Non-Thermal Emission from Galaxy Clusters

University of Amsterdam

MSc Physics Gravitation AstroParticle Physics Amsterdam

Master Thesis

Predictions for X-Ray Satellites

Richard Tony Bartels 10508333

June 2014 60 ECTS August 2013 - June 2014

Supervisor: Daily Supervisor: Examiner: Dr Shin’ichiro Ando Dr Fabio Zandanel Dr Jacco Vink

GRAPPA and IoP Abstract

Clusters of galaxies are the largest gravitationally bound structures in the Universe and the latest ones to form. Large-scale diffuse synchrotron emission is observed in many clusters proving the presence of relativistic electrons and magnetic fields in the intra-cluster medium. The same population of electrons can inverse-Compton scatter off the photons of the cosmic microwave background. This can generate non-thermal hard X-ray emission, on top of the thermal X-ray bremsstrahlung observed in all clusters. However, so far, non-thermal hard X-ray detections have been claimed in just a few clusters and are not confirmed. A definitive detection of the inverse-Compton emission from galaxy clusters would allow us to disentangle the magnetic fields and relativistic electron distributions. Upper limits on this emission can be used to place lower limits on the magnetic field. In this Master’s thesis, we estimate upper limits for the volume averaged magnetic field that still allow for a detectable non-thermal hard X-ray signal by next-generation X-ray telescopes, in particular ASTRO-H and the already launched NuSTAR, for all known radio halos and relics. Acknowledgements

There are various people that I would like to thank for different reasons. First of all, I would like to thank Tera for another year of support and especially for cheering me up when frustration gets the better of me. Also the kittens you offered a temporary home at our place, without me being aware of that, where a nice form of distraction in the final weeks of this project. Finally, there are certain people I have to thank at the university. Thanks to Jacco Vink for being willing to be my second reader and for useful suggestions. Thanks to everyone in Shin’ichiro’s ’thursday’ group for listening to my presentation. Especially to Irene, who has been very helpful. Also thanks to the other Master’s students, with whom I had a lot of fun this year. Thanks to the faculty at GRAPPA, Christoph and Shin’ichiro in particular, for having faith in my future research career. Finally, thanks to my supervisors for all their help. To Shin’ichiro for being willing to guide my project, even though he already had 4 students under his wings. And Fabio, to whom I am most thankful, for being the best supervisor I could have wished for.

ii Contents

Abstract i

Acknowledgements ii

Contents iii

List of Figuresv

List of Tables vi

Abbreviations vii

Physical Constants ix

Symbols x

1 Introduction1

2 Theoretical Background: Radiative Processes6 2.1 Synchrotron Radiation...... 6 2.1.1 Motion of a Particle in a Magnetic Field...... 6 2.1.2 Spectrum of a Single Electron...... 7 2.1.3 Spectrum for a Distribution of Electrons...... 8 2.1.4 Magnetic Field Orientation...... 9 2.1.5 Photon Spectrum...... 10 Photon spectral index...... 10 2.2 Inverse Compton Radiation...... 11 2.2.1 IC scattering in the Thomson limit...... 11 2.2.1.1 Klein-Nishina limit...... 13 2.2.2 Inverse Compton Spectrum...... 13 Photon spectral index...... 14 2.3 The Electron Spectrum...... 14 2.3.1 Loss Functions...... 17 2.3.1.1 γmin ...... 18 2.3.1.2 γmax ...... 20 2.4 Analytical Magnetic Field Estimates...... 20 Correction for Isotropically Distributed Magnetic Fields.. 21

iii Contents iv

3 Methods 24 3.1 Cluster Selection and Data...... 24 Radio Data...... 25 3.1.1 Non-Thermal X-Ray Data...... 25 3.2 Background Modelling...... 26 3.2.1 APEC model...... 26 3.2.1.1 Thermal Gas Density...... 27 Clusters without a gas density model...... 28 Thermal emission in the halo region...... 28 Thermal emission in the relic region...... 29 3.2.1.2 PyXspec...... 31 3.3 ASTRO-H Sensitivity...... 33 3.4 Analysis of the Spectrum...... 36

4 Results and Discussion 38 4.1 Promising Targets...... 43 4.1.1 Comments on Good Targets...... 45 4.2 Spectra with a Spectral Break...... 60 4.3 Discussion...... 64 4.3.1 Low Energy Cutoﬀ: Potential in EUV/SXR and Low Frequency Radio Emission...... 64 4.3.2 NuSTAR and Background Modelling...... 65 4.3.3 Primary Targets in a Broader Science Perspective...... 67

5 Conclusion 69

A Some (Astro-)Physics 71 A.1 Cosmology...... 71 A.1.1 Distance scales...... 72 A.2 Equipartition Magnetic Field...... 73 A.3 Parameter Dependence on Cosmology...... 75

B Radio Data 77

C Comments on Less Good Targets 86

D Cluster Spectra 93

Bibliography 103 List of Figures

1.1 Abell 1689...... 2 1.2 Radio emission in clusters...... 2 1.3 Non-thermal emisson...... 4

2.1 Cooling processes...... 15 2.2 Loss timescales...... 19

3.1 APEC metallicity dependence...... 27 3.2 Normalisation for radio halos...... 29 3.3 APEC normalisation for relics...... 30 3.4 ASTRO-H sensitivity curves...... 34 3.5 ASTRO-H sensitivity curve scaling...... 35 3.6 Spectrum Analysis...... 36

4.1 1E0657-56...... 46 4.2 A0085...... 47 4.3 AS753...... 48 4.4 A1367...... 49 4.5 Coma...... 51 4.6 A1914...... 52 4.7 A2255...... 53 4.8 A2319...... 54 4.9 A2744...... 56 4.10 A3667...... 57 4.11 A4038...... 58 4.12 MACSJ0717.5+3745...... 59 4.13 ZwCl0008.8-5215...... 61 4.14 Broken Power Law Spectra...... 63 4.15 NuSTAR vs. ASTRO-H...... 66

A.1 Equipartition condition...... 73

v List of Tables

2.1 γ for maximum loss timescale...... 18

3.1 Thermal data...... 33 3.2 ASTRO-H Properties...... 33

4.1 Cluster Sample...... 39 4.2 Results for halos...... 41 4.3 Results for relics...... 42 4.4 Equipartition magnetic ﬁeld estimates...... 44 4.5 Results Broken Power Law...... 62 4.6 NuSTAR Properties...... 65

B.1 Radio Data: Halos...... 77 B.2 Radio Data: Relics...... 80

vi Abbreviations

AGN Active Galactic Nucleus ATCA Australia Telescope Compact Aarray cgs centimetre gram second CMB Cosmic Microwave Background CR Cosmic Ray CRe Cosmic Ray electron CRp Cosmic Ray proton DM Dark Matter d.o.f. Degree of Freedom EoM Equation of Motion EUV Extreme UltraViolet FoV Field of View FWHM Full Width at Half Maximum HPD Half-Power Diameter HXI Hard X-ray Imager HXR Hard X-Rays IC Inverse Compton ICM Intra-Cluster Medium KN Klein-Nishina LOFAR Low-Frequency Array for Radio Astronomy NFW Navarro-Frenk-White NuSTAR Nuclear Spectroscopic Telescope Aarray NVSS NRAO VLA Sky Survey RM Rotation Measure REXCESS Representative XMM-Newton Cluster Structure Survey

vii Abbreviations viii

SKA Square Kilometre Array SXI SoftX-ray Imager SXR Soft X-Rays SXS SoftX-ray Spectrometer VLA Very Large Array VSSRS Very Steep Spectrum Radio Source WENSS Westerbork Northern Sky Survey WSRT Westerbork Synthesis Radio Telescope Physical Constants

speed of light c = 2.997 924 58 1010 cm s−1 × elementary charge e = 4.803 205 10−10 esu × gravitational constant G = 6.673 10−8 cm3 g−1 s−1 × Planck constant h = 6.626 068 85 10−27 erg s × − Planck constant, reduced ~ = 1.054 571 73 10 27 erg s × −16 Boltzmann constant kb = 1.380 649 10 erg K × −28 electron mass me = 9.109 382 15 10 g × classical electron radius r = 2.817 940 29 10−12 cm 0 × Thomson cross-section σT = 0.665 245 856 barn

present day CMB temperature T0 = 2.726 K −13 4 −3 Average CMB energy density UCMB = 4.19 10 (1 + z) erg cm ×

ix Symbols

a acceleration cm s−2 B Magnetic ﬁeld esu cm−2 γ Lorentz factor

νc Critical frequency Hz

νg Gyration frequency Hz P Power erg s−1 q Charge esu

r200 Virial radius kpc

rc Core radius kpc −3 UB Magnetic energy density erg cm

x Chapter 1

Introduction

Clusters of galaxies are the largest virialized structures in the universe and as such the latest ones to form according to current paradigm of ΛCDM and hierarchical structure 15 formation. Their mass is typically of the order of 10 M , most of which consists of ∼ dark matter, about 70 80%. The remaining mass is baryonic matter which is distributed − among galaxies ( few%) and a hot gas called the intra-cluster medium (ICM) which ∼ makes up 15 20% of the cluster mass. The thermal plasma component of the ICM − emits in X-rays mainly through bremsstrahlung. This is one of the many ways to identify clusters (Fig. 1.1).

Being such enormous systems, clusters are excellent probes in the study of both cosmology and astrophysics. Cluster mergers are the most energetic phenomena since the Big Bang, with 1063 1064 erg being dissipated into shocks and ICM motions per cluster − crossing. Therefore, clusters are powerful laboratories for the study of high energy astrophysics, which is the focus of this thesis. In particular it will deal with non-thermal emission coming from galaxy clusters. It is believed that a fraction of the energy that is dissipated during cluster mergers can go into non-thermal plasma components, such as cosmic rays (CRs) and magnetic fields. Evidence for non-thermal plasma components can indeed be found in clusters that appear to have undergone a recent merger. This evidence comes in the form of large-scale diffuse radio emission. Large regions ( Mpc) ∼ of diffuse radio emission, so-called radio halos, can be found at the center of clusters. Additionally, diffuse emission is observed at the outskirts of clusters. This kind of emission is called a radio relic (Fig. 1.2). They differ from haloes in their morphology. It

1 Chapter 1. Introduction 2 is often elongated and appears to trace a shock front (Feretti et al., 2012; Brunetti and Jones, 2014).

Figure 1.1: An image the cluster Abell 1689. The purple colour scale is X-ray emission from the ICM. Galaxies are observed in the optical and depicted in yellow (http: //chandra.harvard.edu/photo/2008/a1689/).

Figure 1.2: Left: The X-ray emission from the ICM in Abell 3562 with radio emission in white contours (Giacintucci et al., 2005). Right: The ’Sausage’ radio relic in CIZA J2242.8+5301 (R¨ottgeringet al., 2013). In terms of morphology it appears to trace a shock front. The colour coding is radio emission.

If charged particles travel through a magnetic ﬁeld they are accelerated and therefore will radiate (Fig. 1.3b). In the case of highly relativistic electrons this radiation is called synchrotron radiation (Rybicki and Lightman, 1979). Therefore, the fact that Chapter 1. Introduction 3 radio emission is observed in clusters proves the presence of both relativistic electrons and magnetic ﬁelds. Moreover, the observed radio spectrum follows to a large extent a power law. As a result, the spectrum of the relativistic electrons producing the emission must also follow a power law (see section 2.1). Particles that do not follow a Maxwell- Boltzmann distribution are referred to as non-thermal particles and their emission is dubbed non-thermal emission. The general shape of a Maxwell-Boltzmann distribution compared to a power law is plotted in Fig. 1.3a.

Diffuse synchrotron radio emission has now been established in a few dozen clusters. Yet, radio observations alone are insufficient to disentangle the electron distribution from the magnetic field. However, these relativistic electrons are also expected to produce X- rays through inverse-Compton (IC) scattering. If they scatter off cosmic microwave background (CMB) photons these gain some energy at the expense of the electron and thereby become X-ray photons (Fig. 1.3c). Given the average energy of the non-thermal electrons as deduced from radio observations, the emission is expected to be mainly in hard X-rays (HXRs), i.e. > 10 keV. Be that as it may, hard X-rays from clusters have not yet been detected. Non-thermal emission in X-rays has been searched for extensively (e.g. Feretti and Neumann, 2006; Rephaeli et al., 2006; Wik et al., 2011) and whereas some detections have been claimed, more recent observations do not confirm them (Ajello et al., 2009, 2010; Wik et al., 2012; Ota et al., 2013; Wik et al., 2014). Intense background emission from the thermal plasma is the most prominent obstruction in detecting IC radiation in the X-ray spectra of clusters.

This project sets out to study the detectability of IC radiation from galaxy clusters by next generation satellites. In particular the detectability by the ASTRO-H telescope which is currently scheduled for launch in 20151 (Takahashi et al., 2010). In order to do so the entire spectrum in both radio and X-ray is studied and compared to the background radiation from the thermal plasma and the sensitivity estimates for ASTRO-H. A ﬁrm detection of X-rays from non-thermal electrons will not only give us a better understanding of magnetic ﬁelds and the particle spectra in clusters, but will also help in studying the injection mechanism of these non-thermal particles. In this work, however, we take a phenomenological approach and are fully agnostic towards the injection mechanism of non-thermal particles. The only assumption that is made is that the same electrons that emit in radio should also be responsible for X-rays through IC radiation.

1http://astro-h.isas.jaxa.jp/ Chapter 1. Introduction 4

log-log Power law Maxwell-Boltzmann # Particles

Energy

(a) Maxwell-Boltzmann and power law distributions

(b) Synchrotron radiation (c) Inverse Compton scattering

Figure 1.3: Top panel: Diﬀerent particle distributions. The units on the axes are arbitrary. The red line is a thermal (Maxwell-Boltzmann) distribution which is de- 3 2 mev me 2 2 − 2kT scribed by N(v) 2πkT v e . The green line is a power law, often represen- ∼ −p tative for a non-thermal distribution, and can be described by N(γ) K0γ , with γ being the Lorentz gamma factor. For relativistic particles the Lorentz∼ factor is a dimensionless measure of the energy: γ P . Bottom left: Synchrotron emission ≈ m (http://abyss.uoregon.edu/~js/glossary/synchrotron_radiation.html). Bot- tom right: Inverse Compton scattering (http://www.astro.wisc.edu/~bank/).

Additionally, for the ﬁrst time, we study the IC radiation for all clusters where a halo or relic is detected, and where radio data is present for at least two diﬀerent frequencies such that the radio spectral index can be determined.

This work is set up as follows: in chapter2 the theory behind synchrotron radiation, inverse Compton scattering and their spectra due to a power law distribution of electrons are studied. In addition, we discuss the eﬀects of electron cooling on the resulting spectrum. In chapter3 we discuss how we model the thermal background and analyse the spectrum. Results are presented and discussed in chapter4 and chapter5 concludes Chapter 1. Introduction 5 this thesis. We work in centimetre gram second (cgs) units and adopt a cosmological −1 −1 model with Ωm = 0.27, ΩΛ = 0.73 and H0 = 70 km s Mpc . Chapter 2

Theoretical Background: Radiative Processes

In order to understand the radiation coming from the ICM we have to understand its origin. Emission coming from the thermal pool of electrons is mostly due to thermal bremsstrahlung, while the relativistic electron population generates synchrotron and IC emission. We discuss the latter two mechanism below followed by a discussion of electron cooling. Our method for modelling the thermal bremsstrahlung is discussed in section 3.2.

2.1 Synchrotron Radiation

The discussion on synchrotron radiation is mostly based on Blumenthal and Gould (1970) and Rybicki and Lightman(1979). Another useful, but more concise, discussion can be found in Pinzke(2010).

2.1.1 Motion of a Particle in a Magnetic Field

Synchrotron radiation is due to a charged particle of mass m and charge q, an electron in our case, moving in a magnetic ﬁeld B. In classical electrodynamics the equations of

6 Chapter 2. Theoretical Background 7 motion (EoMs) of such a system are:

d q (γmv) = v B (2.1a) dt c × d (γmc2) = qv E = 0. (2.1b) dt ·

These equations can be derived by equating Newton’s equation for the four-force with the equation for the Lorentz four-force

µ e µ ν mea = F U . (2.2) c ν

µ ν Here Fν is the electromagnetic field tensor, U the four-velocity, e the electron charge and me the electron mass. Eq. (2.1b) implies that the Lorentz factor, γ, and thus also the norm of the velocity, v , are constant. From Eq. (2.1a) it follows that the velocity parallel | | 2 2 2 to the magnetic field (v ) is constant and consequently v⊥ = v v = constant. k | | | | − | k| Therefore, the particle’s motion is helical, with its acceleration being perpendicular to both the magnetic field and its velocity vector. Its gyration frequency is given by

eB νg = . (2.3) 2πγmec

2.1.2 Spectrum of a Single Electron

For non-relativistic accelerated charges, the total emitted power is given by Larmor’s formula 2 q2a2 P = (2.4) 3 c3

with a the three vector acceleration. However, for our purpose we want to look at relativistic electrons. In order to ﬁnd the emitted power for relativistic particles we have to go to the instantaneous rest frame of the particle. The idea is that if we ﬁnd a covariant expression in this frame, it must be valid in any frame. It turns out that Eq. (2.4) is already in covariant form, but it can be cast in a more convenient form:

0 2e2 P = γ4(a2 + γ2a¡2¡) 3c3 ⊥ ¡k 2 = r2γ2B2 v 2 sin2 θ. (2.5) 3c 0 | | Chapter 2. Theoretical Background 8

e2 Here we have introduced the classical radius of the electron r = 2 and the so-called 0 mec pitch angle θ, which is the angle between the velocity vector v and the magnetic ﬁeld B. Integrating over all pitch angles yields the total power emitted:

4 2 2 Psync(γ) = σT cβ γ UB (2.6) 3

B2 where UB = 8π is the energy density of the magnetic ﬁeld, B.

We will now look at the spectrum emitted by a single electron. There are two things that should be mentioned. First, there exists a beaming effect for the radiation emitted by relativistic particles. The emitted synchrotron radiation is confined to a cone with opening angle 2/γ or, in other words, the emitted radiation makes at most an angle 1/γ with the instantaneous velocity vector. This effect is at the origin of the crit- ∼ ical frequency and the appearance of the modified Bessel function in Eq. (2.7) below. Secondly, there is a difference between the emitted and received power for pitch angles θ = π/2, this difference comes from a Doppler shift due to the particle’s spiralling 6 motion. For a detailed discussion see pp. 261-262 in Blumenthal and Gould(1970). 2 Ultimately, Preceived(ν) = Pemitted(ν)/ sin θ. The emitted spectrum for a single electron becomes:

√3e3B sin θ ν +∞ P (ν, γ, θ) = Fsyn( ),Fsyn(x) = x dξK (ξ) (2.7) emitted m c2 ν 5/3 e c Zx

with K5/3(ξ) the modiﬁed Bessel function of second kind and νc the critical frequency given by,

3 3 νc = γ νg sin θ 2 3 eBγ2 sin θ B = 4.199 γ2 sin θ Hz. (2.8) 4π m c ≈ 1 µG e

Above the critical frequency the spectrum rapidly falls.

2.1.3 Spectrum for a Distribution of Electrons

Finally, we have to take into account the electron distribution, which is a function of the energy of the cosmic-ray electrons (CRes) and the pitch angle. The former can be expressed in terms of the Lorentz factor. Our assumption is that the non-thermal Chapter 2. Theoretical Background 9

electrons follow a power law in some energy range, [γmin, γmax], which is based on observations of halos and relics. We can write for the number of electrons per unit volume, sin θ N(γ, θ) = K γ−p. (2.9) 0 2

sin θ The factor 2 comes from assuming the electrons are distributed isotropically with respect to the pitch angle. Blumenthal and Gould(1970) point out that electrons emitting from some ﬁxed region of space are only observed to emit for a fraction of sin2 θ.

