X-Ray Study on Supernova Remnants Interacting withDense Clouds
Hiromichi Okon

Department of Physics, Graduate School of Science, Kyoto University
Kitashirakawa Oiwake-cho, Sakyo, Kyoto, Kyoto, 606-8502, Japanokon@cr.scphys.kyoto-u.ac.jp

January 2021

Abstract
A supernova remnant (SNR) is the astrophysical object resulting from an explosion of a star,
and acts as the major energy source in the Universe. We study X-rays from SNRs interactingwith dense clouds, which are unrivaled targets to investigate injection process of energy releasedin the explosions into the interstellar space. We perform spatial resolved spectroscopy of thermal X-rays from SNRs, W44 and IC 443, with XMM-Newton, and construct a model to predict
X-ray line emission from dense clouds bombarded by sub-relativistic particles accelerated in
SNRs.
Previous observations of SNRs interacting with clouds, including W44 and IC 443, unveiled
the presence of peculiar plasmas in “recombination dominant phase”, so-called over-ionizedrecombining plasmas (RPs). Such plasma is not anticipated in the standard picture of SNR evolution. Although the physical process of the over-ionization has not yet been fully understood,a key seems to be an efficient dissipation of internal energy of SNR plasma into interacting
clouds. We compare spatial variations of plasma parameters of RPs in W44 and IC 443 with
distributions of clouds hit by their blast wave. We find that combination of lower electron temperature and shorter recombination timescale is achieved in the region interacting with dense
clouds. Moreover, a clear anticorrelation between the electron temperature and the recombination timescale is found. The results are well explained if the plasma was overionized by rapid
cooling of electrons through thermal conduction with the dense clouds hit by the blast waves of
the SNRs. Given that a few other overionized SNRs show evidence for adiabatic expansion as
the major driver of the rapid cooling, our new result indicates that both processes can contributeto overionization in SNRs, with the dominant channel depending on the evolutionary stage.
Our recent X-ray studies revealed the presence of the neutral Fe Kα line emission fromdense gas in the vicinity of some SNRs, which can be best interpreted as K-shell ionization of
Fe atoms in the gas by sub-relativistic particles accelerated in the SNRs. The results indicatethat the Fe Kα line is a new diagnostic tool to probe sub-relativistic particles at accelerationsites, which were almost unexplored until recently. Information on such particles is key toestimating total energy transferred into accelerated particles in SNRs and to considering theinjection mechanism of thermal particles into the acceleration process. We construct a modelfor the Fe Kα line structures by various projectile ions utilizing atomic-collision data. Whenenergetic heavy ions collide with target atoms, their strong Coulomb field can easily cause
simultaneous ejection of multiple electrons of the target. This results in shifts in characteristic
X-ray line energies, forming distinctive spectral structures. Detection of such structures in theneutral Fe Kα line strongly supports the particle ionization scenario, and furthermore provides
direct evidence of heavy ions in the accelerated particles. An ∼ eV energy resolution by X-ray
micro-calorimeters onboard future X-ray satellites will be able to resolve the structures.

Contents
1 Introduction

1

2 Supernova and Supernova Remnants
2.1 Supernova . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Classification of Supernovae . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Supernova Remnant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Shock Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Evolution of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.3 Morphology of SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . .

3
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3 Thermal Plasma and Particle Acceleration in SNRs
3.1 Thermal Plasma in SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 X-rays from Thermal Plasma . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 Standard Evolution of SNR Plasma . . . . . . . . . . . . . . . . . . .
3.1.3 Over-ionized Recombining Plasma . . . . . . . . . . . . . . . . . . .
3.2 Particle Acceleration in SNRs . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 SNRs as Galactic Cosmic Ray Sources . . . . . . . . . . . . . . . . .
3.2.2 Diffusive Shock Acceleration Theory . . . . . . . . . . . . . . . . . .
3.2.3 Nonthermal Emissions from Accelerated Relativistic Particles . . . . .
3.2.4 Exploration of Sub-relativistic Particles . . . . . . . . . . . . . . . . .

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4 Instruments
4.1 XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.1 X-ray Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.1.2 EPIC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 XRISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Resolve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Xtend . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Physical Origin of RPs in SNRs
5.1 Our Objective and Target Selection . . . . . . . . . . . . . . . . . . . . . . . .
5.2 W44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Overview of W44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.2 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . .
5.2.3 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Discussion on W44 . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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i

CONTENTS

ii
5.3

5.4

IC 443 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.1 Overview of IC 443 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.2 Observations and Data Reduction . . . . . . . . . . . . . . . . . . . .
5.3.3 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3.4 Discussion on IC 443 . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6

Probing Sub-Relativistic Particles with the Neutral Fe Kα Line76
6.1 Previous Works and Our Objective . . . . . . . . . . . . . . . . . . . . . . . . 76
6.1.1 Detection of Neutral Fe Kα Line . . . . . . . . . . . . . . . . . . . . . 76
6.1.2 Neutral Fe Kα line as a Diagnostic Tool to Study Sub-Relativistic Particles 79
6.2 Multiple Ionization Processes in Collisions of Ion-Atom . . . . . . . . . . . . 81
6.3 Modeling of Kα Lline Structures by Impacts of Mono-energetic Ions . . . . . . 82
6.3.1 Kα Line Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.3.2 Intensity of KαLi Line . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3.3 Comparison between Our Model and Experimental Data. . . . . . . . . 85
6.4 Fe Kα Structures Produced by Cosmic Rays . . . . . . . . . . . . . . . . . . . 89
6.4.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

7Conclusions

91

List of Figures
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9

Classification scheme of SNe based on their light curves and line features in them 4
Comparison of light curves for Type I, II-P and II-L supernovae . . . . . . . .
4
Scheme of the profiles of synthesized elements in a massive star . . . . . . . .
6
Reaction networks of pp-chain and CNO cycle . . . . . . . . . . . . . . . . . .
6Abundance profiles of elements synthesized in core-collapse SNe . . . . . . . .
8Schematic view around the shock front . . . . . . . . . . . . . . . . . . . . . .
9Sectional drawing of an SNR in the free expansion and adiabatic phases. . . . . 10
Cooling coefficient for an optically-thin thermal plasma . . . . . . . . . . . . . 11
X-ray and radio images of four type SNRs. . . . . . . . . . . . . . . . . . . . 13

3.1
3.2

15

Thermal emission from X-ray emitting plasma simulated by XSPEC . . . . . .
Schematics of an emission mechanism for RRCs and transition lines after freeelectrons are captures in ions . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Emitted RRCs and emission lines after the recombination between electrons
and Fe ions computed with XSPEC . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Center energies of the Fe Kα and Fe Kβ emission, and the Kβ/Kα flux ratio asa function of the charge number of Fe ions . . . . . . . . . . . . . . . . . . . .
3.5 Schematic Grotrian diagram for a Helium-like ion . . . . . . . . . . . . . . . .
3.6 Temperature ratios of ions (Ne, Mg, Si, and Fe) to protons in SN 1987A . . . .
3.7 Fe ion fraction in CIE plasma , IP, and RP . . . . . . . . . . . . . . . . . . . .
3.8 X-ray spectra for Cas A and Tycho’s SNR obtained with Tenma and deviationsof the mean energies of observed lines from that expected in a CIE model . . .
3.9 Ionization states of plasma in SNR . . . . . . . . . . . . . . . . . . . . . . . .
3.10 Confidence contours in kTe -kTz space for IC 443 and W49B . . . . . . . . . . .
3.11 W49B spectra obtained with Suzaku . . . . . . . . . . . . . . . . . . . . . . .
3.12 X-ray images of the W28 taken with ROSAT and Suzaku . . . . . . . . . . . .
3.13 Plasma parameters in W28 from Okon et al. (2018) . . . . . . . . . . . . . . .
3.14 kTe -net plot in W49B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.15 Composition of cosmic rays and the solar abundance as a function of nuclear
charge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.16 Energy spectra of cosmic rays . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 Schematic drawing of the scattering of particles in the DSA mechanism . . . .
3.18 X-ray images and spectra of SN 1006 taken with ASCA . . . . . . . . . . . . .
3.19 Gamma-ray map and differential energy spectra of SN 1006 obtained with
H.E.S.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.20 Cross section for inelastic proton-proton interaction as a function of the proton
kinetic energy in the laboratory system . . . . . . . . . . . . . . . . . . . . . .
iii

16
17
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20
22
22
23
23
25
26
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31
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34

LIST OF FIGURES

iv

3.21 Spectrum of gamma-ray generated by π 0 -decay . . . . . . . . . . . . . . . . .
3.22 π 0 -decay spectra for different proton collision energies . . . . . . . . . . . . .
3.23 Gamma-ray spectra of decays of π 0 -mesons by nonthermal protons . . . . . . .
3.24 GeV–TeV data of IC 443 and W44 overlaid with the best-fit model curves . . .
3.25 NuSTAR spectra of W49B. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

34
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4.1 Artistic views of XMM-Newton and XRISM satellites . . . . . . . . . . . . . .
4.2 In-orbit configuration of the XMM-Newton . . . . . . . . . . . . . . . . . . . .
4.3 X-ray Telescope assemblies of XMM-Newton . . . . . . . . . . . . . . . . . .
4.4 Effective area and vignetting factor of XRT . . . . . . . . . . . . . . . . . . .
4.5 MOS fractional encircled energy as a function of angular radius . . . . . . . .
4.6 Field of view of the two types of EPIC cameras. . . . . . . . . . . . . . . . . .
4.7 Energy resolution of EPIC cameras. . . . . . . . . . . . . . . . . . . . . . . .
4.8 Net effective area of EPIC cameras and RGS spectrometer. . . . . . . . . . . .
4.9 Instrumental background spectra for MOS and pn cameras . . . . . . . . . . .
4.10 Position-to-position variations of the intensity of fluorescent lines on MOS detector plane in instrumental background spectra. . . . . . . . . . . . . . . . . .
4.11 Blocking diagram of Resolve . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12 Photograph of X-ray calorimeters on board Hitomi . . . . . . . . . . . . . . .
4.13 Perseus spectrum obtained with SXS onboard Hitomi . . . . . . . . . . . . . .
4.14 Blocking diagram of Xtend . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.15 Photograph of SXI onboard Hitomi . . . . . . . . . . . . . . . . . . . . . . . .

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5.1 Schematic illustration of identified CO features around W44 . . . . . . . . . . 49
5.2 MOS+pn X-ray images of W44 . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.3 MOS spectra of W44 extracted from the four representative sub-regions . . . . 53
5.4 Reduced chi-squared map of W44. . . . . . . . . . . . . . . . . . . . . . . . . 53
5.5 MOS spectra of W44 plotted with the plasma model . . . . . . . . . . . . . . . 54
5.6 Distribution of X-ray absorption column density NH . . . . . . . . . . . . . . . 56
5.7 Maps of the electron temperature kTe and the recombination timescale net of W44 58
5.8 kTe -net plot in W44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.9 Schematic view of the W44 blast wave interacting with the giant molecular clouds 59
5.10 Multi-wavelength view of the SNR IC 443 and spatial tendency of kTe of RPs . 60
5.11 Distribution of dense gas around IC 443 . . . . . . . . . . . . . . . . . . . . . 61
5.12 MOS+pn X-ray images of W44 . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.13 MOS spectra of IC 443 extracted from the four representative sub-regions . . . 65
5.14 MOS spectra of IC 443 plotted with the plasma model . . . . . . . . . . . . . . 66
5.15 Reduced chi-squared map of IC 443 . . . . . . . . . . . . . . . . . . . . . . . 67
5.16 Distribution of X-ray absorption column density NH . . . . . . . . . . . . . . . 68
5.17 Maps of the electron temperature kTe and the recombination timescale net of
IC 443 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.18 kTe -net plot in IC443 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.19 Comparison between CRP and ∆C, and the kTe -net plot, and maps of ∆C . . . . 73
5.20 Si ion fraction in RPs in IC 443 . . . . . . . . . . . . . . . . . . . . . . . . . . 74
6.1
6.2

Intensities of the neutral Fe Kα line in the five regions. . . . . . . . . . . . . .
H.E.S.S. gamma-ray map. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77
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LIST OF FIGURES
6.3
6.4

Fe-K band images of W28, Kes 67, Kes 69, Kes 78, and W44. . . . . . . . . .
Equivalent width of the Fe Kα line by sub-relativistic particles as a function of
their spectral index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.5 Calculated X-ray emission produced by sub-relativistic particles interacting witha dense cloud. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6 Fe Kα spectra produced by impacts of protons and O5+ ions. . . . . . . . . . .
6.7 Schematic view of ionization process in collisions of ion-atom. . . . . . . . . .
6.8 Spectrum of Cl Kα line emitted from thick KCl targets bombarded by Kr ions. .
6.9 Energy shift of Kα line due to multiple ionization. . . . . . . . . . . . . . . . .
6.10 Ionization parameter pXL as a function of the universal variable Xn . . . . . . . .
6.11 Fe Kα structures emitted from solid Fe targets under bombardment by protons,
O8+ , and Fe26+ ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.12 Same as Figure 6.11 but for gas Fe targets. . . . . . . . . . . . . . . . . . . . .
6.13 Comparison between experimental data and our model. . . . . . . . . . . . . .
6.14 Stopping power for projectile Kr ion in solid KCl targets. . . . . . . . . . . . .
6.15 Fe Kα structures expected from Fe atoms bombarded by particles accelerated
in SNRs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v
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List of Tables
2.1

Explosive nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

4.1

Key parameters of Resolve and Xtend . . . . . . . . . . . . . . . . . . . . . .

47

5.1
5.2
5.3

Observation log of W44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Best-fit model parameters of the background spectrum of W44 . . . . . . . . .
Best-fit model parameters of the spectra from the representative sub-regions in
W44 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Observation log of IC 443 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Best-fit model parameters of the background spectrum of IC 443 . . . . . . . .
Best-fit model parameters of the spectra from the representative sub-regions in
IC443 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Comparison between three RP-SNRs, W44, IC 443, and W49B . . . . . . . . .

49
52

5.4
5.5
5.6
5.7

vi

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Chapter 1
Introduction
A supernova remnant (SNR) is the astrophysical object resulting from an explosion of astar, i.e., supernova. SNRs inject a large amount of kinetic energy released in supernovae into
the interstellar space via shock waves formed by collision between ejected materials (ejecta)
and the interstellar medium (ISM). The major forms of the released energy are fluxes of thermal particles that constitute shock heated plasma (∼ 107 K) emitting thermal X-rays and ofnonthermal particles accelerated at shocks in SNRs which are indeed believed to constitute asignificant fraction of galactic cosmic rays. These particles supply energy required to trigger
star formation, and furthermore spread throughout the galaxy cluster by a galactic superwind,
resulting in the galaxy formation. Therefore, SNRs play an important role as the major energy
sources in the Universe.
SNRs interacting dense clouds have been attracting attention in terms of energy conversion and dissipation processes in both aforementioned thermal and nonthernal aspects because
recent multi-band observations enabled us to investigate detailed properties of both the energized particles in SNRs and their ambient gas. One of the topics that we cover is SNR plasmas
in “recombination dominant phase”, so-called over-ionized recombining plasmas (RPs). The
presence of such plasma, revealed by recent X-rays studies (Yamaguchi et al., 2009; Ozawa etal., 2009), is not anticipated in the standard picture of SNR evolution. The physical process ofthe over-ionization has not yet been fully understood, but, as pointed out by some authors such
as Itoh & Masai (1989) and Zhang et al. (2019), a key seems to be a process where thermalenergy of a SNR plasma is somehow efficiently dissipated into interacting clouds.
In this thesis, we perform spatial resolved spectroscopy of thermal X-rays from RP-SNRsaiming to comprehensively understand the physical origin of the RPs in SNRs. We select W44
and IC 443 as the best targets to carry out this study. Radio and infrared observations revealed
the detailed distribution of interacting clouds with these SNRs. W44 and IC 443 have large
apparent sizes, which help us perform spatially resolved spectroscopy. We discuss implicationsof the obtained results by comparing them with those of previous works on other RP-SNRs.
The other topic concerning studies of SNRs interacting dense clouds is neutral Fe Kα line
emission from dense gas in the vicinity of some SNRs, which can be best interpreted as K-shellionization of Fe atoms in the gas by sub-relativistic particles accelerated in the SNRs (e.g., Okon
et al., 2018; Nobukawa et al., 2018). The results, if the authors’ claims are correct, indicate that
the Fe Kα line can serve as a diagnostic tool to probe sub-relativistic particles at accelerationsites, which were almost unexplored until recently. Information on such particles is importantto estimate total energy transferred into accelerated particles in each SNR and to consider the
injection mechanism of thermal particles into the acceleration process.
1

2

CHAPTER 1. INTRODUCTION

In this thesis, we construct a model to predict structures of lines from multiple-ionized
Fe ions in dense clouds bombarded by sub-relativistic particles accelerated in SNRs using theknowledge from beam experiments. Based on this model, we propose a novel method of providing clear evidence for sub-relativistic particles and furthermore of constraining their composition, with high resolution spectroscopy enabled by future X-ray satellites such as XRISM.
In Chapter 2, we summarize the overviews of supernovae and SNRs. In Chapters 3, we
review the current understandings of SNR plasma, and galactic cosmic rays and particle acceleration in SNRs. Chapter 4 gives brief descriptions of XMM-Newton and XRISM. Chapter 5
describes the analyses and results on W44 and IC 443, and discussion on the physical origin
of RPs. In Chapter 6, we explain the detailed calculation of the line structures as evidence of
sub-relativistic particles, and show a model curve expected with XRISM. The final conclusionsof this thesis are given in Chapter 7.

Chapter 2
Supernova and Supernova Remnants
2.1 Supernova
A Supernova (SN) is an explosion of a star at the end of its lifetime. The luminosity ofan SN is comparable to that of the host galaxy, and its explosion energy is typically ∼ 1051
erg. Modern estimates predict that in every few decades one SN event should occur in a galaxy(e.g., van den Bergh & Tammann, 1991). Once the SNe occur, they brightly shine in multibands from optical to gamma-rays. The observed light curves and spectra are well known toshows very diversity and they are considered to reflect the properties of the pre-explosion star
and a gas environment, and so on. In this chapter, we explain the classification of the SNe andnucleosynthesis in stars.

2.1.1 Classification of Supernovae
Classically, SNe have been typed based on their optical spectra around their peak luminosity.
Figure 2.1 shows the scheme of the classification. The SNe are first divided into two types,
Types I and II (e.g., Minkowski, 1941). The former exhibit no hydrogen lines, whereas thelatter do show the hydrogen lines. Type I SNe are further divided into Type Ia, Type Ib, andType Ic, according to the presences of Si and He lines (e.g., Elias et al., 1985). The difference ofthe line features is considered to be attributed to whether or not the pre-explosion stars have thehydrogen, He, and Si outer layers. On the other hand, Types II-P and II-L, which are subclassesof Type II SNe, are characterized by the shapes of their light curves as shown in Figure 2.2.
Light curves of Type II-L SNe decline linearly in magnitude after their peaks, whereas thatof Type II-P SNe have a plateau with almost constant brightness for a period of nearly 100
days (e.g., Barbon et al., 1973). The plateau phase can be seen if the star loses a hydrogenenvelope before its explosion as discussed by some authors (e.g., Filippenko, 1997). Based on
the underlying explosion mechanisms, above SNe classes are meaningfully classified into two
broad categories, Type Ia and core-collapse SNe. We describe the characteristics of the two
types in the following paragraphs.
Type Ia Supernovae
Type Ia SNe are considered to be caused by thermonuclear disruption of carbon-oxygen
white dwarfs in binary systems. The nuclear disruption advances violently so that the progenitor star is totally disrupted by the nuclear reaction energy, leaving no compact objects such as a3

CHAPTER 2. SUPERNOVA AND SUPERNOVA REMNANTS

4

Maximum Light Spectrano H

HType I
strong Si

Type II

weak Si

Light curve

Ib / Ic

Type Ia
He

Type II-P

Type II-L

othersno He

Core-collapse
Type Ib

Type Ic

GRB

Figure 2.1: Classification scheme of SNe based on their light curves and line features in them.

Figure 2.2: Comparison of light curves for Type I, II-P and II-L supernovae (Wheeler et al.,1990).

2.1. SUPERNOVA

5

neutron star nor a black hole behind. The thermonuclear-disruption mechanism was originallyproposed by Hoyle & Fowler (1960). Arnett (1969) and Nomoto et al. (1976, 1984) developed
this idea into a carbon supersonic burning (detonation) and a subsonic carbon burning (deflagration) models, respectively. The two are widely regarded as the standard models for Type Ia
SNe.
Two plausible channels for Type Ia SNe have been mainly proposed. One is the singledegenerate (SD) scenario (Whelan & Iben, 1973), where a white dwarf accretes matter from a
non-degenerate companion star, typically main sequence or red giant stars, subsequently leading
to the SNe. Under the mass accretion, the white dwarf builds up its mass until it approaches
the Chandrasekhar limit of ∼ 1.4 M⊙ (Mch ), and eventually ignites. The other is the doubledegenerate (DD) scenario (Webbink, 1984). In this scenario, an SNe occurs by a dynamical
merger of two white dwarfs forming a binary system. Recent multi-wavelength observations
provided indirect evidence for both scenarios. For instance, Li et al. (2011) reported no presenceof the companion star in the images of SN 2011fe, which agrees with the DD scenario. On
the other hand, Yamaguchi et al. (2015), based on the X-ray spectral analyses of SNR 3C
397, constrained an abundance pattern of iron group elements, which is naturally expected in
the SD scenario. These results, along with the data of Perseus cluster with Hitomi (Hitomi
Collaboration et al., 2017), imply that both channels make a significant contribution to the SN
Ia rate in the galaxies.

Core-collapse Supernovae
Core-collapse SNe are considered to be the results of implosions of cores of massive stars
with typically ≳ 10 M⊙ . While the detailed explosion mechanism is still under debate, several promising scenarios are proposed based on theoretical and observational works. The beststudied one is the neutrino heating mechanism, whose basic idea was first proposed by Colgate& White (1966) and later reinforced by Bethe & Wilson (1985). We focus on the mechanism
and briefly explain it. A massive star evolves through the change of its composition via stellar
nucleosynthesis as discussed in Section 2.1.2. As shown in Figure 2.3, massive stars have a Fe
core at the final stage of its stellar evolution. Fe is the most stable element so that the heavier
elements than Fe are not synthesized, resulting in continuing to increase the internal temperature of the core. In the very hot core, Fe absorbs gamma-rays emitted from it, and decays via a
photo-dissociation process. Once the photo-dissociation of Fe and subsequently reactions occur
in the hot core as follows,
56

Fe + γ → 134 He + 4n − 124.4 MeV
4He → 2p + 2n − 28.3 MeV
p + e− → n + νe ,

(2.1)
(2.2)
(2.3)

the core cannot be supported by any further nuclear fusion reactions or electron degeneracypressure, leading to the core collapsing to a neutron star or black hole. The core collapse
is halted by neutron degeneracy so that the falling materials are bounced and form a bounce
shock. Although the bounce shock decays once inside the star, the shock is reenergized byneutrino energy deposition, resulting in the explosion.

6

CHAPTER 2. SUPERNOVA AND SUPERNOVA REMNANTS

H
He
C, O
O, Ne, Mg
SiFe

Figure 2.3: Scheme of the profiles of synthesized elements in a massive star. The scale is notexact.

Figure 2.4: Reaction networks of (left) pp-chain and (right) CNO cycle (Adelberger et al.,2011).

