一委員 石蹟「欣向   委員 田原 該

 物理学 1366

     Hoshino Akio

氏名 星野晶夫

X−ray Study of the Outer Regions of Clusters of Galaxies

Akio Hoshino

Deραr￠me励0∫Pん鋼C3， Zb勧o凡4e roρol甑ηση初er5吻 1−1M仇α禰一〇ん8αωα，1了αcんτoカ7b伽192−039ち」αραη

February 2010

首都大学東京 博士（理学）学位論文（課程博士）

論文名

  X線による銀河団外縁部の研究（英文）

著者 星野晶夫

審査担当者

  委員 政埠舜叩

一委員 石蹟「欣向   委員 田原 該

上記の論文を合格と判定する  平成之2年3 ．月2仁日

 首都大学東京大学院理工学研究科教授会 研究科長

 DISSERTATION FOR A DEGREE OF DOCTOR OF PHILOSOPHY IN SCIENCE

TOKYO METROPOL，ITAN UNIVERSITY

TITLE：

X−ray Study of the Outer Regions of Clusters of Galaxies

AUTHOR：Akio Hoshino

EXAMINED BY

E…i…in噸三㍉巳広

Examiner 匡＿，μ9弓一二

QuAHFIED BY THE GRADuATE SCHOoL   OF SCIENCE AND ENGINEERING  TOKYO METROPOLITAN UNIVERSITY

Date   lしへ0、卜cl〜 2C， 之δ／・

1 1ntroduction       1

2 Review of Cluster of Galaxies      5

  2．1  Structure and evolution of the universe ．．．．．．．．．．．．．．．．．．．．  5       2．1．1 Expansion dynamics ．．．．．，．．．．．．．．．．．．．．．．．．．． 5       2．1．2 Hierarchical s七ructure forma七ion．．．．．．．．．．．．．．．．．．．．． 6       2．1．3  Collapse condition  ．．．．．．．．．．．．．．．．．．．．．．．．．．．  8       2．1．4 Warm−Hot Inter−cluster Medium．．．．．．．．．．．．．．．．．．．． 9   2．2 Clusters of Galaxies．，．．．．．．．．．．．．．．．．，．．．．．．．．．．．． 10       2．2．1 Virial radius and the virial density ．．．．．．．．，．．．．．．．．． 10       2．2．2 X−ray emission process．．．．．．．．．．．．．．．．．．．．．．．．．12       2．2．3 Mass Distribution．．，，．，．．，．．．．．．，．．．．．，，．．．．．14       2．2．4 Previous studies up toγ・200  ＿ ．．．．．．．．．．．．．．．．．．．． 18       2．2．5 Self−Similarity of Cluster Structure ．．．．．，．．．．．．．．．．．．19       2．2．6 Evolution of Clusters of Galaxies ．．．，．．．．．．，．、．．．．．． 22       2．2．7 Heavy Element Enrichment of the ICM．．．．．．．．．．．．．．．．23

31nstrumentation      27

  3、1 The S批α輪Satellite ．．．．．，．．．．．．．．．．．，．．．．．．．．．．．． 27       3．1．1 Mission Description．．．．．．．．．．．．．．＿．．．．．．．．．．．27       3．1．2 X−Ray Telescopes（XRTs）．．．．＿．．．．．．．．．．．．．．．．． 30       3．1．3 X−ray Imaging Spectrometer（XIS）．．．．．．．．．．．．．．．．．．37       3．1．4 Uncertainties of Metal Abundance．．．，．．．．．．．．．．．．．．．47   3．2 XMM lVe庇oη．．．．．．．．．．．．．．，．．．．．．，．．．，．．・．、，．．．49       3．2．1 X−ray Telescopes ．，．．．．．．．．．．．．．，．．．．．．．．．．．． 50       3．2．2 European Photon Imaging Camera（EPIC）．．＿．．．．．．．．．．54       3．2．3 EPIC Background ．．．．．．．．．．．．．．．．．．．．．．．．．．． 57

4 0bservation and Data Reduction      61   4．1 Sample clusters．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．61       4．1．1 A1413 ．．．．．．．．．．．．．．．．．．．，．．．．．．．．．．，，．．61       4．1．2 A2204 ．．．．．．．．．．．．．．．．．．．．．，．．．．．．．．．．．． 65   4．2 Data Reduction．．，．．．．．．．．．．．，．．．，．．．．．．．，．．．．．． 66

ii       cONTENTS

4．2．1  Sμzα1ヒrμ．．．． ．．．． ．． ．．．．． ．．．． ． ．．．．．． ．． ．． ． ．．． 66

4．2．2  XM］匹Neψτoη．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 67

5 Background Analysis       71

  5．1 Point Source Analysis．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 71   5．2 S七ray Light ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 72   5．3Solar Wind Charge Exchange．，．．．．．．．．．．．．，．．．．．．．．．．75   5．4 Cosmic X−ray Background．．．．．．．．．．．．．．．．，．．．．．．．．．．78   5．5 Non X−ray Background．．．．．．．．．．．．．．．．．．．．．．．．．．．．．79   5．6 Galac七ic Componen七s．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．80   5．7 Background Fraction in Each Region ．．．．．．．．．．．．．．．．．．．．． 82