Therefore, the observed distribution is related to the actual distribution by Nobs(γ, θ) = 2 sin θN(γ, θ). As a result: Pemitted(ν, γ, θ)N(γ, θ) = Preceived(ν, γ, θ)Nobs(γ, θ). The total emissivity is now given by multiplying the distribution by Eq. (2.7) and integrating over pitch angle and energy:

γ2 π P˜sync(ν) = Pemitted(ν, γ, θ)N(γ, θ)dγdθ Zγ1 Z0 γ2 π (2.10) −22 ν 2.344 10 sin θFsyn( )N(γ, θ)dγdθ. ≈ × ν Zγ1 Z0 c

2.1.4 Magnetic Field Orientation

Before moving on to compute the flux density we observe on earth, we should make a comment about the orientation of magnetic fields in relation to Eq. (2.10). This is the standard result for the power coming from a population of electrons as can be found in the literature (e.g. Blumenthal and Gould, 1970; Rybicki and Lightman, 1979). However, it does not account for the orientation of the magnetic field. So far this has been mostly ignored in the literature, apart from a work by Murgia et al.(2010). In order to account for this effect we include an extra factor:

H(θ0) δ(θ θ0) dΩ0. (2.11) − 4π

Here θ0 is the angle between the line of sight and the magnetic field and H(θ0) is the distribution of the magnetic field orientations. δ(θ θ0) accounts for the fact that, due − to the beaming effect, the emitted photons are confined to a narrow solid angle with an opening angle equal to θ, the pitch angle. Therefore, only if the the angle between the magnetic field and the line of sight is approximately the pitch angle will radiation be observed (e.g. Rybicki and Lightman, 1979, pp. 177-178). If one looks at magnetic fields Chapter 2. Theoretical Background 10 that are tangled on sizes much smaller than the volume under consideration, such as in radio halos and relics, H(θ0) = 1, corresponding to an isotropic distribution of magnetic sin θ 0 fields. Eq. (2.11) then reduces to 2 after integrating over θ . On the other hand for a magnetic field that is completely ordered H(θ0) = δ(θ0 x) and Eq. (2.11) becomes − δ(θ x) sin x . As a result, we modify Eq. (2.10): − 2

γ2 π π 0 0 H(θ ) 0 Psync(ν) = Pemitted(ν, γ, θ)N(γ, θ)δ(θ θ ) dγdθdΩ − 4π Zγ1 Z0 Z0 γ2 π π 0 −22 ν 0 0 sin θ 0 2.344 10 sin θFsyn( )N(γ, θ)δ(θ θ )H(θ ) dγdθdθ . ≈ × ν − 2 Zγ1 Z0 Z0 c (2.12)

2.1.5 Photon Spectrum

Ultimately, we want to determine the ﬂux density Sν which is what we observe with our telescopes. This is given in units of energy per unit time, area and frequency, and can be obtained by multiplying Eq. (2.12) by the emitting volume and dividing by the 1 surface of a sphere that is characterised by the luminosity distance DL :

erg 2 Ssync(ν) = Psync(ν) V/(4πD ). (2.13) cm2 s Hz · L

Photon spectral index Let us brieﬂy look at the spectral index of the photon spectrum. The synchrotron kernel function, F (x) (Eq. 2.7), peaks at x 1 (Blumenthal ∼ ν 2 and Gould, 1970), where x = with νc γ . Therefore, the radio photon spectrum is νc ∼ proportional to ν γ2. Looking at the spectrum (Eq. 2.13) one ﬁnds ∼

−(p+2) Ssync(ν) νγ dγ ∼ −(p+1) − p−1 νγ ν 2 . ∼ ∼

−α p−1 So the resulting spectrum is Ssyn(ν) ν where α = . ∝ 2 1For more on cosmological distance scales see appendix A.1.1. Chapter 2. Theoretical Background 11

2.2 Inverse Compton Radiation

Another process that should take place in the ICM is IC scattering. Non-thermal electrons inverse Compton scatter off CMB photons, thereby transferring some of their momentum to the photons. As a result, the CMB photons can be up-scattered to the X-ray regime. In this section we will first discuss inverse Compton scattering of a single electron followed by a discussion of the spectrum resulting from CMB photons scattering off a population of electrons.

2.2.1 IC scattering in the Thomson limit

In the case of IC scattering we can discern between two limits. The ﬁrst one is the 0 2 Thomson limit, which corresponds to mec in the rest frame of the electron, where 0 is the energy of the incoming photon. The corresponding cross-section is the Thomson 8π 2 cross-section, σT r , which is independent of the energy of the incoming photon. ≡ 3 0 The second regime is described by the Klein-Nishina formula, which will be covered in more detail below.

Using energy and momentum conservation the energy transfer from a photon to an electron in its rest frame (K0) can be shown to be

0 0 1 = 0 (2.14) 1 + 2 (1 cos θ) mec −

0 0 where and 1 are the initial and ﬁnal energy of the photon, respectively. Eq. (2.14) c can be expressed in terms of wavelength using = hν and λ = ν as

0 λ λ = λc(1 cos θ), (2.15) 1 − −

h where λc = mc is the Compton wavelength.

dN1 0 The scattering rate dt is, by considering the scattering rate in the rest frame, K , and then boosting to the lab frame K,

dN dN 0 1 = γ−1 1 = c σ(1 β cos θ)dn. (2.16) dt dt0 − Z Chapter 2. Theoretical Background 12

Here n is the distribution of photons. For an isotropic distribution of photons with energies that satisfy the Thomson limit (σ = σT ) this reduces to:

dN1 = σT cn (2.17) dt

Since the background photons in our problem consist mostly of CMB photons we are dealing with an isotropic blackbody distribution at temperature T. The number of photons per unit volume per unit initial photon energy is then given by

1 2 n() = 2 3 . (2.18) π (~c) exp(/kbT ) 1 − Next, we will consider the total energy-loss rate of the electrons, which corresponds to the energy going into X-ray photons. By deﬁnition this equals dN with dN = h 1i dt dt σT c n()d. Following Eqs (7.9 - 7.16) of Rybicki and Lightman(1979), we ﬁnd that the totalR power going into up-scattered photons equals:

4 2 2 PIC (γ) = σT cγ β n()d 3 Z (2.19) dN . ≡ h 1i dt

This leads to a mean energy of the Compton up-scattered photons of

4 2 n()d = γ where = = 2.70kbT. (2.20) 1 3 n()d h i h i h i R R So we can write the total power going into X-ray photons in the Thomson regime as:

4 2 2 PIC (γ) = σT cβ γ UCMB. (2.21) 3

4 −13 4 −3 Here UCMB = 2.7kbT n()d(1 + z) 4.19 10 (1 + z) erg cm is the CMB 0 ≈ × energy density with T0 theR CMB temperature at present. From Eqs (2.6) and (2.21) we note that the ratio of synchrotron to IC luminosity at low redshift is

2 Psync(γ) U B = B 0.095 . (2.22) P (γ) U ≈ 1 µG IC CMB Chapter 2. Theoretical Background 13

Finally, the total spectrum resulting from inverse Compton scattering of photons oﬀ a relativistic electron in the Thomson limit is given by:

dN (γ, ) 3 σ cn() 1 1 = T f 1 dtd 4 γ2 4γ2 s erg2 1 (2.23) n() = 1.4958 10−14 f 1 , × γ2 4γ2 where f(x) = 2x ln x + x + 1 2x2. This function is known as the IC kernel function − (see Eq. 2.24).

2.2.1.1 Klein-Nishina limit

The photon spectrum described by Eq. (2.23) is only valid in the Thomson limit, where 2 9 γ mec in the K frame. For a CMB photon this corresponds to γ 10 . The ∼ complete energy range is described by the Klein-Nishina (KN) formula. The IC kernel function describing the resultant photon spectrum in the KN regime is

dN1(γ, ) FIC (, γ, 1) ≡ dtd1 3σT c n() = (2.24) 4γ2 1 (Γq)2 2q ln q + (1 + 2q)(1 q) + (1 q) × − 2 1 + Γq − where, 4γ 1 Γ = 2 , q = 2 . (2.25) mec Γ(γmec ) − 1 The range of allowed energies follows purely from the kinematics of the problem:

4γ2 1 or 1 q 1. (2.26) ≤ 1 ≤ 1 + Γ 4γ2 ≤ ≤

2.2.2 Inverse Compton Spectrum

In order to ﬁnd the total Compton spectrum we have to convolve the electron distribu- −p tion, N(γ) = K0γ , with the IC kernel function and integrate over the electron energy given by γ and the initial photon spectrum characterised by . Note that we omitted the pitch angle dependence of the electron distribution, since this is only relevant for interactions with magnetic ﬁelds and in the case of IC scattering thus integrates out to Chapter 2. Theoretical Background 14 unity. The power per unit of energy per unit of volume becomes:

∞ γmax dNtot PIC ( ) = = N(γ)FIC (, γ, )dγd. (2.27) 1 1 dtd dV 1 1 Z0 Zγmin

Similarly to what we did for the synchrotron radiation, we can also ﬁnd a ﬂux density related to the inverse Compton scattering:

2 SIC ( ) = PIC ( ) V/(4πD ). (2.28) 1 1 · L

Photon spectral index The reasoning behind ﬁnding the spectral index related to inverse Compton scattering is analogous to the argument provided earlier for synchrotron radiation. Using the average energy of an IC scattered photon γ2, it follows that h 1i ∼

p−1 −(p+2) − 2 SIC ( ) γ dγ . 1 ∼ 1 ∼ 1

p−1 Thus again α = 2 . For the full details please see either Blumenthal and Gould(1970) or Rybicki and Lightman(1979).

2.3 The Electron Spectrum

Clusters of galaxies are excellent at hosting cosmic rays (CRs). For particles with en- 6 ergies . 10 GeV the diﬀusion time is longer than the Hubble time, this makes it likely that CRs are very abundant in the ICM (Berezinsky et al., 1996; Sarazin, 1999; Brunetti and Jones, 2014). Moreover, cosmic ray protons (CRps) have cooling times that are of the same order as the diﬀusion time, cooling mainly through collisions with other protons. As a result, CRps are expected to accumulate in clusters during their assembly history. On the other hand, CRes have cooling times that are much shorter. At energies of γ . 100, they cool through Coulomb cooling, whereas at higher energies γ & 100, IC and synchrotron cooling dominate (see Fig. 2.1).

In this study we take an agnostic approach for the origin of CRes. Their spectrum is assumed to be a power law, this is supported by radio observations. Moreover, it was shown that the observed power law is related to the electron distribution through p−1 α = 2 . However, it only extends over some ﬁnite range of energies, [γmin, γmax]. Chapter 2. Theoretical Background 15

(a)

(b)

Figure 2.1: Top: The diffusion and cooling times plotted as a function CR energy. CRps can accumulate in the cluster for the Hubble time, while CRes have much shorter cooling times (figure from Brunetti and Jones(2014)). Bottom: Energy loss rate for electrons. At low energies Coulomb cooling dominates whereas at high energies IC −3 −3 losses dominate. The plot is for ne = 10 cm , B = 1 µG and z = 0 (figure from Sarazin(1999)). Chapter 2. Theoretical Background 16

Thus, γmin and γmax correspond to a break in the spectrum at low and high energies, respectively. In particular, cooling processes can alter the shape of the spectrum over time. In our modelling, we will allow γmin and γmax to be free parameters, except when there is not enough data to ﬁt for them, in which case they are ﬁxed to theoretically motivated values (e.g. Sarazin, 1999).

The two main models for injecting CRes into the ICM are primary electron models and secondary, or hadronic, models. Primary electrons can be injected into the ICM as a power law through various possible accelerating mechanisms, such as in Active Galactic Nuclei (AGN). Sarazin(1999) discusses various primary electron models. If electrons are injected in a single event, their initial power law spectrum would soon start to deviate due to cooling, producing, amongst others, a cutoff. However, primary electrons from a single injection cannot be uniquely responsible for radio halos with sizes 1 Mpc since their diffusion length is of ∼ the order 10 kpc (Liang et al., 2002). Turbulent reacceleration models are proposed as ∼ a solution. They argue that seed CRes are reaccelerated through turbulence, produced on Mpc scale during cluster mergers. First, this allows the CRes to maintain their ∼ energy levels. In addition, since these processes are not very efficient, the time scales on which they occur are short. Thereby it links radio halos to recent cluster mergers. Finally, the electrons are predicted to have a maximum energy γ 105, producing a ∼ cutoff in the spectrum (see Feretti et al., 2012, and references therein). Sarazin(1999) also discusses a continuous injection model, to which reacceleration can be compared during the timescale of the merging event. In such a model the electron population reaches a steady state. It is then shown that, starting from an initial population with spectral index p, the population will over time steepen at high energies to a steady state 2 solution of p + 1. Moreover, at low energies, typically γ = bCoulomb∆t, the spectrum

will flatten to p 1. Here bCoulomb is the loss function due to Coulomb cooling and will − be discussed in more detail below. It has been suggested that a different form of reacceleration can explain the radio emission in radio relics, which typically have a low Mach number and therefore should not be efficient particle accelerators. Pinzke et al.(2013) showed how reacceleration can explain the observed spectrum. Reacceleration in relics would typically be a first order Fermi process, accelerating particles through shocks rather than turbulence.

2 1 This would lead to a diﬀerence of 2 in the photon spectral index of the injected and observed pinj −1 pobs−1 pinj −1+1 1 spectrum. If αinj = 2 and pobs = pinj + 1 then αobs = 2 = 2 = αinj + 2 . Chapter 2. Theoretical Background 17

In secondary models CRes are produced through p-p collisions. These hadronic collisions lead to pions which in return produce electrons and gamma rays through the following channels (Dennison, 1980; Pinzke and Pfrommer, 2010):

π0 2γ (2.29a) −→ ± ± ± π µ + νµ e + νe + νµ + νµ (2.29b) −→ −→

Although secondary models are not viable for relics, since the proton density is low at the cluster outskirts (Feretti et al., 2012), they are popular for explaining radio halos. Unlike CRes, CRps can diﬀuse through the cluster volume without cooling. Therefore, CRes can be injected in-situ. Although the hadronic model is attractive for various reasons (e.g. Pfrommer and Enßlin(2004)), the non-detection of γ-rays (see Eq. 2.29) from clusters to date puts heavy constraints on hadronic models (Zandanel and Ando, 2013).

2.3.1 Loss Functions

In this section we will discuss the energy losses of CRes in clusters following Rephaeli (1979) and Sarazin(1999). The loss rate function of a single particle is deﬁned as

dγ = b(γ, t) (2.30) dt − from which one can then deﬁne the lifetime3 as

γ tloss (2.31) ≡ b(γ)

The total loss rate function consists of parts due to bremsstrahlung, Coulomb cooling, IC

scattering and synchrotron radiation, i.e. b = bbremsstrahlung+bCoulomb+bIC +bsynchrotron.

3By lifetime we mean the time it takes for the electron to loose a large fraction of its energy and go towards thermal equilibrium. Chapter 2. Theoretical Background 18

The diﬀerent loss functions for these processes are:

−16 −1 bbremsstrahlung(γ, ne) 1.51 10 neγ (ln γ + 0.36) s (2.32a) ≈ × −12 ln(γ/ne) −1 bCoulomb(γ, ne) = 1.2 10 ne 1.0 + s (2.32b) × 75 4 σT 2 bIC (γ) = γ UCMB 3 mec 1.35 10−20γ2(1 + z)4 s−1 (2.32c) ≈ × 4 σT 2 bsynchrotron(γ, B) = γ UB 3 mec B 2 1.3 10−21γ2 s−1 (2.32d) ≈ × 1 µG

Figure 2.1b shows that for typical cluster values of the electron density and magnetic ﬁeld, Coulomb losses dominate at relatively low energies and IC losses dominate at the highest energies.

To see how the total lifetime (Eq. 2.31) depends on the electron density and magnetic ﬁeld we calculate the value of the Lorentz factor that maximises the lifetime of a CRe. −3 −3 Our reference scenario is z = 0, B = 1 µG and ne = 1 10 cm for which γ = 301 × maximises the cooling time. Next, we vary either ne or B with respect to the reference scenario and see how γ changes. The results are given in table 2.1. In addition, Fig. 2.2 provides the cooling time as a function of γ for the parameter values in table 2.1.

−3 B( µG) γ ne( cm ) γ 0.01 315 10−1 2549 1 301 10−2 911 2 268 10−3 301 5 171 10−4 97 10 97 10−5 31

(a) Magnetic ﬁeld dependence (b) Electron density dependence

Table 2.1: The Lorentz factor for which the loss timescale (Eq. 2.31) is maximised. −3 −3 The reference scenario is z = 0, B = 1 µG and ne = 1 10 cm for which γ = 301. One parameter is varied to see the eﬀect on the Lorentz× factor.

2.3.1.1 γmin

Given the values from table 2.1 and ﬁgure 2.2, in case there is not enough data to constrain γmin, we decide to ﬁx the lower bound of the power law to γmin = 300 for Chapter 2. Theoretical Background 19

1010

109

108 Time (yr)

107 B = 0.01µG B = 1µG B = 2µG B = 5µG B = 10µG 6 10 0 1 2 3 4 5 log10 γ (a)

1011

1010

109

108 Time (yr) 7 10 1 3 ne = 1 10− cm− × 2 3 ne = 1 10− cm− × 3 3 106 ne = 1 10− cm− × 4 3 ne = 1 10− cm− × 5 3 ne = 1 10− cm− 5 × 10 0 1 2 3 4 5 log10 γ (b)

Figure 2.2: Cooling time as a function of γ for various values of the magnetic ﬁeld and the electron density. The default values are the same as those in table 2.1.

radio halos. For radio relics we set γmin = 200; slightly smaller than for halos since the electron density is expected to be lower at the cluster outskirts, however, this does not have a major impact on our results as we will see. Note that for these values of the Lorentz factor the electron cooling time is of the order Hubble time, H−1 1010 yr. 0 ∼ Chapter 2. Theoretical Background 20

2.3.1.2 γmax

Deciding upon an upper limit for the power law is somewhat harder. We settle for a 5 value of γmax = 2 10 in case there is no spectral steepening in radio observations. × This value corresponds to an average energy of IC scattered photons of 104 keV h 1i ' (Eq. 2.20). We note that, e.g., Pinzke and Pfrommer(2010) consider electrons up to E 102 TeV, corresponding to γ 108, which is based on the maximum electron ∼ ∼ energy observed in young supernova remnants. For our purpose such high energies are not necessary, because only the position of the cutoff in our spectrum would change. Only if one starts to study the gamma-ray spectrum should we consider changing our allowed energy range. However, for the observed radio spectral index very-high energy emission is almost unimportant. Finally, fixing the cutoff energy to γ = 2 105 is in × accordance with the cutoff in halos predicted by turbulent reacceleration models, as discussed earlier (Feretti et al., 2012).

2.4 Analytical Magnetic Field Estimates

In sections 2.1 and 2.2 we discussed how the spectrum due to synchrotron radiation and inverse Compton scattering is computed. In our analyses, we assume a power −p law spectrum of electrons, N(γ) = K0γ , in some range [γmin, γmax]. However, the magnetic ﬁeld can also be estimated analytically without modelling the spectrum by assuming the power law extends from 0 to . In this case the synchrotron power ∞ becomes (Blumenthal and Gould, 1970, Eq. (4.59)):

3 (p+1)/2 (p−1)/2 4πK0e B 3e −(p−1)/2 Psyn(ν) = a(p)ν , (2.33) mc2 4πmc and for IC radiation (Blumenthal and Gould, 1970, Eq. (2.65)):

dNtot 3πσT (p+5)/2 −(p+1)/2 PIC (1) = 1 = 3 2 K0(kT ) b(p)1 dtd1dV h c (2.34) 3πσT (p+5)/2 −(p−1)/2 PIC (ν) = K (kT ) b(p)(hν) . h2c2 0 Chapter 2. Theoretical Background 21

The functions a(p) and b(p) are given by (see Blumenthal and Gould(1970) Eq. (4.60) & (2.66)): (p−1)/2√ 3p−1 3p+19 p+5 2 3Γ 12 Γ 12 Γ 4 a(p) = (2.35a) 1/2 p+7 8π Γ 4 2 p+5 p+5 (p + 4p + 11)Γ 2 ζ 2 b(p) = 2p+3 (2.35b) (p + 3)2(p + 1)(p+ 5)

Since Psyn and PIC are related to the same CRe population, we can use Eq. (2.33)

and (2.34) to solve for the magnetic field. Let sr be the radio flux density at a given 4 frequency and fx the X-ray flux . For a pure power law they can be defined through

νmax erg −α fx 2 = kx νx dνx (2.36a) cm s ν h i Z min

erg −α sr = krν (2.36b) cm2 s Hz r h i where kx and kr are normalisation factors. Using,

3 3mek σT esu b = 2.46 10−19 4h2e3 × cm2 K3 4πmeck esu b = 4962 3eh cm2 K we obtain (Harris and Romanishin, 1974; Sarazin, 1988; Longair, 2011):

−α −19 3 3 α fxνr 2.46 10 TCMB b(p) 4.96 10 TCMB νmax −α = × × (2.37) sr νx dνx B a(p) B νmin R 3 where TCMB = (1 + z) T0. In case one uses the differential flux in X-ray, rather than the flux, this expression becomes:

−α −19 3 3 α sxν 2.46 10 T b(p) 4.96 10 TCMB r = × CMB × (2.38) s ν−α B a(p) B r x

erg −α with sx cm2 s Hz = kxνx .