2.1.2 Nucleosynthesis
Stellar Nucleosynthesis
Stellar nucleosynthesis is a process where heavy elements are synthesized within stars. As
the stars evolve first by burning hydrogen (main sequence star), then He (red giant star), andprogressively burning higher elements, their abundance composition changes over their life.
Figure 2.4 and Equations 2.4–2.6 show the p-p chain and CNO (carbon-nitrogen-oxygen) cycle,
and triple α reaction, respectively,
He +4 He →4
He +8 Be →
12 ∗
C →

4

Be − 92 keV,C∗ − 287 keV,
12
C + 7.65 MeV.

8

12

(2.4)
(2.5)
(2.6)

Abundant hydrogen and He are synthesized into elements such as C and O through these processes. If the stellar mass is ≲ 10 M⊙ , subsequently C and O burnings do not progress. Therefore, the stars have a core composed of C and O. Near the end of the nuclear burning stage, lowmass stars are considered to expel most of their outer hydrogen and He layers. Only the hotcore remains and becomes a white dwarf.

2.1. SUPERNOVA

7

Massive stars (≳ 10 M⊙ ) have higher core-temperatures than low mass stars (≲ 10 M⊙ ).
Therefore, the synthesized C and O burnings occur, and heavy elements up to Fe are synthesized
through continues reactions as follows,
C +12 C → Mg∗→ 23 Na +1 H + 2.238 MeV,
→ 20 Ne +4 He + 4.616 MeV,
→ 23 Mg + n − 2.605 MeV,
→ 24 Mg + 13.931 MeV,
→ 16 O + 2α − 0.114 MeV.

(2.7)

O +16 O →
→
→
→
→

32

S + 16.541 MeV,
P + 7.677 MeV,
31
P + n + 1.453 MeV,28
Si + α + 9.593 MeV,24
Mg + 2α − 0.393 MeV.

(2.8)

Si + α →28
Si +28 Si →32

S + α →36 Ar... →56 Fe,
56
Fe.

(2.9)
(2.10)

12

16

28

31

As the nuclear reactions progress one after another inside the star, newly synthesized elements
accumulate inside the star. Abundance profiles in the massive star is an onion-like at the final
stage of its evolution (Figure 2.3).
Explosive nucleosynthesis

Table 2.1: Explosive nucleosynthesis.
Burning Process
C/Ne burning
O burning
Incomplete Si burning
Complete Si burning

Main Products
Ne, O, Mg, Si
O, Si, S, Ar, Ca
Si, S, Ar, Ca
Fe, Co, Ni, Zn

Ignition temperature (109 K)
∼2
∼ 3–4
∼4
>∼ 5

Detail parameters from Thielemann et al. (1996).

Explosive nucleosynthesis is a nuclear fusion process in SNe. In both Type Ia and corecollapse SNe, a shock wave propagating inside a star rapidly elevate its internal temperatureso that nuclear reactions drastically progress, resulting in changing of the composition in thestar in a very short time. Table 2.1 summarizes dominant nucleosynthesis processes and theirignition temperatures. The abundances of synthesized elements strongly depend on the type ofa SN and the mass of a star before a SN. Figure 2.5 shows one example of abundance profilesof elements synthesized in a core-collapse SN of a massive star, calculated by Thielemann et al.

8

CHAPTER 2. SUPERNOVA AND SUPERNOVA REMNANTS

Figure 2.5: Abundance profiles of elements synthesized in core collapse SNe with stellar massof 15 M⊙ (Thielemann et al., 1996). The horizontal axis indicates a mass occupied by a spherewith a radius, inside a star. The vertical axis represent a mass fraction of each element in thesphere.
(1996). Our target SNRs in Chapter 5 are indeed considered to be the remnants of core-collapseSNe (e.g., Wolszczan et al., 1991; Olbert et al., 2001). It is notable that large amounts of heavy
elements such as Ca, Fe, and Ni in addition to light elements of Ne, Mg, Si, S, and so on, aresynthesized through the process. The produced 56 Ni decays to 56 Fe as follows,56

t1/2 =6.1 days

t1/2 =77 days

Ni −−−−−−−→ 56 Co −−−−−−→ 56 Fe,(2.11)

where t1/2 is a half-life.

2.2 Supernova Remnant
A SNR is the remains of an SN. SNRs have expanding shock waves formed by interaction
between ejecta in the SN and the swept-up ISM, and hot plasma consisting of them. The section
gives brief descriptions for the formation of the shock wave in SNRs, the dynamical evolutionof the SNRs, and the classification of SNRs.

2.2.1 Shock Wave
We summarize useful relations for strong (plane) shock waves formed by expanding materials into a stationary surrounding gas. Across the shock front, the conservations of mass,
momentum, and energy are given by below equations,
ρu vu
2
ρu vu + pu
1 2
v + ωu2 u= ρd vd ,= ρd v2d + pd ,1 2=
v + ωd ,2 d(2.12)(2.13)(2.14)

2.2. SUPERNOVA REMNANT

9vs ≠ 0v2

vs` = 0v1 = 0

ISM

SNR

vd

vu = v s

ρd , pd

ρu, puSNR(downstream)

ISM(upstream)

Observer rest frame

Shock rest frame

Figure 2.6: Schematic view around the shock front in (left) observer rest frame and (right) shock
rest frame.
where ρ, v, p, and ω are the density, velocity, pressure, and specific enthalpy, respectively. The
notations u and d correspond to the upstream and downstream as shown in Figure 2.6. The
specific enthalpy in ideal gas is described as,ω = Cp T =γp,(γ − 1)ρ

(2.15)

where γ is the specific heat ratio (= Cp /CV ). Under the assumption of the shock conditions(pd /pu ≫ 1), above equations can be translated into the ratio of pressure p, velocity v, density
ρ, and temperature T ,pd
2γMu 2,(2.16)=puγ +1vdρu γ − 1==,(2.17)vu
ρd γ + 1
Td2γ(γ − 1)Mu 2=,(2.18)
Tu(γ + 1)2√where M is the Mach number (= v/ γ p/ρ). For monoatomic gas (γ = 5/3), the ratio of thedensity, velocity, temperature are 4 (= ρd /ρu ), 1/4 (= vd /vu ), and 5/16 Mu 2 (= Td /Tu ), respectively.
Assuming that the upstream velocity vu equals to the shock speed vs , we can derive the mean
post-shock temperature kTs (= kTd ) as,kTs =2(γ − 1) µ mH vs 2
3
µ mH v2s ,=(γ + 1)216(2.19)

where k, µ, and mH are the Boltzmann constant, the mean atomic weight, and the hydrogenmass, respectively. Equation 2.19 can be interpreted as the conversion equation from the kinetic
energy of ejecta into internal energy of SNR plasma. We can see that the shock (vs ∼ 103 km/s)
in young SNRs (typically ≲ 103 yr) can heat the plasma up to ∼1 keV.

CHAPTER 2. SUPERNOVA AND SUPERNOVA REMNANTS

10

Forward ShockContact Discontinuity

HeatedISM
free expanding(unshocked) ejecta

HeatedEjectaISM
Reverse Shock

Figure 2.7: Sectional drawing of an SNR in the free expansion and adiabatic phases.

2.2.2 Evolution of SNRs
SNRs typically last several 105 years before they disperse into the ISM. In an initial phase,the so-called free expansion phase, the mass of the swept-up ISM (MISM ) is smaller than that ofejecta (Mej ) so that the ejecta is hardly decelerated and keeps most of the kinetic energy releasedin the SNe. Therefore, the expansion velocity vs can be expressed as,
√
vs =

2E
∼ 1.0 × 104
Mej

(

E
1051 erg)1/2 (

Mej
M⊙

)−1/2

km s−1 ,(2.20)

where E is the explosion energy. The formed shock wave precedes the expanding ejecta so thatthe shock is called the forward shock as shown in Figure 2.7. The free expansion phase lasts for
100–200 years.
As the mass of the swept-up ISM increases, the ISM starts to impede the free expansionof the ejecta. Until the energy loss by a radiation cooling is still negligible compared to theinitial energy, the SNR evolves adiabatically. The phase is called the adiabatic or Sedov phase.
Sedov (1959) proposed a self-similar solution that describes the dynamical evolution of an SNR
under the assumption of a point explosion in a uniform medium. The shock radius Rs , the shock2.2. SUPERNOVA REMNANT

11

Figure 2.8: Cooling coefficient for an optically-thin thermal plasma as a function of the plasma
temperature (Sutherland & Dopita, 1993).

12

CHAPTER 2. SUPERNOVA AND SUPERNOVA REMNANTS

velocity vs , and the mean temperature Ts just behind the shock front can be written as,()2/5 ()1/5 (tEn0 )−1/5
14km,
Rs = 4 × 10
104 yr10 erg1 cm−3()−3/5 (
)1/5 (
dRstEn0 )−1/5
2
vs == 5 × 10km s−1 ,dt
104 yr10 erg1 cm−3)−3/5 (
)1/5 ((
En0 )−1/5t
6K.
Ts = 3 × 10
104 yr10 erg1 cm−3(2.21)(2.22)(2.23)

The adiabatic phase lasts for 10,000–20,000 years. Until the end of this phase, ∼ 70% of theinitial explosion energy is converted to thermal energy of the swept-up ISM (Chevalier, 1974).
In the transition from the free expansion to adiabatic phases, the outer ejecta is decelerated by the swept-up ISM (see Equation 2.22) whereas the inner ejecta keeps freely expanding(see Equation 2.20). The inner ejecta is pushed back on the outer ejecta, and generates a reverse
shock that propagates inward as discussed in McKee (1974). The forward shock heats surrounding the ISM, whereas the reverse shock does the ejecta component as shown in Figure 2.7.
When the SNR age exceeds ∼ 104 yr, the radiative energy loss cannot be negligible. The
SNR loses its internal energy by the radiative cooling so that the plasma temperature and density
decreases and increases, respectively. Figure 2.8 shows the cooling coefficient for an opticallythin thermal plasma. The plot means that, as the plasma becomes cooler, the cooling speed
increases. Eventually, when the shock slows down and its velocity is comparable to the soundspeed in the ISM, the shock wave stands no longer. The SNRs merge into the ISM and cannot
be identified.

2.2.3 Morphology of SNRs
SNRs are identified by radio emissions from GeV electrons accelerated at shocks formed
by interaction between the ejecta and ISM. Currently, Green (2019) cataloged 265 SNRs and
SNR candidates in our Galaxy. Most of the SNRs are well known to brightly shine in multibands in addition to radio. Some authors (e.g., Rho & Petre, 1998) pointed out morphologicalsimilarities among some SNRs in radio and X-ray bands. They are considered to reflect similar
properties among the SNRs such as their environment and evolution history. Here, we explain
the classification based on the radio and X-ray morphologies of the SNRs, and the properties.
Figure 2.9 shows the four representative types of SNRs, shell-like, plerionic, composite, andmixed-morphology (MM). Shell-like SNRs have limb-brightened radio and X-ray morphologies. Most of young SNRs are categorized into this type. Radio emission is mainly synchrotron
radiation emitted from electrons accelerated in the blast wave. X-rays are thermal emission
from shock heated plasma and/or X-ray synchrotron from electrons in a TeV order. The shell
type is currently considered to be the most basic type. The plerionic SNRs have center-filled
X-rays and radio emission which are from a pulsar (PSR) and pulsar wind nebulae (PWNe).
The Crab Nebula is the most famous remnant of this type, and, therefore, the plerionic type
is often called Crab-like. Green (1986) claimed that the type can be seen if the SN occurs invery tenuous ISM or the SN energy is small. Composite SNRs have shell-like and center-filled
morphologies in X-ray and radio bands. In this type, both emissions from the PSR/PWN andfrom the plasma and/or accelerated particles are observed. MM-SNRs are characterized by thecenter-filled X-rays and the limb-brightened radio emission. Although ∼ 25 % of the X-raydetected SNRs in our Galaxy are categorized into this class (Rho & Petre, 1998), the formation

2.2. SUPERNOVA REMNANT

13(a) Tycho’s SNR (Shell type)(b) Crab (Plerion type)(c) G11.2–0.3 (Composite type)(d) W44 (MM type)
01 40

(a)

35

DECLINATION (J2000)

30
25
20
15
10
05

18 57 15 00

56 45 30

1500 55 45 30

1500

RIGHT ASCENSION (J2000)

Figure 2.9: X-ray and radio images of four type SNRs, (a) Tyhco’s SNR (Credit Radio; Credit
Radio: NSF/NRAO/VLA), (b) Crab (X-ray: NASA/CXC/SAO; Radio: NSF/NRAO/VLA), (c)G11.2−0.3 (Borkowski et al., 2016), (d) W44 (Castelletti et al., 2007). For all panels, the left
and right correspond to X-ray and radio band images.
mechanism has not been understood. Most MM-SNRs are actually known to be interacting withmolecular clouds (e.g., Lazendic & Slane, 2006), suggesting the association of the formation
mechanism and the interaction.

Chapter 3
Thermal Plasma and Particle Accelerationin SNRs
3.1 Thermal Plasma in SNRs
Studies of SNR plasma provide us with important information on the SNR’s environment
and evolution history. SNR plasma often emits thermal X-rays reflecting its electron temperature, ionization degree, and abundances of elements. Therefore, X-ray plasma diagnosis has
been a powerful tool to investigate the properties of SNR plasma. Here, we summarize theradiation mechanisms of the X-ray emission form the SNR plasma and the previous works
concerning the SNR plasma.

3.1.1 X-rays from Thermal Plasma
Figure 3.1 shows models of X-ray emission from optically thin plasma found in SNRs. The
typical X-ray spectra of SNRs have continuum components and many line emissions whose
information such as intensity and center energy is a key to constraining plasma parameters.
In the subsection, we focus on bremsstrahlung, radiative recombination continua (RRCs), andemission lines.
Bremsstrahlung
When charged particles are slowing down or deflected by other particles, the charged particles emit electromagnetic radiation, called bremsstrahlung. Generally, bremsstrahlung fromelectrons is more intense than that from ions in the astrophysical plasma since electrons arescattered more easily than protons because of its smaller mass. The emissivity ϵff of thebremsstrahlung emitted by electrons obeying the Maxwell-Boltzmann distribution is given by,
32πe6
ϵff =
3 me c3

(

2π
3kme

)1/2

Te −1/2 Zi 2 ne ni exp (−E/kTe ) g f f ,(3.1)

where e, c, k, me , Zi , ne , ni , E, and g f f are the electron charge, light speed, Boltzmann constant,electron mass, atomic number of ions, number densities of electrons and ions, photon energy,
and velocity averaged Gaunt factor, respectively (Rybicki & Lightman, 1979). For thermal
143.1. THERMAL PLASMA IN SNRS
10 100100010

15

10 10 10 10 10 10 10 10 10 0.01 0.1 1

Emissivity (arb .unit)

105

1.0

10-5

10-10
0.4 0.5

1
1.0

2

5
5.0

9.0

Energy (keV)
Figure 3.1: Thermal emission from X-ray emitting plasma. Black, red, and blue curves represent the models of CIE plasma, and IP, and RP, respectively.
plasma emitting X-rays, the Gaunt factor g f f is simply approximated as,(
gf f =

3kTe
πE

)1/2
.

(3.2)

The asymptotic behavior of the emissivity is written as,{
E −0.4(E ≤ kTe )ϵff ∝exp (−E/kTe ) (E > kTe ).

(3.3)

Therefore, electron temperature can be constrained based on the spectral shape of the bremsstrahlung
continuum. The luminosity L is calculated by the emissivity integrated over the volume and frequency, and summed of contributions of ions in plasma as follows,∑∫∑L=
Zi 2 ne ni V [erg s−1 ](3.4)
ϵff dV dν ∼ 1.7 × 10−27 Te −1/2
i

i
−27

∼ 2.9 × 10

Te

−1/2

nH ne V[erg s−1 ],where nH is the number density of hydorogen nucleus. Here, we used a helpful relation
1.7 nH in typical SNR plasma with solar abundance.

(3.5)
∑

i Zi

2

ni ∼

Radiative Recombination Continuum
RRCs are continua emitted by free electrons when they are captured in free orbits of ionizedions. Figures 3.2 and 3.3 show schematics of the radiation process and energy spectra of RRCs,
respectively. The energy of the emitted photon is the sum of the kinetic energy of electron before

16

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

freeelectron
Unbound Continuum

RRC(n = 4)

Energyn=4
RRC(n = 3)n=3RRC(n = 2)

n=2

n=1

RRC
(n = 1)Figure 3.2: Schematics of an emission mechanism for RRCs and transition lines after freeelectrons are captured by ions.
the recombination and the binding energy of the captured electron after the recombination. The
spectrum has an edge reflecting the binding energy, and the continuum shape depends on the
kinetic energy. Therefore, the behavior of the emissivity of RRCs from thermal plasma isapproximately written as{
0(E < I)(3.6)
ϵbf ∝exp (−E/kTe ) (E ≥ I),
where I is the binding energy.
Line Emission
Emission lines are caused by bound-bound transitions of electrons between two discrete
quantum levels due to inner-shell ionization, excitation, and cascade decay after the recombination. Energy of the emission line corresponds to the difference between the two levels. In thecases of a hydrogen atom or other H-like ions, the Bohr model gives remarkably good approximations of the energies of the line emissions. The line energy due to the transitions between
the levels with principal quantum numbers n and n′ can be described as,
)
(
1
1
2
(3.7)
Ebb ∼ Z Ry 2 − ′ 2 ,nnwhere Z and Ry is the atomic number and Rydberg constant (= 13.6 eV), respectively. Figure 3.4
shows the energies of the Fe-Kα and Fe-Kβ emission lines as a function of the charge numberof Fe ions. In general, as the ion is more ionized and the Coulomb screening between electrons
in orbits become weaker, the line energy increases.
Figure 3.5 presents an example of Grotrian diagrams showing allowed electronic transitions
between energy levels of atoms. Here, we show the diagram for one He-like ion. Energy

0.01

3.1. THERMAL PLASMA IN SNRS

17

He series

10

FeXXVI RRCs

10

10

1.0

10

10–2

10

Emissivity (arb .unit)

10

102

Ly series
He series

Cascade lines

10

10

10–4

5

10

5.0

10

15

Energy (keV)
Figure 3.3: Emitted RRCs and emission lines after the recombination between electrons and Fe
ions.
9

10

11

6700
6600

(a) Kα centroid

6500

7800

Flux Ratio

6400

Energy [eV]

Energy [eV]log(ne t [cm-3 s]) 8

0.15(b) Kβ centroid

7400
7000

(c) Kβ/Kα flux ratio

0.1
0.05
0

0

5

10

15

20

Charge Number
Figure 3.4: Center energies of the (a) Fe Kα and (b) Fe Kβ emission, and (c) the Kβ/Kα flux
ratio as a function of the charge number of Fe ions (Yamaguchi et al., 2014).

18

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

ge (CX) process sim- st.wt: g=1 g=3 g=5
term: SPD

g=1,3,5 g=3,5,7 g=5,7,9
plus
F
S
P
D
F
higherUnbound Continuum (DE=0)
L values...

n=7

g=7

g=3

n transfer itself. In- n=6
n=5

resonance linet in a highly-excited n=3
tively stabilizes. Typcharge exchange in- n=2

‘w ’

n=4

Singlets

z’
e‘ o
n
li
ati
en bind
id om
rb terc
o
f in

s ‘x
ine
l
n

,y ’

Triplets

ors can be metals or n=1
Ground State of Ion ( DE= ‒Binding Energy)
ng the impact of thisFigure 3.5: Grotrian diagram for a He-like ion with selected radiative transitions marked asdashed lines (Smith et al., 2014).
levels of atoms with multi electrons are more complicated because of the interactions of theelectrons with each other. In Figure 3.4, each energy level reflects the differences of total spin
angular momentum S or total orbital angular momentum L of the two electrons in addition to
the principal quantum number n. Transition paths are restricted by selection rules based on
quantum mechanics (e.g., conservation of spin angular momentum of electrons; conservationof orbital angular momentum between one electron and the emitted photon).
The line intensity has important information to constrain abundances and ionization degrees
of ions in plasma. The line intensity (and the intensity of RRC) is proportional to ne ni whereas
the flux of bremsstrahlung is almost proportional to ne nH (see Equation 3.5). Therefore, we candetermine the relative abundance ion (ni /ne ) with the flux ratio of the components. Figure 3.4
shows the intensity ratio of Fe Kα to Fe Kβ emission lines. It is well known that the intensity
ratio strongly depends on the number of or the arrangement of electrons in the atom. Note that
we also must consider the rate of ionization and excitation, and recombination processes in aplasma in spectral analysis.

3.1.2 Standard Evolution of SNR Plasma
Thermalization of Particles in Plasmas
Particles in SNR plasma are thermalized through shock heating so that their temperatures
are considered to follow Equation 2.19. The temperature of each particle species is proportional
to its mass so that protons and ions have much higher temperature than that of electron. The
particles, immediately after the shock heating, are considered to be kinematically in a nonequilibrium state. Miceli et al. (2019) succeed in measuring ion temperatures of the youngest
nearby SNR, SN 1987A, with the Chandra X-ray telescope. The Chandra data indeed revealed
that the temperature ratios of ions to protons are significantly large and increase linearly in3.1. THERMAL PLASMA IN SNRS

19

2007 and 2011 combinedFe60

Ti /TpTi = ATp
40

Si
Ne Mg
20

Ti = Tp

p
0
0

10

20

30
Atomic number

40

50

60

Figure 3.6: Temperature ratios of ions (Ne, Mg, Si, and Fe) to protons in SN 1987A. The redline marks the mass-proportional trend predicted by Equation 2.19, while the black line shows
the best-fit curve with the 90 % confidence ranges indicated by the green lines (Miceli et al.,2019).
proportion to their mass ratio as shown in Figure 3.6.
After the heating of particles at the shock, electrons in the plasma are gradually heatedthrough proton-electron and electron-ion collisions. The energy exchange continues until eachparticle has the same temperature, and the particles finally reach in a thermal equilibrium state.
Masai (1984) gave the thermalization timescales of electron-electron te−e and electron-proton(ion) te−i due to Coulomb collision as,()−1ne )−1 ln Λs,
(3.8)
= 5.1 × 10
1 cm−330()3/2 (()−1kTene )−1 ln Λ
11−2
= 3.2 × 10 < Ai >< Zi >s, (3.9)
1 keV
1 cm−330(

te−e
and te−i

8

kTe
1 keV

)3/2 (

respectively, where kTe , ne , < Ai >, < Zi >, and the ln Λ are the electron temperature, density, the averaged ion mass in atomic unit, the average ion charge, and the Coulomb logarithm(∼ 25 − 30). The timescales te−e and te−p are few 100 years and few 10 thousand years at< Ai >=< Zi >= 1, ne = 1 cm−3 , and kTe = 1 keV, respectively. Generally, the electronelectron thermalization timescale te−e is considered to be much smaller than the proton-electron
thermalization te−p , suggesting that the equilibrium between electrons precedes that between
electrons and protons (and ions).
Evolution of Ionization State in Plasma
Besides the thermalization, heated electrons also ionize ions, which are nearly neutral immediately after the SNe. As ions are more ionized, the electron-ion recombination rate increases.

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

1

20

Ar-likeBare

He-likeH-like

0.01

0.1

1

10

1010
1011
n e t (cm 3 s)

1012

kTe (keV)

1

0.01

Fraction
0.1

Ne-like1

Fraction
0.1

Ionizing Plasma

0.01

Fraction
0.1

Recombining Plasma

109

Figure 3.7: Charge fraction of Fe ions in (upper) CIE plasma and (middle) non equilibrium
plasmas in ionization dominant phase and (bottom) in recombination dominant phase (Smith etal., 2014).