6 Analysis and Results       87   6．1 A1413 ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．87        6．1．1 Surface Brightness ．．．．．．．．．．．．．．．．．．．．．．．．．．． 87       6．1．2 Spec七ral Fitting  ．．．．．．．．．．．．．．．．．．．．．．．．．．．． 87        6．1．3 Results．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 88        6．1．4 Systematic Errors．．．．．．．．．．．．．．．．．．．．．．．．．．．．92       6．1．5Search for WHIM Lines．．．．．．．．．．．．．．．．．．．．．：．．92   6．2 A2204 ．．．．．．．．．．．．．．．．，．．．．．．．．．．．．．．．．．．．．．93       6．2．1 Surface Brightness ．．．．．．．．．．．．．．．．．．．．．．．．．．． 94       6．2．2 Spectral Fitting．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 95       6．2．3 Results．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 95       6．2．4 Systematic Errors．．．．．．．．．．．．．．．．．．．．．．∴．．．．96

7 Discussion       101   7∴1 Temperature and Brightness Profiles ．．．．．．．．．．．．．．．．．．．．．101   7．2 Entropy Profile ．．．．．，．．．．．．．．．．．．．．．．．．．．．．．．．．．102   7．3 Equilibration Timescale ．．．．．．．．．．．．．．．．．．．．．．．．，．．．103   7．4 Difference between Electron and Ion Temperatures ．．．．．，．．．．．＿107   7．5 Mass Estimation七〇r200．．．．．．．．．．．．．．．．．．．．．．．．．．．．109

8The Polytropic SSM−NFW Model      113

  8．1 Method for Model Fitting．．．．．．．．．．．．．．．．．．．．．．．．．．．113   8．2 Results．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．114   8．3 Comparing with Simultaneous Fitting．．．．．．．．．．，．．．．．．．．．．117   8．4Performance of the Polytropic SSM−NFW Model．．．．．．．．．．．．．．．118

9Summary and Conclusion       121

AProjection      123

CONTENTS ⁱⁱⁱ

BDeviation of SSM−NFW Mode1       125

  B．1Assumption．．．．，．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．125   B，2 Calculation ．，．．．．．．．．．．．．．．．，，．．．．．．．．，．．．．．．．125

CIndividual spectra of clusters      129

Llist of Figures

2．1 Evolution of energy densities with redshift for different cosmological mod−

    els（Vbit 2005）． Solid lines：the concordance model withΩM＝0．3，ΩA＝

    0．7，andωニー1；dotted lines：adark−energy model withΩM＝0．3，ΩA＝

    0．7，andψ＝−0．8；10ng−dashed lines：an open−universe model withΩM＝

    0．3，ΩA＝0．0；short−dashed lines：acri七ical−universe model withΩM＝

    1．0，ΩA＝0（Einstein−de−Sitter model）．．．．．．．．．．，．．．．．．．』．．． 6 2．2 Evolution of gravita七ional clustering simulated using all N−body code for

    七wo different models（Borgani＆Guzzo 2001）． Each of the three red shift     snapshots shows a region with sides of 250ん一1Mpc and thickness of 75ん一1     Mpc comoving with the cosmic expansion． The upper panels describe a     flat low−density model withΩm＝0．3 andΩA＝0．7， and the lower panels     show an Eins七ein−de−Sitter model（EdS）withΩm＝1． In both cases the     amplitude of the power spectrum is consisten七with the number density of     nearby galaxy clusters and with七he large−scale CMB anisotropies． Yellow     circles mark the positions of galaxy clus七ers wi七h認「＞3keV． The size of     the circles is proportional to tempera七ure．．．．．．．．．．．．．．．．．．． 7 2．3 The dynamics of over−dense spheres in the expanding universe．（Rees 1992） 9 2．4 Temperature dependence of the cooling function with its components for     optically七hin plasma containing cosmic abundances of elements（Gehrels     ＆Williams（1993））＿．．．．．．．．．．．．．．．．．．．．．．．．．．．．．13 2．5 Calculated X−ray spectra from optically thin hot plasma with various tem−

    peratures． ．．．．．．．．．．．．．．．．．．．．．．．．．．．，∴．．．．．．． 14 2．6 Normalized radial density pro丘1e in politropes．．．．．．，，．．．．．．．，17 2．7 Temperature pro丘les for clusters and groups observed by Oみαη∂rα（left）

    and XMM−1Veω舌oη（right）． Left：Vikhlinin et al．（2005）， and Right：Pratt

    et al．（2007）．  ． ． ． ． ． ． ． ． ． ． ， ， ， ． ， ． ． ． ， ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． 20