Correction for Isotropically Distributed Magnetic Fields Eq. (2.37) and (2.38) are frequently used in the literature to provide lower limits on the volume averaged magnetic ﬁeld in clusters (e.g. Ajello et al.(2009, 2010); Wik et al.(2009); Ota et al. (2013)). However, these expression do not properly take into account the orientation

4The flux is the flux density or differential flux integrated over some energy range. Chapter 2. Theoretical Background 22 of the magnetic fields as discussed in section 2.1.4. Here we calculate the correction to Eq. (2.35a) for an isotropic distribution of magnetic fields.

The gamma function in Eq. (2.35a) arise from the integral over pitch angles as performed in Blumenthal and Gould(1970) (see Eqs. 4.58-4.60). In general an integral of this form evaluates to p+n+2 π p+n Γ 4 dθ(sin θ) 2 = √π . 0 p+n+4 Z Γ 4 In the literature one ﬁnds n = 3. Here one sin θ comes from the dependence of the power on the pitch angle (Eq. 2.7). Another sin θ comes from the isotropic distribution p−1 of pitch angles (Eq. 2.9). Finally, there is a sin 2 θ coming from the integral over γ. To illustrate this last point recall that we have

∞ ∞ −p dγγ x dξK5/3(ξ), Z0 Zx

ν 2 − 1 − 1 − 1 − 3 where x and νc γ sin θ. Therefore, γ x 2 sin 2 θ and dγ sin 2 θx 2 dx. So ≡ νc ∝ ∝ ∝ overall the above integral is proportional to

∞ ∞ p−1 p−1 sin 2 θ dxx 2 dξK5/3(ξ). Z0 Zx

p+3 Combining all the terms we have sin 2 θ. However, as discussed in section 2.1.4, there is sin θ an extra 2 term if one considers an isotropic distribution of magnetic ﬁeld orientations. Thus, the integral over pitch angles becomes,

p+7 π 1 p+5 √π Γ 4 dθ(sin θ) 2 = . 2 0 2 p+9 Z Γ 4 Therefore the correct factor a(p) to be used in expression (2.37) and (2.38) when estimating magnetic ﬁelds is:

(p−1)/2√ 3p−1 3p+19 p+7 2 3Γ 12 Γ 12 Γ 4 a(p) = . (2.39) 1/2 p+9 16π Γ 4 As a result of this modification, lower limits on the magnetic field in cluster halos and relics have been underestimated. Consequently the gap between the magnetic field Chapter 2. Theoretical Background 23 strength estimates through equipartition and Faraday rotation measurements on the one side, and IC non-detection on the other, becomes smaller. Chapter 3

Methods

This work aims at making predictions for the detectability of non-thermal IC radiation from radio halos and radio relics. We model the radio and X-ray spectrum by fitting Eq. (2.13) and (2.27) to flux density measurements from the literature. In order to predict when IC emission becomes detectable, we model the thermal bremsstrahlung and compare this to the ASTRO-H sensitivity curves. We argue that IC emission is detectable if it dominates over the background components. This provides a lower limit on the detectable value of the electron distribution normalisation, K . Since Ssyn K B 0 ∝ 0 this consequently yields a maximum value for the magnetic field B that allows for the detection of IC radiation. All steps are discussed in detail below.

3.1 Cluster Selection and Data

We analyse all known radio haloes and relics based on the September2011-Halo and September2011-Relic collection from Feretti et al.(2012), with the condition that they have at least two radio measurements at diﬀerent wavelengths in order to determine the spectral index of the power law. We searched the literature for radio data that was published after this date. This led to some new radio data for previously studied clusters and, in addition, it led to the inclusion of 1RXS J0603.3+4214, A3411 and ACT-CL J0102-4915 which all host one or more radio relics. In this section, our use of archival radio and non-thermal X-ray measurements is discussed. Our full sample of

24 Chapter 3. Methods 25 halos and relics, including X-ray upper limits if available, can be found in table 4.1. All radio data, including the relevant references, can be found in appendixB.

Radio Data Radio data is presented as a flux density in units of Jansky1 ( Jy). In the literature one often comes across the term integrated flux density, which means that the flux density is integrated over the entire source. This is the value we are interested in. Flux density integrated over the full source must be a fixed quantity, independent of the telescope and its beam size. Moreover, we are interested in the volume averaged magnetic field, therefore we should consider the radio emission from the full volume. Some radio data is presented without errors, in these cases we adopt an error of 10% unless mentioned otherwise. For more on radio astronomy see for example Wilson et al. (2009).

3.1.1 Non-Thermal X-Ray Data

Studying non-thermal inverse Compton emission from galaxy clusters faces the problem

of a huge background due to the thermal plasma. However, at high energies & 10 keV, so-called hard X-rays (HXRs), the thermal spectrum quickly falls oﬀ and non-thermal emission could eventually dominate over thermal emission. A small number of detections of non-thermal X-rays have been claimed in the literature (Rephaeli and Gruber, 2002; Nevalainen et al., 2004; Fusco-Femiano et al., 2004; Rephaeli et al., 2006; Rephaeli et al., 2008; Murgia et al., 2010). However, more recent observations have ruled out most of these detections and placed upper limits on the non-thermal ﬂux from clusters (Ajello et al., 2009, 2010; Wik et al., 2011; Ota et al., 2013; Wik et al., 2014). Additionally, some attempts have been made to detect non-thermal emission in soft X-rays (SXRs). A non-thermal excess has in fact been observed, however, it has not been exclusively attributed to cosmic rays (Sarazin and Lieu, 1997; Bonamente et al., 2002). In our analysis we use upper limits on non-thermal X-rays if available (e.g. Million and Allen, 2009; Ajello et al., 2009, 2010; Wik et al., 2012).

As a result of the limited sensitivity of our current telescopes, upper limits in X-rays are determined as the excess ﬂux in some large energy range (e.g. 20 80 keV or 50 100 keV). − − However, in order to model accurately the current lower limits on the magnetic ﬁeld, we

11 Jy = 10−23 erg cm−2 s−1 Hz−1 Chapter 3. Methods 26 have to determine the flux density at some energy. Therefore, we model the flux back to a flux density by applying Eq. (2.36a):

νmax erg −α fx 2 = kx νx dνx. cm s ν h i Z min

The flux, fx, and the energy interval, [νmin, νmax], are given in the literature. For the photon spectral index we use the value corresponding to the best fit in determining the upper limit (for values and references see table 4.1). Using these values to determine kx we can then find the flux density through:

−2 −1 −1 −α sx(ν) erg cm s Hz = ν kx. (3.1) Finally, unless mentioned otherwise, the upper limits we take from the literature are at 99% c.l. or 3σ.

3.2 Background Modelling

The most important background for our purposes is thermal bremsstrahlung. In order to model this component we use an APEC model as provided in the XSPEC code (Arnaud, 1996).

3.2.1 APEC model

The Astrophysical Plasma Emission Code (APEC)2 models emission spectra from collisionally-ionized diffuse gas and is used to model the thermal emission in clusters. Four parameters have to be provided. The plasma temperature in keV, which we take from the literature (Ota, 2001; Chen et al., 2007), the metallicity in solar units, the redshift, and the normalisation in cm−5. We fix the metallicity to 0.30 for all clusters in our analysis. Whereas this value can vary a lot from cluster to cluster, 0.30 is a reasonable average value which is also used in other studies in the literature (e.g. Ota et al., 2013). Moreover, for our purpose we do not require to have exact knowledge of the background, a good estimate should suffice. Changing the metallicity mostly influences the intensity of the atomic transitions, as can be seen from Fig. 3.1.

2For more information see http://atomdb.org/. Chapter 3. Methods 27

9 10− Z1 = 1.0Z ] Z2 = 0.3Z /s 10 2 10− Z3 = 0.0Z

/ 11 10− [erg ν

S 12 10− · ν 13 10− Z Z 1− 2 100 Z1 × Z Z 30 2− 3 100 Z2 ×

10 Diﬀerence [%]

0 1016 1017 1018 1019 ν[Hz]

Figure 3.1: Plasma emission in Coma for different metallicities, Z = 0.0Z , Z = 0.3Z and Z = 1.0Z . The other parameters are kept fixed (z = 0.0231, kT = 9.0 keV and the normalisation is 0.51 cm−5). The difference is of the order 5% except at the atomic transitions (e.g. iron line) and the high frequency end.

3.2.1.1 Thermal Gas Density

The normalisation for the APEC model contains information about the ICM gas distribution. The exact deﬁnition, with DA the angular diameter distance to the source in −3 cm, and ne(r) and nH (r) the electron and hydrogen number densities in cm , is:

−14 10 2 r ne(r)nH (r)dr. (3.2) D2 (1 + z)2 A Z

The electron and hydrogen density are not completely independent and are both de- creasing functions of the radial distance to the cluster core. For our purpose the electron number density is well described by the phenomenological beta model (Cavaliere and Fusco-Femiano, 1976), Chapter 3. Methods 28

− 3 β r 2 2 2 ne(r) = n 1 + , (3.3) 0 r c !

where n0 and rc are the core electron number density and the core radius. Some clusters are described better by a multi-component beta model,

1 −3βi 2 2 2 2 r ne(r) = n 1 + . (3.4)  0,i r  i c,i ! X  

The parameters of the beta proﬁle, n0, rc and β are taken from the literature (e.g. Ota, 2001; Pinzke et al., 2011).

Clusters without a gas density model. If there exists no gas density model for a cluster in the literature we model the gas density using the phenomenological model by Zandanel et al.(2014) which is based on X-ray observations of the representative XMM- Newton cluster structure survey (REXCESS) sample (Croston et al., 2008; Pratt et al.,

2009). The model is only dependent on the cluster mass (M500), providing an average gas proﬁle at all masses by using an observational gas fraction-mass relation. Moreover, in case there is no cluster temperature available in the literature we use Eq. (4) and (5) and table (7) in Mantz et al.(2010) to estimate the cluster temperature. In a few cases where no mass estimate is present in the literature, we model the mass using the

LX M or Lbol M relation, also deﬁned in the above-mentioned expressions from − 500 − 500 Mantz et al.(2010). Here LX is the ROSAT 0.1 2.4 keV luminosity, which for many − sources can be found in Voges et al.(1999). Finally, in one case we determine M500 from

M200 assuming a Navarro-Frenk-White (NFW) proﬁle (Navarro et al., 1997) and using the Duﬀy et al.(2008) concentration-mass relation.

Thermal emission in the halo region. For halos, we integrate over the entire 3 cluster, where we set the cluster boundary to be at the virial radius, r200. It is important to note that for a more accurate approximation of the plasma emission we should integrate only over the volume of diﬀuse radio emission. The radius of a radio halo, typically 0.5 Mpc, is smaller than the cluster virial radius. However, this has only minor ∼ 3Strictly speaking, this is not the virial radius, but the radius where the average density of the cluster is 200 times the critical density. Chapter 3. Methods 29

10 10− ] N : 0.0528cm 5 2 1 − 5 N2 : 0.0257cm− cm / s

/ 11 10− [erg ν S · ν 12 10− 0.8 2 1

N N 0.6

= 0.4 R 0.2

0.0 1017 1018 1019 ν[Hz] Figure 3.2: Top: plasma emission for A0754 computed for two diﬀerent volumes. The green line is the emission from a sphere with radius r200 = 2360 kpc from the cluster centre. The red line corresponds to a radius of 300 kpc, which is similar to the region of radio emission. The temperature, redshift and metallicity are set to 9.0 keV, 0.0542 and 0.3 Z , respectively. Bottom: the ratio between the two lines. By integrating out to the virial radius we overestimate the plasma emission by about a factor of 2. This ratio can be trivially deduced from the values of the normalisation.

inﬂuence on the normalisation. We choose to integrate up to the virial radius, slightly overestimating the thermal emission, and thereby obtain more conservative predictions for the detectability of IC emission. We show that the eﬀect is small for the cluster A0754 in Fig. 3.2.

Thermal emission in the relic region. As opposed to radio halos, we do take into account the weakening of plasma emission for radio relics. Relics are located at the cluster outskirts, so thermal emission is expected to give a much smaller background there. Therefore, it is important to model this more accurately. For this purpose we integrate over part of the volume of a sphere. The following formula is used for the normalisation in this case,

−14 Rcc+0.5Rh 10 2 (1 cos θ) r ne(r)nH (r)dr. (3.5) 2D2 (1 + z)2 − A ZRcc−0.5Rh Chapter 3. Methods 30

��

� ��

��

Figure 3.3: The geometry that is used in determining the normalisation of the APEC model for radio relics (Eq. 3.5). Rcc corresponds to the distance between the relic and the cluster center as projected on the sky. Rv is approximately the relics largest −1 0.5Rv linear size and Rh is the relics ’width’. θ is given by tan . Eq. (3.5) thus Rcc−0.5Rh integrates over a solid angle represented by the dashed line. Relic image taken from R¨ottgeringet al.(2013).

Figure 3.3 illustrates how we deﬁne the region over which we integrate and the param-

eters used in Eq. (3.5). Rv is the relics largest linear size and Rcc its distance from the cluster centre as projected on the sky. For most relics these values can be found in

Feretti et al.(2012). Rh is the width of the box we use to enclose the relic. Correspond-

ingly we define the surface of the relic to be Rv Rh. For relics that are classified as × roundish by Feretti et al.(2012) we use Rh = Rv, for elongated relics we estimate Rh based on radio images. Finally, we define the angle over which the solid angle subtends

−1 0.5Rv as θ = tan and integrate from Rcc 0.5Rh to Rcc + 0.5Rh. Since we inte- Rcc−0.5Rh − grate over a region that covers a larger region of the sky than our relic region (Rv Rh) × we are prone to slightly overestimate the thermal bremsstrahlung. Chapter 3. Methods 31

3.2.1.2 PyXspec

To obtain the plasma spectra we use PyXspec4, an object oriented python interface to the XSPEC spectral-ﬁiting program5. In table 3.1, the values for the redshift, normalisation and temperature used in this work are shown. We model the background from 0.01 − 82.5 keV in 100 bins.

Cluster z Norm. kT Reference ( cm−5) ( keV) Halos 1E0657-56f 0.296 1.61 × 10−2 14.20 6 A0520 0.199 1.56 × 10−2 7.10 7, 8 A0521a 0.2533 7.80 × 10−3 5.85 11, 13 A0665 0.1819 2.71 × 10−2 6.96 2 A0697 0.282 2.12 × 10−2 8.19 2 A0754 0.0542 5.28 × 10−2 9 1 A1300 0.3072 1.15 × 10−2 8.33 2 A1656 0.0231 5.1 × 10−1 8.38 1 A1758 0.279 1.15 × 10−2 6.88 2 A1914 0.1712 2.52 × 10−2 10.53 1 A2163 0.203 3.6 × 10−2 13.29 3 A2218 0.1756 1.3 × 10−2 7.63 2 A2219 0.2256 3.33 × 10−2 9.22 2 A2255 0.0806 3.57 × 10−2 6.87 1 A2256 0.0581 1.03 × 10−1 7.50 1 A2319 0.0557 1.99 × 10−1 9.20 1 A2744 0.308 1.82 × 10−2 8.95 2 A3562 0.049 4.68 × 10−2 5.16 1 CL0217+70a,b 0.0655 9.90 × 10−3 3.54 14 MACSJ0717.5+3745 0.5458 3.82 × 10−4 11.60 10 PLCK G171.9-40.7a 0.27 1.30 × 10−2 10.65 12 RXCJ1514.9-1523a,b 0.22 1.20 × 10−2 7.83 13 RXCJ2003.5-2323a,b 0.3171 6.90 × 10−3 7.62 13 Relics 1RXS J0603.3+4214a,c 0.225 6.40 × 10−4 7.80 16 A0013 0.0943 2.98 × 10−3 6 5 A0085 0.0551 5.1 × 10−3 6.10 1 Continued on next page

4https://heasarc.gsfc.nasa.gov/xanadu/xspec/python/html/. 5Standard XSPEC uses the Tool Command Language (Tcl). Chapter 3. Methods 32

Table 3.1 – continued from previous page Cluster z Norm. kT Reference ( cm−5) ( keV) A0521a 0.2533 3.20 × 10−4 5.85 11, 13 A0610ab,e 0.0954 1.30 × 10−4 2.44 21 AS753a 0.014 4.20 × 10−4 2.50 20 A0754 0.0542 8.5 × 10−4 9 1 A1240 N 0.159 3.70 × 10−6 6 4 S 0.159 1.50 × 10−6 6 A1300 0.3072 6.80 × 10−4 8.33 2 A1367 0.022 2.70 × 10−4 3.55 1 A1656 0.0231 8.5 × 10−4 8.38 1 A1664 0.1283 6.00 × 10−4 6.80 7 A2048a,b,d 0.0972 4.00 × 10−4 4.21 19 A2061 0.0784 6.60 × 10−4 4.52 9 A2063 0.0349 3.60 × 10−3 3.68 1 A2255 0.0806 3.20 × 10−4 6.87 1 A2256 0.0581 2.3 × 10−2 7.50 1 A2345ab E 0.1765 2.60 × 10−4 6.51 13 W 0.1765 8.50 × 10−4 6.51 A2433a,b,e 0.108 2.70 × 10−5 1.80 18 A2744 0.308 5.4 × 10−5 8.95 2 A3376 E 0.0456 5.40 × 10−3 4.30 1 W 0.0456 3.10 × 10−5 4.30 A3411a 0.1687 3.20 × 10−3 6.40 22 A3667 NW 0.0556 6.60 × 10−4 7 1 A4038 0.03 2.80 × 10−4 3.15 1 ACT-CL J0102-4915a E 0.87 2.70 × 10−2 14.50 15 NW 0.87 2.70 × 10−2 14.50 SE 0.87 2.70 × 10−2 14.50 CIZAJ2242.8+5301a,b,c 0.1912 1.10 × 10−5 5.55 17 PLCK G280+32.0a,c N 0.39 7.40 × 10−5 12.86 17 S 0.39 5.20 × 10−7 12.86 ZwCl0008.8-5215a,b E 0.1032 1.30 × 10−4 4.98 13 W 0.1032 9.80 × 10−6 4.98

aGas density from Zandanel et al.(2014).

b Temperature from T − M500 relation (Mantz et al., 2010). c M500 from ROSAT LX − M500 relation (Mantz et al., 2010). d M500 from bolometric Luminosity (Mantz et al., 2010). e M500 scaled from M200. Continued on next page Chapter 3. Methods 33

Table 3.1 – continued from previous page Cluster z Norm. kT Reference ( cm−5) ( keV) fNormalisation taken straight from the reference.

Table 3.1: Thermal data for our cluster sample. References: [1] Chen et al.(2007); Pinzke et al.(2011); [2] Ota(2001); [3] Ota et al.(2013); [4] Barrena et al.(2009); Cavagnolo et al.(2009); [5]Juett et al.(2008) [6] Wik et al.(2014) ; [7] Govoni et al. (2001); [8] Govoni et al.(2004); Vacca et al.(2014); [9] Marini et al.}(2004); [10] Ma et al.(2008); [11] Ferrari et al.(2006); [12] Collaboration et al.(2011); [13] Planck Collaboration et al.(2013); [14] Brown et al.(2011b); [15] Menanteau et al.(2012); [16] Ogrean et al.(2013); [17] Piﬀaretti et al.(2011); [18] Popesso et al.(2007); [19] Shen et al.(2008); [20] Subrahmanyan et al.(2003); [21] Yoon et al.(2008); [22] van Weeren et al.(2013).

3.3 ASTRO-H Sensitivity

ASTRO-H is a next generation X-ray satellite that is scheduled for launch in 2015. The instruments that are of interest for this study are the Hard X-ray Imager (HXI) and the Soft X-ray Imager (SXI). All instruments are co-aligned and will operate simultaneously (Takahashi et al., 2012). The properties of aforementioned instruments, and also of the Soft X-ray Spectrometer (SXS), are given in table 3.2.