3.1. THERMAL PLASMA IN SNRS

21

When the ionization and recombination rates are eventually equal, the plasma reaches collisional ionization equilibrium (CIE). The time evolution of ion fraction of each ion species iscalculated by following:ordni= −ne Ii ni + ne Ii−1 ni−1 − ne Ri ni + ne Ri+1 ni+1 ,dt
1 dni= Ii−1 ni−1 − (Ri + Ii ) ni + Ri+1 ni+1 ,ne dt(3.10)

where ni , Ii , Ri , and ne are the ion fraction of the i-times ionized ion, the ionization rate fromthe (i − 1)-times ionized ion to i-times ionized ion, the recombination rate from (i + 1)-times
ionized ion to i-times ionized ion, and the electron density, respectively. Masai (1994) computed
the characteristic timescale tion to reach the CIE state as,∫
ne dt ∼ 3 × 1012 cm−3 s.
(3.11)In Figure 3.7, we present ion fraction of Fe ions in CIE and non-equilibrium plasmas in “ionization dominant phase” and “recombination dominant phase”. SNR plasma is often in the nonequilibrium ionization (NEI) state because the timescale is comparable to or longer than SNR
ages.
The standard scenario of SNR plasma evolution has been established based on the above
theoretical works and following observational data taken with many rocket experiments andsatellite missions. After the opening of the X-ray window into the universe by Giacconi et al.
(1962), surveys with the payload rockets revealed that the locations of some X-ray sources are
consistent with those of SNRs such as Cassiopeia A, Tycho’s SNR, and the Crab. Gorenstein
et al. (1970) and Burginyon et al. (1975) discovered thermal bremsstrahlung and emission lines
in the X-ray spectra of Cas A, Tycho’s SNR, the Cygnus Loop, Vela X, and Puppies A, directly
indicating the presence of hot plasmas at ∼ 107 K. Tsunemi et al. (1986) measured the meanenergies of lines from Si, S, Ar, Ca, and Fe ions with Tenma, and revealed that the energies are
smaller than those expected in a CIE model. Figure 3.8 shows the spectra and the difference ofcenter energies of line emissions. Tsunemi et al. (1986) found that the spectra can be naturally
explained by an ionizing-dominate NEI model. The similar results were confirmed in many
SNRs so that the observed plasma in SNRs had been considered to be in the transition fromionizing plasma (IP) to CIE plasma as illustrated in Figure 3.9.

3.1.3 Over-ionized Recombining Plasma
Discovery of RPs
The standard scenario from IP to CIE plasma was questioned by Kawasaki et al. (2002,
2005). Analyzing ASCA data of IC 443 and W49B, they claimed that the measured Lyα-toHeα line intensity ratios of S, Ca, and Ar are higher than those expected from CIE models withthe electron temperatures determined by the bremsstrahlung continua (Figure 3.10). However,based on subsequent observations of these SNRs with XMM-Newton, Miceli et al. (2006) andTroja et al. (2008) showed that the line intensity ratios can be reproduced by multi CIE components, and claimed that the over-ionization is only marginal. In principle, arbitrary Lyα-to-Heαratio can be reproduced by a superposition of multiple-temperature CIE plasmas. Therefore,
other evidence were needed to conclude whether the over-ionization is real or not.

22

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

Figure 3.8: X-ray spectra for (upper left) Cas A and (upper right) Tycho’s SNR obtained with
Tenma. The black curves show the best-fit models. Deviations of the mean energies of Si, S,
Ar, Ca, Fe Kα lines are constrained in the spectral fitting from that expected in a CIE modelfor (bottom left) Cas A and (bottom right) Tycho’s SNR. The horizontal axis represents theionization time scale net in Equation 3.10. The black boxes and curves show the constrained
ranges with the 90 % confidence levels and IP models, respectively. (taken from Tsunemi et al.,
1986)
Ionization dominant

Recombination dominant

IP n t ~ few 10 cm s CIE n t ~ few 10 cm s RP
e

12

-3

e

12

-3

Figure 3.9: Ionization states of plasma in SNR.

3.1. THERMAL PLASMA IN SNRS

23

Figure 3.10: Confidence contours in kTe -kTz space for (left) IC 443 and (right) W49B (Kawasaki
et al., 2002, 2005). The black curves show the 1 σ, 90 %, and 99 % confidence levels. The ionization temperature kTz is equal to the electron temperature kTe if the Lyα-to-Heα line intensity
ratio described in plasmas with the kTz is equal to that in CIE plasmas. For instance, IPs havea smaller value of kTz than kTe , and the CIE plasmas have the same value of kTz than kTe . The
dashed line corresponds to the relation between kTe and kTz in CIE plasmas.

(b)

(a)

Fi

3 ( )

S

i

h 5 12 k

b d

h b

f

A

C

Figure 3.11: (a) W49B spectra obtained with Suzaku. Black line represents the best-fit CIE
model with additional Cr and Mn Kα lines. (b) Same as the left figure but plotted with the
RRC (red), recombination lines (orange), and Fe Lyα line (blue) line. (taken from Ozawa et al.,2009).

24

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

A breakthroughs concerning studies of the over-ionization was brought by detections ofstrong RRCs with Suzaku observations of W49B (Ozawa et al., 2009) and IC 443 (Yamaguchi
et al., 2009). Figure 3.11 shows the Suzaku spectra of W49B overlaid with (left) a CIE model,and (right) the CIE model and additional He-like Fe RRC and line components. We can see thata CIE plasma is not able to reproduce the spectra, leaving the characteristic residuals aroundthe energies of the Fe RRC. Even with multiple-temperature CIE plasmas, the overall spectrum
cannot be reproduced well. Currently, this plasma is called over-ionized recombining plasmas(RPs).
Recent Works concerning Formation Process of RPs
Recent X-ray studies have revealed RPs in a dozen of SNRs. All of them are classified as
MM SNRs (e.g., Uchida et al., 2015) as discussed in Section 2.2.3. Most of the MM-SNRs are
known to be interacting with molecular clouds. These facts imply that the presence of RPs issomewhat common among MM SNRs, and that shock-cloud interactions seem to be related tothe origin of RPs. Although some scenarios (e.g., Itoh & Masai, 1989; Kawasaki et al., 2002,
2005) are proposed to explain the RPs, the formation process of the RP has been not fully
understood yet.
The physical origin of RPs have been studied based on spatial variations of plasma parameters (e.g., kTe and net), and their comparison with distribution of ambient gas. Some authors
such as Matsumura et al. (2017b) and Okon et al. (2018) reported spatial correlations between
the electron temperature kTe of SNR plasmas in IC 443 and W28 and surrounding dense molecular clouds, respectively. Matsumura et al. (2017a) and Katsuragawa et al. (2018) also reported
the same kTe tendency in G166+4.3 and CTB 1, respectively. In Figures 3.12 and 3.13, we show
the overview of W28 and the kTe obtained with Suzaku data, respectively. The electron temperature kTe decreases in the region where the shocks in W28 interact with clouds. The results
can be explained by a rapidly cooling due to thermal conduction with the clouds, suggesting theformation of the RPs as the thermal conduction scenario originally proposed by Kawasaki et al.
(2002) and Kawasaki et al. (2005).
Itoh & Masai (1989) and Shimizu et al. (2012) predicted another scenario concerning theformation of RPs, the so-called rarefaction scenario, by using numerical simulations. In this
scenario, rapid adiabatic expansion in the SNRs is responsible for the overionization. Someauthors, e.g., Miceli et al. (2010), Lopez et al. (2013), Greco et al. (2018), and Sezer et al.
(2019), indeed claimed that their X-ray spectroscopy results support the scenario. The clearest
evidence was presented by Yamaguchi et al. (2018), who analyzed NuSTAR data of W49B
and performed spatially resolved spectroscopy, focusing on the Fe RRC. They found a clear
correlation between the values of kTe and net derived for each region (Figure 3.14). The result
suggests lower electron temperatures are achieved in the lower density regions, qualitatively
consistent with a rapid adiabatic expansion scenario as an origin of the overionization.

3.1. THERMAL PLASMA IN SNRS

25

Right Ascension
01:00.0

00:00.0

18:02:00.0

01:00.0

00:00.0

outside20:00.0

2
1
3-23:30:00.0

Declination

10:00.0

18:02:00.0

4

0.030

0.061

0.13

0.25

0.50

1.0

Figure 3.12: (upper) 0.5–2.4 keV X-ray image of the entire W28 taken with ROSAT overlaid
the 328 MHz radio contours (Rho & Borkowski, 2002). The cyan boxes correspond to two
Suzaku fields. (bottom left) Images of W28 in the energy band of 0.65–4.0 keV obtained by
Suzaku. The cyan solid and dash lines denote the source and background regions, respectively.
The white contours indicate the radio 325 MHz emission. The magenta contours and green
crosses show the spatial distribution of the 12 CO (J = 2 − 1) line emission and the locations of1720 MHz OH maser emission, respectively. These emissions are interpreted as evidence forshock-cloud interactions. (bottom right) Same as the bottom right panel but overlaid the white
contours indicating the radio 325 MHz emission (Okon et al., 2018).

26

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

0.6

kTe (keV)

0.5
0.4
0.3
0.2
0.1
region 1

region 2

region 3

region 4

Figure 3.13: Electron temperature kTe of two RP components obtained for the four source
regions of W28 in Figure 3.12. The red and blue points represent kTe for the higher-kTe RPs andthose for the lower-kTe RPs, respectively (Okon et al., 2018). In the region 1, the hot component
is not observed.

6

C1

D1

A2

B2

C2

D2

A3

B3

C3

D3

(b)
A3

ne t [1011 cm-3 s]

B1

15

B1

4
C3

B2
A2

C2

D3

B3

A1

10

East

D1

ne (t / kyr) [cm-3]

(a)
A1

C1

2

D2

West
1

5
1.2

1.4
kTe [keV]

1.6

1.8

Figure 3.14: (a) Image of 1.64 µm [FeII] line around W44 indicating an ambient gas distribution. The green contours are the exposure corrected Fe Heα flux map. The boxes are sub-regions
used in the X-ray spatial spectroscopy. (b) Relationship between kTe and net. The region names
labeled near the data points correspond to those given in panel (a). The dashed line is a powerlaw function with an index of 1.5 which is derived from the relation T V 2/3 = const between thegas volume V and temperature kTe expected in an adiabatic process of an ideal gas. (taken from
Yamaguchi et al., 2018).

3.2. PARTICLE ACCELERATION IN SNRS

27

Figure 3.15: Composition of CRs and the solar abundance as a function of nuclear charge(George et al., 2009).

3.2 Particle Acceleration in SNRs
It is widely believed that particles accelerated in SNRs constitute a significant fraction ofcosmic rays in our Galaxy. Cosmic rays (CRs) are one of the major components of the interstellar space in terms of energy density, and hence play an important role for the structure andevolution of our Galaxy. This section gives the relation between SNRs and cosmic rays, the diffusive shock acceleration theory as the most plausible mechanism for cosmic-ray production,
and a summery of evidence for particle acceleration in SNRs.

3.2.1 SNRs as Galactic Cosmic Ray Sources
CRs are high energy particles in the space. The origin and the acceleration mechanism
have been the important issues in physics since the discovery of them by Victor F. Hess in1912. Currently, arriving cosmic rays are known to consist of mainly protons and ionizedatomic nuclei (∼ 98 %), as shown in Figure 3.15, and the rest are electrons and positrons. A
noteworthy point is that the energy spectra dN/dE presented in Figure 3.16, are represented byan almost featureless nonthermal distribution over a very wide range of energies, from below∼ 109 eV up to ∼ 1020 eV. The spectra can be described by a power-law function as{
E −2.7 (E ≳ 3 × 1015 eV)
dN/dE ∝
(3.12)
E −3.1 (E ≲∼ 3 × 1015 eV),
where E is the kinetic energy per nucleon. The steepening at an energy of around ∼ 3 × 1015
eV is called “knee”.
CRs up to the knee are thought to be accelerated in astrophysical objects in our Galaxy.
The gyro radii of such particles actually are much smaller than the thickness of our Galaxy sothat they should be confined in our Galaxy. Therefore, CRs up to the knee energy are often
called Galactic Cosmic Rays (GCRs). Currently, SNRs are believed to be the most probable

28

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

Flux (m2 sr GeV sec)-1

Cosmic Ray Spectra of Various Experiments
104
10

LEAP - satellite

2

Proton - satellite(1 particle/m2-sec)

Yakustk - ground array
Haverah Park - ground array
Akeno - ground array

10-1

AGASA - ground array
Fly’s Eye - air fluorescence

10-4

HiRes1 mono - air fluorescence
HiRes2 mono - air fluorescence
HiRes Stereo - air fluorescence

10-7

Auger - hybridKnee(1 particle/m2-year)

10-10
10-13
10-16
10-19

C

t
va

LH

Te
n

4
(1

ro
(2
V)
Te

10-28
10

9

10

10

V)
Te

10-25

Ankle
(1 particle/km2-year)

RN

AL

CE

FN

10-22

1011 1012 10

13(1 particle/km2-century)1014 10

15

10

16

18

1017 10

19

20

10 10
Energy (eV)Figure 3.16: Energy spectra from 108 eV to 1021 eV of CRs.
<https://www.physics.utah.edu/~whanlon/spectrum.html>

3.2. PARTICLE ACCELERATION IN SNRS

29

Figure 3.17: Schematic drawing of the scattering of particles in the DSA mechanism.
candidates for the acceleration sites of GCRs (Ginzburg & Syrovatskii, 1964) for the following
two reasons.
One reason is that SNe are almost the only known astrophysical objects capable of providing
kinetic energy needed to explain the injection rate of GCRs. The injection rate LCR can be
estimated as follows,
ϵCR VGal∼ 5 × 1041 erg s−1 ,(3.13)
LCR ∼τCR
where ϵCR is the observed energy density (∼ 1 eV cm−3 ), VGal is the confinement volume of
GCRs (∼ 3 × 1067 cm3 ) taken to be the disk with a radius of 10 kpc and a thickness of 1 kpc, andτCR (∼ 3 × 1014 s) is the resident timescale of GCRs within the confinement volume estimatedby abundance of radioisotope (10 B) in GCRs. One SN event typically releases the kinetic energyof ∼ 1051 erg, and is considered to occur per ∼ 30 yr in our Galaxy. Therefore, we can see thatthe energy budget for the production of GCRs can be satisfied if about 10 % of the total energy
released in the SNe is somehow transferred to particle acceleration in SNRs.
The other reason is that SNRs can naturally explain the spectral property of GCRs. As
discussed in Section 2.2.3, SNRs have extended radio morphologies formed by synchrotron
emissions. The radio spectra of SNRs, especially shell type SNRs, are described by a powerlaw distribution, ϵ · dnγ /dE ∝ E −0.5 , indicating the presence of relativistic electrons in a GeV
order whose population is represented by dN/dE ∝ E −2 . Here, the generation spectrum of
GCRs at the acceleration sites should be harder and close to 2 because a part of the accelerated
particles are escaping from the confinement volume during their propagation. Therefore, we cannaturally explain the characteristic energy spectra of GCRs assuming SNRs are GCRs sources.

3.2.2 Diffusive Shock Acceleration Theory
Fermi (1949) first proposed an acceleration mechanism where charged particles gain energy
in a stochastic manner via scattering by magnetized clouds in the ISM. The acceleration mechanism is often called the second-order Fermi acceleration mechanism. Bell (1978) and Blandford

30

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

& Ostriker (1978) developed the Fermi’s idea into Diffusive Shock Acceleration (DSA) theory,
which is widely accepted as the standard mechanism of particle acceleration in SNRs. Here, wesummarize the DSA theory and explain the expected energy spectrum.
Figure 3.17 presents a schematic drawing of particle acceleration in the DSA theory. In thistheory, charged particles undergo being repeatedly reflected by Alfvén waves in upstream anddownstream of the shock waves. When a particle with energy E moves into the downstream
from upstream, its energy E ′ in downstream can be derived by the Lorentz transformation,
E ′ = γ(E +V p cos θ).

(3.14)

Here, the parameter V represents the difference of the shock speeds vu − vd in upstream andin down stream as shown in Figure 2.6, p is the momentum of the particle, and θ is the angle
between the moving direction of the particle and the axis perpendicular to the shock. Assuming
the shock is non-relativistic, V ∼ 1, and the particle is relativistic, E ∼ cp, we can obtain theenergy gain δE asV(3.15)
δE = E ′ − E = E cos θ.
c
The average energy gain is calculated as
∫
V π/2
2V
< δE >= E
2 sin θ cos θ dθ =E.
(3.16)c 0
3c
The particle again gain the same fractional energy increase as before, < δE >= (2/3)(V /c)E,
when it moves into the upstream from downstream. Therefore, particles gain the average fractional energy, δE/E = (4/3)(V /c), through one round trip across the shock (see Bell, 1978).
Considering the energy increase is very tiny, δE/E ≪ 1, we can give the the average energy En
after n-times round trips,
(
)
)n
(
4V
4V
En = E0 1 +n ,(3.17)∼ E0 exp3c3cwhere E0 is the energy of the particles before the scattering.
In the downstream, a part of accelerated particles escape by their convective motion. The
number of particles crossing the shock is N c/4, where N is the number density of the particles.
The number of escaping particles by the convective motion is n vd . Therefore, we can obtain
the probability of the particles escaping as (N vd )/(N c/4) = 4 vd /c. The probability that theparticles remain in the acceleration site just after n round trips is,
(
)n
(
)
4vd
4 vd
Pn = 1 −∼ exp −
n .
(3.18)cc
We can rewrite Equation 3.18 as Pn = (En /E0 )−3vd /V , using Equations 3.17. With ∫a relation∞dE,
between the differential energy spectrum dN/dE of the particles, and En and Pn , Pn ∝ En dN
dE
we can derive dN/dE as follows,dN∝ E −s ,dE

s=vu /vd + 2.
vu /vd − 1(3.19)For strong shocks in a monoatomic gas (vu /vd = 4, see Equation 2.17), accelerated particles
obey a power law distribution dN/dE ∝ E −2 . The index expected in DSA is consistent with theones obtained in the observations of radio synchrotron in SNRs in Section 3.2.3.

3.2. PARTICLE ACCELERATION IN SNRS

31

Figure 3.18: (left) X-ray images of SN 1006 in the energy band of 0.4–8.0 keV taken with
ASCA. (upper right) Spectrum from the bright northeast rim. The solid line shows the best-fit
model. (bottom right) Same as the upper right panel but for the interior region. (taken from
Koyama et al., 1995).

3.2.3 Nonthermal Emissions from Accelerated Relativistic Particles
Particle acceleration in SNRs has been widely studied through detection of nonthermal
emissions from accelerated particles. Here, we summarize radiation mechanisms and previous works concerning their detection of them in SNRs.
Synchrotron Radiation
Synchrotron radiation, which is from electrons accelerated in the magnetic field by Lorentz
force, is a powerful tool to probe high energy electrons. The synchrotron radiation power per
unit frequency from one relativistic electron is given by (Rybicki & Lightman, 1979)√ 3
3 e B sin θF(ω/ωc ).
(3.20)
P(ω) =
2π me c2
Here, θ is the pitch angle, ωc is the characteristic frequency described as
ωc =3 γ 2 e B sin θ,
2 me c(3.21)and the function F(x) gives the spectral energy distribution from a single electron expressed as∫ ∞K5/3 (ξ)dξ,(3.22)
F(x) = xx

32

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS

with a modified Bessel function K5/3 . The Function F(x) has a peak at ∼ 0.29 so that P(ω) has
also a peak at ω ∼ 0.29 ωc . The photon energy at the peak frequency ∼ 0.29 ωc can be regarded
as the average synchrotron photon energy from one electron, and is approximately written as(Bϵ ∼ 3.3
10 µG

)(

Ee
100 TeV)2
keV,(3.23)√√
where Ee is the electron energy. We assumed the average angle of sin θ (= ⟨sin2 θ⟩ = 2/3).
By integrating of Equation 3.20 over frequency, we calculate total power as
4
Psync = σT c β 2 γ 2 UB ,3

(3.24)

where UB (= B2 /8 π) is the energy density of the magnetic field. We can derive the synchrotron spectrum from electrons with any energy distribution by using the spectrum fromsingle-electron. Assuming the electrons obeying a power law distribution dN/dE ∝ E −s , thebehavior of the synchrotron energy spectra ϵ · dnγ /dϵ can be approximately described as,∫
ϵ · dnγ /dϵ ∝ P(ω)dN/dEdE ∝ B(s+1)/2 ϵ−(s−1)/2 , α = −(s − 1)/2.
(3.25)
Koyama et al. (1995) discovered synchrotron X-ray emissions from SN 1006 with the ASCA
X-ray observatory. They found that the rim of the remnant is dominated by the synchrotron
component as shown in Figure 3.18, and concluded that electrons are accelerated up to ∼ 100
TeV at the shock waves (see Equation 3.23). In several other SNRs, such as RX J1713.7−3946(Koyama et al., 1997) and RX J0852.0−4622 (Slane et al., 2001), the synchrotron X-ray emissions have also been detected. Recently, some authors (e.g., Uchiyama et al., 2007; Tsuji &Uchiyama, 2016) have studied key topics in particle accelerations such as an amplification of
the magnetic fields in the shock waves and measurements of shock velocity, through the spatially resolved spectroscopy of synchrotron X-rays in SNRs.
Inverse Compton Scattering
Another piece of evidence for accelerated electrons in SNRs is gamma-ray emissions emitted via inverse Compton up-scattering. In this process, the low energy seed photons are scatteredby high energy electrons to higher energies. Generally, in the case of SNRs, the Cosmic Microwave Background (CMB) photons are a dominant as seed photons. The total power of the
gamma-rays emitted from a single electron, in the Thomson regime, is given by,
PIC =4
σT c β 2 γ 2 UCMB ,3(3.26)

where σT is the Thomson cross section and UCMB (= nCMB ϵCMB ) is the the average energy densityof the CMB photons. The nCMB and ϵCMB are the number density of the CMB photons and theaverage energy per one CMB photon, respectively. Dividing Equation 3.24 by Equation 3.26,
we obtain
Psync
UB
=
.
(3.27)PIC
UCMB

3.2. PARTICLE ACCELERATION IN SNRSFi 7 Di

33

ti l

t

f SN 1006

t

t df

th t

Figure 3.19: (left) H.E.S.S. gamma-ray map of SN 1006. The white solid contours show the
X-ray image in the 2.0-4.5 keV energy range. (right) Energy spectra of SN 1006 extracted
from the northeastern and southwestern shells. The shaded bands correspond to the range of thepower-law fit with the 1 σ confidential levels. (taken from Acero et al., 2010)
This equation means that, if the energy density of seed photons are well known such as the
CMB, we can probe the strength of the magnetic field with the flux ratio of synchrotron emission
to inverse Compton emission. We can derive the average energy ϵ of the scattered photon as
ϵ=

4 2 2
β γ ϵCMB .
3(3.28)

Here, we obtaine this equation dividing Equation 3.26 by the number of photons scattered perunit time is c σT nCMB . For instance, the scattered photon energy is about 10 GeV when electronsof 5 TeV (β ∼ 1, γ ∼ 107 ) scatter the CMB photons (ϵCMB ∼ 2.73 K ∼ 2.3 × 10−4 eV).
The gamma-ray spectra of the inverse Compton emission were calculated by some authors(e.g., Jones, 1968; Blumenthal & Gould, 1970). We can calculate the gamma-ray spectra dnγ /dϵ
as follows,∫∫dN d 2 nγ
dn0dγ,(3.29)
dnγ /dϵ ∝ dϵ0
dϵ0
dγ dt dϵwhere dn0 /dϵ0 is the differential density spectrum of the seed photons, dN/dγ is the differential
spectrum of electrons, and d 2 nγ /dt dϵ is the differential production rate of scattered photons.
Assuming electrons are relativistic, Jones (1968) gave d 2 nγ /dt dϵ as[]
d 2 nγ2 π r0 2 c
1 (4α0 γ q)2=2 q ln q + (1 + 2 q)(1 − q) +,(3.30)dt dϵ
α0 γ 22 1 + 4α0 γ q
where r0 is the classical electron radius, q = α/4 α0 γ 2 (1 − α γ), α = ϵ/me c2 , and α0 = ϵ0 /me c2 .
With Equations 3.29 and 3.30, Blumenthal & Gould (1970) calculated the asymptotic behaviorof the energy spectra ϵ · dnγ /dϵ of gamma-rays from nonthermal electors, dN/dE ∝ E −s , as
∝ ϵ(−s+1)/2 . Here, the seed photons are assumed to be the CMB photons.
Recently, the observations of high energy phenomena in the GeV–TeV bands was enabled by
the advent of gamma-ray telescopes such as Large Area Telescope on Fermi Gamma-ray Space
Telescope (Fermi) and the high energy stereoscopic system (H.E.S.S.) of Cherenkov Telescopes.