2．8 Density profiles and concentration parameter observed by Oんαη∂rα（Vikhlinin

    eta1．2005）．   ． ． ． ， ． ． ． ． ． ． ， ． ． ． ． ． ， ． ． ． ． ． ． ． ． ． ． ． ， ． ． ． ． ． 20

2．9 S一えTrelation and erltropy profiles（left：Ponman et al．（2003）， right：Pratt     ＆Arnaud（2005））． ．．．．．．．，．，．．．．．，，．．．．．．．．．．．．．． 21

V

vi LIST OF FIGσRE8

2．10The contours of XMM image of the cluster RXJ1053．7十57350verlaid on a     CFHT l band image（Hashimo七〇et a1．2004）． The image was created by     combining all events in the O．2−8．O keV band from three（pn， MOS1， and     MOS2）cameras． North is up and East is left． The image is 2，．3×1，．50n     aside． The raw data were smoothed with a Gaussian withσニ7 ． The

    lowest contour is 1．9 counts arcsec−2 and the con七〇ur in七erval is O．2 counts

    arcsec−2． ． ． ． ． ． ． ．、． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． 23

2．111ron Mass−to−Light Ratio as a function of the system mass（Makishima

    et al．2001）． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． 24

2．12Left：The number ratio of SN II to SN Ia． It is almost〜3． Right：The     number of SN Ia to gas mass（Sato 2007）．．．．．．．．．．．．．．．．．．．26 3．1 The 96 minute S鵬α肋orbit（The S批αえμtechnical Discription）．．．．．．．27 3．2 Left：Schematic picture of the S屹αえ秘satellite． Right：Aside view of the      instruments and telescopes on Sμzαえμ（Serlemitsos et al．2007）． ．＿．．．28

3．3 Left：XIS Effective area of one XRT十XIS system， for the FI and BI   CCDs． no contamination． Right：The Encircled Energy FUnction（EEF）

    showing the ffactional energy within a given radius for one quadrant of七he     XRT二I telescopes on S批αえμat 4．5 and 8．O keV（Serlemitsos e七a1．2007）．．、．．30

3．4 Total effective area of the HXD detectors， PIN and GSO， as a function of

、  energy（Kokubun et al．2006）． ．．．．．．．．．．．．．．．．．．．．．．．． 31 3．5 Layout of the XRTs on七he S鵬磁μspacecraft（Serlemi七sos et al．2007）．．．31 3．6 AS批α勧X−Ray Tblescope（Serlemitsos et al．2007）．．．．．．．．．．．．．33 3．7 Athermal shield（Serlemitsos et al．2007）．．．．．．．．．．．．．．．．．．．34 3．8 1mage， POint−Spread Function（PSF）， and EEF of the four XRT−I modules     in the focal plane（Serlemitsos e七al．2007）．．．．．．．．＿．．．．．．．．．35

3．9 1mages and PSFs are shown in the upper， middle， and lower panels for the     XIR−10 through XRT−13 from leftg to righ七．．．．．．．．．．．．．．．．．．．36

3．10Locations of the optical axis of each XRT−I module in the focal plane     determined from the observations of the Crab Nebula in 2005 August−

    September． ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．36 3．11Vignetting of the four XRT−I modules using the data of the Crab Nebula     taken during 2005 August 22−27 in七he two energy bands 3−6 keV and     8−10keV．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．37

3．12Focal plane images formed by stray light（Serlemi七sos et a1．2007）．．．．．．38 3．13Angular responses of the XRT−I at 1．5（1ef七）and 4．5 keV（right）up to 2     degrees（Serlemi七sos et al．2007）． ．．．．．．．．．．．．．．．．．．．．．．．38 3．14The four XIS detectors before installation onto 5μzα抗（Koyama et al．2007）．39 3．15Left：The XIS background rate for each of the four XIS detec七〇rs， with     prominent fluorescent lines marked． Right：The XIS background rate for     each of the four XIS detectors， showing only energies between O．1−2，0 keV． 44

L」凹丁OF FIGσRE8       vii 3．16Definition of GRADE of CCD events， ．．．．．．．．．．．．．．．，．．．． 46 3．17Left：The time history of the con七amination of all four XIS detectors，

    measured at the center of the OBF． Right：The radial prole of the contam−

    ination of the BI（XIS1）．．．．．．．．．．．．．．．．．．．．．．．．．．．．．47 3．18 Sketch of the XM1レ匹」Vεω‡oγ↓payload． ．．．．．．．．．．．．．．．．．．．．． 49 3．19The ligh七path in X1班匹Nεψ紘oη，s XRT wi七h七he PN camera in focus．．．．51 3．20The ligh七path in XM4Z−1Vε励oη s XRT with the MOS and RGA．．．＿．51 3．210n−axis images of the MOS1， MOS2 and PN XRTs（left to right）．．．．．．52 3．22Left：Radial counts distribution for the on−axis PSF of the MOSI XRT in     the O．75−2．25 keV energy range． Right：The encircled energy function as a     function of angular radius（on−axis）at di」田erent energies． ．．．．．．．．．． 52 323Left：The net effective area of all XMM−1Ve砿oηXRT， combined with the     response characteristics of the focal detectors． Right：Vignetting function     as a function of ofFaxis angle at several different energies（based on simu−