SXS SXI HXI Energy range (keV) 0.3-12.0 0.4-12.0 5-80 Angular resolution (arcmin) 1.3 1.3 1.7 Field of view (arcmin2) 3.05 3.05 38 38 9 9 × × × Energy resolution (eV) 5 150 < 2000 (@6keV) (@60keV) Eﬀective area (cm2) 50/225 214/360 300 (@0.5/6keV) (@30keV) Instrumental background 2 10−3/0.7 10−3 0.1/0.1 6 10−3/2 10−4† × × × × (s−1 keV−1 FoV) (@0.5/6keV) (@0.5/6keV) 2 10−3/4 10−5‡ × × (@10/50keV) † for 4 layers, relevant for hard x-rays (20 80keV) − ‡ for 1 layer, relevant for soft x-rays (< 30keV)

Table 3.2: Properties of the relevant ASTRO-H instruments, the Soft X-ray Spectrom- eter (SXS), Soft X-ray Imager (SXI) and the Hard X-ray Imager (HXI). Values adopted from the ASTRO-H Quick Reference (http://astro-h.isas.jaxa.jp/ahqr.pdf).

To estimate the detectability of the non-thermal X-ray component in galaxy clusters we make use of the sensitivity curves as published by the ASTRO-H collaboration. These Chapter 3. Methods 34 are shown ﬁgure 3.4 for both point and extended sources (ASTRO-H Quick Reference6, Takahashi et al.(2010, 2012)). In our analysis we use the sensitivity curve for 1 Ms of observation. For diﬀerent observation times one can assume the sensitivity to improve as √time (see Fig. 3.5).

(a)

(b)

Figure 3.4: Sensitivity curves for ASTRO-H. The curves correspond to 1 Ms of observation time. Top plot refers to point sources, whereas the bottom plot is for uniform sources of 1 degree2. The ﬁgure is taken from Takahashi et al.(2010).

6http://astro-h.isas.jaxa.jp/ahqr.pdf. Chapter 3. Methods 35

10 8 − 100 ks 1 Ms 1Ms √10 × 9 ] 10− 2 cm / sec

/ 10 10− [erg ν S ·

ν 11 10−

10 12 − 1018 1019 ν[Hz]

Figure 3.5: Comparison of the 100 ks HXI detection limits from the ASTRO-H quick reference (http://astro-h.isas.jaxa.jp/ahqr.pdf) and the 1 Ms curve from Taka- hashi et al.(2010). Scaling this latter curve by a factor of √10 reproduces to 100 ks line.

The bottom plot in Fig. 3.4 is for a uniformly distributed source of 1 degree2. Since the ﬁeld of view (FoV) of HXI is 90 90, this means that the number of photons observed × by HXI is 9×9 S photons cm−2 s−1 keV−1 , where S is the HXI sensitivity for a 60×60 × 1 degree2 source (Fig. 3.4b). For our analysis, we will assume that the halos and relics are uniform sources, whereas in reality they are clearly non-uniform. Emission will be higher in certain regions and ASTRO-H could in fact observe emission from a smaller region. Let us assume we have a source of a certain size on the sky, x arcmin2. We can then rescale the sensitivity curve assuming that the source is uniform by

x arcmin2 S photons cm−2 s−1 keV−1 . (3.6) 3600 arcmin2 × As long as the source size is larger than the HXI FoV, we can assume this scaling to hold since it will yield the same number of photons for the HXI instrument. However, several sources in our sample are smaller than the HXI FoV. Nevertheless, we use the same scaling, since the source should in that case be resolvable as an extended object. 2 Only for sources that have a size . 10 arcmin we use the point source sensitivity, since Chapter 3. Methods 36 there our scaling starts to fall short, making HXI too sensitive.

Concluding, for sources 10 arcmin2 we use Eq. (3.6) and the point source sensitivity ≥ is used otherwise7.

3.4 Analysis of the Spectrum

Having established the theoretical framework for synchrotron and inverse Compton radiation, a model for the background and the sensitivity for our instrument of reference, ASTRO-H, we now provide a step-by-step walkthrough of spectral analysis. Abell 754 is used as an example. For illustrative purposes all steps are presented in Fig. 3.6.

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.06µG BV = 0.06µG Plasma

10 11 10 11 − − X-ray background ] ] 2 2 12 12 10− Non-thermal spectrum 10− cm cm / / sec sec

/ 13 / 13 10− 10− [erg [erg ν ν

S 14 S 14 · 10− · 10− ν ν

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 − 107 109 1011 1013 1015 1017 1019 1021 ν[Hz] ν[Hz] (a) (b) E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.06µG BV = 0.06µG Plasma Plasma ASTRO-H 1Ms ASTRO-H 1Ms 11 11 10− 10− BV = 0.31µG ] ] 2 2 12 ASTRO-H sensitivity 12 10− 10− cm Takahashi et al. (2010) cm Non-thermal spectrum / / detectable by ASTRO-H sec sec

/ 13 / 13 10− 10− [erg [erg ν ν

S 14 S 14 · 10− · 10− ν ν

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 − 107 109 1011 1013 1015 1017 1019 1021 ν[Hz] ν[Hz] (c) (d)

Figure 3.6: Analysis of the non-thermal spectrum in a cluster. Data corresponds to Abell 754 (Bacchi et al., 2003; Ajello et al., 2009).

First, Eq. (2.27) is fit to the upper limit in X-ray if available. To do this we fix the high 5 energy cutoff to γmax = 2 10 , as, unless the energy of the upper limit in X-ray is close × 7Madoka Kawaharada (private communication) Chapter 3. Methods 37 to the cutoff energy, fixing the cutoff does not impact our result. From this fit we fix the normalisation of the electron distribution, K0. Next, Eq. (2.13) is fit to the available radio data. If spectral steepening is observed, the lower and/or higher cutoff are kept free during the fit. The spectral index is taken from the literature, unless it returns a poor fit, in which case we determine a new spectral index. The resultant spectrum provides the current lower limit on the magnetic field (see Fig. 3.6a).

Next, we compare the resulting broadband spectrum to the thermal background (Fig. 3.6b) and ASTRO-H sensitivity (Fig. 3.6c). We use the intersection between the thermal background and ASTRO-H sensitivity to ﬁx a new normalisation of the electron distribution. This point is the lower limit on the normalisation detectable by ASTRO-H, whilst not being obscured by bremsstrahlung emission. If no upper limits on the X-ray ﬂux exist for a cluster, we start from this step.

Finally, we ﬁt Eq. (2.13) to the radio data, again. The resulting value of the magnetic ﬁeld is the highest volume averaged value for which non-thermal IC radiation will still be detectable by ASTRO-H. All results are presented in the next chapter. Chapter 4

Results and Discussion

This chapter contains the results of our analysis. Our full halo and relic sample is given in table 4.1, including the approximate area they cover on the plane of the sky, and the upper limit on the non-thermal X-ray flux where presents. Results for halos are shown in table 4.2 and for relics in table 4.3. The first column of these tables contains the name of the cluster. The photon spectral index observed in radio can be found in the second column. Columns 3-5 contain the current lower limit on the magnetic field and the values for γmin and γmax. Note that there are only lower limits for clusters that have an upper limit on the IC flux. Moreover, we only fit for γmax and/or γmin if spectral steepening is observed, otherwise they are fixed to 2 105 and 300 respectively. Columns 6-8 are × essentially the same as 3-5, but now the magnetic field (Bu.l.) corresponds to the upper limit for which ASTRO-H can still detect non-thermal X-rays within 1 Ms of observation time. Columns 9 and 10 give χ2 and the number of degrees of freedom, respectively. These refer solely to the fit to the radio data, i.e. the last step described in section 3.4. Finally, columns 11 and 12 contain the flux density and energy at which the ASTRO-H sensitivity curve intersects the thermal background spectrum. Comments on individual clusters are given in sections 4.1. Section 4.3 contains a more general discussion.

38 Chapter 4. Results and Discussion 39

Table 4.1: Cluster Sample

† ‡ * Cluster z Surface Fx Band Γ Ref. Comments arcmin2 (keV) Halos

1E0657-56 0.296 19 1.1 50-100 1.86 x Bullet A0520 0.199 25 A0521 0.2533 20 A0665 0.1819 58 4.2 0.6-7 1.63 vi A0697 0.282 20 A0754 0.0542 57 6.5 50-100 2 i A1300 0.308 18 A1656 0.0231 680 4.2 20-80 2 viii Coma A1758N 0.279 28 A1914 0.1712 43 1.09 50-100 2 i A2163 0.203 104 1.7 20-80 1.5 vii A2218 0.1756 p A2219 0.2256 50 A2255 0.0806 76 2.73 20-80 2 ix A2256 0.058 254 2.41 50-100 2 ii A2319 0.0557 200 0.67 50-100 2 i A2744 0.308 39 0.4 0.6-7 1.66 vi A3562 0.049 50 5.52 20-80 2 ix CL0217+70 0.0655 79 MACSJ0717.5+3745 0.5458 13 PLCK G171.9-40.7 0.27 16 RXCJ1514.9-1523 0.22 39 RXCJ2003.5-2323 0.3171 20 Relics

1RXS J0603.3+4214 0.225 18 Toothbrush A0013 0.0943 p A0085 0.0551 26 2.51 50-100 2 ii A0521 0.2533 18 A0610 0.0954 p AS753 0.014 300 A0754 0.0542 130 A1240 N 0.159 15 S 43 A1300 0.3072 p Continued on next page Chapter 4. Results and Discussion 40

Table 4.1 – continued from previous page

† ‡ * Cluster z Surface Fx Band Γ Ref. Comments arcmin2 (keV) A1367 0.022 82 8.24 20-80 2 ix A1656 0.0231 310 0.32 0.3-10 2.2 iii Coma A1664 0.1283 66 A2048 0.0972 p A2061 0.0784 49 A2063 0.0349 p 7.58 20-81 2 ix A2255 0.0806 32 A2256 0.058 136 A2345 E 0.1765 35 W 45 A2433 0.108 p A2744 0.308 12 0.4 0.6-7 1.66 vi A3376 E 0.0456 162 14 4-8 2 iv W 94 21 4-8 2 v A3411 0.1687 121 A3667 0.0556 320 0.62 10-40 1.8 v A4038 0.03 16 7.43 20-80 2 ix ACT-CL J0102-4915 E 0.87 p El-Gordo NW p SE p CIZAJ2242.8+5301 N 0.1921 18 Sausage PLCK G287.0+32.9 N 0.39 p S p ZwCl0008.8-5215 E 0.1032 33 W p

†Upper limit on the non-thermal X-ray ﬂux in 10−12erg cm−2 s−1 ‡Spectral index used to derive non-thermal upper limit. ∗Reference refers to the non-thermal X-ray upper limit.

p 2 Considered a point source in our analysis (. 10arcmin ). iAjello et al.(2009); iiAjello et al.(2010); iiiFeretti and Neumann(2006); ivKawano et al.(2009); vNakazawa et al.(2009); viMillion and Allen(2009); viiOta et al.(2013); viiiWik et al.(2011); ixWik et al.(2012); xWik et al.(2014). Chapter 4. Results and Discussion 41 ‡ E (keV) † 067 35 140 38 110 52 028 25 140 19 174 36 200 44 160 41 300 40 270 48 066 46 850 57 310 54 084 33 220099 63 051 40 210 30 094 38 450 44 074 56 41 x ...... F f . o 3 0 . d 4 10 60 2 0 00 1 0 00 1 0 17 1 0 56 3 0 961500 2 2 1 1 - 0 - 21 2 0 08 1 0 53 1 0 37 1 0 11 7 0 9403560003 624 100 403 0 111 0 4 0 1 0 1 11 0 0 1 0 - 0 - 2 ...... × χ 05 . ) 5 313 9 271 0 . . 10 max × γ (1Ms) )( 3 3 2 1 3 2 0 3 2 0 3 2 1 3 2 0 3 0 33 2 2 0 0 3 2 2 3 2 0 2 2 1 3 2 0 7 2 3 3 233 2 0 46 0 33 23 23 23 2 0 0 2 4 0 0 ...... 10 min γ × Results for halos ASTRO-H . 14 0 62 0 08 0 26 0 63 0 46 0 37 0 51 0 71 0 27 0 57 13 48 0 12 1 89 0 40 0 46 0 4308 0 0 53 0 05 0 92 0 G) ( ...... u.l. 1 µ − B ( s 2 − ) 5 681 0 603 0 389 - - - 64 . . . 10 max Table 4.2: erg cm × γ 12 − )( 3 3 0 3 2 - - - 7 33 2 2 0 0 3 2 0 3 2 0 3 2 1 3 233 0 2 0 0 3 0 ...... 10 min × Current Limits 10 0 70 0 20 0 29 0 32 0 13 0 59 2 38 0 11 0 09 0 32 0 G) ( ...... B γ µ ( 32 1 60 0 84 1 98 2 20 0 30 0 80 0 35 0 92 0 60 0 72 0 60 0 18 0 95 0 7650 1 0 16 0 5012 0 810452 0 10 0 0 1 0 ...... α 1 1 ∗ ∗ ASTRO-H sensitivity curve does not intersect thermal plasma spectrum. No improvement possible due to large size on the sky. Energy where non-thermal X-rays will start to dominate over the plasma emission. Non-thermal ﬂux detectable by ASTRO-H (1Ms) in 10 RXCJ2003.5-2323 1 RXCJ1514.9-1523 1 PLCK G171.9-40.7 1 MACSJ0717.5+3745 0 CL0217+70 1 A2319 A3562 1 A2256A2744 1 0 A2255 1 A2219 0 A2218 1 A2163 1 A1914 1 A1300A1656 A1758N 1 1 ‡ ∗ Cluster 1E0657-56A0520A0521A0665A0697 1 A0754 1 1 1 1 1 † Chapter 4. Results and Discussion 42 ‡ 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...... E (keV) † 039 25 040 33 077 33 026 16 010 8 099 6 240 20 027 20 079 20 080 10 180 0 100 17 019 17 062 14 024 24 056 19 058 0 510 39 048 15 078 19 011 10 014 14 260 18 170 20 230 21 310 10 018 12 093 53 930 53 093 53 017 10 020 18 011 10 032 10 011 10 x ...... F f . o . d 34 9 0 61 4 0 98 6 0 11 5 0 05 1 0 16 2 0 41 1 0 1110 1 1 0 0 04 1 0 80 5 0 19 2 0 00 1 0 44 2 0 09 12 0 04 1 0 04 1 0 01 2 0 9900 1 1 0 0 69 1 0 35 1 0 51 1 0 54 1 0 85 2 0 12 4 0 75 7 0 2285 158 2 1 0 0 0 47 6 0 0000 1 1 0 0 4042 3 2 0 0 2 ...... χ ) 5 067 13 097 3 038 16 059 0 154 3 156 1 058 42 336 35 ...... 10 max × γ (1Ms) )( 3 2 2 1 5 2 4 3 0 2 2 3 2 2 0 2 0 2 2 2 22 2 2 0 1 2 2 0 2 2 3 2 2 5 2 2 0 2 2 1 2 0 2 2 0 2 2 0 2 2 2 22 2 2 1 0 2 0 2 2 0 2 0 2 0 2 2 0 2 2 3 2 0 222 2 2 2 0 4 0 2 0 22 2 2 0 0 29 2 2 2 2 ...... 10 min γ × ASTRO-H 70 0 15 2 36 1 40 0 96 0 70 0 42 0 2612 0 0 86 0 31 0 90 0 19 0 47 0 02 0 71 0 33 0 43 0 0825 0 0 48 0 39 0 79 0 95 0 46 0 73 0 79 0 1328 0 42 0 0 85 0 1379 0 0 3774 0 3 G) ( ...... u.l. µ B ( ) . 5 1 Results for relics − 157 2 143 6 560 0 617 0 251 3 s . . . . . 10 max 2 × γ − )( erg cm 3 1 0 2 2 1 2 2 1 2 0 2 2 1 2 0 2 0 2 2 2 2 0 12 ...... 10 min − × Table 4.3: Current Limits 43 3 27 0 95 0 42 0 32 0 06 0 06 0 86 0 20 0 G) ( ...... B γ µ ( 10 2 30 2 62 0 45 1 40 1 10 4 10 0 86 0 71 0 90 0 18 0 10 0 29 3 03 0 21 0 40 0 40 1 81 0 30 1 56 1 74 3 10 0 88 0 00 0 00 0 25 1 18 0 90 0 1940 0 0 06 1 26 2 54 3 59 2 86 2 ...... α 1 S 0 W 1 NWSE 1 1 S 1 W 1 Non-thermal ﬂux detectable by ASTRO-HEnergy (1Ms) where in the 10 non-thermal x-rays will start to dominate over the plasma emission. Cluster 1RXS J0603.3+4214 1 † ‡ A0013 2 A0085 1 A0521 1 A0610 1 AS753 2 A0754 1 A1240 N 0 A1367 1 A1656 1 A1664 1 A2048 2 A2061 1 A2063 1 A2255 1 A2256 0 A2345 E 1 A2433 1 A2744 1 A3376E E 0 A3376W W 1 A3411 1 A3667 NW 1 A4038 1 ACT-CL J0102-4915 E 0 CIZAJ2242.8+5301 N 1 PLCK G287.0+32.9 N 1 ZwCl0008.8-5215 E 1 Chapter 4. Results and Discussion 43

4.1 Promising Targets

In order to decide which halos and relics are good targets for the detection of IC emission, we will compare our results with equipartition estimates. Another way of estimating the magnetic field is through Faraday rotation measures (RM), but since these are present for only a few clusters, we will not consider them apart from an individual case. Comparing various estimates is not straightforward, since the different methods are subject to different assumptions and sensitive to the magnetic field on different scales.

The prototype radio halo and relic are in the Coma cluster, for which magnetic field estimates exists using all three methods: RM, equipartition and limits from IC non- detection. Bonafede et al.(2010) studied the central magnetic field through RM. The authors estimate the average magnetic field within the inner 1 Mpc3 to be 2 µG. This ∼ volume is slightly smaller than the radio halo. At the same time there exist theoretical arguments from equipartition. These estimates are usually for a larger volume. Thier- bach et al.(2003) reports 0 .7 1.9 µG for the Coma halo, consistent with Bonafede − et al.(2010) (also see table 4.4). Current lower limits from IC non-detection from Wik et al.(2011) are 0.3 µG. From these considerations, we conclude that for good targets ∼ ASTRO-H should be able to detect IC emission for magnetic fields & 1 µG. In tables 4.2 and 4.3 we report the upper limits on the magnetic field (Bu.l.) for which IC radiation will be detectable in 1 Ms of observation by ASTRO-H.

In order to be more precise we compare Bu.l. with estimates from equipartition (table 4.4). Such predictions are not available for all clusters. Note that the revised equiparti- 0 tion magnetic field (Beq) provides the most reliable estimate (for details see Appendix (0) A.2). Good targets are clusters for which Bu.l. & Beq and/or Bu.l. & 1 µG. Following the above arguments, we propose the following targets: A0085, AS753, A1367, A1656, A1914, A2255, A2319, A2744, A3667, A4038, MACSJ0717.5+3745 and ZwCl0008.8- 5215. However, we consider AS753, A1367 and ZwCl0008.8-5215 to be less good targets for different reasons (see section 4.1.1). In addition, note that the above reasoning, and therefore the above selection of targets, is by no means all-embracing. Most importantly, any estimate of the volume-averaged magnetic field is still highly uncertain and can vary from cluster to cluster. Therefore, other targets should by no means be completely ignored. In particular, we consider the following clusters to host interesting targets as well: A0013, A0521, A0610, A2345, A3376, RXCJ2003.5-2323, Toothbrush Chapter 4. Results and Discussion 44

0 and Sausage. For example, Bu.l. for the Toothbrush is much lower than Beq, but it is nevertheless interesting since this estimate is uncertain and one could simultaneously perform diﬀerent studies. E.g. one can study both IC emission and the shock nature of the relic (for more details please see the discussion, section 4.3). However, for now we will focus on the narrowed down sample based on the comparison with equipartition estimates. For individual comments on the clusters in this sample see section 4.1.1. For comments on all remaining clusters please see appendixC.