34

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRS80
PDG data
Fit formula
Kelner(2006)
Kamae(2006)

70

σinel [mb]

60
50
40
30
20
10

0 1
0
10
10

1

10

2

10

3

4

10 10
Tp [GeV]

5

10

6

10

7

10

8

10

Figure 3.20: Cross section for inelastic proton-proton interaction as a function of the proton
kinetic energy in the laboratory system. (taken from Kafexhiu et al., 2014)

dnγ/d

log(

log( )

Figure 3.21: Spectrum of gamma-ray generated by π 0 -decay.
Figure 3.19 presents a gamma-ray map of SN 1006 with H.E.S.S. (Acero et al., 2010). The map
shows strongly spatially correlations between the gamma-ray emissions and the shock waves,and the synchrotron X-rays. These X-ray and gamma-ray observations established the picturethat electrons can be accelerated to energies of ∼ TeV at shock waves in SNRs.
π 0 decay gamma-rays
A direct signature of high energy protons, which are major components of GCRs, is provided by gamma-ray emissions through the decay of π 0 -mesons generated by inelastic collisions
between protons in GCRs and that in the ISM as follows,p (GCRs) + p (ISM) → p + p + π +,−,0 ,π 0 → 2 γ.

(3.31)(3.32)

3.2. PARTICLE ACCELERATION IN SNRS

Tp=0.300 GeV

10

0.8
1

10

10

E [GeV]

3

1.2

Data
Fit formula
Dermer(1986)
Kamae(2006)

1

1

1.2

1

10

Data
Fit formula
Dermer(1986)
Kamae(2006)

2

10

0.8
1

10

10
E [GeV]

γ

0

10

3

10

1

10

2

1
0.8
10

2

10
Eγ [GeV]γ

Tp=0.400 GeV

ratio

2

1

10

γ

10

dσ/dE [mb/GeV]γ

1d /dE [mb/GeV]

Data
Fit formula
Dermer(1986)
Kamae(2006)

ratio

3

10

1

ratio

2

1.2

10

Tp=0.800 GeV

2

10

10

dσ/dE [mb/GeV]10

Tp=0.400 GeV
01γdσ/dE [mb/GeV]

10

35

10

1

1

Figure 3.22: π 0 -decay spectra for different proton collision energies Tp (left: Tp = 0.3 GeV;
center: Tp = 0.4 GeV; right: Tp = 0.8 GeV).

Figure 3.23: Gamma-ray spectra of decays of π 0 -mesons by nonthermal protons (dN/dE ∝E −s ). If protons are relativistic, the protons distribution can be written as dN/d p ∝ p−s p . The
index s p is equal to s. (Figure from Dr. Tanaka)

10-10

E2 dN/dE (erg cm-2 s-1)

E2 dN/dE (erg cm-2 s-1)

10-10

10-11

10-12

10-11

10-12

8

10

9

10

10

10

Energy (eV)

1011

1012

8

10

9

10

10

10

1011

1012

Energy (eV)Figure 3.24: (left) GeV–TeV data of IC 443 taken from Fermi, VERITAS, MAGIC, and AGILE.
Solid line denotes the best-fit curve with a π 0 -decay model. Dashed, dash-dotted lines show thethe best-fit models with a bremsstrahlung model, a bremsstrahlung model with an energy break,respectively. (right) Same as but for W44. (taken from Ackermann et al., 2013).

36

CHAPTER 3. THERMAL PLASMA AND PARTICLE ACCELERATION IN SNRSIn the rest system of the produced pions, they decay with the mean lifetime 8.4 × 10−17 s, andemit two gamma-rays with the energy of a half of the π 0 rest mass (mπ c2 /2 = 67.5 MeV).
In Figure 3.21, we show the gamma-ray spectrum dnγ /dϵ expected through the decay of
mono-energetic π 0 -mesons. The gamma-rays are symmetrically distributed around 67.5 MeV(= mπ c2 /2) in the log energy scale (Stecker, 1971), and show a flat spectrum. The behaviorof the gamma-ray spectrum can be understood as follows. We can derive energy ϵ of observed
gamma-rays using the Lorentz transformation from the rest frame of π 0 -mesons to the observer
frame,
ϵ = γ(ϵ∗ + vp∗ cos θ∗ ),(3.33)
where γ and v are gamma factor and velocity of π 0 -mesons in the observer frame, respectively,and ϵ∗ (= mπ0 c2 /2), p∗ and θ∗ are energy, momentum of emitted gamma rays, and the angle
between the observer and themoving√direction of π 0 -mesons, in the in rest
respectively.
√ frame,√√2
2
The maximum ϵmax = mπ c 1 + β/2 1 − β and minimum ϵmin = mπ c 1 − β/2 1 + β energies in Figure 3.21 correspond to the cases in Equation 3.33 with θ∗ = 0◦ and 180◦ , respectively.
We can describe a helpful relation between the maximum and minimum energies,
(
)
1
1
2
(log(ϵmax ) + log(ϵmax )) = log
m 0c .
(3.34)
22 π
Equation 3.34 means that the center of the interval is half of the pion mass in log-log scale. The
isotropic distribution dnγ /dΩ∗ of emitted photons in the π 0 rest frame can described as
1
dnγ
dnγ
=
= const.
dΩ∗ 2π d(cos θ∗ )(3.35)

With this equation and a variation of Equation 3.33, dϵ = d(cos θ∗ ), we can see that gamma-ray
spectrum dnγ /dϵ is constant. Therefore, the gamma-ray emissions have a flat spectrum.
Figure 3.22 shows π 0 -decay spectra for different proton collision energies. The spectrum
is also symmetric because the spectrum is a superposition of the spectra of decays of monoenergetic π 0 -mesons. In Figure 3.23, we present the νFν spectra (ϵ2 · dnγ /dϵ) of gamma-raysby the protons with dN/dE ∝ E −s . The spectra above ∼ 200 MeV are power law with indiceswhich are the same as that of the proton distribution. On the other hand, the spectra below∼ 200 MeV do not depend on the proton distributions, and shows the characteristic “break”
structures. The behavior in the low-energy band reflects the rapid increasing of the protonproton inelastic cross section around 200 MeV–1 GeV (Figure 3.20).
Although the promising channel to prove accelerated protons have been considered to be the
gamma-ray emissions through the π 0 -decay, the identification of the gamma rays has been difficult. Gamma-rays via π 0 -decay process show power law spectra in the energy range of above∼ 1 GeV. However, for example, as discussed in the section of Inverse Compton Scattering, thegamma-rays via this process can also represent the same featureless spectra. Ackermann et al.
(2013) focused on the characteristic break signature below ∼ 200 MeV only in the π 0 -decay
spectrum, and succeed in detecting the structures in spectra of W44 and IC 443 with Fermi.
Figure 3.24 show the GeV–TeV spectra overlaid with π 0 -decay and bremsstrahlung models.
One can see the spectral breaks in the energy band of below 300 MeV.

3.2.4 Exploration of Sub-relativistic Particles
Sub-relativistic particles are one of the important components in particle acceleration because information on such particles are key to estimating total energy transferred into particle

3.2. PARTICLE ACCELERATION IN SNRS

37

Figure 3.25: (a) Background-subtracted spectra of W49B from NuSTAR FPMA (black) andFPMB (red). The solid curves are the background models. (b) Same as the left figure but
plotted with the best-fit model. The dotted and dashed curves indicate the RRC and powerlaw components, respectively. The bottom panel shows residuals from the model. (taken from
Tanaka et al., 2018)acceleration and to considering the injection mechanism of particle acceleration. However, subrelativistic particles at acceleration sites are almost unexplored. This fact is because it is difficult
to explore sub-relativistic particles through above radiation channels. Fluxes of synchrotron Xrays from and gamma-rays via Inverse Compton off sub-relativistic electrons are known to be
extremely weaker than those by relativistic electrons. The threshold energy of protons for π 0
production is ∼ 280 MeV (= mp c2 + 2 mπ c2 + mπ 2 c2 /2 mp ) in the rest system of protons in the
ISM so that sub-relativistic protons cannot generate π 0 -mesons. Therefore, other diagnostic
tools are required to probe them.
Ramaty et al. (1979) pointed out nuclear gamma line emissions in MeV band as one of thepromising tools to probe sub-relativistic particles. However, the even most prominent lines fromcelestial objects are only marginally detectable because of limited sensitivities of instruments
and huge background (e.g., Schönfelder et al., 2000). Tanaka et al. (2018) found a significant
power-law component, which can be best interpreted as nonthermal bremsstrahlung from subrelativistic electrons, extending up to ∼ 20 keV in NuSTAR data of W49B. Figure 3.25 shows
the NuSTAR spectrum of W49B.

Chapter 4
Instruments
We perform an observational study of RPs utilizing spectral data taken with XMM-Newton
and a theoretical study toward probing sub-relativistic particles accelerated in SNRs with XRISM.
Figure 4.1 shows overviews of the X-ray satellites. Both X-ray observatories are equipped with
X-ray mirror optics, and enable us to perform X-ray imaging spectroscopy. In the chapter, we
briefly summarize basic properties of both satellites.

4.1

XMM-Newton

The X-ray Multi-Mirror Mission (XMM-Newton) is the X-ray astronomy mission of the European Space Agency. The XMM-Newton observatory was successfully launched on December
10, 1999, with an Ariane-V from the Guiana Space Centre. It was thrown into a highly ellipticalorbit with an apogee of about 115000 km and a perigee of 6000 km. Its orbital period is about
48 hours. As of 2020, the satellite is in operation and provides us with highly worth data.
Figure 4.2 shows a sketch of XMM-Newton. XMM-Newton is equipped with three identical
X-ray reflective mirrors, and carries three distinct types of cameras which make it possible tosimultaneously access X-ray and optical/UV emissions. One of the cameras is the European
Photon Imaging Camera (EPIC) consisting of three charge coupled devices (CCDs) for X-ray
imaging and moderate resolution spectroscopy. Another is the Reflection Grating Spectrometer(RGS; den Herder et al., 2001) achieving high resolving power (150 to 800) over a range from
5 to 35 Å. The other is Optical/UV Monitor that is CCDs for optical/UV imaging and grism
spectroscopy (Mason et al., 2001).

4.1.1 X-ray Telescope
The XMM-Newton X-ray Telescope (XRT) utilizes total reflection under the Wolter typeI configuration, which employs paraboloidal and hyperboloidal surfaces as primary and secondary mirrors, respectively. Figure 4.3 shows the overviews of the XRT assemblies. Incident
X-rays are focused by the XRT, and ∼ 40 % of the total light is dispersed with the gratingassemblies in their light paths. The non-dispersed light passes to the EPIC cameras, and the intercepted one is detected by the CCD cameras of the RGS. Each of the three XRT assemblies iscomprised of 58 Wolter I grazing-incidence mirrors which are nested in a coaxial and confocal
configuration. The grazing angle is as shallow as 30′ , which enables to achieve high effective38

4.1. XMM-NEWTON

39

Figure 4.1: Artistic views of (left) XMM-Newton and (right) XRISM satellites.
<https://www.esa.int/Enabling_Support/Operations/XMM-Newton_operations;
https://xrism.isas.jaxa.jp>

Figure 4.2: In-orbit configuration of the XMM-Newton satellite.
<https://heasarc.gsfc.nasa.gov/docs/xmm/xmmhp_gal_hard_schem.html>

Figure 4.3: (left) Wolter type-I X-ray reflecting optics. (right) Light path in the XMM-Newton
with grating assemblies. (taken from XMM-Newton Users Handbook)CHAPTER 4. INSTRUMENTS

40

2000

Aeff (cm2)

1500

1000

500

0
0.1

1.0
Energy (keV)

10.0

Figure 4.4: (left) Effective area as a function of energy. (right) Vignetting factor defined as theratio of the effective area against incident angle to that on on-axis. (taken from XMM-Newton
Users Handbook)Figure 4.5: MOS fractional encircled energy as a function of angular radius (on-axis). (takenfrom XMM-Newton Users Handbook)4.1. XMM-NEWTON

41

Figure 4.6: Field of view of the two types of EPIC camera; (left) MOS and (right) pn. The
shaded circle depicts a 30 diameter area. (taken from XMM-Newton Users Handbook)area over a wide energy range from 0.15 keV to around 7.0 keV as shown the left panel in
Figure 4.4.
Figure 4.4 shows dependences of the effective area of one XRT of XMM-Newton against energy of incident X-rays and incident angle to that on on-axis. The dependence of effective area
on incident angle is generally called “vignetting” effect. Figure 4.5 shows fractional encircled
energy defined as the fraction of X-ray photons collected in a circular region as a function ofa diameter. The diameter that encircles 50 % energy is called a Half Power Diameter (HPD),
which are used a parameter to compare angular resolution in different satellites.

4.1.2 EPIC
EPIC is composed of two Metal Oxide Semi-conductor (MOS) type CCD cameras, namely
MOS1 and MOS2 (Turner et al., 2001), and one pn CCD camera (Strüder et al., 2001). Each
MOS camera is comprised of 7 front-illuminated (FI) CCDs as shown in Figure 4.6. The imaging area of the MOS camera is ∼ 2.5 × 2.5 cm and is equivalent to about a 30 arcmin-diametercircle. One CCD has 600 × 600, 40 µm square, pixels. The pn camera is comprised of 12
back-illuminated (BI) CCDs with 200 × 64 pixels. The pixel size is 150 × 150 µm. The layoutof the pn CCDs is represented in Figure 4.6. The pn array has the imaging area of about 6 ×6
cm, and almost completely covers the same 30 arcmin-diameter circle as MOS cameras.
Figure 4.7 shows energy resolutions of the MOS and pn CCDs immediately after the launchof the satellite. The quoted values are full widths at half maximum (FWHM) of the Al Kα
and Mn Kα lines for on-board calibration after corrections for charge transfer inefficiency. The
MOS cameras have better energy resolutions than pn. In Figure 4.7, the energy resolution
rapidly degraded by ∼10 % early in the mission. In order to suppress thermal noise in CCDs
and improve the energy resolution, the decreasing of operation temperature was performed
between November and December 2002 (Rev.#530 to #560). After the cooling, the resolution
was improved to almost the same value as the pre-launch. Since then, the resolutions of the
MOS cameras remain nearly at the improved values. For the pn camera, the energy resolution
degrades at about constant small rate as reported by Meidinger et al. (2004). For instance, therate for the Mn Kα line is ∼ 1.2 eV yr−1 .

42

CHAPTER 4. INSTRUMENTS

Figure 4.7: (left) Temporal evolution of MOS energy resolution (FWHM) as a function ofenergy. The solid line is a best-fit curve with a E 0.5 -function based on ground calibration data.
Data points represent the FWHM value of the Al Kα (1.478 keV) and Mn Kα (5.893 keV)lines in five different epochs. (right) pn energy resolution for singles. The black, blue, red,green curves correspond to energy resolution calculated with single event data at the bore-sight,
single event data closest to the readout node, double event data at the bore-sight, and double
event data closet to the readout node, respectively. (taken from XMM-Newton Users Handbook)Figure 4.8: Net effective area of EPIC cameras and RGS spectrometer (taken from XMMNewton Users Handbook)4.1. XMM-NEWTON

43

Figure 4.9: Instrumental background spectra of (left) MOS and (right) pn cameras. (taken from
XMM-Newton Users Handbook)Figure 4.10: Position-to-position variations of the intensities of fluorescent lines on MOS detector plane in instrumental background spectra (Kuntz & Snowden, 2008).
Figure 4.8 shows net effective areas of MOS and pn cameras which is calculated frommultiplying the XRT effective area by the quantum efficiencies of them. In contrast to theenergy resolution, the pn cameras have larger effective area than MOS. The difference of thecurve shape reflects whether the CCDs are FI or BI types. Low-energy X-rays are largely
absorbed by the optical blocking filter and by the gate structures of the CCD chips. Since BI
chip has the gate on the opposite side from the XRT, the quantum efficiency of the BI CCD usedin the pn camera is larger than those of the FI CCD in MOS cameras, in a low-energy band.
EPIC background
EPIC background includes X-ray emission from celestial objects and instrumental background. The latter can be divided into detector noise which becomes dominant at low energies(i.e. below 300 eV) and a component caused by interaction of high energy particles with thestructure surrounding the detectors and the detectors themselves. Figure 4.9 shows the instrumental background spectra of MOS and pn cameras. In the energy band above 300 eV, theCHAPTER 4. INSTRUMENTS

44

Figure 4.11: Blocking diagram of Resolve (Ishisaki et al., 2018).
spectra have continuum components which are mainly X-rays caused by interaction between
cosmic rays and the satellite, and charge generated by invasion of cosmic ray in the CCDs fromthe direction of the XRT. Further, one can see florescence Al Kα, Si Kα, Ni Kα and Kβ, and Au
Lα, Lβ and Mα from materials of the spacecraft. The intensity of these lines has been known
to have a very strong spatial dependence as shown in Figure 4.10 (Kuntz & Snowden, 2008).

4.2

XRISM

The X-ray Imaging and Spectroscopy Mission (XRISM), formerly known as the X-ray Astronomy Recovery Mission (XARM), is the 7th Japanese X-ray astronomy satellite, which is
to be launched in fiscal year 2022 on a JAXA H-IIA rocket. The XRISM satellite carries two
X-ray mirror assemblies (XMAs), which are basically identical to those on the Hitomi satellite
launched in 2016. One of the focal plane detectors, Resolve, is an X-ray micro calorimeter
array which will achieve unprecedented high-resolution spectroscopy (FWHM: 5–7 eV) in the
0.3–12 keV bandpass. The other is Xtend using an X-ray CCD camera with a moderate energy
resolution and a large field of view of 38′ × 38′ . With these two complementary instruments,
XRISM will precisely measure plasma condition and kinematics, and open up a new view of the
X-ray universe. In this section, we briefly explain the properties of both modules.

4.2.1 Resolve
Resolve is a soft X-ray spectrometer using silicon-thermistor micro-calorimeters. Microcalorimeters are instruments to measure the energies of X-ray photons by using slightly increasings of temperatures of their elements that the X-rays hit. Therefore, during their operations,micro calorimeters are required to be kept in a very low temperature. In Figure 4.11, we show
a blocking diagram of Resolve. The Resolve system is divided into the four sub-systems, optics, refrigeration, sensor, and calorimeter electronics. The X-ray micro calorimeters are built
into the sensor system, which is cooled in a dewer in the refrigeration system. Calorimeter4.2. XRISM

45

Figure 4.12: Photograph of SXS onboard Hitomi. <https://svs.gsfc.nasa.gov/12120>

Figure 4.13: Perseus spectrum obtained with SXS onboard Hitomi (Hitomi Collaboration etal., 2016). Red line denotes simulated X-ray emission from Perseus folded with instrumental
response of the X-ray CCD (XIS) onboard Suzaku.

CHAPTER 4. INSTRUMENTS

46

Figure 4.14: Blocking diagram of Xtend (Hayashida et al., 2018).
electronics control the X-ray micro calorimeters and act as a processor of signals output by the
micro-calorimeter. Optical system is equipped with filters used if the satellite observes brightcelestial objects and an X-ray generator for energy calibration.
Resolve uses a 36-pixel array of X-ray micro calorimeters as shown in Figure 4.12. The Resolve instrument is mostly a copy of the X-ray calorimeter onboard the Hitomi (SXS) and its soft
X-ray telescope design, though several changes are applied based on the lessons learned from
Hitomi (e.g., Takei et al., 2018). The instrument was designed to achieve an energy resolution
better than 7 eV over the 0.3–12 keV energy range, operated at only 50 mK. The actual energy
resolution of the instrument is 4–5 eV as demonstrated during extensive ground tests. Figure 4.13 shows X-ray spectrum of Perseus cluster obtained by the SXS onboard Hitomi overlaid
with a model folded with instrumental response of Suzaku CCDs (XIS) (Hitomi Collaboration
et al., 2016). In table 4.1, we summarized key parameters of Resolve.

4.2.2 Xtend
Xtend is a soft X-ray imaging spectrometer with CCDs. Figure 4.14 shows a blocking
diagram of the Xtend system. Xtend consists of the camera part (SXI-S) which includes CCDs,
analog electronics (the Video Boards and SXI-S-FE), and mechanical coolers (SXI-S-1ST), thepixel processing electronics (SXI-PE), the digital electronics (SXI-DE), and the cooler driver(SXI-CD). The Video Boards digitize singles output by the CCDs and sent them to SXI-PE.
Subsequently, the digitized signals are applied to some corrections in SXI-PE and SXI-DE, andevent data are extracted from them. During operations of the CCDs, they are cooled down to−120◦ C with the SXI-S-1ST. SXI-S-1ST is controlled by SXI-CD based on house keeping data
(e.g., CCD temperature) monitored by SXI-S-FE.
The Xtend detectors are four P-channel CCDs manufactured by Hamamatsu Photonics K.
K, and are designed almost the same as SXI on Hitomi. Figure 4.15 shows a layout of the
CCDs and a schematic view of one CCD. Each CCD is comprised of 1280 × 1280 pixels with a
24 µm × 24 µm pixel size, which yields an imaging area size of 30 mm × 30 mm. Considering4.2. XRISM

471280 pixels

Segment AB

Segment CD

Frame-store region
1280 pixels

640 pixels

Serial shift register
Readout nodes A

Imaging area
1280 pixels

Charge injection
gate

B

C

D

Figure 4.15: (right) Photograph of SXI onboard Hitomi, and (left) schematic view of one CCD.
(taken from Tanaka et al., 2018)the advantage of high resistance to damage by micrometeoroids, we employed BI type device.
As demonstrated in the case of Hitomi, we used the n-type substrates with high resistivity,
resulting in higher quantum efficiency for the hard X-ray band compared to BI CCDs onboard
previous X-ray satellites. Some improvements have been applied by Kanemaru et al. (2020)
and Uchida et al. (2020). Table 4.1 summarizes the required performance of the Xtend.
Table 4.1: Key parameters of Resolve and Xtend.
Item
Angular resolution (HPD)
Focal length
Energy band
Energy resolution (FWHM)
Field of view
Effective Area (at 1 keV)
Effective Area (at 6 keV)Time resolution
Instrumental background
Operation temperature

Resolve≤ 1.3′
5.6 m
0.4–12 keV≤ 7 eV
2.9′ × 2.9′
≥ 160 cm2
≥ 210 cm25 µs
≤ 2 × 10−3 counts/s/keV/array
50 mK

Xtend
≤ 1.3′
5.6 m
0.3–12 keV≤ 200 eV∗ /250 eV†
38′ × 38′
N/A
≥ 360 cm2
4 s (normal)/0.1 s (burst)≤ 1 × 10−6 counts/s/keV/arcmin2 /cm2−120 ◦ C

Detailed parameters from Ishisaki et al. (2018) and Hayashida et al. (2018).
∗ Required FWHM in begin of life.
† Required FWHM in end of life.