    1ations）． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． 53

3．24The effect of strayligh七appeared in PN image of GRS 1758−258．．．．．．．53 3．25Arough sketch of七he field of view of the two types of EPIC cameras（MOS，

    lef予；PN， right）．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．∵．． 54 3．26Left：The EPIC MOS energy resolution（FWHM）as a function of energy．

    Right：The EPIC PN energy resolution（FWHM）as a function of energy．．55 3．27Left：Quantum e伍ciency of the EPIC MOS camera as a function of photon     energyL Right：Quantum ef丘ciency of the EPIC PN camera as a function     of photon energy． ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 56 3．28Event patterns recognised by the MOS（pn）detector．．．．．．．．．．．．．57 3．29Light curve badly affected by soft proton flares． ．．．．．．．．．．．．．．． 58 3．30MOS1（left）and PN（right）background spectrum仕om a blank sky region．．59 3．31MOS and PN background image．．．．，．．．．．．．．．．．＿．．．．＿ 60 4．1 （a）XMM−Ne庇oηMOS1十MOS2 image（0．35−1．25 keV）and S酩αんμXIS     image（0．5−5．O keV）of A1413．．．．．．．．．．．．．．．．．．．．．．．．．．．62 4．2 XMM−1Vεω‡oηMOS1十MOS2 image（0．35−1．25 keV）and S鵬αえμFI十BI     image（0．5−5．O keV）for outskirts of A2204．．．．．．．．．．．．．．．．．．．65 4．3Light curve and its count ra七e histogram of AWM7 reprocess6d data（MOS1（a）

    and MOS2（b））．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．69 5．1 Power−1aw model fit to七he sum of all point source spectra．（a）MOS1十MOS2，

    （b）FI， and（c）BI（black：source spectra， grey：best−fit model）． ．．．．．．74

5．2 Light curve of Flow speed（upper）and proton density（10wer）by ACE     satellite．（a）A1413 and（b）A2204 ．．．．．．．．．．．．．．．．．．．．．．76 5．3 The best一丘t oxygen line spectra model of A2204．．．．．．．．．．．．．．．77 5．4 Rosat AL，L Sky Survay map（R45 band：R4＝52−69， R5＝70−90）．．．．．．．81

viii L18T OF 1η「GσRE8 6．1 Radial profile of temperature， abundance， surface brightness and electron

    density for A1413。．．．．．．．．．．．．．．．．．．，．．．．．＿．．．．．91 6．2  0vII（cyan）and OvIII（pink）line spectra in 10 −15／and 15ノー20／annuli．  93 6．3 Surface brightness profile of A2204 in O．5−5．O keV energy band in Suzaku

    （a）and XMMNeω oηin O．35−1．25 keV（b）． ．．．．．．．．．．．．．．．．．94 6．4 Radial pro丘le of temperature， abundance， surface brightness and electron     density for A2204 、．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．99   7．1 Averaged temperature profiles observed with S鵬αん銀＿．．．．．．．．．．102   7．2 Entropy and equilibration time scale of A1413．．．．．．．．．．．．．．．．104  7．3 Entropy and equilibration time scale of A2204．．．．．．．．．．．．．．．．104  7．4 Entropy（a）and equilibration time scale（b）of PKS−0745191（George et       al．2008）．（a）：entropy profile（black diamond：Suzaku， black solid line：

      fitted mode1）．（b）：τei profile（diamonds）compared withτelapsed（black solid

      line）．  ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． ． 105

 7．5 Entropy（a）and equilibration time scale（b）of A1795（Bautz et a1．2009）．

御   （a）：entropy profile（black diamond：Suzaku， black solid line：fitted       model）．（b）：舌ei profile（diamonds）compared withτelapsed（black solid line）．105  7．6 Entropy（a）and equilibration time scale（b）of A1689（Kawaharada， et al．