0 Cluster Beq Beq Reference Halos 1E0657-56 1.2 1 A0520 1.4 2 A0665 0.6 3 A0754 0.7 4 A1656 0.5 0.7-1.9 1, 5, 6, 21 A1914 0.6 1.3 1, 4 A2163 0.7 1.0 1, 3 A2219 0.4 0.7 7 A2255 0.5 8 A2256 > 1 1.1 1, 9 A2319 0.5 10 A2744 0.5 1.0 1, 7 A3562 0.4 11 MACSJ0717.5+3745 3.4 6.5 12 RXCJ2003.5-2323 1.7 13 Relics 1RXS J0603.3+4214 9.2 14 A0085 1.1-2.4 15, 20 A0754 0.3 15 AS753 1.3 15 A1240 N 1 2.4 16 S 1 2.5 16 A1367 1 15 A1656 0.6 0.7-1.7 5, 6, 21 A1664 0.9 2, 17 A2255 0.5 8 A2256 > 1 9 A2345 E 0.8 2.2 16 W 1 2.9 16 A2744 0.6 1.3 7 A3667 NW 1.5-2.5 6, 18 A4038 3 17 ZwCl0008.8-5215 E 2.5 6.6 19 W 3.4 7.9 19

Table 4.4: Magnetic field estimates based on the equipartition theorem. Beq is the 0 equipartition magnetic field and Beq the so-called revised equipartition magnetic field, the latter is considered to provide a more realistic value (see Appendix A.2 for more details). All values are scaled to the cosmology adopted in this work. References: (1) Petrosian et al.(2006); (2) Govoni et al.(2001); (3) Feretti et al.(2004); (4) Bacchi et al.(2003); (5) Giovannini et al.(1991); (6) Govoni and Feretti(2004); (7) Orru et al.(2007); (8) Feretti et al.(1997); (9) Clarke and Ensslin(2006); (10) Feretti et al.(1997); (11) Venturi et al.(2003); (12) Pandey-Pommier et al.(2013); (13) Giacintucci et al.(2009); (14) van Weeren et al.(2012); (15) Chen et al.(2008); (16) Bonafede et al.(2009b); (17) Kale and Dwarakanath(2012); (18) Johnston-Hollitt(2004); (19) van Weeren et al.(2011b); (20) Ensslin et al.(1998); (21) Thierbach et al.(2003) Chapter 4. Results and Discussion 45

4.1.1 Comments on Good Targets

1E0657-56 The bullet cluster (z = 0.296) contains a radio halo and has been a popular target for detecting non-thermal emission. Ajello et al.(2010) see an excess of 1 .58 × 10−12 erg cm−2 s−1 in the 50 100 keV band. Recently it has been analysed for 266 ks − of NuSTAR observations by Wik et al.(2014), who place a conservative 90% c.l. upper limit of 1.1 10−12 erg cm−2 s−1, barely consistent with Ajello et al.(2010). From our × estimates, ASTRO-H can obtain limits close to the equipartition estimates ( 1 µG). ∼ However, the radio spectrum still suffers from uncertainties as discussed in Liang et al. (2000) and Shimwell et al.(2014). In our analysis (Fig. 4.1), we used the spectral index and data from Shimwell et al.(2014), in whose work the area of diffuse emission is 18.5 arcmin2. In addition, we also use the data from Liang et al.(2000) for a similar sized region. Since the latter data corresponds to a flatter spectral index, fitting to all data together yields a bad χ2. Naturally, this is not the case when fitting to the Shimwell et al.(2014) data only. It should be noted that this yields similar values for the magnetic field.

1E0657-56 has been used to prove the existence of Dark Matter (DM) (Clowe et al., 2006). It is important to note that both the region of highest mass density and the radio halo ﬁt within the SXS FoV (30 30). Therefore, the Bullet cluster is an excellent × target for studying simultaneously non-thermal IC emission in both hard and soft X- rays, as well as the recently claimed detection of a line at 3.5 keV, which can potentially be attributed to decaying DM (Bulbul et al., 2014; Boyarsky et al., 2014).

A0085 Abell 85 (z = 0.0551) hosts a radio relic and was one of the ﬁrst clusters to be detected in X-ray (Mitchell et al., 1979). Our estimate for the volume averaged

magnetic field, Bu.l. = 2.36 µG, that still allows for a detectable IC signal by ASTRO-H in 1 Ms, is comparable to predictions from equipartition (Chen et al., 2008; Ensslin et al., 1998). However, it is smaller than estimates by Slee et al.(2001), who report B 9 µG ∼ following the minimum energy condition1 as defined given in Miley(1980). The relic source only partially fills the HXI FoV. The entire cluster can be contained in the SXI FoV. A detection of non-thermal IC radiation, corresponding to B = 0.95 µG has been claimed in the past (Bagchi et al., 1998), this excess is also observed in soft X-rays by

1The minimum energy condition corresponds roughly, but not exactly, to equipartition between CRs and magnetic ﬁelds (see Miley, 1980). Chapter 4. Results and Discussion 46

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.38µG BV = 0.89µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.1: 1E0657-56

Bonamente et al.(2002). However, it has been questioned whether this excess really corresponds to the relic region (Durret et al., 2005).

The data is best fit keeping both γmin and γmax free (see Fig. 4.2). Using Eq. (3.4) and Pinzke et al.(2011) we model the gas density at the relic location, 42 kpc from the ∼ cluster centre. The derived electron density of 1.6 10−3 cm−3 corresponding to γ 300 × ≈ is in tension with to our best fit value of 1.3 103. In addition, a relatively large value × γmin, as suggested by the radio data, weakens an interpretation of the above-mentioned soft X-ray excess as IC emission (see the IC spectrum in Fig. 4.2). Future observations with ASTRO-H can probe non-thermal X-rays for reasonable values of the magnetic field and shed light on the soft X-ray excess.

AS753 Abell S753 (z = 0.014) contains a radio relic, 1401-33. The value of the average spectral index of the relic is uncertain. The brightest region has a spectral index of 1.4, whereas for a larger area, including some fainter emission, it is 2.1. We considered this Chapter 4. Results and Discussion 47

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.43µG BV = 2.36µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.2: A0085 larger area. A 3σ IC upper limit of 1.47 10−13 erg cm−2 s−1 in the 0.3 10 keV band, × − corresponding to B & 2.2 µG, is reported by Chen et al.(2008). Using the same data, we estimate this upper limit to be & 4.8 µG for α = 1.4 and & 14 µG for α = 2.1. Although we used the revised analytic expression (see section 2.4), also the old expression yields a somewhat higher limit (& 3.4 µG).

In addition, the results from Chen et al.(2008) are in tension with our predictions for ASTRO-H. In fact, their upper limit on the X-ray flux is more constraining than what we expect is achievable by ASTRO-H in 1 Ms. However, this tension can be resolved if γmin is relatively large, in which case there is very little flux at low energies (see Fig. 4.3). Finally, the flux is possibly contaminated by the bright galaxy NGC 5419 (Subrahmanyan et al., 2003; Chen et al., 2008). More detailed observations are required, in both radio and X-ray, to pin down the value of α, to study the role of NGC 5419 and to reconcile our estimates with the upper limit reported in Chen et al.(2008). For the aforementioned-reasons, we do not consider AS753 to be an ideal target for now. Chapter 4. Results and Discussion 48

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 4.70µG γmin = 1000 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.3: AS753. The upper limit is from Chen et al.(2008). Note that the tension with our estimate can be resolved if γmin is relatively large.

A1367 Abell 1367 (z = 0.0220) is part of a larger filamentary supercluster structure that includes Coma (Farnsworth et al., 2013). The relic was initially discovered by Gavazzi and Trinchieri(1983) who doped it a radio halo. Ensslin et al.(1998) concluded it is more likely a relic. The integrated flux of the relic measured by Farnsworth et al. (2013) (232 28 mJy) with the 100m Green Bank Telescope at 1.4 GHz is 7 times larger ± ∼ than that measured by Gavazzi and Trinchieri(1983) (35 mJy). Moreover, they find a largest linear size of 27.50 which is 4 times bigger than that of Gavazzi and Trinchieri ∼ (1983). However, since no spectral index information is available from Farnsworth et al. (2013) we decided to use the data by Gavazzi and Trinchieri(1983).

An X-ray excess has been claimed by Wik et al.(2012), but the relic, at a distance of 220 from the cluster centre, is not contained in their extraction region. However, if the relic size reported by Farnsworth et al.(2013) is correct, the edge of the relic would now be close to the region considered by Wik et al.(2012). On the other hand, also the Chapter 4. Results and Discussion 49

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 1.86µG γmin = 1000 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.4: A1367. The upper limit is from Wik et al.(2012), corresponding to BV & 0.27 µG. Predictions for ASTRO-H are for the relic size reported in Gavazzi and Trinchieri(1983). We also show what the spectrum looks like for γmin = 1000. existence of a radio halo is not ruled out by Farnsworth et al.(2013), but detecting it is diﬃcult due to the contaminating source 3C264.

Our estimates show that IC emission is detectable for B . 1.9 µG. However, if the relic has the size reported by Farnsworth et al.(2013) and if the emission is more or less uniform, the sensitivity of ASTRO-H as used in this study would deteriorate by a factor 10, leading to a detection threshold of B 0.9 µG. Due to these uncertainties, it ∼ . is difficult to definitively associate any IC emission with the relic, therefore, we do not consider this to be an ideal target. Finally, from the gas density profile we estimate the density at the relic to be 8 10−4 cm−3, corresponding to a maximum electron lifetime, × and therefore a possible cutoff, at γmin 250. For these electron energies, the photon ∼ spectrum peaks in the extreme ultra violet (EUV) (Fig. 4.4). Chapter 4. Results and Discussion 50

A1656 The Coma cluster (z = 0.231) is the best studied cluster and contains the prototype radio halo and relic. Clear spectral steepening can be observed in the halo. An excess in X-ray was claimed by Rephaeli and Gruber(2002) for the radio halo, but later refuted (Wik et al., 2009, 2011). Due to the large size of the halo, it is doubtful whether ASTRO-H can make substantial improvements in constraining the magnetic ﬁeld (see Fig. 4.5a).

The relic (1253+275) is located at 750 from the cluster centre. Improvements can be made with respect to current upper limits (Feretti and Neumann, 2006), by observing in soft X-rays. We obtained a detectable limit at 0.5 keV of Bu.l. = 1.31 µG (see Fig. 4.5b), which implies that the lower cutoff should be γmin . 700. From the beta profile (Pinzke et al., 2011), we estimate the electron density at the relic location to be 6 10−5 cm−3, ∼ × 2 corresponding to γmin 1 10 . As we show, ASTRO-H can probe IC emission from . × 1253+275 for magnetic fields stronger than the current equipartition estimates.

A1914 The halo in Abell 1914 (z = 0.1712) is a so-called Very Steep Spectral Radio Source (VSSRS) (Bacchi et al., 2003). Most radio data is from Komissarov and Gubanov (1994), who refer to it as source 4C 38.39. Since Komissarov and Gubanov(1994) use old data, they assume errors of at least 15%. There is an indication of spectral flattening 3 around 50 MHz (see Fig. 4.6). Our best fit yielded γmin 1.7 10 if one assumes a ≈ × cutoff. This seems reasonable in comparison with the gas density profile, from which we estimate that electrons have their maximum lifetime around γ 800 (Pinzke et al., ∼ 2011). A1914 has already been studied in X-ray by Ajello et al.(2010). ASTRO-H will be able to probe IC emission for magnetic fields close to the estimate from the revised 0 equipartition theorem, with Bu.l. = 1.12 µG and B 1.3 µG, respectively. Moreover, eq ≈ the full halo fits within the ASTRO-H FoV.

A2255 Abell 2255 (z = 0.0806) hosts a radio halo and relic (Feretti et al., 1997). Since the relic is at a projected distance from the core of 100 and the XMM-Newton FoV ∼ is 300, current HXR upper limits likely contain contributions from both the halo and the relic (Turner et al., 2001; Wik et al., 2012). For both sources, ASTRO-H is able to detect IC emission corresponding to magnetic ﬁelds that are slightly stronger than Chapter 4. Results and Discussion 51

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.32µG BV = 0.63µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] (a) Halo. Note that here the dashed spectrum is not detectable by ASTRO-H, but is included for comparison. E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.95µG BV = 1.31µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] (b) Relic

Figure 4.5: Coma Chapter 4. Results and Discussion 52

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.59µG BV = 1.12µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.6: A1914

equipartition estimates, with Bu.l., = 0.71 µG and Beq, 0.5 µG for the halo; halo halo ≈ and Bu.l., = 0.71 µG and Beq, 0.5 µG for the relic. From the gas density, the relic relic ≈ electron cutoff energy is estimated to be at γmin 300 for the halo as well as the relic, ∼ making a detection in soft X-ray viable. Unfortunately, the halo and relic do not fully fit in the ASTRO-H HXI FoV together, since the relic is offset by 80. However, the SXI can study both objects simultaneously.

A2319 The radio halo of Abell 2319 (z = 0.0557) shows an irregular structure (Feretti et al., 1997). This cluster has a long history of non-thermal HXR searches, resulting in no-detection (Gruber and Rephaeli, 2002; Feretti and Neumann, 2006). According to our estimates, the upper limit by Feretti and Neumann(2006) is already probing B0 0.7 µG. It should be noted that we ﬁnd a more constraining lower limit for the eq ∼ Chapter 4. Results and Discussion 53

E[keV] 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.32µG BV = 0.71µG 11 γ = 1000 10− min Plasma ASTRO-H 1Ms

] 12 ASTRO-H SXI 1Ms 2 10− cm / 13 10− sec /

[erg 10− ν S · 15 ν 10−

16 10−

10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

(a) Halo. The dashed-dotted line shows the spectrum for γmin = 1000. E[keV] 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.71µG γmin = 1000 11 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 12

2 10− cm / 13 10− sec /

[erg 10− ν S · 15 ν 10−

16 10−

10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

(b) Relic. The dashed-dotted line shows the spectrum for γmin = 1000.

Figure 4.7: A2255 Chapter 4. Results and Discussion 54 magnetic ﬁeld due to assuming an isotropic distribution of the magnetic ﬁeld (see section 2.1.4).

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.70µG BV = 1.14µG 10 γ = 1000 10− min Plasma ASTRO-H 1Ms

] 11 ASTRO-H SXI 1Ms 2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.8: A2319. Similar to the Coma halo, due to the halos large size no great improvements seem possible. Again, the green dashed line is not detectable by ASTRO- H. However, for this cluster current satellites are already probing the equipartition estimates (Beq 0.53 µG). Finally, the dashed-dotted line shows the spectrum for ≈ γmin = 1000. In this case the prospects in soft X-ray deteriorate severely.

Similar to Coma, we do not obtain a major improvement for ASTRO-H in terms of hard X-ray detectability due to the large size of the halo on the sky (see Fig. 4.8). However, the SXI instrument can resolve the full halo region. From the central gas density we estimate the Lorentz factor that maximises the electron lifetime at γ 600, ∼ corresponding to 0.3 keV photons. Yet the radio data seems to be giving a hint of spectral 1.4 steepening at higher energies as the data is not ﬁt well by a spectral index of α0.4 = 1.8. However, the data at 610 MHz is from Harris and Miley(1978) and was taken with the Westerbork Synthesis Radio Telescope (WSRT). Feretti et al.(1997) their data is from both WSRT and the Very Large Array (VLA). Also, they report that their emission Chapter 4. Results and Discussion 55 is more extended at identical wavelengths. Therefore, concluding that there is spectral steepening is unfounded since some ﬂux might be missing.

A2744 Abell 2744 is a distant cluster (z = 0.3080). The cluster hosts both a radio halo and relic. Together, both sources ﬁt precisely within the ASTRO-H HXI FoV, allowing to probe two targets simultaneously. Moreover, we showed that ASTRO-H can probe IC emission for magnetic ﬁeld strengths similar to equipartition estimates in both 0 sources (for the halo: Bu.l., = 0.51 µG, Beq, 0.5 µG and B 1.0 µG. For halo halo ≈ eq, halo ≈ 0 the relic: Bu.l., = 1.39 µG and B 1.3) relic eq, relic ≈

Million and Allen(2009) provide an upper limit in soft X-ray, the residuals being best +0.40 fit by a power law with α = 1.66−0.13. In the fit (Fig. 4.15a and 4.9b) we assumed all excess is coming from one object, either the halo or the relic. Orru et al.(2007) present a spectral index in radio of α0.3 = 1.0 0.1 and α0.3 = 1.1 0.1 for the halo 1.4 ± 1.4 ± and relic respectively. This raises doubts about whether this emission is from the same electron population as that claimed by Million and Allen(2009). Nevertheless, A2744 is a good target in soft X-ray. The central electron density is 4.4 10−3 cm−3, thus no × lower cutoff due to coulomb cooling is expected at electron energies γ & 400 (Ota, 2001; Govoni et al., 2001). Future observations by ASTRO-H can elucidate the origin of the excess seen by Million and Allen(2009) and detect, or severely constrain, hard X-rays from this cluster.

A3667 Abell 3667 (z = 0.0556) hosts double relics. We analyse the 1.9 Mpc northwest- ern relic, which contains most diffuse emission (Rottgering et al., 1997). HXR emission from A3667 has been studied by Ajello et al.(2009) and Nakazawa et al.(2009). We use the latter limits, since this work specifically studies the relic, which is offset from the cluster centre by 330. Because the cluster is relatively close and the relic is large, ∼ only a third of the relic fits inside the ASTRO-H HXI FoV. The full relic can be resolved in the SXI FoV. From the gas density profile we expect no low energy cutoff above γ 100. Since ASTRO-H can probe equipartition magnetic field values with the HXI ∼ and no cutoff is expected in soft X-rays this relic appears an excellent target in both Chapter 4. Results and Discussion 56

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.29µG BV = 0.51µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] (a) Halo E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 0.36µG BV = 1.39µG 10 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] (b) Relic

Figure 4.9: A2744 Chapter 4. Results and Discussion 57 regimes. However, no soft X-ray excess has been seen yet (Nakazawa et al., 2009; Aka- matsu et al., 2012a), whereas one might have expected this from the dashed spectrum in Fig. 4.10. This could possibly be due to a large (γmin > 200) or because the magnetic ﬁeld is higher than what is suggested by equipartition. In the latter case, one might

still hope to detect emission in soft X-ray for magnetic ﬁelds up to Bu.l. = 5.27 µG (see dotted line in Fig. 4.10).

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 1.86µG BV = 2.73µG 10 B = 5.27µG 10− V Plasma ASTRO-H 1Ms

] 11 ASTRO-H SXI 1Ms 2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.10: A3667. Note that we determined a second limit (Bu.l. = 5.27 µG) that can be obtained by the soft X-ray imager if γmin 200. The dotted line is corresponding spectrum. ≤

The radio spectrum is studied by Rottgering et al.(1997). They find a spectral index of α = 1.1. ATCA data is present at 1380 MHz and 2380 MHz, here the spectral index is much steeper. As the authors point out, either the radio spectrum steepens or about 20% of the emission is missing in the ATCA study. They consider the latter scenario to be the most likely. We find that the spectrum over the entire frequency range is well fit by a power law with α = 1.3. Chapter 4. Results and Discussion 58

A4038 This nearby cluster (z = 0.0300) hosts a small scale relic ( 0.13 Mpc) close ∼ to the cluster centre ( 40 kpc). Our analysis suggests that ASTRO-H can detect hard ∼ X-ray IC emission for B . 4 µG. Most likely, this cluster is not a good target in soft X-ray. First, since the relic is close to the center, the soft X-ray regime will be dominated by thermal emission. Secondly, the electron density at the relic location is high 1 102 µG, making γ 9 102 CRes the longest lived electrons. A spectral ∼ × ∼ × analysis in radio was done by Slee et al.(2001) and with more recent data by Kale and Dwarakanath(2012). The data at 80 MHz from Slee et al.(2001) is high compared to the data at 74 MHz from Kale and Dwarakanath(2012) (see Fig. 4.11). Following Kale and Dwarakanath(2012), we omit the observations at 74 and 160 MHz, both from Slee et al.(2001), from our analysis.

E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 3.79µG Plasma 10 ASTRO-H 1Ms 10− ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.11: A4038. Open circles are the data at 80 and 160 MHz from Slee et al. (2001). These points are omitted in our analysis (see Kale and Dwarakanath, 2012).

MACSJ0717.5+3745 This distant cluster (z = 0.5458) hosts the most powerful radio halo (Bonafede et al., 2009a). The source is relatively small, 13 arcmin2. Our ∼ Chapter 4. Results and Discussion 59 analysis shows that IC emission can be detected for magnetic ﬁelds B . 2.26 µG. This is smaller than equipartition and revised equipartition estimates from Pandey-Pommier et al.(2013)(3 .4 6.5 µG), but higher than revised equipartition estimates from Bonafede − et al.(2009a)( 1.2 µG). Data at 74 MHz and 325 MHz have been left out of the analysis, ∼ since it refers to the full cluster rather than just the halo (Bonafede et al., 2009a; Pandey- Pommier et al., 2013) (open circles in Fig. 4.12). Recently more low frequency data was published by Pandey-Pommier et al.(2013), they report a spectral index of α = 0.98, which we adopt. As can be seen from Fig. 4.12 the radio has some scatter. An extensive discussion can be found in the aforementioned work. E[keV] 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10− BV = 2.26µG Plasma 10 ASTRO-H 1Ms 10− ASTRO-H SXI 1Ms

] 11

2 10− cm / 12 10− sec /

[erg 10− ν S · 14 ν 10−

15 10−

10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz]

Figure 4.12: MACSJ0717.5+3745. Open circles are ignored in the analysis (see text).

