2: Comparison between the spectra (MOS2) of region 1 (black) and region 6 (red). The inset represents the same two spectra but plotted on a linear scale. The peak from the C emission is clearly visible. region 2, while the Si line is exactly the opposite. We also compared the spectra from region 6 and region 1. They are shown in ﬁgure 7.2 This increase of the abundances toward the edge of the remnant together with the low temperatures in the northeastern part of the FOV suggests that we are witnessing the encounter of the incident shock and a cloud (possibly the cavity walls). In the previous chapter, we stated that the radial variation of the EI is similar to what one would expect to se from an adiabatic blast wave described by the Sedov self similar solution. If this is true, then we can in principle calculate the position of the shock front. To do this, we used the approximate formula presented by Cox & Franco (1981[70]) that describes the variation of the density with radius. The formula is

5 3 3(3 ω) x(r) + r8−4ω r(9−5ω)/2 exp − [r8−4ω 1] (7.1) ∼ 8 8 8(2 ω) − − In this formula r and x are deﬁned as R = Rs(t)r and ρ = ρs(t)x(r) where R is the distance from the explosion site, ρs is the density just behind the shock front, ρ is the density at R and Rs is the shock radius at a certain epoch t. The model also assumes that the explosion took place in a medium with a density gradient ρ R−ω, where ρ is the density of the ambient medium, and A ∝ A γ = 5/3 (i.e. the ambient medium is a monoatomic gas). We took this formula, then squared and integrated it along the line of sight to obtain the

EI. Next we tried several diﬀerent values for ω, Rs, and ρs and after numerically calculating the CHAPTER 7. DISCUSSION 63

Figure 7.3: Comparison between the variation of the electron density obtained from the data and that predicted by the Sedov model for ω = 3 −

Figure 7.4: A circle with its center in the center of the Cygnus Loop and having a radius of 790 overlayed on our selection regions. integral, compared the result with our data. Unfortunately none of the values we assigned to our variables produced a plot that could reproduce our data. The values of our parameters that came closest to a reasonable fit were: ρ = 2.65cm−3, R = 790, and ω = 3. The result is plotted in s s − figure 7.3. The reason why the model does not fit our data to well could be the assumption of spherical symmetry of the shock wave which is not necessarily true in our case. However, by looking at figure 7.3, we see that the shock front should be located somewhere between 790 and 840. Figure 7.4 represents the 790 radius circle overlayed on our regions. CHAPTER 7. DISCUSSION 64

Figure 7.5: Our selection regions overlayed on images of the northeastern limb of the Cygnus Loop taken in X-rays (ROSAT, top left), optical (DSS, top right), infrared (IRAS 60µ, bottom left), and radio (WENS, bottom right)

If we were indeed witnessing the interaction between the blast wave and an interstellar cloud, and what we are seeing in the northeastern part of the FOV is the cloud itself, the results of this interaction should show up in other wavelength as well, especially in radio and optical. Figure 7.5 represents images of the northeastern limb of the Cygnus Loop taken in X-rays (ROSAT PSPC), optical (DSS), infrared (IRAS 60µ), and radio (WENS 93 cm). All images were taken from skyview. From the ROSAT image we see that our FOV lies entirely inside the shock wave. The optical image shows that a ﬁlament is crossing our FOV, suggesting that in those regions, the shock wave is already interacting with clouds. The IRAS image shows that in almost all of our regions we have infrared emission, suggesting again interaction with dusty clouds. The radio image is very similar CHAPTER 7. DISCUSSION 65

Figure 7.6: Blowups of the radio and optical images. The optical ﬁlaments and the radio emission are indicated by arrows to the optical one. Figure 7.6 is a blowup of the optical and radio images. We notice the faint radio emission in the northeastern part of the FOV and the fact that in the optical image we have ﬁlaments (indicated by arrows) near and running through this region. These are all signs of shock cloud interaction. In what the western part of the FOV is concerned, here we have a cool dark region with high

NH . The first thing that comes into mind is another cloud located on the near side of the Loop. If this cloud was only partially engulfed by the shock wave (i.e. only a part of the far side of the cloud was shock heated), that would explain the lower than average abundances, the high NH and the low temperatures. However, when we look again at figure 7.6 at the position corresponding to the western part of our FOV we see no radio or optical emission. In the second part of our analysis we established that region 2 showed an N excess of H ∼ 4 1020cm−2. If we assume that the extent of the cloud along the line of sight is 2.3 1018cm (twice · · the semi-minor axis of the ellipse we used to extract the spectrum for region 2) than the density of the cloud would be 120cm−3. If we consider that the density at the shock front is 2.7cm−3 ∼ that means that the ambient medium has a density of 0.7cm−3. This would represent a density ∼ contrast of 171. This “cloud” could also be a side effect of our fitting the data with a single temperature model. Further research is needed to establish wether this is the case. Chapter 8

Conclusions

1. We observed the northeastern limb of the Cygnus Loop with XMM-Newton

2. For the ﬁrst time, we have detected emission from C in our spectra.

3. We found two regions, one in the northeastern part of the FOV and the other in the western part of the FOV, with low temperatures. The northeastern part is characterized by high

abundances and low NH , while the western region is characterized by low abundances and

high NH .

4. the abundances are depleted (suggesting that what we are seeing is probably the shocked ISM and not the ejecta), but their radial proﬁles show an increase toward the edge of the remnant. At the northeastern region, all the heavy element abundances jump to higher than average values.

5. In the bright X-ray ﬁlament the elemental abundances are approximately constant.

6. Taking into consideration the observations taken in other wavelengths, we suppose that in the northeastern part of our FOV we are witnessing the interaction between the shock wave and and interstellar cloud (possibly the cavity wall), while in the western part of the FOV the “cloud” might be a side eﬀect of our using a single temperature model to ﬁt the data. It it were indeed a cloud, its density would be 120cm−3. ∼

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