Chapter 5
Physical Origin of RPs in SNRs
5.1 Our Objective and Target Selection
We analyzed XMM-Newton data of RP-SNRs, W44 and IC 443, aiming to comprehensively
understand the physical origin of RPs in SNRs. Previous studies of RP-SNRs (e.g., Okon etal., 2018; Yamaguchi et al., 2018) demonstrated that spatial comparison between distributionsof plasma parameters and that of interacting gas is a powerful tool to investigate the formation
process of RPs. These SNRs are ideal targets to carry out this study because interaction between their shock waves and ambient clouds have been studied in detail with radio and infraredobservations (e.g., Seta et al., 2004; Lee et al., 2008). W44 and IC 443 have large apparent sizesof ∼ 40′ and ∼ 65′ , respectively. In addition to a high angular resolution with XMM-Newton,
the large sizes of them help us to investigate detailed spatial variations of plasma parameters.
Throughout this chapter, errors are quoted at 90% confidence levels in the tables and text. Error
bars shown in figures correspond 1 σ confidence levels.

5.2 W445.2.1 Overview of W44
W44 (a.k.a., G34.7−0.4 or 3C 392) is a Galactic MM SNR with an estimated distance of∼ 3 kpc (Claussen et al., 1997; Ranasinghe & Leahy, 2018). The age of W44 is estimatedto be ∼ 20 kyr (Smith et al., 1985a; Wolszczan et al., 1991; Harrus et al., 1997). Wolszczan
et al. (1991) discovered a radio pulsar, PSR B1853+01, in the southern part of the remnant,indicating that W44 is a remnant of a core-collapse supernova. W44 is known to be interactingwith molecular clouds as evidenced by radio observations of OH masers 1720 MHz (Frail &Mitchell, 1998; Claussen et al., 1999) and 12 CO lines (Seta et al., 1998, 2004; Yoshiike et al.,2013). Figure 5.1 show the known interacted gas distribution Seta et al. (2004). In the Xray band, Jones et al. (1993) observed W44 with Einstein and reported that the emission is
predominantly thermal, based on the presence of Mg, Si, and S emission lines. In Suzaku data,
Uchida et al. (2012) found RRCs of Si and S, and concluded that the plasmas in the central
bright region (Figure 5.2) are in an over-ionized state.
48

5.2. W44

49

Figure 5.1: Schematic illustration of identified CO features around W44. The colors represent
the different velocity ranges of the features. The gray scale shows the radio continuum emissionof 1.4 GHz (Jones et al., 1993). The black contours represent the X-ray emission reproduced
from Rho et al. (1994). (taken from Seta et al., 2004)

Table 5.1: Observation log of W44.
TargetW44 PWN
W44
W44
W44

Obs. ID
0551060101
0721630101
0721630201
0721630301

Obs. date2009 April 24
2013 October 18
2013 October 19
2013 October 23(R.A., Dec.)(18h 56m 11s .00, + 01◦ 12′ 28′′ .0)(18h 56m 06s .99, + 01◦ 17′ 54′′ .0)(18h 56m 06s .99, + 01◦ 17′ 54′′ .0)(18h 56m 06s .99, + 01◦ 17′ 54′′ .0)

Exposure
65 ks
110 ks92 ks
93 ks

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

50

Right Ascension
18:57:00

56:30

56:00

18:57:00

55:30

(a)

56:30

56:00

(b)

55:30

18:57:00

56:30

56:00

(c)

30:00

2
4

20:00

1

3
1:10:00

Declination

55:30

0.06

0.13

0.25

0.50

1.0 0.02

0.08

0.21

0.47

1.0

Figure 5.2: MOS+pn images of W44 in the energy band of (a)(b) 0.5–4.0 keV and (c) 4.0–
8.0 keV after NXB subtraction and correction for the vignetting effect. The coordinate refers
to the J2000.0 epoch. The white contours in panel (a) indicate a radio continuum image at
1.4 GHz taken with the Karl G. Jansky Very Large Array whereas those in panel (c) are the
0.5–4.0 keV X-ray image. The source and background spectra were extracted from the regions
enclosed by the solid and dashed lines in panel (a). The source region was divided into 70
sub-regions as shown in panel (b). The regions enclosed by the green lines in panel (c) are thefour representative sub-regions whose spectra are plotted in Figure 5.3. The cyan ellipses are
regions excluded in the spectral analysis to remove bright point sources.

5.2.2 Observations and Data Reduction
W44 was observed several times with XMM-Newton from 2003 to 2013. We discarded
datasets whose effective exposures are extremely short because of flaring backgrounds, As aresult, four datasets (Obs.ID=0551060101, 0721630101, 0721630201, and 0721630301) wereleft for further analysis. The details of the observations used are summarized in table 5.1. In
what follows, we analyze data obtained with two MOS (Turner et al., 2001) and one pn (Strüder
et al., 2001) CCD cameras.
Following the cookbook for analysis procedures of extended sources1 , we reduced the datawith the Science Analysis System software version 16.0.0 and the calibration database version 3.9 released in January 2, 20172 . We estimated the non-X-ray background (NXB) with
mos-back. We generated the redistribution matrix files and the ancillary response files byusing mos-spectra. We used version 12.9.0u of the XSPEC software (Arnaud, 1996) for
the following spectral analysis. In the image analysis, we merged MOS1, MOS2 and pn data ofthe each observation for better photon statistics. In the spectral analysis, we only used the MOS
data because of their lower detector background level than the pn data.

12

ftp://xmm.esac.esa.int/pub/xmm-esas/xmm-esas.pdf
http://xmm2.esac.esa.int/docs/documents/CAL-TN-0018.pdf

5.2. W44

51

5.2.3 Analysis and Results
Imaging Analysis
Figure 5.2 shows vignetting- and exposure-corrected images of W44 taken with the EPIC
after NXB subtraction. The soft-band image in Figure 5.2(a) reveals the center-filled morphology and small bright knots as already reported by Shelton et al. (2004) based on Chandra data.
In order to perform a spatially resolved spectroscopic analysis, we applied the contour binningalgorithm (Sanders, 2006) to the 0.5–4.0 keV image, and divided the source region in Figure 5.2(a) into 70 subregions as displayed in Figure 5.2(b). The algorithm generates subregions
along the structure of the surface brightness so that each subregion has almost the same signalto-noise ratio. We manually excluded bright point sources identified in the hard band image in
Figure 5.2(c).
Background Estimation
To estimate the X-ray background, we extracted spectra from the off-source region (Figure 5.2) in the field-of-views of each observation. After subtracting the NXB from each of
the spectra, we co-added them to perform spectral fitting. The applied model consists of thecosmic X-ray background (CXB), the Galactic ridge X-ray emission (GRXE), and Al and Si
Kα lines of instrumental origin which are not included in the NXB spectra estimated with
mos-back (Lumb et al., 2002). By referring to Kushino et al. (2002), the CXB component was expressed as a power law with a photon index of 1.4 and a 2–10 keV intensity of
6.38 × 10−8 erg cm−2 s−1 sr−1 . We employed the GRXE model by Uchiyama et al. (2013),
which is composed of the foreground emission (FE), the high-temperature plasma emission(HP), the low-temperature plasma emission (LP), and the emission from cold matter (CM). We
used the Tuebingen-Boulder interstellar medium (ISM) absorption model (TBabs; Wilms et al.,2000) to estimate the column density (NH GRXE ) for the total Galactic absorption in the line ofsight toward W44. Most of the parameters of GRXE were fixed to those shown by Uchiyama etal. (2013). Free parameters are NH GRXE , kTe of the LP, and the normalization of each component.
The best-fit parameters are summarized in table 5.2. We used the best-fit model to account for
the X-ray background in the source spectra in §5.2.3.
Spectral Analysis
Figure 5.3 shows background-subtracted MOS spectra extracted from the representative
four sub-regions shown in Figure 5.2(c), where emission lines from highly ionized Ne, Mg,
Si, S, Ar and Ca are clearly resolved. The Lyα-to-Heα ratios and the continuum shape below∼ 2 keV are different from each other, suggesting significant region-to-region variations ofplasma parameters and of absorption column densities. We first fitted spectra from all 70 subregions with a CIE model. The result implies that the X-ray emitting plasma in W44 is overionized not only in a part of the remnant, as reported by Uchida et al. (2012) based on Suzaku
data of the central region, but in the whole remnant.
We then fitted all spectra with the RP model, VVRNEI (Foster et al., 2017), in XSPEC. The
model describes emission from a thermal plasma net after an abrupt decrease of the electron
temperature from kTinit to kTe under an assumption that the plasma initially was in CIE. Using
the TBabs model, we took into account photoelectric absorption by the foreground gas withthe solar abundances of Wilms et al. (2000). We allowed the column density NH , the electron

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

52

Table 5.2: Best-fit model parameters of the background spectrum of W44..
Component function
FE

Model function
TBabs (Absorption)
APEC (FElow )APEC (FEhigh )GRXE

TBabs (Absorption)
APEC (LP)APEC (HP)Power law (CM)CXB

TBabs (Absorption)
Power law

Parameter
NH FE (1022 cm−2 )kTe (keV)
Zall (solar)
NormakTe (keV)
Zall
Norma
GRXE
NH
(1022 cm−2 )kTe (keV)
ZAr
ZotherNormakTe (keV)
ZAr
Zother
Norma
Γ
Normb
NH CXBΓNormbχ2ν (ν)cValue
0.56 (fixed)
0.09 (fixed)
0.05 (fixed)
1.05+0.12−0.16
0.59 (fixed)
0.05 (fixed)≤ 1.68 × 10−3
1.71+0.10−0.03
0.56+0.03−0.03
1.07 (fixed)
0.81 (fixed)−2
1.53+0.02−0.01 × 10
6.64 (fixed)
1.07 (fixed)
0.81 (fixed)= LP Norm. × 0.29
2.13 (fixed)≤ 0.20= NH GRXE × 2
1.40 (fixed)
9.69 (fixed)
1.64 (229)∫The emission measure integrated over the line of sight, i.e., (1/4πD2 ) ne nH dl in the unit of 10−14 cm−5 sr−1 .
b
The unit is photons s−1 cm−2 keV−1 sr−1 at 1 keV.
c
The parameters χν 2 and ν indicate a reduced chi-squared and a degree of freedom, respectively.

a

Table 5.3: Best-fit model parameters of the spectra from the representative sub-regions in W44.
Model function
TBabs
VVRNEIχ2ν (ν)b

Parameters
NH (1022 cm−2 )kTe (keV)
kTinit (keV)
ZNe (Solar)
ZMg (Solar)
ZSi (Solar)
ZS = ZAr = ZCa (Solar)
ZFe = ZNi (Solar)
net (1011 cm−3 s)
NormaRegion 1
1.51+0.01−0.03
0.503+0.019−0.0031.0 (fixed)
1.29+0.06−0.07
1.55+0.07−0.05
2.68+0.09−0.05
2.1±0.1
0.14+0.02−0.01
5.3+0.2−0.1
0.048+0.005−0.0031.45 (217)

Region 2
1.43±0.07
0.55+0.04
0.03
1.0 (fixed)
0.8±0.1
1.1±0.1
1.7±0.1
1.3±0.2
0.17+0.05−0.04
6.0±0.1
0.026+0.006−0.005
1.12 (104)

Region 3
1.83±0.03
0.239+0.004−0.0021.0 (fixed)
1.7±0.1
1.5±0.1
2.6+0.2−0.1
3.1+0.4−0.2
1.1±0.1
6.0±0.2
0.11±0.04
1.57 (215)

Region 4
2.8±0.1
0.26±0.01
1.0 (fixed)
3.0±1.0
2.2+0.8−0.4
2.6+0.9−0.5
3.2±1.0
1.0+0.6−0.5
4.0±0.3
0.19+0.02−0.01
1.25 (104)∫The emission measure integrated over the line of sight, i.e., (1/4πD2 ) ne nH dl in the unit of 10−14 cm−5 sr−1 .
b
The parameters χν 2 and ν indicate a reduced chi-squared and a degree of freedom, respectively.

a5.2. W44

53

Ne

Mg

Si

1

1.0

0.1

normalized counts s 1 keV 1

0.1



Ar
Ca

0.01



10 3

0.01

10-3


10 4

Counts s-1 keV-1

S

10-4
10 5



10-5
0.6


1
1.0

2
2.0
Energy (keV)

5
5.0

7.5

Energy (keV)

Figure 5.3: MOS (MOS1 + MOS2) spectra extracted from the sub-regions 1 (black), 2 (red),3 (blue), and 4 (green), whose locations are shown in Figure 5.2(c). The NXB and X-ray
background are subtracted. For a display purpose, the spectra of Regions 3 and 4 are scaledby factors of 0.05 and 0.1, respectively. The vertical solid and dashed lines denote the centroid
energies of the Heα lines and Lyα lines, respectively.
temperature kTe , recombining timescale net, and normalization of the VVRNEI component tovary. The parameter kTinit was fixed in the fittings. We tried kTinit of 1.0 keV, 2.0 keV, 3.0 keV,and 5.0 keV, and found that the data are best reproduced with kTinit = 1.0 keV. We thus show
results obtained with kTinit fixed at 1.0 keV in what follows. We note that parameters such as NH ,kTe , and net are insensitive to the choice of kTinit . The abundances of Ne, Mg, Si, S, and Fe wereleft free, whereas Ar and Ca were linked to S, and Ni was linked to Fe. The other abundanceswere fixed to the solar values. To the model for the W44 emission, we added the backgroundmodel with the parameters fixed to those in Table 5.2. We allowed the normalizations of the
Al and Si Kα lines to vary since the line intensities are known to have location-to-location
variations on the detector plane (Kuntz & Snowden, 2008).

0.9

1.3

1.7

2.1

Figure 5.4: Reduced chi-squared map of W44.

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

54

1.01

0.1
0.1

0.1
0.1

1



(b)

data and folded modelCounts s-1 keV-1

1

normalized counts
s keV-1
Countss-1 keV

(a)
1.01



0.01
0.01

10-3
10
3


10-4
10
4

-5
10
10
44
22
00
2
-2
4
-4

χ

(data model)/error

0.6

10-3
10-4
10-5
44
22
00
-22
-44

5



0.01
0.01

1

1.0

2
Energy (keV)

2.0

5

5.0

7.5

0.6

1

1.0

Energy (keV)
(c)

5

7.5

5

7.5

(d)
1.01

0.1
0.1

0.1
0.1

Counts s-1 keV-1

Counts s-1 keV-1

5.0

Energy (keV)

1.01

0.01
0.01

10-3
10-4
10-5
44
22
00
-2
-4
0.6

2

2.0

0.01
0.01

10-3
10
3

10-4
10
4

-5
10
10
44
22
00
-22
-44
5

1

1.0

2

2.0

Energy (keV)

5

5.0

7.5

0.6

1

1.0

2

2.0

5.0

Energy (keV)

Figure 5.5: (a) MOS1 (red) and MOS2 (black) spectra from Region 1 plotted with the model
without a Gaussian for Fe L lines (see text for details). The blue, orange, and black curves
represent the RP model, the background, and the sum of the models, respectively. The black
dotted curve represent a Gaussian at 1.23 keV added to the model (the black dotted curve).
(b)–(d) Same as panel (a) but for Regions 2–4. Since Region 3 is contaminated by the southernhard source (PSR B1853+01 and its PWN), the model includes a power law shown as the green
curve. Only MOS2 data are available in Regions 2 and 4 because of malfunction of CCD chipsof MOS1.

5.2. W44

55

In the fittings, we noticed line-like residuals at ∼ 1.2 keV in most of the sub-regions. However, the used NEI plasma code takes into account of the Fe-L lines (Foster et al., 2017). The
residuals could be attributed to uncertainty in emissivity data of Fe-L lines in the code or tophysical processes such as charge exchange that are not taken into account here. While the reason for the residuals is not clear, an addition of a Gaussian at 1.23 keV significantly improved
the fits. In the case of Region 1 shown in Figure 5.5(a), the fitting statistic was improved fromχ2ν = 1.54 with ν = 218 to χ2ν = 1.45 with ν = 217. On the other hand, the addition of the Gaussian does not change the parameters obtained beyond the 90% confidence level. In the spectral
analyses, therefore, we used the model including the Gaussian.
Additional components are necessary to fit the spectra from the sub-regions where two extended hard sources are detected (Figure 5.2(c)). Nobukawa et al. (2018) pointed out that thenortheastern source, which was discovered by Uchida et al. (2012), is probably a galaxy cluster. To account for the emission, therefore, we employed a CIE model, in which the abundance
and kTe were fixed to the values as determined by Matsumura (2018) while the normalization
was left free. The southern source encompasses PSR B1853+01 and its associated pulsar wind
nebular (PWN) detected with Chandra (Petre et al., 2002). Since their X-ray emissions havefeatureless continuum spectra (Petre et al., 2002), we used a power law model for the southernsource, in which the photon index Γ and the normalization were free parameters.
All 70 spectra are well reproduced by the above RP (with an additional component) model.
In addition to the result from Region 1 in Figure 5.5(a), we plot the best-fit models overlaid on
the observed spectra from Regions 2–4 in Figure 5.5(b)–(d). In a map in Figure 5.4, we present
χ2ν values of each sub-region, which range from 0.98 to 2.15. Among all 70 sub-regions, 20
sub-regions have χ2ν ≥ 1.5, and 4 sub-regions have χ2ν ≥ 2.0.

5.2.4 Discussion on W44
Foreground Gas Distribution
The X-ray absorption column densities (NH ) obtained from the spectral fittings present a
tool to probe the spatial distribution of the gas in front of W44. Figure 5.6 shows a map of NH ,where a significant spatial variation is clearly visible. The values, ranging from 1.3×1022 cm−2
to 2.8×1022 cm−2 , are roughly consistent with the previous studies with Suzaku by Uchida etal. (2012) and Matsumura (2018), but the present map revealed a spatial distribution in muchfiner angular scales. We found that the X-ray absorption column densities are higher in theouter regions and are peaked in the northwestern rim. Based on CO line data, Seta et al. (2004)
estimated the column density of foreground gas of ∼ 1 × 1022 cm−2 and ∼ 2 × 1022 cm−2 inthe inner and outer regions, respectively, which agree well with our X-ray results. Note that
the ISM around W44 is dominated by molecular gas and that the contribution from atomic gas
amounts to only ∼ 10% of the total mass (Yoshiike et al., 2013). In the northwestern region
with the highest X-ray absorption column density, it is known that a giant molecular cloud in
the near side of W44 was hit by the SNR shock (Seta et al., 2004). When we select a velocity
range of 40–50 km s−1 , which includes the most of the gas in the giant molecular cloud, theCO contours show almost a perfect match with the X-ray column density map (Figure 5.6(b)).
According to Seta et al. (2004), the foreground gas in the northeastern rim has a column densityof NH ∼ 3 × 1022 cm−2 , which is again consistent with the values estimated from our X-ray
analysis.

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

56
(a)

(b)

1.4 GHz Radio continuum

1.2

1.5

1.8

12CO(J=1–0) VLSR = 40–50 km s-1

2.1

Absorption column density NH

2.4

2.7
(1022 cm-2)

N

Figure 5.6: Distribution of X-ray absorption column density NH . The same radio continuum
image as that in Figure 5.2(a) are overlaid as cyan contours in panel (a). The green contours
in panel (b) denote 12 CO(J = 1–0) emissions in a velocity range of VLSR = 40–50 km s−1 asobserved with the Nobeyama 45 m radio telescope in the FUGIN project (Umemoto et al.,2017).
Physical Origin of RPs on W44
We now discuss the physical origin of the RPs in W44 based on spatial distributions of
the parameters such as kTe and net, and their comparison with interacting gas distributions.
Figure 5.7(a) shows a kTe map. In panel (a-ii), we overlaid a 12 CO(J = 2–1)-to-12 CO(J = 1–0)
intensity ratio map. The line ratio serves as a good indicator of shock-cloud interactions. A
ratio well above the typical value in the unshocked part of the cloud, 0.6, indicates that the gas
is shocked and/or heated (Yoshiike et al., 2013). The electron temperature kTe tends to be lower
at the locations where the 12 CO(J = 2–1)-to-12 CO(J = 1–0) ratio is higher. Similar tendencies
were found also in other MM SNRs with RPs, IC 443 and W28 (Matsumura et al., 2017b; Okon
et al., 2018). Those authors claimed that the tendencies are most probably explained by thermalenergy exchanges between the plasmas and clouds via thermal conduction (Zhang et al., 2019).
Thus, our result on W44 would also be suggestive of significant thermal conduction between
the X-ray emitting plasma and interacting gas.
Information from another parameter, net, whose spatial distribution is presented in Figure 5.7(b), has revealed far more convincing evidence for thermal conduction. In Figure 5.8,
we plot kTe and net derived for each sub-region. The data points are divided into two groups.
The blue points come from regions where Seta et al. (2004) discovered 12 CO(J = 1–0) lines
broader than ∆V = 7 km s−1 in full width at half maximum (see panels (a-iii) and (b-iii) of
Figure 5.7 and also Figure 5.8(a) for the locations), referred to as spatially extended moderately
broad emission (SEMBE) by Seta et al. (2004). The red points, on the other hand, are from theother regions. The two groups are clearly separated from each other, and each of the two groups
shows a clear anti-correlation between kTe and net.

5.2. W44

57

The result in Figure 5.8(b) can be well understood in a context of the thermal conduction
scenario as follows. Let us assume that the X-ray emitting plasma initially had an ionization
degree close to CIE (net ∼ 1012 cm−3 s) and an electron temperature of kTinit ∼ 1 keV as we
assumed in the spectral fittings in 5.2.3. After the shock encountered the molecular cloud, theplasma was rapidly cooled due to thermal conduction. At this point, the plasma switched into
an over-ionized state since the cooling proceeded in a timescale shorter than the recombination
rate. Once the cooling rate became slower, recombination started to dominate to make theionization degree gradually approach CIE. What we are currently observing in W44 would beemission from the plasma in this phase. Figure 5.8(c) presents schematic trajectories of theplasma on the kTe -net plane in the above scenario. The clear separation between the SEMBE
and non-SEMBE regions suggests that the plasma was more efficiently cooled in the SEMBE
regions.
Although the nature of the SEMBE is not clear yet, a plausible interpretation would be that
the SEMBE is emitted by unresolved dense clumps shocked and disturbed by the SNR shock(Seta et al., 2004; Sashida et al., 2013) (Figure 5.9). Since those clumps are embedded in
the hot X-ray emitting plasma, cloud evaporation would occur through thermal conduction between the plasma and the clumps, making the plasma in the SEMBE regions efficiently cooled.
Cloud evaporation in SNRs are numerically studied with hydrodynamical simulations (e.g.,
Zhou et al., 2011; Zhang et al., 2019) as well as with magneto-hydrodynamical simulations(e.g., Orlando et al., 2008). According to the result by Zhang et al. (2019), cloud evaporation plays a role in rapid cooling of hot plasma and thus also in over-ionization. Sashida etal. (2013) estimated the clumps in the SEMBE region have a size of ≪ 0.3 pc. The typicalevaporation timescale of the clumps through thermal conduction can be evaluated as tevap ≈5.4 × 1010 (ne /1 cm−3 )(l/1 pc)2 (kTe /1 keV)−5/2 s ≪ 1011 s (e.g., Orlando et al., 2005) , assuming the plasma density ne = 1 cm−3 , the clump size l ≪ 0.3 pc, and the average plasma
temperature kTe = 0.3 keV. The evaporation timescale is sufficiently smaller than the timescale
for a plasma to reach CIE (tCIE ≈ 1012 (ne /1 cm−3 )−1 s), and, therefore, cloud evaporation canmake the plasma over-ionized. ALMA would be able to resolve dense clumps of the SEMBE
gas in W44 as pointed out by Sashida et al. (2013). Spatially resolved spectroscopy in X-rays
with angular scales similar to that of ALMA then should observationally reveal the process ofcloud evaporation and resulting over-ionization.