Due to the complex radio spectrum, and the uncertainties in the equipartition estimates, this target is not ideal.

ZwCl0008.8-5215 Zwicky Cluster 0008.7-5215 (z = 0.1032) hosts double relics, both at a distance of 90 from the cluster centre (van Weeren et al., 2011b). The eastern ∼ Chapter 4. Results and Discussion 60 relic is the brighter of the two sources, and much more extended. Its longest linear size is approximately two times the ASTRO-H HXI FoV. Our estimates show that ASTRO-H can detect IC emission for magnetic fields comparable to equipartition estimates, but not field strengths predicted by the revised equipartition theorem. This holds for both relics. In the western relics, there is an indication of a cutoff at low energies. This feature is ignored by van Weeren et al.(2011b). Therefore, we plot the spectrum for 3 both γmin = 200 and our best fit value of γmin = 3.9 10 . For the eastern relic we also × plot the spectrum for a cutoff at γmin = 1000. In such a scenario, the prospects in soft X-rays deteriorate (Fig. 4.13). Since there is no gas density profile for this cluster we cannot make an estimate for the cutoff. Since a cutoff in the electron spectrum is likely to be at low energies, the revised equipartition estimates are probably most accurate. We conclude that, ZwCl0008.8-5215 is not an excellent target for ASTRO-H. Moreover, since half of eastern relic is outside the FoV, our estimate for Bu.l. deteriorates by roughly a factor 1.3.

4.2 Spectra with a Spectral Break

In addition to the analysis discussed above, we also ﬁtted a spectrum with a spectral break to a small number of clusters. In order to do this at least four data points have to be present in radio. Such a spectrum is well motivated theoretically (e.g. see section 2.3 and Sarazin, 1999).

For our analysis we change the electron distribution and include two additional parameters, a second spectral index (α1, α2) and a break energy, γbreak. The electron distribution can now be described by:

sin θ −p1 K0 2 γ if γ < γbreak N(γ, θ) =  , (4.1) sin θ −p1+p2 −p2 K γ γ if γ γbreak  0 2 break ≥ 

where θ is the pitch angle and pi = 2αi +1. In order to fit the spectra, we first determine the spectral indices, p1 and p2, by fixing a simple power law of the form Eq. (4.1), without adding any further details related to synchrotron emission. This is done because there Chapter 4. Results and Discussion 61

E[keV] 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10− BV = 2.37µG γmin = 1000 11 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 12

2 10− cm / 13 10− sec /

[erg 10− ν S · 15 ν 10−

16 10−

10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] (a) Eastern relic. The dashed-dotted line shows the spectrum for γmin = 1000. E[keV] 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10− BV = 2.74µG γmin = 1000 11 Plasma 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 12

2 10− cm / 13 10− sec /

[erg 10− ν S · 15 ν 10−

16 10−

10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] (b) Western relic. Note that also the spectrum is plotted for a cut-oﬀ at γmin = 200 (see discussion in the text).

Figure 4.13: ZwCl0008.8-5215 Chapter 4. Results and Discussion 62

is too little data for most clusters to fit for all parameters at once. The value for γmin 5 is fixed to 200 for relics and 300 for halos. γmax is fixed to 2 10 . Having fixed × the spectral indices we then apply the same procedure as discussed in chapter3, only replacing the electron distribution by Eq. (4.1). The results can be found in table 4.5 and the corresponding spectra in Fig. 4.14.

Only the fit for Abell 3562 improves over the regular power law case. However, for this cluster there are relatively few data points and by eye the spectrum does not appear realistic. This suspicion is strengthened by the large difference between the spectral indices α α = 1.77, while you would expect the difference to be approximately 2 − 1 1 (see section 2.3). The values obtained for Bu.l. are roughly comparable to those obtained for regular power law distribution. Only for A2063 and A3562 are the obtained values somewhat smaller. This can be understood as follows in the case of A1914. The point where the background spectrum and the ASTRO-H limiting sensitivity intersect corresponds to the steep part of the spectrum, α2. Had this point been on the other side of the spectral break, the normalisation, K0, would have to be smaller to force the spectrum through this point. Consequently, B would be larger. For A3562 the situation is somewhat more complex, as can be seen in Fig. 4.14, but in essence the problem is the same. Again, the difference in the value of B obtained is due to the different values of the spectral index at the intersection point. Finally, we conclude that, currently, there is not enough data to conclusively discern between a normal and a broken power-law spectrum. In addition, the consequences for our predictions appear to be negligible if the spectra are not too different.

Current Limits ASTRO-H (1Ms) 2 † ‡ Cluster α1 α2 B γbreak Bu.l. γbreak χ d.o.f.Fx E (µG) ( 103) (µG) ( 103) (keV) × × Relics A0013 1.10 2.11 6.350 1.96 3.440 1.99 4 0.040 33 A0085 0.77 2.92 0.38 8.320 1.98 3.640 19.31 7 0.081 34 A2063 1.21 2.51 0.45 6.870 4.66 2.140 20.89 12 0.024 24 Halos A1914 1.33 1.95 0.57 4.090 1.03 3.020 3.76 7 0.310 54 A1656 1.14 2.88 0.31 29.778 0.62 21.222 66.66 11 1.240 20 A3562 0.37 2.14 0.01 108.430 0.19 2.128 3.46 3 0.175 36 †Non-thermal ﬂux detectable by ASTRO-H (1Ms) in 10−12erg cm−2 s−1. ‡Energy where the non-thermal x-rays will start to dominate over the plasma emission.

Table 4.5: Results for clusters whose spectra can be ﬁt by a broken power law. Chapter 4. Results and Discussion 63

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 1.96µG BV = 0.38µG Plasma BV = 1.98µG ASTRO-H 10ks 10 10 Plasma 10 11 − − ASTRO-H 1Ms Plasma + BV (= 1.98µG) ASTRO-H 10ks

] ] 11

2 2 10− ASTRO-H 1Ms 12 10− cm cm / / 12 10− sec sec

/ 13 / 10− 13

[erg [erg 10− ν ν

S 14 S · 10− · 14 ν ν 10−

15 10− 15 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (a) A0013 (b) A0085 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.45µG BV = 0.57µG BV = 4.66µG BV = 1.03µG Plasma 10 10 Plasma 10 11 − − Plasma + BV (= 4.66µG) Plasma + BV (= 1.03µG) ASTRO-H 10ks ASTRO-H 10ks

] ] 11

2 ASTRO-H 1Ms 2 10− ASTRO-H 1Ms 12 10− cm cm / / 12 10− sec sec

/ 13 / 10− 13

[erg [erg 10− ν ν

S 14 S · 10− · 14 ν ν 10−

15 10− 15 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (c) A2063 (d) A1914 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.31µG BV = 0.01µG BV = 0.62µG BV = 0.19µG 10 Plasma 10 Plasma 10− 10− Plasma + BV (= 0.62µG) Plasma + BV (= 0.19µG) ASTRO-H 10ks ASTRO-H 10ks

] 11 ] 11

2 10− ASTRO-H 1Ms 2 10− ASTRO-H 1Ms cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (e) Coma Halo (A1656) (f) A3562

Figure 4.14: Spectra with a broken power law for the clusters in table 4.5. Chapter 4. Results and Discussion 64

4.3 Discussion

Above, we commented on the best targets for ASTRO-H to probe non-thermal IC emission. Here we will discuss some general aspects that return for many clusters in our sample. In particular, the behaviour of the spectra corresponding to emission from the least energetic electrons, i.e. near the low energy cutoff. In addition, we briefly touch upon the potential of NuSTAR, which by now is fully operational. Based on a recent work (Wik et al., 2014), we also discuss some of the difficulties in extracting an IC component from NuSTAR observations; these considerations will also apply to ASTRO-H. Finally, we make some specific suggestions for the primary targets that can be observed by ASTRO-H in the near future, taking into account related science goals.

4.3.1 Low Energy Cutoﬀ: Potential in EUV/SXR and Low Frequency Radio Emission

Many of the spectra corresponding to the clusters discussed in section 4.1.1 have a 2 steep spectral index. For a cutoﬀ in the electron spectrum of the order γmin 1 10 ∼ × the spectrum peaks in the extreme ultra violet (EUV). In addition, the non-thermal spectrum often dominates over the X-ray background at low frequencies. In many cases, this behaviour is most likely not realistic, since IC emission should already have been

seen then (e.g. the dashed line in Fig. 4.4, corresponding to γmin = 200). Therefore, the spectrum probably cuts oﬀ at higher energies. For this reason, we also plotted the

spectrum with a cutoff at γmin = 1000 in many of the figures. However, a cutoff around γ 103 is not always easily explained when compared to our back-of-the-envelope ∼ estimates for the cutoff based on the observed electron density, since these favor γmin ∼ 102. Another scenario is a flattening of the spectrum at these energies. As discussed in section 2.3, flattening is a viable possibility.

In order to gain more insight in the low energy part of the spectrum more observations are needed. Not only will it help in modelling the spectrum more accurately, but it also allows for studying the injection mechanism of the CRe more accurately, since this for a large part determines the shape of the spectrum. Observing these clusters with the SXI Chapter 4. Results and Discussion 65 aboard ASTRO-H can help in pinning down the behaviour of the spectrum if the instru- 2 ment is sensitive enough to detect an IC signal. In addition, since for γmin 1 10 ∼ × the spectrum peaks in EUV, there might also be a potential for detecting IC emission in that regime. In the past, this domain has already been subject of investigation (e.g. Sarazin and Lieu, 1997). Finally, low frequency observations in radio (< 100 MHz) provide the most promising opportunity to scrutinise the spectrum. In radio, one has a clue about the approximate ﬂux at low energies from extrapolating higher frequency measurements. Observations with the Low-Frequency Array for radio astronomy2 (LOFAR), and in the more distant future the Square Kilometre Array3 (SKA) will certainly shed more light on the spectrum of CRes in clusters and are of vital importance in assessing the contribution of IC emission to the cluster soft X-ray spectrum.

4.3.2 NuSTAR and Background Modelling

The Nuclear Spectroscopic Telescope Array (NuSTAR) mission was launched on June 13, 2012 (Harrison et al., 2013). Its performances for hard X-rays are comparable to ASTRO-H. For detailed speciﬁcations see table 4.6, but note that the sensitivity refers to point sources.

Parameter Value Energy range 3 78.4 keV Angular resolution (HPD†)− 58” Angular resolution (FWHM‡) (arcsec) 18” Field of View @ 10 keV 100 100 Field of View @ 68 keV 60 × 60 Energy resolution 400 eV @ 10 keV;× 900 eV @ 69 keV Background in HPD (10 30 keV) 1.1 10−3 erg cm−2 s−1 Background in HPD (30 − 60 keV) 8.4 × 10−4 erg cm−2 s−1 − × †Half-Power Diameter ‡Full Width at Half Maximum

Table 4.6: NuSTAR properties. Table adopted from Harrison et al.(2013).

Recently, Wik et al.(2014) analysed 266 ks NuSTAR observations of the Bullet cluster, deriving a 90% upper limit on the IC ﬂux of 1.1 10−12 erg cm−2 s−1 in the 50 80 keV × − band. The study contains a detailed discussion on background modelling. The authors point out that an IC signal has to be extracted from both the thermal and instrumental background, with the former dominating over IC emission at low and the latter at high

2http://www.lofar.org/ 3https://www.skatelescope.org/ Chapter 4. Results and Discussion 66 energies. In fact, the instrumental background is likely to dominate the count rate in the Hard X-ray regime. Since the instrumental background can be modelled by a power law, any claimed detection of IC emission will be extremely sensitive to the applied model. The HXI onboard ASTRO-H will not improve hard X-ray observations compared to NuSTAR (see Fig. 4.15b). On the other hand, Wik et al.(2014) indicate that, since SXI will take observations simultaneously, the low energy regime can be modelled more accurately. In particular, since cluster hosting relics and halos are believed to be in a merging state, there might exist multiple thermal components with diﬀerent temperatures. ASTRO-H will be able to better model the spectral behaviour at low energies, thereby reducing the overall uncertainty on a possible IC component.

E[keV] 100 101 102 10 11 − ASTRO-H HXI 1Ms ASTRO-H SXI 1Ms NuSTAR 1Ms 12 10− ] 2 cm

/ 13 10− sec /

[erg 14 ν 10− S · ν

15 10−

10 16 − 1017 1018 1019 1020 ν[Hz] (a) (b)

Figure 4.15: Comparison between NuSTAR and ASTRO-H 1 Ms continuum sensitivity for point sources. The left plot is from Koglin et al.(2009). The right plot compares the sensitivity of both instruments. In hard X-ray, NuSTAR appears slightly more sensitive. However, ASTRO-H has a larger ﬁeld of view, which is beneﬁcial for extended sources such as clusters.

To conclude, it is fair to say that NuSTAR is comparable to ASTRO-H when it comes to observing clusters in HXR, but ASTRO-H will improve over NuSTAR due to su- perior performance in the soft regime allowing for a better modelling of the complete background, both thermal and instrumental. In addition, certain targets are better for ASTRO-H since improvements are mainly expected in the soft X-ray regime, in particular A2319 and Coma. Targets that have a comparable potential for both telescopes are A0085 and A1914. Chapter 4. Results and Discussion 67

4.3.3 Primary Targets in a Broader Science Perspective

So far, searches for non-thermal X-ray emission from cluster halos or relics have yielded no deﬁnitive detection. Our study selects targets for which the odds of detection are highest. However, it is by no means certain that ASTRO-H will conclusively detect the long sought IC emission. Here we consider diﬀerent science objectives and relate them to our suggested targets.

One of the primary questions in modern day cosmology and particle physics is detection and identification of dark matter. Decaying or annihilating DM can produce line emission in either X-rays or γ-rays depending on the mass of the DM particle. Recently, a new line line was detected at 3.5 keV in the stacked spectrum of several galaxy clusters (Bulbul et al., 2014) and individually in the Perseus cluster and the Andromeda galaxy (Boyarsky et al., 2014). This line could be produced by a light DM particle, such as a decaying sterile neutrino. The ASTRO-H soft X-ray spectrometer (SXS) will provide unprecedented sensitivity that is needed to identify the origin of such a line (see table 3.2). Since the decay rate is proportional to the density, one expects the strongest signal at the cluster centre. As such, studying halos that reside at the cluster centre, might simultaneously provide an excellent opportunity to study the nature of this line. Among the suggested targets Bullet, Coma, A1914, A2255, A2319, A2744 and MACSJ0717.5+3745 host a radio halo. The core radius of Coma and A2319 is much bigger than the ASTRO-H FoV, so one would lose part of the flux from a potentially decaying particle4. This also holds for A2255. For A2744 and MACSJ0717.5+3745, a much larger section of the cluster ( 1 Mpc2) can be studied with SXS, since they are ∼ more distant. Note though that, for A2744, both the halo and the relic precisely fit in the HXI FoV, but we are unsure about the exact configuration of the FoV of HXI and SXS. Therefore it is not clear whether a simultaneous observation of both the halo and relic with HXI, and the cluster centre with SXS, is possible. The best target is the Bullet cluster, where the majority of the mass fits in a 30 30 region. In particular, this × cluster is interesting to study because the thermal gas has an offset with respect to the DM distribution (Clowe et al., 2006). Finally, the relic in A4038 is located sufficiently close to the centre, such that it can be resolved with a pointing in this region.

4For an NFW proﬁle, the density falls as r−1 inside the core radius and as r−3 outside. Chapter 4. Results and Discussion 68

Another interesting objective is to study the temperature profile in the cluster outskirts. In particular, if relics really correspond to shock fronts, then there should be a temperature jump at the relic location. So far, only a few of such temperature jumps have been identified, all with the Suzaku satellite5 (e.g. Akamatsu et al., 2012b,a; Akamatsu and Kawahara, 2013). With improved spatial resolution and FoV over Suzaku, ASTRO-H its SXI can hopefully confirm the relation between shocks and relics. Note that among the targets proposed in this work, there are four roundish relics6, namely A0085, AS753, A1367 and A4038. Morphologically, these relics do not obviously trace a shock front. The others, Coma, A2255, A2744 and the double relics in A3667 and ZwCl0008.8-5215, are elongated. Of the aforementioned relics, only A3667 has been studied. A temperature jump has been seen in both the northwest and southeast relic (Akamatsu et al., 2012a; Akamatsu and Kawahara, 2013). An advantage that ASTRO-H has over Suzaku is that the Coma relic entirely fits in the SXI FoV. In addition, the double relics in ZwCl0008.8-5215 can be resolved simultaneously. Finally, note that such studies are also interesting for relics outside our proposed sample. In particular, the Sausage7 and Toothbrush. Although the magnetic field estimates from equipartition suggest that it is unlikely for ASTRO-H to detect IC emission, it is nevertheless worthwhile to study them.

5http://www.astro.isas.jaxa.jp/suzaku/ 6See Feretti et al.(2012) for the distinction between roundish and elongated relics. 7The temperature jump in the Sausage cluster has already been studied by Akamatsu and Kawahara (2013). Chapter 5

Conclusion

In this work we presented predictions for the detectability of non-thermal IC emission from radio halos and relics by the ASTRO-H telescope. IC emission should be produced in these objects at some level by the same electrons that generate synchrotron emission. Our approach is phenomenological, being agnostic towards the generation mechanism of CRes.

We analysed all halos and relics with radio flux measurements at two or more frequencies, in order to be able to determine the CRe spectral index. Maximum values for the volume averaged magnetic field which would yield a detectable IC signal in 1 Ms of ASTRO-H observation were obtained. In predicting these values, we take into account that the magnetic field orientation is likely to be isotropic in halos and relics. This yields slightly higher values compared to past computations in the literature (see sections 2.1.4 and 2.4). After comparing these values with, most importantly, equipartition estimates, our results show that there are about a dozen targets where IC emission might be detected, either in hard or soft X-rays. Here we list the primary targets once more: A0085, A1367, A1656, A1914, A2255, A2319, A2744, A3667, A4038, MACSJ0717.5+3745 and ZwCl0008.8- 5215. These targets have been discussed in detail in section 4.1. Additional targets that have potential are A0013, A0521, A0610, A2345, A3376, RXCJ2003.5-2323, the Toothbrush and the Sausage. They are discussed in appendixC.

There is potential to observe IC emission, not only in hard, but also in soft X-rays and possibly EUV. However, as discussed in section 4.3, it is possible that the spectrum cuts of at higher values of γmin or that there is a ﬂattening in the spectrum at lower energies.

69 Chapter 5. Conclusion 70

Low frequency observations with LOFAR and in the future SKA will be of great value in determining more precisely the spectrum in radio, and thereby predicting the spectrum in X-ray.

Although we have discussed which targets seemingly have most potential in IC searches, this list should by no means be considered exclusive. The magnetic field in clusters is estimated to be of the order 1 µG through Faraday rotation measures and the equipar- ∼ tition theorem. However, one should bare in mind that also these estimates suffer from uncertainties. For this reason, it is by no means certain that ASTRO-H will in fact observe HXR emission from the clusters in the above-mentioned list, or any of the other clusters, in a 1 Ms pointing. For this reason we believe that it is important to make use of the multiple instruments aboard ASTRO-H to simultaneously study other phenomena. For example, while studying halos, which reside at the cluster centre, one can simultaneously study the tentative dark matter line (Bulbul et al., 2014; Boyarsky et al., 2014). While for relics, the shock nature can be studied in SXR through temperature jumps (e.g Akamatsu et al., 2012a; Akamatsu and Kawahara, 2013). Finally, in selecting targets it is important to compare your target size to the field of view of your instrument and to consider whether multiple sources can be studied simultaneously.