      2010）．（a）：entropy profile（black diamond：Suzaku， black solid line：丘tted       model）．（b）：ちi profile（diamonds）compared withτelapsed（black solid line）．106  7．7 （a）Entropy profiles（black diamond：Suzaku， grey diamond：XMM−Newton，

      black solid line：fitted model to Suzaku in 7L 20，， black dashed line：fitted       mode1七〇XMM−Newton in Oノ．5−7ノ， grey sglid cross：PKSO745−191， grey       dotted cross：A1795， grey diamond：A1689）．（b）Entropy normalized to       O（r1・1 profile．（c）ヱ』／Zξa， pro丘les compared with the simulated result by       Rudd＆Nagai（2009）． ．．．．．．＿．．．．．．．．．．．．．．．．．．．．．108  7．8 Comparing profiles ofんエωwithんZ』I andんヱ5d which we assumed same as       the projected temperature． and Integrated mass pro丘1es of A1413 ．．．．．111  7．9 Comparing pro丘1es ofえZ』ωwi七h姐U and認5d which we assumed same as       the projec七ed temperature． and Integrated mass profiles of A2204 ．．．．．111

8．1 The best−fit profiles with Oんαη∂rαand Sμzαえμdata of A1413．（a）integral     mass，（b）temperature and（c）surface brightness．．．．．．．．．．．．．．．115 8．2 The best−fit pro丘les wi七h XMM一ハreωτoηand Sμzαんμdata of A2204．（a）

    integral mass，（b）tempera七ure and（c）surface brightness． ．．．．．．．．．115 8．3 ）（2distribution for temperature model with S酩αえμ十ぴα閲rαdata set freezed     r20bニ1995 kpc， rsニ350 kpc．  ．．．．．．．．．．．．．．．．．．．．．．．．116 8．4 （a）Tbmperature and（b）surface brightness profile by simultaneous丘tting． 117 8．5 Radial pro丘le of（a）temperature，（b）surface brightness，（c）integral mass，

    and（d）density fromη＝1toηニ40． Green line meansη＝1． Red line：

    the best−fit pro丘1e． ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．119

L」BT OF F∫GσRE8       ix A．1deprojection image．，．．．．．．．．．．，．．．．，．．．．．．．．．．．．．123 C．1 A1413：The point source spectra of FI（black）， BI（red）， and the best一丘t FI     model（green）． ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．130

C．2 A1413 spectra for the individual annular regions observed with the FI sen−

    sors． The七〇tal observed spectrum minus the estimated NXB is the black     crosses， the estimated NXB is七he grey crosses， and the fitted CXB com−

    ponent is the solid line． The screening used are COR2＞8GV and 100     ＜PINUD〈300 cts s−1．55Fe calibration source regions， namely cαImα5え，

    are excluded except for（a）． ．．．．．．．．．．．．．．．．．．．．．．．．．．．131 C．3 Same as figure C．2， but for the BI de七ector， All the 55Fe calibration source     regions are excluded． ．．．．．．．．．．．．．．．．，．．．．．．．．．．．．．132

C．4 The upper panels show the observed spectra of A1413 after subtracting the     NXB， that is fitted with the ICM：ωα65×αρec model plus the GAL十CXB：

    αpec1十搬65×（αpec2十ρoωerl脚）model in the energy range O．5−10 keV     for FI and O．4−10 keV for BI． The annular regions are：（a）2ノ．7−7，（b）

      ン 

    5 −10 ，（c）10 −15 ，（d）15ノー20 ，and（e）20，−26 ． The symbols denote     BI da七a（red crosses）， FI da七a（black crosses）， CXB of BI（purple），αρεcl     of BI（grey），ψαb5×αρεc20f BI（light blue）， ICM of BI（orange）， the total     model spectra of BI（green）， and that of FI（blue）． The lower panels show

    the residuals in units ofσ．  ．．，．．．．．．．．．．．．．．．．，，，．，．．133 C．51CM and background spectra of A2204 at the annular regions for（a）一（e）

    FI sensors 2T−III mode1：The colors indicate ICM（black cross），NXB（grey     cross）， CXB（solid line）respectively Estima七ed components of the NXB is     subtracted in actual model fitting． The COR＞8GV and PINUD 100−300     cts／s screening are applie（！． The 55Fe calibration source areas are excluded     excep七（e）・  ・・・・・・・・・・・・・…   ．．．．．．．．．．．．．．．，．．．134 C．6 Same as figure．C．2except for BI sensors． All 55Fe calibration source areas     are excluded． ．．．，．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．135 C．7 The upper panels show the observed spectra of A2204 after subtracting the

    NXB， that is丘t七ed with the ICM：助α65×αρεc model plus the GAL十CXB：

    αρec1十・ωα65 x（αpec2十ρoωerlαω）model in七he energy range O．7−10 keV     for FI and BI． The annular regions are：（a）0ノー3，．5，（b）3 ．5−7 ，（c）