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

58

(a-i)

(a-ii)(a-iii)12CO J=2–1/J=1–0
VLSR = 30–40 km s-1
VLSR = 40–50 km s-1

SEMBE

.10

34

1.4 GHz Radio continuum

0

0.2

0.3

0.4

0.5

0.6
(keV)

Electron temperature kTe(b-i)(b-ii)(b-iii)12CO J=2–1/J=1–0
VLSR = 30–40 km s-1
VLSR = 40–50 km s-1

SEMBE

.10

34

1.4 GHz Radio continuum

0

3.5

4.7

6.3

Recombination timescale net

8.5

11.4
(1011 cm-3 s)Figure 5.7: Maps presenting the distributions of (a) kTe and (b) net. The white contours in
the panels (a-i) and (b-i) indicate the same radio continuum image as that in Figure 5.2(a). The
green and magenta contours in panels (a-ii) and (b-ii) denote a 12 CO(J = 2–1)-to-12 CO(J = 1–0)
intensity ratio map drawn every 0.1 from 0.7 in VLSR = 30–40 km s−1 and VLSR = 40–50 km s−1
taken from Yoshiike et al. (2013). The velocity ranges correspond to that of the giant molecular
cloud interacting with W44. In panels (a-iii) and (b-iii), the cyan contours denote the halfintensity line width diagram for the 12 CO(J = 1–0) in VLSR = 20–60 km s−1 obtained with theNobeyama 45 m radio telescope by Seta et al. (2004). Each contour represents 7, 10, and
13 km s−1 .

5.2. W44

59

1.2

0.6

1.0

SEMBE
regionkTe (keV)

kTe (keV)

0.5

0.4

0.3

0.2

0.8 SEMBE
region
0.6
0.4

SEMBE
region
3.0

4.0

0.2
5.0

6.0

7.0

8.0

2.0

9.0

net (1011 cm-3 s)

5.0

10

20

40

net (1011 cm-3 s)Figure 5.8: (a) Same as Figure 5.2(a) but with the definition of the SEMBE regions in cyan. (b)Relationship between net and kTe . The blue points are from the SEMBE regions whereas thered points are from the other regions. (c) Schematic trajectories of plasma during its evolution
after a shock-cloud collision. The color scheme is the same as that of panel (b). The shaded
area corresponds to the range plotted in panel (b).

wing gasquiescent
gas

SEMBE

cores
shock front

W44 GMC
Figure 5.9: Schematic view of the W44 blast wave interacting with the giant molecular cloud(GMC).

60

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

Figure 5.10: (left) Multi-wavelength view of IC 443. The red, green, and, blue correspond to
optical (670 nm) taken with the Second Palomar Observatory Sky Survey, 1.4 GHz radio takenby the DRAO Synthesis Telescope, and 0.1–2.4 X-ray images taken by ROSAT, respectively.
The bright source at the west of IC 443 is a star (Gaensler et al., 2006). The cyan boxes indicate
three fields covered by Suzaku. (b) Maps of normalization ratio of cold RPs (kTe ∼ 0.15–
0.30 keV) to hot RPs (kTe ∼ 0.4–0.6 keV) obtained with Suzaku data. The red contours show
the 12 CO(J = 2–1) intensity ratio intensity ratio (Yoshiike, 2017). (taken from Matsumura etal., 2017b)

5.3 IC 443
5.3.1 Overview of IC 443
IC 443 (a.k.a., G189.1+3.0) is a Galactic MM-SNR at a distance of ∼1.5 kpc (Welsh & Sallmen, 2003) toward the Galactic anticenter. The age of IC 443 is estimated to be ∼ 20–30 kyr(Olbert et al., 2001; Lee et al., 2008). Olbert et al. (2001) found a PWN 1SAX J0617.1+2221
in the southeastern part of the remnant, suggesting the SNR is of a core-collapse origin. IC 443
is known to be interacting with dense clouds through detections of 12 CO lines (Denoyer, 1979;
Xu et al., 2011) and H2 emissions (Rho et al., 2001; Kokusho et al., 2020). Figure 5.11 showsa spatial distribution of ambient clouds traced by 12 CO lines (Lee et al., 2012). Previous observations of IC 443 with Einstein revealed a centrally concentrated X-ray morphology and thepresence of thermal emissions from the bright center (Petre et al., 1988). Kawasaki et al. (2002)
claimed that the ionization degree of the plasma is higher than that expected in CIE based on ameasurement of the Lyα to Heα line intensity ratio with ASCA, as summarized in Section 3.1.3.
Yamaguchi et al. (2009) discovered RRCs of Si and S in Suzaku data, and showed unequivocal
evidence of RPs in IC 443. Subsequent observations with Suzaku revealed that that heavier ionssuch as Ca and Fe are also in the over-ionized state (Ohnishi et al., 2014).
The formation process of RPs in IC 443 has been discussed by some authors such as Matsumura et al. (2017b), Greco et al. (2018), and Hirayama et al. (2019). Matsumura et al. (2017b)
found a tendency that the plasma temperature is lower in the region where the shock waves interact with ambient clouds. They claimed that this result is caused by a rapidly cooling of the5.3. IC 443

61

23◦ 00cniioRadio Continuum Halo

C

δ2000

22◦ 4522◦ 30koc
shA

molecular shockB

22◦ 1510 (23 pc)
6h 19m6h 18m6h 17mα2000

6h 16m6h 15mFigure 1. (a) Schematic showing the overall morphology of IC 443 adopted

Figure 5.11: (left) Three color (red, green and blue) maps of the integrated intensity of 12 CO(J =1–0) line obtained with the FCRAO 14 m telescope. The difference of the colors corresponds
to the difference of radial velocities of the identified CO clouds. The white contours show HI
image taken with the Very Large Array. (right) Schematic view of the shell morphology ofIC 443. The asterisk indicates the position of PWN 1SAX J0617.1+2221. (taken from Lee etal., 2012)
plasma due to thermal conduction with interacting clouds, and the same mechanism can account for RPs as well. With XMM-Newton data, Greco et al. (2018) claimed that an adiabatic
expansion in rarefaction scenario proposed by Itoh & Masai (1989) and Shimizu et al. (2012)is responsible for the over-ionization. Their analysis showed that metal-rich plasma, which isinterpreted as an ejecta dominant plasma, is in a strongly over-ionized state. Hirayama et al.
(2019) focused on the neutral Fe line which would be due to K-shell ionization of Fe atoms in
the gas by sub-relativistic protons accelerated in IC 443 (Nobukawa et al., 2019), and proposeda new scenario that is completely different from the above two scenarios. In this scenario, subrelativistic protons promote ionization of ions in plasma and generate RPs. Given ionization
cross sections for them, such protons can more efficiently ionize them than electrons in the
SNR plasma. These authors’ claims contradict each other and the physical origin of RPs havebeen still under debate.
In the case of W44, we found that kTe and net of RPs is in the region where the shock isinteracting with molecular clouds (Section 5.2). This finding indicate an efficiently cooling
via thermal conduction between X-ray emitting and the cold dense gas as the origin of theover-ionization. Therefore, if thermal conduction between SNR plasma and ambient clouds is
responsible for RPs in IC 443 as the same as the W44 case, we would expect RPs in a strongly
over-ionized sate in the shock-cloud regions.

5.3.2 Observations and Data Reduction
IC 443 was observed with XMM-Newton several times from 2003 to 2013. Table 5.4 summarizes the details of the used observations. Once all the observations are combined, the entire

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

62

Table 5.4: Observation log of IC 443.
TargetIC 443
IC 443
IC 443
IC 443
IC 443
IC 443
IC 443
IC 443Obs. ID
0114100101
0114100201
0114100301
0114100401
0114100501
0114100601
0301960101
0600110101

Obs. date
2000-09-26
2000-09-25
2000-09-27
2000-09-28
2000-09-25
2000-09-27
2006-03-30
2010-03-17(R.A., Dec.)(6h 17m 27s .99, 22◦ 41′ 44′′ .0)(6h 16m 14s .99, 22◦ 41′ 60′′ .0)(6h 17m 27s .99, 22◦ 25′ 14′′ .0)(6h 16m 14s .99, 22◦ 18′ 02′′ .5)(6h 16m 14s .99, 22◦ 41′ 60′′ .0)(6h 17m 27s .99, 22◦ 25′ 14′′ .0)(6h 18m 04s .29, 22◦ 27′ 33′′ .0)(6h 17m 06s .00, 22◦ 43′ 24′′ .0)

Exposure
11 ks
5 ks
22 ks
23 ks
15 ks
4 ks
46 ks
26 ks

region of IC 443 is completely covered by the field of view of XMM-Newton. In what follows,
we analyze data obtained with the MOS and pn CCD cameras.
We reduced the data with the Science Analysis System software version 16.0.0, following
the cookbook for analysis procedures of extended sources3 . We used the calibration database
version 3.9 released in 2017 January 2.94 . We generated the redistribution matrix files and theancillary response files by using mos-spectra. In the image analysis, we merged MOS1,
MOS2, and pn data of the each observation for better photon statistics, whereas, in the spectral
analysis, we only used the MOS data because of their lower detector background level than thepn data.

5.3.3 Analysis and Results
Imaging Analysis
Figure 5.12 shows vignetting- and exposure-corrected images of IC 443 in the energy bandsof 0.5–4.0 keV and 4.0–8.0 keV. The source region is overlaid in Figure 5.12(a). To performspatially resolved spectroscopic analysis, we applied the same method as that used in the image
analysis of W44. We applied the contour-binning algorithm (Sanders, 2006) to the 0.5–4.0
keV image, and divided the source region into 110 subregions as displayed in Figure 5.12(b).
We found the PWN 1SAX J0617.1+2221, its PSR, and some bright point sources in the the4.0–8.0 keV image (Figure 5.12(c)), which are reported by Bocchino & Bykov (2003). For
the following spectral analysis, we manually excluded the identified point sources whereas we
performed a model fitting of X-rays from the PWN and its PWN according to the work by
Bocchino & Bykov (2003).
Background Estimation
For X-ray background estimation, we used spectrum extracted from the source-off region in
Figure 5.12(c). After subtracting the non-Xray background (NXB) estimated with mos-backfrom the spectra, we fitted the spectra with a model consisting of the X-ray background modelby Masui et al. (2009) who studied the soft X-ray emission from the the Galactic anticenter. The
model consists of the cosmic X-ray background (CXB), the local hot bubble (LHB), two thermal
34

ftp://xmm.esac.esa.int/pub/xmm-esas/xmm-esas.pdf
http://xmm2.esac.esa.int/docs/documents/CAL-TN-0018.pdf

5.3. IC 443

63

(a)

(b)
18:00

17:00

16:00

6:19:00

(c)
18:00

17:00

16:00

6:19:00

18:00

40:00 22:50:00

6:19:00

17:00

16:00

2

30:00

3

10:00

20:00

1

0.02

0.06

0.25

1.0 0.001

0.03

0.2

1.0

Figure 5.12: MOS+pn images of IC 443 in the energy band of (a)(b) 0.5–4.0 keV and (c) 4.0–
8.0 keV after NXB subtraction and correction for the vignetting effect. The coordinate refers to
the J2000.0 epoch. The cyan contours in panel (a) indicate a radio continuum image at 1.4 GHz
taken with the the NRAO VLA Sky Survey whereas those in pane (c) are the 0.5–4.0 keV Xray image. The source and background spectra were extracted from the regions enclosed by thesolid and dashed lines in panel (a). The source region was divided into 110 sub-regions as shownin panel (b). The regions enclosed by the green lines in panel (c) are the three representative
sub-regions whose spectra are plotted in Figure 5.13. The cyan ellipses are regions excluded in
the spectral analysis to remove bright point sources. The magenta arrow indicates PWN 1SAX
J0617.1+2221.
components for the Galactic halo (GHcold and GHhot ). The photon index of the CXB component
was fixed to 1.4 in Kushino et al. (2002) whereas the normalization and the column density(NHCXB ) for the total Galactic absorption were allowed to vary. We used the Tuebingen-Boulderinterstellar medium absorption model (TBabs; Wilms et al., 2000) for the interstellar absorption.
Most of the parameters of the LHB, GHhot , and GHcold models were fixed to values given by
Masui et al. (2009), whereas we sat the electron temperature kTe of GHhot and the normalizationof each component as free parameters. We used additional two Gaussian components to model
neutral Al and Si Kα lines of instrumental background, which are not included in the NXB
spectra (Lumb et al., 2002). The normalization of the Al and Si Kα lines were allowed to vary.
The best-fit parameters are summarized in Table 5.5. In the subsequent spectral analysis, weused the best-fit model to account for the X-ray background.
Spectral analysis
Figure 5.13 shows spectra extracted from the representative regions in Figure 5.12(c). One
can clearly see resolved emission lines from highly ionized O, Ne, Mg, Si, S, and Ar ions, andthe different Lyα-to-Heα intensity ratio and the continuum shape in each spectrum. The different spectral features, as demonstrated in the W44 case, indicate significant region-to-region
variations of plasma parameters and of absorption column densities toward IC 443. When we
tried a collisional ionization equilibrium (CIE) model for all spectra from 110 subregions, almost all fittings left apparent hump-like residuals at ∼ 2.7 keV and ∼ 3.5 keV, which correspondCHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

64

Table 5.5: Best-fit model parameters of the background spectrum of IC443.
Component function
GH

Model function
APEC (GHcold )APEC (GHhot )

LHB

APEC

CXB

TBabs (Absorption)
Power law

ParameterkTe (keV)Norma
kTe (keV)Norma
kTe (keV)Norma
NH CXBΓNormbχ2ν (ν)c

Value
0.658 (fixed)
12.5 ± 1.2
1.22 ± 0.02
66.8+5.7−6.9
0.105 (fixed)
45.1+7.7−7.6
0.60+0.06−0.05
1.40 (fixed)
12.1+1.3−1.1
1.44 (187)∫The emission measure integrated over the line of sight, i.e., (1/4πD2 ) ne nH dl in the unit of 10−14 cm−5 sr−1 .
b
The unit is photons s−1 cm−2 keV−1 sr−1 at 1 keV.
c
The parameters χν 2 and ν indicate a reduced chi-squared and a degree of freedom, respectively.

a

Table 5.6: Best-fit model parameters of the spectra from the representative sub-regions in
IC443..
Model function
TBabs
VVRNEI(RP comp)

APEC(CIE comp)χ2ν (ν)b

Parameters
NH (1022 cm−2 )kTe (keV)
kTinit (keV)
ZO (Solar)
ZNe (Solar)
ZMg (Solar)
ZSi (Solar)
ZS = ZAr = ZCa (Solar)
ZFe = ZNi (Solar)
net (1011 cm−3 s)NormakTe (keV)
Zall (Solar)
Norma

Region 1
1.02+0.4−0.03
0.24 ± 0.02
5.0 (fixed)
0.4 ± 0.1
0.9±0.2
0.7±0.1
0.4±0.1
0.7+0.2−0.1
0.24+0.07−0.08
4.5+0.3−0.2
0.3+0.009−0.0071.07 (224)

Region 20.82±0.04
0.22+0.03
0.02
5.0 (fixed)
0.5±0.2
0.7±0.2
0.7±0.2
1.0+0.3−0.2
1.3±0.2
0.5±0.1
13.0+1.4−1.3
0.13±0.03
0.98 (224)

Region 3 (RP)0.82±0.03
0.35±0.02
5.0 (fixed)
0.7±0.2
1.1±0.2
0.8±0.1
1.2±0.2
1.1±0.2
0.30±0.05
6.1±0.3
0.15±0.02
2.08 (224)

Region 3 (RP+CIE)
0.90±0.01
0.26±0.02
5.0 (fixed)< 1.6
1.6±0.2
1.1+0.1−0.2
1.8±0.2
1.3±0.2
0.4±0.1
5.5+0.4−0.3
0.07±0.01
0.22+0.09−0.08
1.0 (fixed)
0.11+0.02−0.03
1.39 (222)∫
The emission measure integrated over the line of sight, i.e., (1/4πD2 ) ne nH dl in the unit of 10−14 cm−5 sr−1 .
b
The parameters χν 2 and ν indicate a reduced chi-squared and a degree of freedom, respectively.

a5.3. IC 443
100

65
100

Ne
Mg

10

10

O

Si

Ar

1

1.0

0.1

Ca
0.1

0.01

Counts s-1 keV-1

S

0.01

10

10–3
0.5

0.5

1

1.0

2

2.0

5

5.0

Energy (keV)

Figure 5.13: MOS (MOS1 + MOS2) spectra extracted from the sub-regions 1 (black), 2 (red),3 (blue), and 4 (green), whose locations are shown in Figure 5.12(c). The NXB and X-ray
background are subtracted. For a display purpose, the spectra of Regions 3 and 4 are scaledby factors of 0.05 and 0.1, respectively. The vertical solid and dashed lines denote the centroid
energies of the Heα lines and Lyα lines, respectively.
to the edges of the H-like Si and H-like S RRCs, respectively. The result implies that the X-ray
emitting plasma is in over-ionized state not only in a part of IC 443 reported by the previous
works (e.g., Matsumura et al., 2017b; Greco et al., 2018), but also almost in the whole remnant.
We then fitted all spectra with the VVRNEI (Foster et al., 2017) model implemented in the
XSPEC software version 12.10.1f (Arnaud, 1996). To take account for photoelectric absorption
by the foreground gas, we applied the TBabs model with the solar abundances (Wilms et al.,2000). We allowed the column density NH , the present electron temperature kTe , recombining
timescale net, and normalization of the VVRNEI component to vary. The initial plasma temperature kTinit in the spectral fittings is constrained to be ≥ 5 keV, in which, except for Fe, ions such
as O–S are almost fully ionized. We fixed the initial plasma temperature kTinit at 5 keV becauseparameters such as NH , kTe , and net are insensitive to the choice of kTinit . The abundances of O,
Ne, Mg, Si, S, and Fe were left free, whereas Ar and Ca were linked to S, and Ni was linked to
Fe. The abundances of the other elements were fixed to solar. In spectral fittings of the subregions where PWN 1SAX J0617.1+2221 or its pulsar are observed, we applied a model which
consists of the VVRNEI model and an additional power law to account for emission from them.
The photon index Γ and the normalization of the power law component were free parameters.
We allowed the Al and Si Kα line intensity to vary since the line intensities are known to havelocation-to-location variations on the detector plane (Kuntz & Snowden, 2008).
Most spectra from all subregion are well reproduced by the RP model (or the RP modelwith the additional power law). In Figure 5.14(a) and (b), we show the results of the fittings inRegions 1 and 2 indicated in Figure 5.12. We also present a map of χ2ν obtained with all spectral
fittings in Figure 5.15(c-i). Among 110 subregions, 36 sub-regions have 2.0 > χ2ν ≥ 1.5, and17 subregions have χ2ν ≥ 2.0. The locations of all χ2ν ≥ 2.0 subregions are enclosed by the cyanline in Figure 5.15(a). Figure 5.14(c-i) shows the spectral fitting in Region 3, which is one of

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

66

(a)

(b)

data and folded model

data and folded model-1
Countss-1 keVnormalized counts
s keV

1.01
1

1

-1
Countss-1 keVnormalized counts
s keV

1.01

0.01
0.01


10–3
10
3

0.01
0.01


10–3
10
3


10–4
10
4


10–4
10

44
22

44
22

4

(data model)/error(data model)/error

0.1
0.1

1

1

0.1
0.1

00
–22

00
–22

–44

–44

0.5

0.5

1

1.0

2
Energy (keV)

2.0

5

0.5

5.0

0.5

1

1.0

Energy (keV)(c-i)

data and folded model

data and folded model

1-1
Countss-1 keVnormalized counts
s keV

0.1
0.1

1

1

5

5.0

1.01

1

-1
Countss-1 keVnormalized counts
s keV

2.0

Energy (keV)(c-ii)

1.01

0.01
0.01


10–3
10
3

0.1
0.1

0.01
0.01


10–3
10
3


10–4
10
4


10–4
10

4
22

4
22

4

4
0

(data model)/error

4(data model)/error

2
Energy (keV)

00
–22
–44

00
–22
–44

0.5

0.5

1

1.0

2
Energy (keV)

2.0

Energy (keV)

5

5.0

0.5

0.5

1

1.0

2
Energy (keV)

2.0

5

5.0

Energy (keV)

Figure 5.14: (a) MOS1 (red) and MOS2 (black) spectra from Region 1 plotted with the model.
The blue and black curves represent the RP model and the sum of the models for MOS1 data,
respectively. The red line represent the sum of the models for MOS2 data. (b)–(c) Same as
panel (a) but for Regions 2–3. In Region 3, the green curve show the CIE component.

5.3. IC 443

67

(a)

.8
0.8

(b)

0.98

1.2
1.2

1.3

1.5
1.5

1.7

1.9
1.9

2.1

2.2
2.2

2.4

2.
2.6

Figure 5.15: (a) Reduced chi-squared map with the single-RP model. The cyan curve indicatesthe χ2ν ≥ 2.0 subregions. (b) Same as (a) but for the RP+CIE model.
the χ2 ≥ 2.0 subregions. The fitting left remarkable residuals at ∼ 1.0 keV around H-like Ne
Lyα line and ∼ 2.0 keV around H-like Si Lyα line, suggesting that required ion populationof ions are different between the soft-band and hard-band. We obtained similar results in all
fitting with χ2ν ≥ 2.0 subregions. Using Suzaku data, Matsumura et al. (2017b) reported thata cold ISM component is not negligible in addition to the hot RP. Greco et al. (2018) showedsimilar fitting results with XMM-Newton data. Following the previous works, we add the CIEof the ISM origin to the RP model. The CIE+RP model can explain well the overall spectrumof Region 3 in Figure 5.13(c-ii), and the fit statistic was improved from χ2ν = 2.08 with ν = 225
to χ2ν =1.39 with ν = 223. We applied the CIE+RP model for spectral fitting in all χ2ν ≥ 2.0
subregions. Figure 5.15(b) presents a map of χ2ν , and all subregions finally have χ2ν ≤ 2.0.

5.3.4 Discussion on IC 443
Foreground Gas Distribution
In a map in Figure 5.16, we present the X-ray absorption column density NH of each subregion. The map shows higher values in sub-regions where the 12 CO(J = 1 − 0) line is detectedwith the NANTEN2 telescope (Yoshiike, 2017). The match between the 12 CO contours and
NH , pointed out first by Matsumura et al. (2017b), supports an interpretation that most of thegas traced by the CO line present in front of IC 443. We roughly estimated the column densityof the foreground gas to be ∼ 0.6 × 1022 cm−2 by subtracting the low NH in the 12 CO line notobserved sub-regions from the high one in the 12 CO line observed sub-regions. Yoshiike (2017)
estimated the column density NH, CO ∼ 0.6 × 1022 cm−2 of the gas with the CO data of NANTEN2. Given that the amount of the atomic gas traced by HI emissions is less than that of thegas traced by the CO line (Yoshiike, 2017), our measurement can be regarded to be consistent
with the radio one.