With the launch of ASTRO-H next year, and with NuSTAR by now fully operational, we have reached an era in which we can probe IC emission in clusters for magnetic fields > 1 µG. Although, care should be taken in analysing the spectra (e.g. Wik et al., 2014), for a few clusters we might finally break the degeneracy between magnetic fields and the CRe distribution in the coming decade. Appendix A

Some (Astro-)Physics

A.1 Cosmology

For a detailed treatment of cosmology in general see e.g. Weinberg(2008). The Fried- mann equations for an isotropic and homogeneous universe are given by

a˙ 2 8πG k H2(t) = ρ , (A.1a) ≡ a 3 − a2 2¨a a˙ 2 k + = 8πGp . (A.1b) a a − − a2

Here a is the scale factor, ρ = ρm + ρr + ρΛ the total density, p = pm + pr + pΛ the total pressure and k the curvature. Taking the diﬀerence of these two equations one obtains

a¨ ρ = 4πG(p + ). (A.2) a − 3

Moreover, we can define the critical density as the density for which the universe is flat today, i.e. k = 0: 2 3H0 ρc = , (A.3) 8πG and the normalised abundance assuming a flat universe is

ρi Ωi = . (A.4) ρc

71 Appendix A. Some (Astro-)Physics 72

The age of the universe at some redshift z is

1 ∞ dz 1 t = . (A.5) H0 1 + z × Ω (1 + z)3 + Ω (1 + z)3 + Ω + Ω (1 + z)2 Z0 m r Λ k p A.1.1 Distance scales

There are various distance scales that are relevant to cosmology, they are outlined below. Cosmic distances are treated in any book on cosmology or general relativity, but a nice summary on which this section is based can be found in Pfrommer(2005).

The proper distance is the coordinate time that it takes light to travel from the source to an observer

c a(zo) da Dprop(zo, zs) = . (A.6) H −1 −2 2 0 Za(zs) Ωma + Ωra + +ΩΛa + Ωk p The comoving distance is the distance with the scale factor divided out, as if you are locked in the Hubble ﬂow.

c a(zo) da Dcom(zo, zs) = . (A.7) H 2 −3 −4 −2 0 Za(zs) a Ωma + Ωra + +ΩΛ + Ωka p The angular diameter distance relates the angle an object subtends over the sky in radians with its physical size l. One takes the limit sin θ θ for θ 1. One arc second ≈ corresponds to 1 00 4.85 10−6 rad ≈ ×

l θ Dang(zo, zs) (A.8) ≈ × where,

Dang(zo, zs) = a(zs)Dcom(zo, zs). (A.9)

Finally, there is the luminosity distance which relates the luminosity of the source to the ﬂux observed at zo

2 a(zo) Dlum(zo, zs) = Dcom(zo, zs). (A.10) a(zs) kpc/” Although we already discussed angular diameter distance it is still worthwhile to look at the conversion from arc seconds to a distance measure such as kpc. Particularly Appendix A. Some (Astro-)Physics 73 since this is often used in the literature. First of all, the circumference of the sky spans 1296000 ”. So we can ﬁnd this conversion through:

2πDang Mpc/”. (A.11) 1296000

Different cosmologies yield different results and are not only related through the rescaling 1 of H0 (Dany ), but also depend the different normalised abundances Omega. In ∝ H0 old studies one often finds Ωm = 1 and ΩΛ = 0.

A.2 Equipartition Magnetic Field

In the literature the magnetic ﬁeld is often estimated through the equipartition condition. Unlike estimates from IC radiation, this method only requires information about synchrotron radiation. The main idea is to minimise the total energy content of the

source volume, Utot, where

Utot = Ue + Up + UB

with Ue and Up the energy in electrons and protons, and UB the energy in the magnetic ﬁelds (see Fig. A.1).

Figure A.1: The equipartition magnetic ﬁeld, Beq, minimises the total energy content of the source volume (ﬁgure taken from Govoni and Feretti, 2004). Appendix A. Some (Astro-)Physics 74

A detailed derivation of the equipartition magnetic ﬁeld can be found in, e.g., Govoni and Feretti(2004); Feretti and Giovannini(2008). Here we simply state the result:

1 24π 2 Beq = umin (A.12) 7 with,

4 4 4α 7 − 7 4 12+4α ν0 7 I0 d umin = ξ(α, ν , ν )(1 + k) 7 (1 + z) 7 . 1 2 1 MHz 1 mJy arcsec−2 1 kpc Here z is the redshift, k the ratio of energy in relativistic protons to that in electrons1,

I0 the source brightness at frequency ν0, d the source depth, and ξ(α, ν1, ν2) a constant resulting from integrating over photon frequencies (for typical values see Table 1 in Govoni and Feretti(2004)).

The computation of the equipartition magnetic ﬁeld in Eq. (A.12) is based on the in-

tegration of the synchrotron radio luminosity between two ﬁxed frequencies, ν1 and

ν2. However, from the critical frequency (Eq. 2.8), we know that the electron energy corresponding to this frequency depends on the strength of the magnetic ﬁeld. It was pointed out by Beck and Krause(2005) that it is better to integrate over the electron

distribution. Under the assumptions that γmin γmax, α > 0.5 and for Beq evaluated from 10 MHz 100 GHz the so-called revised equipartition magnetic ﬁeld, B0 , becomes − eq (Brunetti et al., 1997; Govoni and Feretti, 2004):

7 1−2α Beq 2(3+α) B0 1.1γ 3+α G. (A.13) eq ≈ min 1 G

1 Finally, since the source depth, d, depends on the Hubble constant through h , we ﬁnd the following dependence of the (revised) equipartition magnetic ﬁeld:

2 Beq h 7 ∝ (A.14) 0 1 B h 3+α . eq ∝ 1Typical values used in the literature are k = 1 and k = 0. Appendix A. Some (Astro-)Physics 75

A.3 Parameter Dependence on Cosmology

In this section the dependence of certain parameters on the cosmological model is discussed. In this study we adopt a model with Ωm = 0.27, ΩΛ = 0.73 and H0 = −1 −1 100h70 km s Mpc where h70 = 0.7. However, in older studies the adopted cosmology diﬀers from the one used here and this impacts the value of certain parameters.

In particular a cosmological model with q0 = 0.5 corresponding to Ωm = 1, ΩΛ = 0 −1 −1 and H0 = 100h50 km s Mpc where h50 = 0.5 is often found in studies until about a decade ago.

Radii For analysing clusters one often uses the virial radius (r200) or the core radius

(rc). They can be found through Eq. (A.8). Therefore,

1 r Dang(z) . ∝ ∝ H0

To be exact, one should really use the ratio of the two diﬀerent angular diameter distances. Although the correction from the density parameter is small, it is present at about the 10% level for the two cosmologies mentioned at the beginning of this section. ∼

Number density The beta model depends on the number density of electrons and 1/2 hydrogen. These roughly scale as ne, H . The exact dependence is 0 ∼ 0

1/2 ne, D . 0 ∝ ang

The electron and hydrogen energy are determined through the surface brightness, which roughly scales as (e.g. eqn 5.2 in Ota(2001)):

rc S ne,0nH,0 2 . ∝ Dang

Using the above relation for rc, and the fact that surface brightness is a measured quantity and thus does not depend on cosmology, used one ﬁnds the above mentioned relation for ne,0. Appendix A. Some (Astro-)Physics 76

Central density Sometimes in the literature one only ﬁnds an expression for the central density, ρ0, which refers to the total, baryonic plus DM, density. Although it is not explicitly used in this work, knowing how to convert this to central electron density is nevertheless useful. It can be done through the following expression (Ota, 2001):

Ω µmpne, B 0.2 = 0 . (A.15) ΩDM ≈ ρ0

Here ΩB is the baryon versus DM mass fraction, and µ 1.14 the ratio of hydrogen ΩDM ≈ to electrons as given in Zandanel et al.(2014). Appendix B

Radio Data

Table B.1: Radio Data for Halos.

† Cluster νradio (MHz) Sν (mJy) Reference 1E0657-56 1300 56.4 ± 2.3 Shimwell et al.(2014) 1340 51.65 ± 5.20 Liang et al.(2000) ‡ 2100 27.5 ± 1.7 Shimwell et al.(2014) 2350 20.21 ± 2.00 Liang et al.(2000) 4860 11.4 ± 1.2 ” 5870 8.1 ± 0.8 ” 8830 3.50 ± 0.35 ”

A0520 325 85 ± 5 Vacca et al.(2014) 1400 16.7 ± 0.6 ”

A0521 153 328 ± 66 Macario et al.(2013) 240 152 ± 15 Brunetti et al.(2008) 325 90 ± 7 ” 1365 6.4 ± 0.6 Macario et al.(2013) 1400 5.9 ± 0.5 Giovannini et al.(2009)

A0665 327 197 ± 6 Feretti et al.(2004) 1400 43.1 ± 0.8 ”

A0697 153 135 ± 27 Macario et al.(2013) 325 47.3 ± 2.7 ” 610 14.6 ± 1.7 ” 1382 5.2 ± 0.5 van Weeren et al.(2011a) Continued on next page

77 Appendix B. Radio Data 78

Table B.1 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference 1714 40 ± 5 ”

A0754 74 4000 ± 400 Kassim et al.(2001) 330 750 ± 75 ” 1365 86 ± 4 Bacchi et al.(2003)

A1300 325 130 ± 7 Giacintucci(2011) 1400 10 ± 1 ”

A1656 30.9 49 000 ± 10 000 Thierbach et al.(2003) 43 51 000 ± 13 000 ” 73.8 17 000 ± 12 000 ” 151 7200 ± 800 ” 326 3810 ± 30 ” 408 2000 ± 200 ” 430 2550 ± 280 ” 608.5 1200 ± 300 ” 1380 530 ± 50 ” 1400 640 ± 35 ” 2675 107 ± 28 ” 2700 70 ± 20 ” 4850 26 ± 12 ”

A1758 325 146 ± 7 Giacintucci(2011) 1400 16.7 ± 0.8 Giovannini et al.(2009)

A1914 26.3 88 000 ± 13 000 Komissarov and Gubanov(1994) 38 54 000 ± 8000 ” 81.5 18 000 ± 2700 ” 151 5600 ± 800 ” 178 3900 ± 600 ” 318 1180 ± 180 ” 408 780 ± 120 ” 608.5 284 ± 42 ” 1465 64 ± 3 Bacchi et al.(2003)

A2163 325 861 ± 10 Feretti et al.(2004) 1400 155 ± 2 Feretti et al.(2001) Continued on next page Appendix B. Radio Data 79

Table B.1 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference

A2218 9 ± 4 Kempner and Sarazin(2001) 1400 4.7 ± 0.5 Giovannini and Feretti(2000) 5000 0.60 ± 0.06 ”

A2219 325 232 ± 17 Orru et al.(2007) 1400 81 ± 4 Bacchi et al.(2003)

A2255 330 536 ± 54 Feretti et al.(1997) 1400 56 ± 3 Govoni et al.(2006) 1500 43 ± 4 Feretti et al.(1997)

A2256 63 6600 ± 1300 van Weeren et al.(2012) 351 760 ± 70 Brentjens(2008) 1369 103 ± 20 Clarke and Ensslin(2006)

A2319 408 1450 ± 145 Feretti et al.(1997) 610 1000 ± 100 ” 1420 153 ± 15 ”

A2744 325 218 ± 10 Orru et al.(2007) 1400 98 ± 7 Govoni et al.(2001)

A3562 240 220 ± 33 Giacintucci et al.(2005) 332 195 ± 5 ” 610 90 ± 9 ” 843 59 ± 6 Venturi et al.(2003) 1400 20 ± 2 Giacintucci et al.(2005)

ACT-CL J0102-4915* 610 29 ± 3 Lindner et al.(2014) 2100 2.43 ± 0.18 ”

CL0217+70 325 326 ± 30 Brown et al.(2011a) 1400 58.6 ± 0.9 ”

s MACSJ0717.5+3745 235 492.50 ± 0.52 Pandey-Pommier et al.(2013) 610 162.0 ± 2.3 ” 1425 118 ± 5 Bonafede et al.(2009a) Continued on next page Appendix B. Radio Data 80

Table B.1 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference 4860 26 ± 1 ”

PLCK G171.9-40.7 235 483 ± 110 Giacintucci et al.(2013) 1400 18 ± 2 ”

RXCJ1514.9-1523 327 102 ± 9 Giacintucci et al.(2011) 1400 10 ± 2 ”

RXCJ2003.5-2323 240 360 ± 18 Giacintucci et al.(2009) 610 96.9 ± 0.5 Venturi et al.(2009) 1400 35 ± 2 Giacintucci et al.(2009) †And references therein. ‡Data extracted using Dexter (http://dc.zah.uni-heidelberg.de/dexter/ui/ui/custom). *Not in our sample.

Table B.2: Radio Data for Relics.

† Cluster νradio (MHz) Sν (mJy) Reference 1RXS J0603.3+4214 74 7600 ± 760 van Weeren et al.(2012) ‡ 150 3430 ± 340 ” 240 2000 ± 200 ” 325 1520 ± 150 ” 610 753 ± 75 ” 1215 350 ± 35 ” 1382 319.5 ± 2.1 van Weeren et al.(2012) 1700 239 ± 24 van Weeren et al.(2012) ‡ 2260 170 ± 17 ” 4870 66 ± 17 ”

A0013 80 6000 ± 1200 Slee et al.(2001) 160 28 000 ± 600 ” 327 630 ± 60 ” 408 490 ± 80 ” 843 90 ± 10 ” 1400 30 ± 3 ”

Continued on next page Appendix B. Radio Data 81

Table B.2 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference A0085 16.7 93 000 ± 24 000 Slee et al.(2001) 29.9 93 000 ± 13 000 ” 80 34 000 ± 3700 ” 160 8330 ± 700 ” 327 3200 ± 320 ” 408 1540 ± 250 ” 843 200 ± 30 ” 1400 43 ± 3 ” 1425 40.9 ± 2.3 ”

A0521 153 297 ± 59 Macario et al.(2013) 235 180 ± 10 ” 327 114 ± 6 ” 610 42 ± 2 ” 1400 14 ± 1 ” 4980 2.0 ± 0.2 ”

A0610 600 59 ± 6 Giovannini and Feretti(2000) 1400 18.6 ± 1.9 ”

A0754 74 1450 ± 150 Kassim et al.(2001) 1365 69 ± 3 Bacchi et al.(2003) A786* 150 933.5 ± 9.0 Kale and Dwarakanath(2012) 345 440.2 ± 3.0 ” 606 306 ± 8 ” 1400 105 ± 5 ”

A1240N 325 21.0 ± 0.8 Bonafede et al.(2009b) 1400 6.0 ± 0.2 ”

A1240S 325 28.5 ± 1.1 Bonafede et al.(2009b) 1400 10.1 ± 0.4 ”

A1300 325 75 ± 4 Giacintucci(2011) 843 33 ± 3 Reid et al.(1999) 1300 15 ± 2 ” 2400 10 ± 1 ”

Continued on next page Appendix B. Radio Data 82

Table B.2 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference A1367 610 180 ± 27 Gavazzi and Trinchieri(1983) 1415 35 ± 5 ”

A1656 151 3300 ± 500 Thierbach et al.(2003) 326 1400 ± 30 ” 408 910 ± 100 ” 610 611 ± 50 ” 2675 112 ± 10 ” 4750 54 ± 15 ”

A1664 150 1250 ± 125 Kale and Dwarakanath(2012) 325 450 ± 30 ” 1400 106.2 ± 0.4 ”

A2048 325 559 ± 61 van Weeren et al.(2011c) 1425 18.9 ± 4.3 ”

A2061 327 104 ± 15 Kempner and Sarazin(2001) 1382 27.6 ± 0.1 van Weeren et al.(2011a) 1714 21.2 ± 2.1 ”

A2063 16.7 337 000 ± 51 000 Komissarov and Gubanov(1994) 22.25 295 000 ± 44 000 ” 26.3 218 000 ± 33 000 ” 38 131 000 ± 20 000 ” 80 61 000 ± 9000 ” 81.5 52 000 ± 8000 ” 86 51 700 ± 8000 ” 102.5 39 000 ± 6000 ” 160 21 200 ± 3000 ” 178 13 200 ± 2000 ” 408 2650 ± 400 ” 750 680 ± 100 ” 1360 96 ± 14 ” 1465 67 ± 10 ”

A2255 330 103 ± 10 Feretti et al.(1997) 1500 12 ± 1 ” Continued on next page Appendix B. Radio Data 83

Table B.2 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference

A2256 63 5600 ± 800 van Weeren et al.(2012) 327 1390 ± 70 Brentjens(2008) 1369 462.0 ± 0.8 Clarke and Ensslin(2006)

A2345-E 325 188 ± 3 Bonafede et al.(2009b) 1400 29.0 ± 0.4 ”

A2345-W 325 291 ± 4 Bonafede et al.(2009b) 1400 30.0 ± 0.5 ”

A2433 74 5310 ± 175 Cohen and Clarke(2011) 325 406 ± 69 ” 1425 6.5 ± 0.5 ”

A2744 325 98 ± 7 Orru et al.(2007) 1400 18.2 ± 0.2 Govoni et al.(2001) A3376E 150 3500 ± 350 Kale et al.(2012) 325 1770 ± 90 ” 1400 122 ± 10 ”

A3376W 150 2962 ± 300 Kale et al.(2012) 325 1367 ± 70 ” 1400 113 ± 10 ”

A3411 74 2074 ± 850 van Weeren et al.(2013) 350 284 ± 50 ” 1395 79 ± 5 ”

A3667 85.5 81 000 ± 12 150 Rottgering et al.(1997) 408 12 200 ± 1830 ” 843 5500 ± 500 ” 1380 2400 ± 200 ” 2380 1400 ± 210 ”

A4038 29.9 32 000 ± 7000 Slee et al.(2001) 74 12 450 ± 1500 Kale and Dwarakanath(2012) Continued on next page Appendix B. Radio Data 84

Table B.2 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference 150 5160 ± 110 ” 240 2960 ± 60 ” 327 1440 ± 150 Slee et al.(2001) 408 910 ± 110 ” 606 380 ± 57 Kale and Dwarakanath(2012) 843 170 ± 30 Slee et al.(2001) 1400 60 ± 4 Kale and Dwarakanath(2012)

ACT-CL J0102-4915 E 610 1.2 ± 0.2 Lindner et al.(2014) 2100 0.41 ± 0.04

ACT-CL J0102-4915 NE 610 19 ± 2 Lindner et al.(2014) 843 18.2 ± 0.2 2100 4.3 ± 0.2

ACT-CL J0102-4915 SE 610 3.0 ± 0.3 Lindner et al.(2014) 2100 0.48 ± 0.04

AS753 330 8500 ± 850 Subrahmanyan et al.(2003) 843 1300 ± 130 ” 1398 460 ± 460 ” 2378 100 ± 100 ”

CIZAJ2242.8-5301N 150 668 ± 69 Stroe et al.(2014) ‡ 320 270 ± 28 ” 600 187 ± 19 ” 1200 107 ± 11 ” 1400 96 ± 10 ” 1700 67 ± 7 ” 2300 28 ± 3 ” 16 000 1.2 ± 0.3 ”

PLCK G287.0+32.9N 150 550 ± 50 Bagchi et al.(2011) 1400 33 ± 5 ”

PLCK G287.0+32.9S 150 780 ± 50 Bagchi et al.(2011) 1400 25 ± 5 ” Continued on next page Appendix B. Radio Data 85

Table B.2 – continued from previous page

† Cluster νradio (MHz) Sν (mJy) Reference

ZwCl0008.8-5215E 241 820 ± 90 van Weeren et al.(2011b) 610 230 ± 25 ” 1382 56.0 ± 3.5 ” 1714 37.0 ± 2.7 ”

ZwCl0008.8-5215W 241 110 ± 30 van Weeren et al.(2011b) 610 56 ± 8 ” 1382 11.0 ± 1.2 ” 1714 8.90 ± 0.12 ” †And references therein. ‡Data extracted using Dexter (http://dc.zah.uni-heidelberg.de/dexter/ui/ui/custom). *Not in our sample. Appendix C

Comments on Less Good Targets

In this appendix we comment on all clusters that were not discussed in section 4.1.1. Spectra of the clusters discussed below can be found in appendixD. Of this remaining sample, we consider A0013, A0521, A0610, A2345, A3376, RXCJ2003.5-2323, Tooth- brush and the Sausage to be particularly interesting. However, they were not discussed in section 4.1.1 for various reasons. For the toothbrush and sausage the magnetic ﬁeld estimates are much higher than Bu.l.. For the remaining sample, apart form A3376, there exists no detailed study of the X-ray brightness of the cluster.

1RXS J0603.3+4214 Toothbrush relic (van Weeren et al., 2012). Currently one of the most studied relics.

A0013 This cluster (z = 0.0943) hosts a small radio relic. We estimate that ASTRO-H can detect IC emission for a volume averaged magnetic ﬁeld of B 2.15 µG. However, ≤ there are no equipartition estimates in the literature. The spectrum of the relic appears to ﬂatten towards low frequencies. However, Juett et al.(2008) report an electron density at the relic of 1 10−3 cm−3, which corresponds to a maximum lifetime of relativistic × −1 −3 electrons at γmin 200. For comparison, if the electron density would be 10 cm , ∼ ∼ γmin shifts to 2000. We conclude that this relic has some potential. ∼

86 Appendix C. Comments on Less Good Targets 87

A0520 Abell 520 hosts a radio halo that has been studied anew (Vacca et al., 2014) recently. They suggest the cluster merger is still ongoing, explaining the ﬂat spectral index.