    7 −11，．5，（d）11 ．5−15 ．5，and（e）15 ．5−19，．5． The symbols denote BI     data（red crosses）， FI data（black crosses）， CXB of BI（purple），αpεcl of     BI（grey），ρんα65×α忽ec20f BI（light blue）， ICM of BI（orange）， the total     model spectra of BI（green）， and that of FI（blue）． The lower panels show

    the residuals in units ofσ．  ．，．．．．．．．，．．．．．．．．．．．．．．．．136

List of Tables

3．1 0verview of S批αえμcapabilities ．．．．．．．．．．．．．．．．．．．．．．．． 29 3．2 Telescope dimensions and design parameters of XRT−1， compared with      ASCA XRT．．．．．．．．．．．，，．．．．．．．．．．．．．．．．．．．．．．．32

3．3 Design parameters for pre−collimator ．．．．．．．，．．．．．．．．．．．．．34 3．4 Major XIS Background Emission Lines．．．．．．．．．．．．．．．．．．．．43 3．5 Parameters used in GTI selection of S鵬αんμ ．．．．．．．．，．．．．．一．．．45 3．6 Basic performance of the EPIC detectors．．．．．．．．．．．．．．．．．．．50 3．7The on−axis in orbit and on ground 1．5 keV HEW of the di任erent XRT．．．51 4．1 Cluster samples ．．．．．．．．．．．．．．．．．．．，．．．．．．．．．．．，61 4．2 List of XMM−Ne碗oηobservations ．．，．．．，．．．．．．．．，．．．．．．63 4．3  1」ist of Sμzα1鋤observa七ions  ．．，．．．，．．．．．．．．．．．．．．．．．．． 64 5．1 Best−fit parameters of detected point sources of A1413．．．．．．．．．．．．73 5．2 Probabilities of point source detection． ．．，，．．．．．．．，．．．．．．．． 74 5．3 Emission weigh七ed radius and es七imated fractions of the ICM photons ac−

    cumulated in detector regions coming from each sky region for FI十BI in     the O．5−5 keV band． ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 75

5．4 1ntensity of redshifted OvII（0．503 keV）and OvIII（0．564 keV）lines ．．．．76 5．5 Estimation of the CXB surface bright皿ess after the point source excision     of A1413， A2204， and AWM7． ．．．．．．．．．．，．．．．．．．．．，．．．80 5．6 Galactic components best fit parameters and 90％con丘dence errors． ．．．83 5．7 Properties of the spa七ial regions used in A1413 ．．．．．．．．．．．．．．．84 5．8 Properties of the spatial regions used in A2204 ．．．．．．．．．．．．．．．85 6．1 Best fitting parameters of the spectral 6ts with 90％confidence errors for     one parameter．．．．．．．．．．．．．．．．．．．．．．．，，．．．．．．．．．．89 6．2 Same as table 6．1except NXB士3％， CXBMAx and CXBMIN and contami士20％．

    Abundance model is Anders＆Grevesse（1989）．．．．．．．．．．．．．．．．90 6．3 1ntensity of redshifted OvII（0．508 keV）and OvIII（0．569 keV）lines in unit     of 10−6 photons cm−2 s−1 arcmin−2 with 2σupper limits or 90％confidence

    errors for a siIlgle parameter． ．．．．．．．．．．．，．．．．．，．．．．，．．93 6．4 Best−fit parameter of double 5βmode1 ＿，．．．．．．．．．．．．．．．．．95

xi

xii       LIST OF TABLE8 6．5 The best fitting parameters of七he spectral fi七s of A2204 with 90％con丘一     dence errors for one parame七er in O．7−10．O keV．．．．．．．．．．．．．．．．97 6．6 Same as table 6．5． Abundance model is Anders＆Grevesse（1989）． Energy     band is in O．7−10．O keV．．．．．．，．．．．．．．．．．．．．．．．．．．．．．98 7．1 The best fit parameters of entropy profile mode1． ．．．．．．．．．．．．．．106 8．1 best−fit parame七ers of integral mass model with XMM十Suzaku．．．．．．．114 8．2 M200，δcandc200 ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．115 8．3 The best−fit parameters of temperature fi七ting．．．．．．．．．．．．．．．．115 8．4 The best−fit parameters of surface brightness丘tting．．．．．．．．．．．．．116 8．5 The best−fit parameters of simultaneously fitting．．．．．．．．．．．．．．．117

Chapter 1 Introduction

Awide variety of cosmological observations now support a model which explains the overall architecture of th6 universe and the development of galaxies and other structures within it． In七his picture， regions in which ma七七er density exceeds the mean density are collapsed， gravitationally bound and evolve to large scale structures hierarchica11）乙 Such evolution model is called bottom−up scenario ， which is one of the reliable model of dynamical evolution of七he universe（Vbit 2005）．