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

68

0.30

0.48

0.66

0.84

1
1.02

1.1

1
1.20

Figure 5.16: Distribution of X-ray absorption column density NH . The cyan contours denote
12
CO(J = 1–0) emissions in a velocity range of VLSR = −18–+2 km s−1 as observed with obtained from the NANTEN2 (Yoshiike, 2017).
Physical Origin of RPs on IC 443
Matsumura et al. (2017b) reported that the decrease of kTe in the shock-cloud region is mostprobably caused by a thermal energy exchange between the plasma and the clouds. They also
claimed that a cooling by the thermal energy exchange can generate RPs in IC 443 as well. In
Figure 5.17, we present maps of kTe and net, and overlay the 12 CO(J = 2−1) to 12 CO(J = 1−0)
intensity ratio (Yoshiike, 2017) and H2 1–0 S(1) line contours, which are good indicators ofshock-cloud interactions. In Figure 5.18, we showed the values of kTe and net derived for each
sub-region, and divided data points into red and blue groups. The red points are from on-cloudsubregions where the 12 CO line ratio or H2 emissions are detected, whereas the blue points arefrom the other subregions. The maps and plot revealed that RPs in the on-cloud subregions tend
to have smaller kTe and net. In the context of the plasma cooling proposed by Matsumura et al.
(2017b), this tendency is naturally interpreted as the result of rapid cooling.
It is notable that our results on IC 443 is similar to the W44 case. Regions with lower kTe
and net in W44 completely coincide with the locations where spatially extended broad 12 CO
line, so called SEMBE, is observed (Subsubection 5.2.4). Although the nature of SEMBE is
not clear yet, the emission is considered to be from small clumps (≪ 0.3 pc) disturbed after theshock propagation (Seta et al., 2004; Sashida et al., 2013). Based on the observational results,
we pointed out that hot plasma is efficiently cooled by the evaporation of the clumps via thermal conduction (Subsubsection 5.2.4). The noteworthy facts suggest that the same mechanism
accounts for the kTe and net tendency in IC 443.
Charge fractions for each ion species, computed with Equation 3.10, and kTe and net, areparameters which enable us to directly evaluate the over ionization degree in RPs. Following
the theoretical work by Zhang et al. (2019), we used the average charge of ions CRP in RPs, and5.3. IC 443

69

the deviation of the average charge ∆C from the CIE state with the same kTe ,
∑
C=
ci Fi
∆C = CRP (kTe , net, kTinit = 5 keV) −CCIE (kTe ),

(5.1)
(5.2)

where ci and Fi are the charge number and fraction of i-times ion, respectively. Larger ∆Cwould be expected in RPs in a strongly over-ionized state.
Figure 5.19(a-i)-(e-i) and (a-ii)-(f-ii) show CRP and ∆C values as functions of net and kTe ,respectively. We overlay the same kTe -net plot as Figure 5.18 on the CRP and ∆C maps. In
Figure 5.19(a-iii)-(f-iii), we present maps of ∆C computed with the best-fit values. RPs in
the on-cloud sub-regions tend to have larger ∆C for Ne-Si ions, which is consistent with theinterpretation of over-ionization by the rapid cooling in the thermal conduction scenario. On
the other hand, the ∆C map for Fe ions shows a different tendency from that of Ne-S ions. The∆C of Fe ions is larger in RPs with higher kTe and smaller net, which seems to be difficult to
explain by simple thermal conduction between the molecular clouds and plasma. In order todiscuss ∆C in more detail, spectral analysis taking account for SNR evolution would be helpful.
For instance, we assumed that plasma initially was in a CIE state and its ionization state isuniform over the entire remnant, but two condition would be not realistic. Inhomogeneous gas
distribution around SNRs should be considered as discussed in Ustamujic et al. (2020).
Another plausible formation process of RPs is a rapid cooling through adiabatic expansion.
Yamaguchi et al. (2018) found a clear positive correlation between kTe and net in W49B, whichis naturally interpreted as the result of the efficient cooling in a rarefied region with a lower
density. IC 443 has northeast and southwest shells with different radii, which reflect an ambientgas density (e.g., Lee et al., 2008). The kTe -net plot in IC 443 shows not a positive but roughly
negative correlation as shown in Figure 5.18. This tendency is indeed similar to the W44 casewhere Okon et al. (2020) claimed the thermal conduction scenario as the formation processof RPs. The rarefaction scenario cannot naturally explain the spatial variation of ∆C. If weconsider rarefaction as the formation process of RPs, larger ∆C would be in the southwest
region with a low ambient gas density.
We also test the possibility of the over-ionization caused by bombardment of sub-relativistic
protons proposed by Hirayama et al. (2019). Figure 5.20 summarizes the Si ion population in
RPs with typical parameters obtained, kTe = 0.3 keV, net = 6.0 × 1011 cm−3 s, and kTinit =5.0 keV, and that in CIE plasma with the same kTe . To explain the strong H-like Si RRC in the
IC 443 spectra, He-like Si ions must be ionized to H-like Si by sub-relativistic protons.
Let us estimate the required energy density of sub-relativistic protons under the condition
that the ionization by the proton bombardment proceeds faster than the relaxation toward CIE
state. The ionization rate ξ and the energy density ϵp can be described as follows,
∫
dnp
dE,
(5.3)
ξ = σi v
dE∫
dnp
ϵp = E
dE,(5.4)
dE
where σi is ionization cross section from He-like Si to H-like Si ion by proton impacts. Assuming the LECRps spectrum dnp /dE ∝ E −2 expected in diffusive shock acceleration at a strong
shock, the ξ and ϵp can be estimated as)( np
× 4.4 × 10−12 s−1 ,
(5.5)
ξ∼
−3
1.0 cmCHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

70

)
np
× 1.2 MeV/cm3 ,(5.6)
1.0 cm−3where the n p is the LECRp density integrated from the energy range from 0.2 MeV to 200 MeV
corresponding to the integral range of equations 5.3 and 5.4. Smith & Hughes (2010) computed
the characteristic timescale toward CIE state at
(
)−1
ne
Λ∼
× 1012 s.
(5.7)−3
1.0 cmϵp ∼(If ξ is larger than Λ−1 , the ionization proceeds faster than the relaxation toward the CIE state.
To realize this condition, the LECRp density n p and energy density ϵ p are required to be≥ 0.22 cm−3 and ≥ 0.24 MeV cm−3 if ne is 1.0 cm−3 . If protons are filled in the entire IC 443,
whose volume is assumed to be a sphere with a radius of ∼ 10 pc, the total proton energy exceeds the typical kinetic energy (∼ 1051 erg) in SNe. Our estimation indicates that the ionization
by LECRp is difficult to generate RPs.

5.3. IC 443

71

(a-i)

(a-ii)

1.4 GHz

(a-iii)

H2

12CO line ratio

VLSR = –60 - –6 km s-1
VLSR = –6 - +20 km s-1

0.13

0.26

0.39

0.52

0.65

8.0

13

kTe (keV)(b-i)(b-ii)

1.4 GHz(b-iii)12CO line ratio

H2

VLSR = –60 - –6 km s-1
VLSR = –6 - +20 km s-1

3.6

4.3

5.5
net (1011 cm–3s)

Figure 5.17: Maps presenting the distributions of (a) kTe and (b) net. The cyan contours in thepanels (a-i) and (b-i) indicate the same radio continuum image as that in Figure 5.12(a). The
green and magenta contours in panels (a-ii) and (b-ii) denote a 12 CO(J = 2–1)-to-12 CO(J = 1–0)
intensity ratio map drawn every 0.8 from 1.0 in VLSR = −6–20 km s−1 and VLSR = −60–6 km s−1
taken from Yoshiike et al. (2013). In panels (a-iii) and (b-iii), the white contours denote H2 1–0
S(1) lines taken with the near-IR camera Simultaneous Infrared Imager for Unbiased Survey
installed on the InfraRed Survey Facility 1.4 m telescope (Kokusho et al., 2020).

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

72

0.7

kTe (keV)

0.6
0.5
0.4
0.3
0.2
4.0

6.0

8.0

10

12

14

net (1011cm–3 s)Figure 5.18: Plot of the values of the kTe and net. The red points are from the on-cloud region
whereas the blue points are from the other regions.

5.3. IC 443

73

0.7

(a-i)
CRP for O ion

0.7

7.8

0.6

(a-iii)(a-ii)
7.6

0.5

7.4

0.4

7.2

kTe (keV)

kTe (keV)

0.6

8.0

0.6

0.4

0.4

0.2

0.2

0

0

0.5
0.4
0.3

0.3

0.6

ΔC for O ion

7.0
0.2

0.2
4.0

6.0

8.0

10

12

14

6.8

4.0

6.0

net (1011cm–3 s)
9.8

(b-i)
CRP for Ne ion

kTe (keV)

9.0
0.4
0.3
0.2
6.0

8.0

10

12

(b-iii)
1.2

1.2

0.8

0.8

0.4

0.4

0

0

0.5
0.4

8.6

0.3

8.2

0.2

14

4.0

6.0

8.0

10

12

14

net (1011cm–3 s)(c-i)
CRP for Mg ion

0.4(c-ii)
0.6

11.0

0.5

1.2

0.7

11.4

10.6

kTe (keV)

0.7

kTe (keV)

14

ΔC for Ne ion

net (1011cm–3 s)

0.6

12

(b-ii)
0.6

9.4

0.5

4.0

10

0.7

kTe (keV)

0.7
0.6

8.0

net (1011cm–3 s)ΔC for Mg ion

0.5(c-iii)

1.2

1.0

1.0

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0.4
0.3

0.3
10.2
0.2

0.2
4.0

6.0

8.0

10

12

14

4.0

6.0

net (1011cm–3 s)(d-i)
CRP for Si ion

12

14

0.5

11.5

0.4
11.0

1.0

(d-ii)

12.0

0.6

kTe (keV)

kTe (keV)

0.6

ΔC for Si ion

10.5

0.2
4.0

6.0

8.0

10

12

0.4

0.2

14

4.0

6.0

net (1011cm–3 s)

0.8

0.8

0.6

0.6

0.4

0.4

8.0

10

12

0.2

0.2

14

0.7

(e-i)
CRP for S ion

kTe (keV)

13.0
0.4
12.0

0.3
0.2
8.0

10

12

ΔC for S ion

0.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.4
0.3
0.2

11.0
6.0

(e-iii)(e-ii)
0.6

14.0

0.5

4.0

14

4.0

6.0

net (1011cm–3 s)

8.0

10

12

14

net (1011cm–3 s)
0.7

0.7

(f-i)
CRP for Fe ion

0.6(f-ii)

18.0
0.6

0.4
0.3
0.2
6.0

8.0

10

net (1011cm–3 s)

1214

kTe (keV)

16.0

1.6

0.5
0.4

15.0

0.3

14.0

0.2

(f-iii)

1.6

ΔC for Fe ion

17.0
0.5

4.0

1.0

net (1011cm–3 s)

0.7
0.6

(d-iii)

0.5

0.3

0.3

kTe (keV)

10

0.7

0.7

kTe (keV)

8.0

net (1011cm–3 s)

4.0

6.0

8.0

10

12

1.2

1.2

0.8

0.8

0.4

0.4

0

0

14

net (1011cm–3 s)Figure 5.19: Average charge CRP and charge deviation ∆C for O-Fe ions in the panels (a-i)(f-i) and (a-ii)-(f-ii), respectively, shown on color scales. We overlay the same plot as that in
Figure 5.18 on each map. In panels (a-iii)-(f-iii), maps of ∆C computed with best-fit values.
The cyan contours denote the same radio H2 image as that in Figure 5.17.

CHAPTER 5. PHYSICAL ORIGIN OF RPS IN SNRS

74

Ion fraction (%)

100
10
1.0
0.1
SiXI

SiXII

SiXIII

SiXIV

SiXV

Figure 5.20: Si ion fraction in CIE plasma with kTe =0.3 keV and RP with kTe = 0.3 keV, kTinit =5.0 keV, and net = 6.0×1011 cm−3 s.

5.4. DISCUSSION

75

5.4 Discussion
Table 5.7: Comparison between three RP-SNRs, W44, IC 443, and W49B.

Age (kyr)kTe (keV)
kTe -net correlation
Shock-cloud interaction
RPs near molecular clouds
Cooling process

W44
∼20a
0.20–0.60
Negative
EntireLower kTe and net e
Thermal conduction

IC 443∼20–30b
0.15–0.65
Negative
Local
Lower kTe and net
Thermal conduction

W49B
∼1–6c
1.1–1.8d
Positive
Local
No correlation
RarefactionaSmith et al. (1985a), Wolszczan et al. (1991), and Harrus et al. (1997).
Olbert et al. (2001) and Lee et al. (2008).
c
Pye et al. (1984) and Smith et al. (1985b).
dYamaguchi et al. (2018).
eRemarkable in the SEMBE region.
b

We discuss the comprehensive physical origin of RPs in SNRs based on our results and theircomparison of other SNRs. Our results provided clear evidence for thermal conduction as theover-ionization in W44 and IC 443. Recent studies showed the same mechanism seems to be
responsible for RPs in other SNRs as well: G166.0+4.3 (Matsumura et al., 2017a), W28 (Okon
et al., 2018), and CTB 1 (Katsuragawa et al., 2018). A clear exception is W49B. Analyzing
NuSTAR data of W49B, Yamaguchi et al. (2018) found a result opposite to this, a positive correlation between kTe and net as shown in Figure 3.14. The correlation can be well explainedby an efficient cooling by adiabatic expansion in low density areas. The result led Yamaguchi
et al. (2018) to conclude that adiabatic expansion plays a predominant role in over-ionizing theplasma in W49B. What is a key to determining the thermal conduction scenario or the rarefaction scenario? Table 5.7 summarizes the observational characteristics of the W44, IC 443, and
W49B. An important hint would be their age. Cooling through adiabatic expansion is expected
to work efficiently in the early phase of SNR evolution when the blast wave breaks out of dense
circumstellar matter into tenuous ISM (Itoh & Masai, 1989; Shimizu et al., 2012). On the contrary, thermal conduction can be effective only after the blast wave hits dense ambient ISM, andthus would be expected to be predominant at later stages. G166.0+4.3, W28, and CTB 1 whose
thermal conduction is the most plausible formation process of RPs are much older (few 10kyr) than W49B, supporting our interpretation. Based on hydrodynamical simulations, Zhang
et al. (2019) reached a similar conclusion that both thermal conduction and adiabatic expansion contribute to plasma cooling in SNRs and that the dominant channel can be changed as
SNRs evolve. Systematic observational studies as well as their comparison with theoretical andnumerical studies are necessary to further clarify the over-ionization process in SNRs.

Chapter 6
Probing Sub-Relativistic Particles with the
Neutral Fe Kα Line
6.1 Previous Works and Our Objective
6.1.1 Detection of Neutral Fe Kα LineWe detected enhanced neutral Fe Kα (∼ 6.4 keV) line emission in the northeastern rimof the SNR W28 (Figures 3.12 and 6.1 1; region 1) (Okon et al., 2018). The line surface
brightness is significantly higher than a level expected for GRXE (e.g., Yamauchi et al., 2016),
which also emits the neutral Fe Kα line. We, therefore, conclude that most of the neutral FeKα line emission can be attributed to W28, not to the GRXE. One possible origin of this lineis thermal emission from the remnant, however, it is less plausible because W28 is one of the
middle-aged and core-collapse SNRs, from which Kα lines of nearly-neutral Fe generally are
not expected (Yamaguchi et al., 2014). Interestingly, this region corresponds to the locations
where the shock is interacting with a molecular cloud. An alternative possibility is thus that theenhanced natural Fe Kα line emission is generated by K-shell ionization of Fe in the cloud by
accelerated particles. GeV and TeV gamma rays also detected there indicate that the cloud isbombarded by particles accelerated in W28 if π 0 decay is the gamma-ray production mechanism
as duscussed by Abdo et al. (2010) and Aharonian et al. (2008) (Figure 6.2). The fact supports
our interpretation of the origin about the neutral Fe Kα line.
In addition to the example of W28, Suzaku data recently revealed the presence of the enhanced neutral Fe Kα line emission in some SNRs interacting with dense clouds: i.e., W44:
Nobukawa et al. (2018); G323.7−1.0: Saji et al. (2018). In most cases, the line emission spatially coincides with dense gas in the vicinity of the SNRs as shown in Figure 6.3. Since thecross section of the neutral Fe Kα production peaks at ∼ 10 MeV and ∼10 keV for protons andelectrons, respectively (Dogiel et al., 2011), the observed line emission would be emitted bysub-relativistic particles regardless of the particle species. These results suggest that the neutral
Fe Kα line emission, along with bremsstrahlung continuum as demonstrated by Tanaka et al.
(2018), would work as a diagnostic tool to study largely unknown sub-relativistic particles.
7610–7 phs s–1 cm–2 arcmin–2

6.1. PREVIOUS WORKS AND OUR OBJECTIVE

77

0.8
0.6
0.4
0.2
outsideregion 1

region 2

region 3

region 4

Figure 6.1: Intensities of the neutral Fe Kα line line of the five regions (Figure 3.12) in W28(Okon et al., 2018). The horizontal dashed lines indicate the GRXE level expected by a phenomenological model in Yamauchi et al. (2016).

80

60

1

2
3
4
40

20

0

RA J2000.0 (hrs)

Figure 6.2: H.E.S.S. gamma-ray map (> 0.1 TeV) (Aharonian et al., 2008). The cyan lines
indicate the same regions as in Figure 3.12.

78CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINE

Figure 6.3: Band images of (a) W28, (b) Kes 67, (c) Kes 69, (d) Kes 78, and (e) W44. The
left, center, and right panels correspond to the soft band (0.5–2 keV), the hard band (5–8 keV),and the Fe-K (6.2–6.5 keV) band that covers the neutral Fe Kα line (6.4 keV), respectively.
Vignetting is corrected and the instrumental background is subtracted. Point-like and slightly
extended sources are marked with the solid lines. In the right panels, those regions are excluded
from the images. The cyan contours in the right panels show the gas distributions. (taken from
Nobukawa et al., 2018).

6.1. PREVIOUS WORKS AND OUR OBJECTIVE

79

Figure 6.4: Equivalent width of the Fe Kα line produced by sub-relativistic particles as a function of their spectral index. The thick solid line indicates electron case. The thin solid anddashed curves represent proton case for injection energy Einj = 80 MeV and Einj = 50 MeV,
respectively. (taken from Dogiel et al., 2011)

6.1.2 Neutral Fe Kα line as a Diagnostic Tool to Study Sub-Relativistic
Particles
Information on accelerated sub-relativistic particles can be exploited using the neutral Fe
line emission. Dogiel et al. (2011) proposed an idea that species of radiating particles canbe distinguished based on the equivalent width of the Fe line with respect to a non-thermal
bremsstrahlung continuum from the same population of particles. In Figure 6.4, we show theequivalent widths for protons and electrons as functions of their spectral indices. Using the idea,
Nobukawa et al. (2018), Nobukawa et al. (2019), and Saji et al. (2018) claimed that protons account for the majority of the Fe line emission in some SNRs. Makino et al. (2019) presented ananalytical model in which they consider energy-dependent escape of CRs from an SNR shock
into an interacting cloud, and calculated emission spectra from the cloud, i.e., Fe line emission from sub-relativistic protons and π 0 -decay emission from relativistic protons. Applying
their model to W44 and W28, they successfully reproduced both the observed Fe line emission
intensity and the gamma-ray spectra.
Fine structures of the Fe Kα line, if detected, can make another step forward in the studyof sub-relativistic particles accelerated in astrophysical objects. Tatischeff et al. (2012) pointed
out that the electron transfer process from ambient neutral atoms to fast heavy ions can produce
broad line structures accompanying narrower K-shell lines. Figure 6.5 shows the line structures,
which are sums of transition lines from captured electron, broadened mainly by the Doppler effect of the fast moving ions. Detection of such structures would allow us to prove the presenceof heavy ions in accelerated particles and to constrain their composition. Apart from electrontransfer, multiple ionization, which is the topic of this dissertation, is another potentially important process caused by accelerated heavy ions, and thus can be a powerful diagnostic tool toprobe accelerated particles.

10
10

-3

10
10
10

O

-4

C N

-1

-1

LX (erg s keV )80CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINE

SS composition
Ar
Ca

-5

fmet=1 fmet=10
-7

23

C
NO

-4

-1

10
10
10
10

Ar
Ca

-5

CRS composition

Fe

Ne Si
Mg S

Ni

-6

fmet=1 fmet=10
-7

23

-2

NH = 10 cm

b)
10

-2

NH = 10 cm-8-1

LX (erg s keV )

Ni

-6

a)
10

Fe

Ne Si
Mg S

-8

1

10

10

2

EX (keV)Figure 6.5: (a) Calculated X-ray emission produced by sub-relativistic particles interacting witha dense cloud. The dashed and solid curves represent the models by the particles with the solar
system composition, and with 10 times metallicity relative to the solar composition. (b) Sameas the above figure but for the cosmic ray source composition from Engelmann et al. (1990) andMeyer et al. (1997) (taken from Tatischeff et al., 2012).

6.2. MULTIPLE IONIZATION PROCESSES IN COLLISIONS OF ION-ATOM

81

1500
K 1

1250

Counts

1000

K L1

K L2

K 2

750

K L3

500
250
K L0

0
6350

6400

6450

6500

6550

Energy (eV)Figure 6.6: Fe Kα spectra produced by impacts of protons (red), and O5+ ions (blue) (data fromBurch et al., 1971). For a display purpose, the O5+ spectrum is scaled by a factor of two.
In this thesis, we qualitatively estimate the effect of the multiple ionization process on the
Fe Kα line emission. We calculate a model to predict line structures due to multiple ionizationby using the knowledge from beam experiments. Based on our model, we show Fe Kα line
structures expected to be detected in SNRs by high resolution X-ray spectroscopy with future
X-ray satellites such as XRISM and Athena.

6.2 Multiple Ionization Processes in Collisions of Ion-Atom
Ionization of target atoms by projectile ions have been widely studied through both experimental and theoretical approaches. With studies by high-resolution crystal spectrometers,
authors such as Burch et al. (1971) and Kauffman et al. (1973) found differences of line structures between proton- and ion-produced Kα spectra. Figure 6.6 shows spectra of Fe Kα line
structures originally presented by Burch et al. (1971). The proton-produced spectrum has only
the neutral Fe Kα1 and Fe Kα2 lines due to the K-L3 and K-L2 transitions, respectively. The
O5+ -produced spectrum, on the other hand, has broad line-like structures in the 6350–6550 eV
band. When projectile particles are heavy ions, their strong Coulomb field can easily cause
simultaneous ejection of multiple inner-shell electrons of the targets, resulting in the significant
characteristic structures.
The multiple ionization structures consist of peaks called KαLi (i = 0–7), each of which
is superposition of the K-L3 and the K-L2 transition lines from ionized Fe atoms with i L-shellvacancies as shown in Figure 6.7. The center energies of the KαLi peaks are higher by ∼ i × 20–
30 eV than those of the Fe Kα1 and Kα2 lines. This is because the K-L3 (K-L2 ) transition lines
shift upwards by ∼ 20–30 eV per L-shell electron ionization (= ∆EL ) (e.g., Wang et al., 2012).
The outer shell (M, N, ...) ionization is mainly manifested in broadenings of the KαLi peaks
because the energy shift ∆EM (and ∆EN , ...) of the transition lines due to additional M-shell

82CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINE

Single Ionization
Vacancy

Projectile
particle

Fe K 1
or
Fe K 2Multiple Ionization
Target Fe atom

Fe K L3

Figure 6.7: Schematic view of ionization process in collisions of ion-atom.
and outer shell vacancies are sufficiently smaller than ∆EL , and is equal to or smaller than thenatural widths of the transition lines.