A0521 This clusters (z = 0.2533) hosts both a radio halo and a relic, where the relic is the brightest feature present. They seem to be connected by a bridge (Macario et al., 2013). Assumptions of spherical symmetry or hydrostatic equilibrium do not apply to this cluster, complicating the estimation of the gas density, temperature profile and mass of the cluster (Ferrari et al., 2006). However, both the relic and halo have relatively good forecasts, IC emission should be detectable for magnetic field strengths of B 1.08 µG ≤ and B 1.40 µG, respectively. In addition, both object fit in the HXI FoV. ≤

A0610 The relic in Abell 610 (z0.0954) has been little studied in the literature (Gio- vannini and Feretti, 2000). Considering there are only two data points in radio, the small size of the relic and the fact that there is no extensive X-ray study we do not consider A610 to be the most interesting target for now. However, with our estimate of the thermal background from the model by Zandanel et al.(2014), we predict that ASTRO-H should be able to detect IC emission if B 1.96 µG. Therefore, the cluster ≤ has some future potential if it is not too X-ray luminous.

A0665 Abell 665 (z = .1819) hosts a radio halo. Although this cluster is not listed among our targets of opportunity, it is one of the more interesting clusters of the remaining cases. Million and Allen(2009) report an SXR excess flux of 4 .2+1.4 −1.2 × 10−12 erg s−1 cm−2 in the 0.6 7 keV band and an average spectral index of α = 1.63+0.10. − −0.21 1.4 In radio, Feretti et al.(2004) and Vacca et al.(2010) obtain a spectral index of α0.3 = 1.04 0.02. The discrepancy between these two values makes it questionable whether ± this soft X-ray radiation is created by the same electron population as the synchrotron radiation1. Moreover, since the radio spectrum is relatively flat, observing the cluster in hard X-rays might be advantageous. The magnetic field in the central 1 Mpc3 is estimated at 0.75 µG(Vacca et al., 2010).

1For a similar case see A2744. Appendix C. Comments on Less Good Targets 88

A0697 The halo shows a regular morphology (van Weeren et al., 2011a; Macario et al., 2013). No steepening or ﬂattening is observed in the spectrum.

A0754 Abell 754 hosts a halo and two relics (Bacchi et al., 2003; Kassim et al., 2001). However, the structure of the radio emission is connected and asymmetric. Moreover, the centres of the radio emission correspond to two optical clumps. Alternatively, the radio emission could also correspond to two halos or two relics. Spectral steepening is observed in the halo.

A1240 The cluster hosts a double relic which is in agreement with an outgoing merger shock scenario (Bonafede et al., 2009b). Bonafede et al.(2009b) obtain a spectral index of α = 1.2 for the northern and α = 1.3 for the western relic in the region where the surface brightness exceeds 3σ. In addition, they observe that the spectral index flattens towards the outer regions of the relic. Taking the integrated flux and deriving the average spectral index for the entire relic region we find α = 0.86 and α = 0.71, respectively. The computed value of the volume-averaged magnetic field strongly depends on the spectral index. The uncertainty on the spectral index in comparison to the total integrated flux leads us to the concluding that our derived values for the magnetic fields might be wrong.

A1300 Abell 1300 is a complex cluster that hosts both a radio halo and relic (Reid et al., 1999; Giacintucci, 2011), The halo and relic are known as source A4 and B3, respectively, in Reid et al.(1999). There exists a discrepancy of a factor two between data taken at 1.3 GHz from the Australia Telescope Compact Array (ATCA) and 1.4 GHz by the NRAO VLA Sky Surve (NVSS) for the radio halo, probably due to missing ﬂux in the ATCA observation. A similar problem exists for the radio relic at 1.4 GHz and 2.4 GHz. For these reasons and since the cluster is quite distant, we do not consider it to be a good target to study HXR emission.

A1664 Kale and Dwarakanath(2012) recently presented multi-frequency data for the relic. The spectrum is ﬂat, with α = 1.1. This is uncommon for a roundish relic, which usually have very steep spectra (Feretti et al., 2012). Appendix C. Comments on Less Good Targets 89

A1758N A1758N hosts a radio halo. Together with A1758S, it forms a merging cluster. The X-ray morphology is complex.

A2048 Abell 2048 contains a roundish relic with a steep spectral index (van Weeren et al., 2011c).

A2061 This cluster is in the vicinity of A2067. The radio relic was first detected by Kempner and Sarazin(2001). More recent observations were carried out by van Weeren et al.(2011a), who report a higher flux density 1 .4 GHz. The spectral index is relatively flat.

A2063 This cluster hosts a relic, known as source 3c318.1 in Komissarov and Gubanov (1994). Spectral steepening is clearly observed. The source is very small ( 40 kpc) and ∼ close to the cluster centre ( 40 kpc). ∼

A2163 One of the hottest and most X-ray luminous clusters. It hosts a radio halo.

A2218 The radio halo of Abell 2218 is one of the smallest reported in the literature ( 0.4 Mpc). Giovannini and Feretti(2000) report a flux density of 4 .7 mJy at 1.4 GHz. ∼ Kempner and Sarazin(2001) report 1 0.6 mJy at the same frequency, but this is because ± the source is badly resolved in the Westerbork Northern Sky Survey (WENSS), which they examine. The spectrum appears to break at low frequencies. From the central gas density ( 6 10−3 cm−3, Ota(2001)), we find that γ 5 102 electrons should have ∼ × ∼ × 5 the longest lifetime. However, our best fit corresponds to γmin = 1.3 10 . However, × this discrepancy can most likely be explained, since the 327 MHz measurement it is also from Kempner and Sarazin(2001). Assuming that, similarly to the data at 1 .4 GHz, the flux density is lower by a factor the same factor compared to that of Giovannini and Feretti(2000), we multiply the data at 327 MHz by 4 .7. In that scenario we would obtain a spectrum with α = 1.6 over the entire frequency range, exactly the same number as reported by Giovannini and Feretti(2000). On the other hand, note that if the cutoff is real ASTRO-H won’t be able to probe IC emission whatsoever (seeD). Appendix C. Comments on Less Good Targets 90

A2219 The radio halo is 10 times more powerful than that of Coma (Bacchi et al., 2003).

A2256 A halo and relic are present in this cluster. Similarly to Abell 2255, the HXR upper limit is for a region containing both the halo and the relic. Ajello et al.(2010) observed out to 100 from the cluster centre, the relic is at 70. ∼

A2345 The cluster (z = 0.1765) hosts double relics, of which the western one shows some unusual properties (Bonafede et al., 2009b). The complex mass distribution indicates that spherical symmetry is not a good approximation for this cluster, making mass estimates highly uncertain Okabe et al.(2010). Therefore, since we used the mass- dependent model by Zandanel et al.(2014) to estimate the gas density, our background estimate is uncertain. However, if our background estimate is reasonable, ASTRO-H should be able to detect IC emission from both relics for values of the magnetic ﬁeld slightly above 1 µG.

A2433 There are indications that this clusters is in an ongoing merger. The relic has an ultra-steep spectrum and we observe spectral steepening (Cohen and Clarke, 2011). 0.3 However, it is also well ﬁtted by a power law (α0.07 = 1.74) and a cutoﬀ. In our analysis, we considered it approximately a point source for ASTRO-H.

A3376 Abell 3376 is a relatively nearby cluster (z = 0.0456) containing a double relic (Kale et al., 2012). Constraints on non-thermal X-rays are derived by Kawano et al. (2009). The western relic has also been studied by Akamatsu et al.(2012b). They place individual limits on both relics in the 4 8 keV band. The most recent radio data is − from Kale et al.(2012). Their data indicates that there is spectral steepening at high frequencies, however, the authors point out that there may be some loss of ﬂux density at 1400 MHz accounting for the steep spectral index (α0.3 1.7) at higher frequencies. .4 ∼ In fact, a slightly higher ﬂux at 1.4 GHz is given by Feretti et al.(2012). Appendix C. Comments on Less Good Targets 91

A3411 The cluster hosts a relic and a halo. For the halo the spectral index is not available. The relic has a peculiar morphology, being broken up into ﬁve segments (van Weeren et al., 2013). Flux densities were retrieved using Dexter2.

A3562 Abel 3562 is one of three clusters in the cluster complex A3558, the others being A3558 and A3556 (Venturi et al., 2000). The radio halo in A3562, the only one in the complex, is one of the smallest and least powerful halos. Clear spectral steepening is observed, as indicated by Giacintucci et al.(2005).

ACT-CL J0102?4915 ”El-Gordo” is the most distant cluster observed to date. It hosts three relics and a radio halo. The spectral index for the halo as obtained by Lindner et al.(2014) for the halo ( α = 1.2) does not match to the ﬂux densities they report, we obtain α = 2.0 for the same values. The origin of the discrepancy is unclear, possibly it is just a mistake. For this reason we left the halo out of our analysis. Finally, the entire cluster would be a point source for ASTRO-H, making it impossible to derive limits on non-thermal X-rays for individual relics.

CIZAJ2242.8+5301 A double relic os present in this cluster. We analyse the northern, so-called, sausage relic, which is at 8.50 from the cluster centre. Radio data was taken from Stroe et al.(2014) using Dexter. Spectral steepening is observed towards higher frequencies (16000 GHz). The magnetic ﬁeld at the relic is estimated to be 5 µG ∼ (van Weeren et al., 2010; R¨ottgeringet al., 2013).

CL0217+70 A radio detected cluster of galaxies hosting a radio halo and double relics. The spectral index is only available for the halo.

PLCK G171.9-40.7 The cluster hosts a newly discovered radio halo (Giacintucci et al., 2013).

PLCK G287.0+32.9 A hot (T 13 keV) and luminous cluster hosting double relics. ∼ 2http://dc.zah.uni-heidelberg.de/sdexter Appendix C. Comments on Less Good Targets 92

RXCJ1514.9-1523 This cluster its halo is faint at 1.4 GHz, the NRAO VLA Sky Survey (NVSS) might have missed some of the ﬂux at this frequency (Giacintucci et al., 2011).

RXCJ2003.5-2323 The cluster (z = 0.3171) hosts one of the largest and most powerful radio halos (Giacintucci et al., 2009). This might in fact be one of the more interesting targets, however, we did not list it among the prima candidates for two reasons. First, no gas density proﬁle exists for this cluster, making the background estimate uncertain.

Secondly, the revised equipartition estimate is slightly higher than Bu.l., 1.7 µG against 1.14 µG, respectively. Appendix D

Cluster Spectra

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.38µG BV = 2.70µG BV = 0.89µG Plasma 10 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.i) 1E0657-56 (D.1.ii) 1RXSJ0603 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 2.15µG BV = 0.43µG Plasma BV = 2.36µG 10 ASTRO-H 1Ms 10 Plasma 10− 10− ASTRO-H SXI 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.iii) A0013 (D.1.iv) A0085

93 Appendix D. Cluster Spectra 94

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.43µG BV = 1.08µG Plasma γmin = 1000 11 ASTRO-H 1Ms 11 Plasma 10− 10− ASTRO-H SXI 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 12 ] 12

2 10− 2 10− cm cm / / 13 13 10− 10− sec sec / /

14 14

[erg 10− [erg 10− ν ν S S · · 15 15 ν 10− ν 10−

16 16 10− 10−

10 17 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.v) A0520 (D.1.vi) A0521 Halo E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 1.40µG BV = 1.96µG γmin = 1000 γmin = 1000 11 Plasma 11 Plasma 10− 10− ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 12 ] 12

2 10− 2 10− cm cm / / 13 13 10− 10− sec sec / /

14 14

[erg 10− [erg 10− ν ν S S · · 15 15 ν 10− ν 10−

16 16 10− 10−

10 17 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.vii) A0521 Relic (D.1.viii) A0610 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.11µG BV = 0.53µG BV = 0.40µG Plasma 10 Plasma 11 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 12

2 10− 2 10− cm cm / / 12 13 10− 10− sec sec / /

13 14

[erg 10− [erg 10− ν ν S S · · 14 15 ν 10− ν 10−

15 16 10− 10−

10 16 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.ix) A0665 (D.1.x) A0697 Appendix D. Cluster Spectra 95

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.09µG BV = 0.42µG BV = 0.46µG Plasma 10 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xi) A0754 Halo (D.1.xii) A0754 Relic E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.26µG BV = 0.12µG Plasma Plasma 11 ASTRO-H 1Ms 11 ASTRO-H 1Ms 10− 10− ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 12 ] 12

2 10− 2 10− cm cm / / 13 13 10− 10− sec sec / /

14 14

[erg 10− [erg 10− ν ν S S · · 15 15 ν 10− ν 10−

16 16 10− 10−

10 17 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xiii) A1240N (D.1.xiv) A1240S E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 1.05µG BV = 0.64µG γmin = 1000 Plasma 11 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 12 ] 11

2 10− 2 10− cm cm / / 13 12 10− 10− sec sec / /

14 13

[erg 10− [erg 10− ν ν S S · · 15 14 ν 10− ν 10−

16 15 10− 10−

10 17 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xv) A1300 Halo (D.1.xvi) A1300 Relic Appendix D. Cluster Spectra 96

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 1.86µG BV = 0.90µG γmin = 1000 Plasma 10 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xvii) A1367 (D.1.xviii) A1664 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.92µG BV = 0.59µG Plasma BV = 1.12µG 11 ASTRO-H 1Ms 10 Plasma 10− 10− ASTRO-H SXI 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 12 ] 11

2 10− 2 10− cm cm / / 13 12 10− 10− sec sec / /

14 13

[erg 10− [erg 10− ν ν S S · · 15 14 ν 10− ν 10−

16 15 10− 10−

10 17 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xix) A1758 (D.1.xx) A1914 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 3.19µG BV = 0.47µG γmin = 1000 Plasma 10 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxi) A2048 (D.1.xxii) A2061 Appendix D. Cluster Spectra 97

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.42µG BV = 0.13µG BV = 6.02µG BV = 0.48µG 10 Plasma 10 Plasma 10− 10− ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxiii) A2063 (D.1.xxiv) A2163 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 11 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.57µG BV = 0.27µG γmin = 1000 Plasma 12 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 13 ] 11

2 10− 2 10− cm cm / / 14 12 10− 10− sec sec / /

15 13

[erg 10− [erg 10− ν ν S S · · 16 14 ν 10− ν 10−

17 15 10− 10−

10 18 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxv) A2218 (D.1.xxvi) A2219 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.32µG BV = 0.71µG BV = 0.71µG γmin = 1000 11 γ = 1000 11 Plasma 10− min 10− Plasma ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 12 ASTRO-H SXI 1Ms ] 12 2 10− 2 10− cm cm / / 13 13 10− 10− sec sec / /

14 14

[erg 10− [erg 10− ν ν S S · · 15 15 ν 10− ν 10−

16 16 10− 10−

10 17 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxvii) A2255 Halo (D.1.xxviii) A2255 Relic Appendix D. Cluster Spectra 98

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.20µG BV = 0.43µG BV = 0.37µG Plasma 10 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxix) A2256 Halo (D.1.xxx) A2256 Relic E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.70µG BV = 1.08µG BV = 1.14µG γmin = 1000 10 γ = 1000 10 Plasma 10− min 10− Plasma ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11 ASTRO-H SXI 1Ms ] 11 2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxxi) A2319 (D.1.xxxii) A2345E E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 1.25µG BV = 3.48µG γmin = 1000 γmin = 1000 10 Plasma 10 Plasma 10− 10− ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxxiii) A2345W (D.1.xxxiv) A2433 Appendix D. Cluster Spectra 99

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.29µG BV = 0.36µG BV = 0.51µG BV = 1.39µG 10 Plasma 10 Plasma 10− 10− ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxxv) A2744 Halo (D.1.xxxvi) A2744 Relic E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.06µG BV = 0.06µG BV = 0.79µG BV = 0.95µG 10 Plasma 10 Plasma 10− 10− ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxxvii) A3376E (D.1.xxxviii) A3376W E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.46µG BV = 0.10µG Plasma BV = 0.46µG 10 ASTRO-H 1Ms 10 Plasma 10− 10− ASTRO-H SXI 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xxxix) A3411 (D.1.xl) A3562 Appendix D. Cluster Spectra 100

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 1.86µG BV = 3.79µG BV = 2.73µG Plasma 10 B = 5.27µG 10 ASTRO-H 1Ms 10− V 10− Plasma ASTRO-H SXI 1Ms ASTRO-H 1Ms

] 11 ASTRO-H SXI 1Ms ] 11 2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xli) A3667 (D.1.xlii) A4038 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 4.70µG BV = 1.85µG γmin = 1000 Plasma 10 Plasma 11 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 12

2 10− 2 10− cm cm / / 12 13 10− 10− sec sec / /

13 14

[erg 10− [erg 10− ν ν S S · · 14 15 ν 10− ν 10−

15 16 10− 10−

10 16 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xliii) AS753 (D.1.xliv) CIZAJ2242N E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.63µG BV = 0.32µG Plasma BV = 0.63µG 10 ASTRO-H 1Ms 10 Plasma 10− 10− ASTRO-H SXI 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xlv) CL0217+70 Halo (D.1.xlvi) Coma Halo Appendix D. Cluster Spectra 101

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 11 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.95µG BV = 0.13µG BV = 1.31µG Plasma 10 Plasma 12 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 13

2 10− 2 10− cm cm / / 12 14 10− 10− sec sec / /

13 15

[erg 10− [erg 10− ν ν S S · · 14 16 ν 10− ν 10−

15 17 10− 10−

10 16 10 18 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xlvii) Coma Relic (D.1.xlviii) El-GordoE E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 11 10− 10− 10− 10− 10− 10 10 10 11 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.28µG BV = 0.42µG Plasma Plasma 12 ASTRO-H 1Ms 12 ASTRO-H 1Ms 10− 10− ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 13 ] 13

2 10− 2 10− cm cm / / 14 14 10− 10− sec sec / /

15 15

[erg 10− [erg 10− ν ν S S · · 16 16 ν 10− ν 10−

17 17 10− 10−

10 18 10 18 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.xlix) El-GordoNW (D.1.l) El-GordoSE E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 2.26µG BV = 1.08µG Plasma γmin = 1000 10 ASTRO-H 1Ms 10 Plasma 10− 10− ASTRO-H SXI 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.li) MACSJ0717 (D.1.lii) PLCKG171 Appendix D. Cluster Spectra 102

E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 9 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 2.13µG BV = 3.79µG Plasma Plasma 10 ASTRO-H 1Ms 10 ASTRO-H 1Ms 10− 10− ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 11 ] 11

2 10− 2 10− cm cm / / 12 12 10− 10− sec sec / /

13 13

[erg 10− [erg 10− ν ν S S · · 14 14 ν 10− ν 10−

15 15 10− 10−

10 16 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.liii) PLCKG287N (D.1.liv) PLCKG287S E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 9 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 0.62µG BV = 1.14µG γmin = 1000 Plasma 11 Plasma 10 ASTRO-H 1Ms 10− 10− ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 12 ] 11

2 10− 2 10− cm cm / / 13 12 10− 10− sec sec / /

14 13

[erg 10− [erg 10− ν ν S S · · 15 14 ν 10− ν 10−

16 15 10− 10−

10 17 10 16 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.lv) RXCJ1514 (D.1.lvi) RXCJ2003 E[keV] E[keV] 10 8 6 4 2 0 2 4 10 8 6 4 2 0 2 4 10 10− 10− 10− 10− 10− 10 10 10 10 10− 10− 10− 10− 10− 10 10 10 10− 10− BV = 2.37µG BV = 2.74µG γmin = 1000 γmin = 1000 11 Plasma 11 Plasma 10− 10− ASTRO-H 1Ms ASTRO-H 1Ms ASTRO-H SXI 1Ms ASTRO-H SXI 1Ms

] 12 ] 12

2 10− 2 10− cm cm / / 13 13 10− 10− sec sec / /

14 14

[erg 10− [erg 10− ν ν S S · · 15 15 ν 10− ν 10−

16 16 10− 10−

10 17 10 17 − 107 109 1011 1013 1015 1017 1019 1021 1023 − 107 109 1011 1013 1015 1017 1019 1021 1023 ν[Hz] ν[Hz] (D.1.lvii) ZwCl0008E (D.1.lviii) ZwCl0008W Bibliography

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