   Clusters of galaxies form ffom such collapse of density perturbation琴having a typical size of the order of 10 Mpc． They are the largest selfgravitating system in the universe which contains dozens七〇thousands of galaxies bound gravitationally within a few Mpc scale． Clusters of galaxies consist of X−ray emitting ho七plasma with typical temperatures of a few七imes 107 K with about 5 times the mass of galaxies． The evolution of structures involving clusters and larger scales is mainly driven by gravi七ational instability of the dark

matter（DM）density perturbations．

   Cluster of galaxies can be used as both invaluable cosmological tools and astrophys−

ical laboratories． These two aspects are clearly interconnected with each other． The evolution of the population of clusters and their overall baryonic content provide powerful constraints on cosmological parameters． Also we learn a lot of unique physics from七he observed properties of七he intra−cluster medium（ICM）and its interaction with the galaxy population．

   Observations of clusters of galaxies offer a number of well established cosmological tests relying on the cold dark matter（CDM）paradigm， in which clusters are composed mostly of collision−less CDM and virialized obj ects form from initial density perturbations． CDM paradigm predicts dynamical evolu七ion and structure of our universe through numerical simulations， and are used七〇calibrate essential theoretical ingredients for cosmological 七ests， such as detailed shape of mass functions or average baryon bias wi七hin clusters． In this framework， clusters of galaxies have self−similarity as their basic properties（Zhang et al．2007；Borgani et al．2004；Roncarelli et a1．2006）． They predict that physical parame七ers such as temperature， surface brightness， gravitational mass profiles distribute in almost the same way when normalized with redshift or virial radius．

   In understanding the structure and evolution of dark−matter dominated clusters， the 1

2       CHAPTERヱ． INTRODσC皿ON most important parameters are temperature and gravitational mass profile because these parame七ers indicates dark matter distribu七ion and its ffaction compared wi七h baryons．

Especially， Navarro et al．（1996）has reported common density profile of dark matter in clus七ers of galaxies called as NFW pro丘le． Suto et a1．（1998）analytically derived gas density and temperature profile（non−isothermal SSM model）based on dark matter distribution in clusters of galaxies in the case of NFW and Moore models．

   The main aim of this thesis is to look into七he mass structure and ICM properties to the outermost regions of clusters of galaxies． Past X−ray observations， even withぴαη由α and XMM−Neω￡oη， have explored only a small fraction of七he to七al volume of clusters．

Outer regions of cluster carry a large frac七ion of baryons． These are the places where matter accretes from the surrounding field and where the ICM is heated． These low surface brightness regions are also connected to the large scale丘lamens which should be丘11ed with warm−hot intergalactic medium（WHIM）， namely the dark baryons in the present universe． With these original sciences， regions near the virial radii of clusters are regarded as a new frontier in the X−ray astronomy． Our aim is to obtain the first real gbservational knowledge about the ICM in these regions．

   Outer regions of clusters have so far escaped from detailed observational study， mainly due to its extreエnely low surface brightness． The flux from a unit solid angle goes down by afactor of more than 104， and X−ray measuremen七has been severely hampered by both X−ray and non−X−ray background． These technical di伍cu1七ies are the reason why cluster temperatures have not been measured much beyond about half of the virial radius and，

until recently，七he shape of the temperature radial profile was a matter of heated debate even to that radius． Now independent measurements using several different observatories are consistent wi七h a factor of〜2decline of the projec七ed temperature from the center to half the virial radius， a七least for relaxed clusters（Markevitch et a1．1998；De Grandi

＆Molendi 2002；Vikhlinin et al．2005；Piffaretti et a12005；Pratt et a12007）．

   、4Sα4 with the first application of CCD instruments along with gas scintillation pro−

portional counters opened the possibilities of imagin X−ray spectroscopy．．4Sα40bserva一 七ions， despite their modest spatial resolution， have established that most of the clusters show significant departures from isothermality， with negative七empera七ure gradients char−

acterized by a remarkable degree of similarity， out to the largest radii sampled（Marke−

vitch et a1．1998）．、Bε四〇一乱4X observations confirmed these features for a larger num−

ber of clusters（e．g． De Grandi＆Molendi 2002）．（既αη伽αand XMM−Nε励oηprovided great knowledge on clusters of galaxies with their improved sensitivity．ぴα閲rαshowed detailed picture of the ICM distribution and central temperature profiles（Vikhlinin et al．2005；Baldi et al．2007）with their ASIS X−ray CCD camera． At the same time， XMM−

」Ve庇oηobservations gave a concrete evidence for the absence of large−scale cooling flows

（Peterson et al．2001）and showed the presence of a negative temperature gradient at radii＞0．1r200（Piffaretti et a1．2005；Prat七et a1．2007；Poin七ecouteau et al．2005）． They revealed clus七ers of galaxies are generally characterized by a declining七emperature profile toward the center and outer region within 60％of virial radius，

3    S酩磁μis the fifth in七he series of Japanese X−ray astronomy satellites devo七ed to observations of celestial X−ray sources by Japan Aerospace Exploration Agency（JAXA）

launched on July 10，2005． One of the main instruments is the X−ray Imaging Spectrom−

e七er（XIS）， consisting of four X−ray charge−coupled devices（CCDs）． Three sensors out of four have ffont−illuminated（FI）CCDs， while the o七her one has a back−illuminated（BI）