6.3 Modeling of Kα Lline Structures by Impacts of Monoenergetic Ions
6.3.1 Kα Line Structures
The KαLi peaks are the sums of the Kα1 Li and Kα2 Li sub-peaks, which are superpositions of the K-L3 and K-L2 transition lines, respectively. The Kα1 Li (Kα2 Li ) sub-peaks are
expressed as superpositions of Lorentzians corresponding to transition lines. According to Horvat et al. (2006) and Horvat et al. (2009), KαLi spectra obtained in ion beam experiments canphenomenologically be reproduced by the sums of the Kα1 Li and Kα2 Li peaks described by
Voigt functions, or a convolution of a Lorentzian and a Gaussian. Figure 6.8 shows one example from Horvat et al. (2006). Here, the Gaussian reflects broadening of the sub-peaks due tosimultaneous ionization of electrons in outer shells. Taking the same approach, we modeled theKα1 Li and Kα2 Li sub-peaks with the Voigt function.
We calculate the center energy of the sub-peaks with the scaling law given by Horvat et al.
(2006). They expressed the energy shift ∆E i (eV) of each Kα1 Li (Kα2 Li ) sub-peak with respect
to the neutral Kα1 (Kα2 ) line emission based on various data obtained by ion beam experiments.

6.3. MODELING OF Kα LLINE STRUCTURES BY IMPACTS OF MONO-ENERGETIC IONS83

Figure 6.8: Spectrum of Cl Kα line emitted from thick KCl targets bombarded by 4 MeV/amu
Kr ions obtained by a crystal spectrometer. The green, blue and brown curves represents thebest-fit fit model for each Kα1 Li line, and the contributions from Kα1 and Kα2 lines, respectively. The gray and magenta lines indicate instrumental background and the Kα line generated
by secondary electrons. The red line shows the sum of all components. (taken from Horvat etal., 2006)

Ei~ i × 20-30 eV< few 10 eV(Ionization of
L-shell electrons)(Ionization of outershell electrons)

σi

K 1
(K 2)

K 1Li
(K 2Li)

EnergyFigure 6.9: Energy shift of Kα line due to multiple ionization. The black and red curves represent Kα1 (Kα2 ) line, and Kα1 Li0 (Kα2 Li0 ) line from ions with single K-shell and i L-shellvacancies, respectively. The blue and red lines indicates Kα1 Li (Fe Kα2 Li ) sub-peaks.

84CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINEpLX = 0.38

Xn = 3.3

Figure 6.10: Ionization parameter pXL as a function of the universal variable Xn determined using
Equation 6.3 for n = 2 (Horvat et al., 2006). The data points represent measurements with solid
targets with Z2 = 17–32 and projectile ions with Z1 = 6–83 at 2.5–25 MeV/amu. The solid anddashed curves show the best-fit logistic model and a curve predicted by the Geometrical Model(e.g., Sulik et al., 1987), respectively. The orange dash lines denote the values of pXL and X2 inthe impacts of Fe26+ ions (10 MeV/amu) on Fe targets calculated with Equations 6.2 and 6.3.
The energy shift ∆E i can be described as∆E i = i(a + b Z2 + c i + d i Z2 ) + pXL [(i − 1)(Z2 − e) + f ] eV,(6.1)

where a = −11.64, b = 1.493, c = 0.755, d = −0.0112, e = 9.11, f = 14.3, and Z2 is the atomic
number of the target. The first and second terms in Equation 6.1 correspond to the energy shifts
due to ionization of L-shell and outer shell electrons, respectively, as shown in Figure 6.9.
The parameter pXL is the ionization probability per L-shell electron in K-shell ionization. We
calculate the pXL with the model by Horvat et al. (2006),′

pXL = a′ /[1 + (b′ /X2 )c ],(6.2)

where a′ = 0.537, b′ = 2.11, and c′ = 2.02. The parameter X2 is a universal function derived by
Sulik et al. (1987), and is described as
X2 = 4V [G(V )]1/2 Z1 /(2v1 ),(6.3)

where v1 , Z1 , V , and G(V ) are the projectile velocity in atomic units, where is normalized to the
Bohr velocity 2.18 × 106 m/s, the atomic number of the projectile, the ratio of v1 to the averagevelocity of electrons in target atoms, and the Gryzinski Geometrical factor, respectively. We
employ an analytical formula in McGuire & Richard (1973) for G(V ).
We then calculate the widths of the sub-peaks, which correspond to the parameter σ i in
Figure 6.9. The scaling law by Horvat et al. (2006) approximates the widths of the Gaussian of
the Voigt function as
σ i = a i (b − i)(Z2 − c) eV,(6.4)

6.3. MODELING OF Kα LLINE STRUCTURES BY IMPACTS OF MONO-ENERGETIC IONS85
where a = 0.0246, b = 9.86, and c = 10.40. Following Horvat et al. (2006), we fix the line widthof the Lorentzian component to the natural widths of the transition lines obtained by Campbell& Papp (2001).
The above scaling laws by Horvat et al. (2006) are derived from experimental data using avariety of solid targets with Z2 = 17–32 and projectile ions with Z1 = 6–83 at 2.5–25 MeV/amu.
In Figure 6.10, we show the plot of the values of X2 and pXL of the used data (Horvat et al.,2006), and overlay the values in the impacts of Fe26+ ions on Fe targets. The X2 of each datais calculated with Equation 6.3, and the ∑pXL is calculated with the intensity Ii of Kα1 Li (Kα2 Li )X
sub-peak obtained by the data and pL = i i Ii /Itot derived from Equation 6.5, respectively. The
values of the Fe26+ impacts are calculated with Equations 6.3 and 6.2. The data cover impacts by
various ions with ∼ 10 MeV/amu, where the cross sections for K-shell ionization of Fe atoms(Z2 ) peak. We applied the scaling laws to the calculation of the Fe line structures generated by
impacts of various ions in 0.5–1000 MeV/amu region, where collision nature is well describedby the perturbation theory and the scaling laws by Horvat et al. (2006) can be considered valid.

6.3.2 Intensity of KαLi LineThe intensity of each Kα1 Li (Kα2 Li ) sub-peak can be expressed as a function of pXL . Under
an assumption of independent L-shell electron ionization, a binomial distribution of( )8 Xi
Ii = ItotpL (1 − pXL )8−i ,
(6.5)
i
where
Itot =

8
∑

Ii ,

(6.6)

i

gives a good description of the relative intensities of the KαLi peaks (Kauffman et al., 1973).
According to Horvat et al. (2009), intensities of the KαLi peaks depend on the phase of thetarget, whether it is gas or solid. Compared to the solid target case, the Fe KαLi peaks become
dominant with gaseous targets. Horvat et al. (2009) derived the scaling law of pXL similar to
the equation (6.2) from atomic data of collisions between various ions at ∼ 10 MeV/amu andmonoatomic Ar gas. The scaling law for gas is the same as equation (6.2), but with a′ = 0.856,
b′ = 2.94, and c′ = 1.71.

6.3.3 Comparison between Our Model and Experimental Data.
In Figure 6.11, we plot the models for the Kα line emitted by solid Fe bombarded by protons
and fully ionized O and Fe ions. Figure 6.12 is the same but for gaseous Fe. The results clearly
indicate that the intensities of the KαLi peaks depend on the charge state and kinetic energyof the projectiles. The larger charge the projectile has, the more significant the KαLi peaks
become. This is naturally explained by a stronger Coulomb field of heavy ions. Regardless ofthe projectile species, the Fe KαLi peaks are the most significant when the projectile kinetic
energy is ∼ 1.6 MeV/amu. Electrons generally are ejected most efficiently when the projectile
ion velocity matches the average velocity of the electrons in orbit of an atom (Bohr, 1948).
Since the kinetic energy of ∼ 1.6 MeV/amu is translated into a projectile velocity close to thatof Fe-L electrons, L-shell electrons are efficiently ionized around this energy.

6500

Energy (eV)

0

0
6700

0.5

0.5

6600

1.0

1.0

0
1.5

1.0

0
1.5

0.5

1.0

0
1.5

proton (100 MeV)

proton (10 MeV)

proton (1.6 MeV)

0
1.5

0.5

1.0

1.5

0.5

6400

K 2

K 1

IntensityIntensity(arb. unit)

0.5

1.0

0
1.5

0.5

1.0

0
1.5

0.5

1.0



IntensityIntensity(arb. unit)

proton (0.5
(0.5 MeV)
MeV)
proton
K 1

6400

K 2





1.5

6600

6700

O8+ (100 MeV/amu)

O8+ (10 MeV/amu)

O8+ (1.6 MeV/amu)

O8+ (0.5 MeV/amu)

Energy (eV)

6500

K L3

K L2

K L1



(a-ii)



(a-iii)

IntensityIntensity(arb. unit)

(a-i)

0

0.5

1.0

0
1.5

0.5

1.0

0
1.5

0.5

1.0

0
1.5

0.5

1.0

1.5

6400

K 2

K 1

K L1

K L7

6600

6700

Fe26+ (100 MeV/amu)

Fe26+ (10 MeV/amu)

Fe26+ (1.6 MeV/amu)

K L6

K L5

K L4

Fe26+ (0.5 MeV/amu)

Energy (eV)

6500

K L2

K L3

86CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINE

Figure 6.11: Fe Kα structures emitted from (a) solid and (b) gaseous Fe targets under bombardment by (i) protons, (ii) O8+ , and (iii) Fe26+ ions. The red and blue dashed curves denote the Fe
Kα1 and Fe Kα2 structures, respectively.

6500

Figure 6.12: Same as Figure 6.11 but for gas Fe targets.

Energy (eV)

0

0
6700

0.5

0.5

6600

1.0

1.0

0
1.5

1.0

0
1.5

0.5

1.0

0
1.5

proton (100 MeV)

proton (10 MeV)

proton (1.6 MeV)

0
1.5

0.5

1.0

0.5

6400

K 2

IntensityIntensity(arb. unit)

0.5

1.0

0
1.5

0.5

1.0

0
1.5

0.5

1.0



IntensityIntensity(arb. unit)

6400

K 2

K 1

L3

6600

6700

O8+ (100 MeV/amu)

O8+ (10 MeV/amu)

O8+ (1.6 MeV/amu)

Energy (eV)

6500

K

K L2

K L1

O8+ (0.5 MeV/amu)

0

0.5

1.0

0
1.5

0.5

1.0

0
1.5

0.5

1.0

0
1.5

0.5

1.0

1.5

6400

K L3

K L7

6600

6700

Fe26+ (100 MeV/amu)

Fe26+ (10 MeV/amu)

Fe26+ (1.6 MeV/amu)

K L6

K L5

Fe26+ (0.5 MeV/amu)
K L4

Energy (eV)

6500

K L2
K L1

K 1

K 2



1.5



proton (0.5 MeV)



K 1





1.5



(b-iii)(b-ii)

IntensityIntensity(arb. unit)(b-i)

6.3. MODELING OF Kα LLINE STRUCTURES BY IMPACTS OF MONO-ENERGETIC IONS87

88CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINE

(a)

(b)
K L4
K L5

K L3

K 1+K 2

K L1

1.00

Intensity (arb. unit)

Intensity (arb. unit)

2.0

1.5
K L6
K L2

1.0
K L7

K L1

0.5

K L2

0.75

K 1+K 2

0.50

K L3

K L4

0.25

0

0
2600

2650

2700

2750

2800

3000

2950

3050

Energy (eV)Energy (eV)Stopping Power (MeV/mg/cm2)

Figure 6.13: (a) Cl Kα spectrum from solid KCl targets under bombardment by 4 MeV/amu
Kr36+ ions (Horvat et al., 2006) and (b) Ar Kα spectrum from a gaseous Ar target under bombardment by 9.4 MeV/amu Ne10+ ions (Horvat et al., 2009) from experiments (the black dots),
compared with our model (the red curves). The gray dashed curves represent the background.
50
40
30
20
10
0

0

1.0

2.0

3.0

4.0

5.0

6.0

Energy (MeV/amu)

Figure 6.14: Stopping power for projectile Kr ion in solid KCl targets. Electronic and nuclear
stoppings are considered (data from Dr. M. Imai).

Figure 6.13 shows a comparison between the computed models and experimental data by
Horvat et al. (2006) and Horvat et al. (2009). In the experimental data, the KαLi peaks (i =0–7) are generated by impacts of projectile ions, while the Kα1 and Kα2 lines in Figure 6.13(a)are mainly induced by secondary electrons and X-rays not included in our model. Our model
reproduces the overall KαLi peaks structures. However, we found some discrepancies of the line
center energies and intensities. The contradiction about the center energy could be explainedby the inaccuracy of Equations 6.1, 6.2, and 6.4, which is estimated to be at a few % level by
Horvat et al. (2006). The discrepancy of the intensities could be brought by continuous changesof energy and charge state of projectile ions in thick (∼ mg cm−2 ) targets, which change thevalue of pXL . In Figure 6.14, we show the stopping power for Kr ions in KCl targets. The
combination of projectile ions and targets is the same as the case in Figure 6.13(a). Anotherpossibility would be contribution of electron captures from the L-shell of the target atoms in
L-shell vacancy production as Rymuza et al. (1989) and Kavčič et al. (2000) pointed out. Thoseeffects are not included in the present model.

6.4. FE Kα STRUCTURES PRODUCED BY COSMIC RAYS

89

6.4 Fe Kα Structures Produced by Cosmic Rays
6.4.1 Assumptions
Using our model, we compute Fe Kα line spectra expected to be observed in SNRs. In
SNR shocks, various ions would be accelerated at the same time, and thus the spectra would besuperpositions of contributions from each ion species. Since the composition of cosmic rays atacceleration sites is unknown, we assume here that it is the same as that observed in the solar
system by referring to Mewaldt (1994). We also assume that ions are fully ionized and that allions follow a common spectrum. We take into account contributions from H, He, ..., Fe, Co,
and Ni ions in an energy range of 0.5–1000 MeV/amu.
The flux of the Fe KαLi peak Fi by each ion species can be described as∫dNion
Fi ∝ ngas σKLi vion
dE,
(6.7)
dE
where ngas , σKLi , vion , and dNion /dE are the number density of Fe atoms in the dense gas, theproduction cross section of the Fe KαLi peak, the velocity of the ions, and the differential
spectra of the ions, respectively. We applied the scaling laws for solid targets assuming that Fe
is mainly in dust grains. Based on Equations 6.5 and 6.6, the production cross section σKLi canbe calculated as( )8 Xi
σKLi = σpp (1 − pXL )8−i , σp = ωK × σion ,
(6.8)
i L
∑
where σp , σion , and ωK are the production cross section of the Fe Kα (= i Fe KαLi peaks) line,
the K-shell ionization cross section, and the florescence yield (= 0.34) (Krause, 1979), respectively. We computed σion with the program by Batič et al. (2013) based on the ECPSSR (EnergyLoss Coulomb-Repulsion Perturbed-Stationary-State Relativistic) theory (Brandt & Lapicki,
1981).

6.4.2 Results
Figure 6.15 presents the result, where the models are folded with the response of the Xray micro-calorimeter Resolve (Ishisaki et al., 2018) aboard XRISM (Tashiro et al., 2018).
Accelerated ions have a power-law spectrum dN/dE ∝ E −s with s = 1 and s = 2 in the panels(a) and (b), respectively. The former is chosen, referring to the measurement of non-thermal
bremsstrahlung in W49B by Tanaka et al. (2018). The latter is the index expected in diffusive
shock acceleration at a strong shock. In both cases, the KαLi (i = 1–7) peaks appear in the
6420–6700 eV band. The intensities of each KαLi peak strongly reflect the composition of
the emitting particles. If particles accelerated in SNRs have a similar ion composition to CRs
arriving at the solar system, the most significant peak is the KαL1 peak, which can be resolved
into Kα1 L1 and Kα2 L1 with the Resolve. The intensities of the two sub-peaks are ∼ 1/10 of
those of Kα1 and Kα2 . The Fe Kα1 L1 and Kα2 L1 sub-peaks are shifted by ∼ 30 eV with respect
to the Fe Kα1 and Kα2 .
An ∼ eV energy resolution by X-ray micro-calorimeters would be necessary to resolve thestructures. In addition to XRISM, future missions such as Athena (Barcons et al., 2017) andSuper DIOS (Ohashi et al., 2018) with X-ray micro-calorimeters will able to detect the line
structures. Such studies will play a complimentary role to CR-ionization rate estimates based

90CHAPTER 6. PROBING SUB-RELATIVISTIC PARTICLES WITH THE NEUTRAL FE Kα LINE
data and folded model

data and folded model

(b)
1.0

K L2



K L3
10 4

K L4

0.01


K L5
K L6

K 1L1
10 3





0.1



K L2



K L3
K L4

10 4

10 3

0.1

K 2L1

K 2
normalized counts s 1 keV 1

K 1L1



K 1

0.01


K L5
K L6
10 5

K 2L1

K 2
normalized counts s 1 keV 1

0.01

K 1

10 5

Intensity (arb. unit)

1.0

Intensity (arb. unit)

0.01

(a)

10-3

10-3





K L7

K L7

10-4




6.35

10 6

10 6

10-4

6.4

6400

6.45

6.5

6.55

6500
Energy (keV)

Energy (eV)

6.6

6600

6.65

6700

6.35

6.4

6400

6.45

6.5

6.55

6500
Energy (keV)

6.6

6600

6.65

6700

Energy (eV)Figure 6.15: Fe Kα structures expected from Fe atoms bombarded by accelerated particles with
spectral indices of (a) s = 1 and (b) s = 2 (black). The red, blue, and green curves represent
contributions from protons, O ions, and Fe ions, respectively.
on absorption lines of H+
3 generated by collisions of the CRs and H2 molecules in a dense cloud(e.g., Indriolo et al., 2010). We finally note that potential targets would not be limited to SNRs,
considering the recent claims of contribution of CR-ionization to the neutral Fe K line in theArches cluster region (Tatischeff et al., 2012; Krivonos et al., 2017) and in the Galactic ridge(Nobukawa et al., 2015).

Chapter 7
Conclusions
We performed spectroscopic analysis of thermal X-rays from SNRs, W44 and IC 443, aiming to understand the physical origin of RPs, and constructed a model to predict X-ray line
emission from dense clouds bombarded by sub-relativistic particles accelerated in SNRs forprobing sub-relativistic particles with the future X-ray satellites. The important results are summarized as follows:
1. We have performed spatially resolved spectroscopy of X-ray emission of W44 with XMMNewton. All spectra extracted from each region are well fitted with an RP model. The
X-ray absorption column densities well correlate with the distribution of foreground gas
in the line-of-sight toward W44 as traced by radio line emissions. The obtained electron temperature kTe and the recombination timescale net of RPs range from 0.18 keV to
0.60 keV and from 3 × 1011 cm−3 s to 9 × 1011 cm−3 s, respectively. We have discoveredthat kTe is lower in the region where the shock is interacting with molecular clouds andthat kTe and net are negatively correlated. These findings indicate thermal conduction between X-ray emitting and the cold dense gas as the origin of the over-ionization. We havealso found that net is especially smaller in the regions with spatially extended moderately
broad emissions of the 12 CO(J = 1–0) line, which are considered to be emitted by clumpy
gas shocked and disturbed by the SNR shock (Seta et al., 2004; Sashida et al., 2013). This
result indicates a rapid cooling of the plasma through evaporation of the clumpy gas.
2. We analyzed XMM-Newton data of IC 443 with the same method applied to the W44
case. The spectra extracted from each region of the remnant are all fitted well with asingle RP model or a model consisting of RP and CIE components. The obtained electron temperature kTe and the recombining timescale net in the RP component range from
0.15 keV to 0.65 keV and from 4 × 1011 cm−3 s to 14 × 1011 cm−3 s, respectively. We
found a good spatial correlation between the X-ray absorption column and the distributionof foreground gas traced by 12 CO lines, in the line-of-sight toward IC 443. Our analysis
revealed that kTe and net decrease in the region where IC 443 is interacting with dense
clouds traced by the 12 CO and H2 observations, and the values show roughly negatively
correlated. These results are very similar to those from W44, and suggest thermal conduction between SNR plasma and the clouds is responsible for the RPs in IC 443. Aiming todirectly evaluate an ionization degree of RP in each region, we calculated average charges
of ions in the RP with obtained kTe and net. We found RPs in the shock-cloud interaction regions tend to have larger ∆C for Ne-Si ions, supporting the thermal conduction
scenario.
91

92

CHAPTER 7. CONCLUSIONS
3. Our analysis of the XMM-Newton data of W44 and IC 443 indicate that thermal conduction between SNR plasma and ambient clouds is the most plausible formation processof the over-ionization. On the other hand, Yamaguchi et al. (2018) found clear evidence
for adiabatic cooling as the formation process of RPs in W49B. A comparison of resultson these SNRs suggests that both thermal conduction and adiabatic cooling are possible
channels of over-ionization in SNRs and that the dominant channel may change as SNRs
evolve. Recent hydrodynamical simulations by Zhang et al. (2019) support this idea as
well. Systematic observational studies as well as their comparison with theoretical andnumerical studies are helpful to further clarify the over-ionization process in SNRs andwill lead us to comprehensive understanding of the injection mechanism of energy in
SNRs into interstellar space. In particular, investigations of charge fractions as demonstrated in the analysis of IC 443 would work as a powerful tool.
4. We constructed a model for the Fe Kα line structures by various projectile ions utilizing atomic-collision data. When energetic heavy ions collide with target atoms, theirstrong Coulomb field can easily cause simultaneous ejection of multiple electrons of thetarget. This results in shifts (∼ a few 10 eV) in characteristic X-ray line energies, forming distinctive spectral structures. Detection of such structures in the neutral Fe Kα line
strongly supports that the Fe Kα line detected in some SNRs are from the dense clouds
bombarded by sub-relativistic particles accelerated in SNRs. An ∼ eV energy resolution
by X-ray micro-calorimeters onboard XRISM and future satellites such as Athena, would
be necessary to resolve the structures.
5. We found that the line structures strongly depend on the composition of sub-relativistic
particles. In particular, as the projectile ion is heavier, the shifts of the line structure
become larger. Detection of such structures would allow us to prove the presence ofheavy ions in particles accelerated in SNRs and to constrain their composition.

Acknowledgments
First of all, I would like to express my best gratitude to Prof. Takeshi Tsuru, Ass. Prof.
Takaaki Tanaka, and Ass. Prof. Hiroyuki Uchida, for guiding me throughout the five years
at Kyoto university. Without their advices, this thesis could not reach the present level. I
am very grateful to my collaborators, Hiroya Yamaguchi, Masumichi Seta, Randall K. Smith,Satoshi Yoshiike, Salvatore Orlando, Fabrizio Bocchino, Marco Miceli, and Makoto Imai, fortheir advices and helpful comments. Many insightful comments were given by H. Sano, T.
Mukoyama, M. Pajek, B. Sulik, V. Tatischeff, and D. Banas. I appreciate the supports andencouragements of all the people in the Cosmic ray group and XRISM team. Finally, I thank myfamily for their support and understanding.

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