CCD（Koyama et al．2007）． The background levels for uni七field of view are much lower than those of the XMM−1Ve？〃toηEPIC and七he O九αηdrαACIS． Suz磁u XIS is， therefore，

best suitable for the measurement of faint and ex七ended sources such as the ou七ermost regions of clusters．

   In七he study of extended X−ray objects， background subtraction is critical in obtaining accurate information about the emission region． The background can be broadly divided into non X−ray background（NXB）， cosmic X−ray background（CXB）and the Galactic emission． The Galactic emission is considered to originate from the local ho七bubble

（LHB）and the Milky Way halo（MWH）． CXB is the sum of emission from all the extra−galac七ic sources in七he X−ray energy band． Reliable modeling of these components is particularly important in studying七he density and temperature of ICM in the outer regions of clusters．

   In this thesis， we present results from Suzaku observations of A1413， A2204 and AWM7． The targets are suitable for the study of outer regions because oftheir re−

1axed nature， high intensi七y， and adequate ICM temperatures． By taking advantage of 七he low−background nature of 5批α肋XIS， we are able to measure the temperture and sur−

face brightness pro丘les near the virial radius． With七hese new data， we look into the ICM properties such as entropy pro丘1e and equilibration time scales， and compared with model predictions． These resul七s are combined for the estima七ion of the gravitational mass pro−

file out to the virial radius， We use Ho＝70 km s−1 Mpc−1，ΩA＝1一ΩM＝0．73． Unless otherwise no七ed， we employ the solar abundance table by Anders＆Grevesse（1989）．

Chapter 2

Review of Cluster of Galaxies

2．1  Structure and evolution of the universe

2．1．1 Expansion dynamics       一

We will brie且y look into七he geheral view about the dynamical evolution of the unverse，

      ノ

following the review by Vbit（2005）・On very large scales， the universe apPears homoge−

nous and isotropic． Time−dependent behavior of the scale factorαobeys the Friedmann−

Lemaitre model of the universe，

i−−G（  3ρρ＋7），   （2・1）

whereρ（τ）c2 is七he mean density of mass−energy andρ（￠）is the pressure due to the energy density If七he equation of state takes the formρニωρc2， density changes with the expansion asρ○（α一3（1†ω）． The scale factor is set to be unity at七he current time．

Then七he cosmological redshift z of dis七ant objects is simply related to the scale factor as α＝（1十z）−1．This de丘nition gives the following relation，

㈲2一田［Ω・（1＋2）3（・＋ω）＋（1一Ω・）（1＋2）2］， （2・2）

whereΩo is the current energy densityρo in units of the current critical densityρcro＝

3田／8πG．Including all the components， we obtain the dynamical equation

∬2（z）一（1）2−Hぎ［ΩM（・＋2）3＋ΩR（1＋2）4＋ΩA＋（・一Ω・）（・＋z）2］，（2・3）

withΩR the radiation energy density and allΩparameters indicating the current mass−

energy density in units ofρcro． Also， the densi七y parameter is given asΩo＝ΩM十Ω．R十ΩA．

If non relativis七ic particles with a mass densityρM contibutes negligible pressure， then 2ρ＝0．The energy densityρRc2 in pho七〇ns and o七her relativistic particles exerts a pressure withω＝1／3． Einstein s cosmological constant acts like an energy density ρAc2 that remains constant while七he universe expands and therefore exerts a pressure corresponding toω＝−1．

5

6      CHAPTER 2． REVZEW OF CLσ8TER OF GALAX工E8

   In丘gure．2．1， we show the evolution of energy densities for ACDM universe． Structure in the univ・erse grows most rapidly whileΩM（2）＝1， because positive density pertur−

bations then exceed the critical density The redshift at whichΩM（z）begins to decline depends on the characteristics of dark energy． Observations of clusters and their evolution provide opportunities to constrain the values ofΩM，ΩA andωbecause these parameters in且uence the properties of the cluster population．

（ o

1

0．1

      Ω翼，ΩA，w＝0．3．0．？．−1     −一一一  Ω貰．ΩA、； 1．0，0．0

一一．一．．＿一．一@ΩH．ΩA，w＝0．3．0．？rO．8       Ω冨，ΩA＝ 03．0．0

° @／  Ω（2）      、、    1≠

1   10   100  1000   104 − 105

       1十z

Fig．2．1：Evolution of energy densities with redshift for different cosmological models（Vbit 2005）．Solid lines：the concordance model withΩM＝0．3，ΩAニ0．7， andψ＝・−1；dotted lines：adark−energy model wi七hΩM＝0．3，ΩA＝0．7， andωニー0．8；10ng−dashed lines：

an open−universe model withΩMニ0．3，ΩA＝・0．0；short−dashed lines：acritica1−universe model withΩM＝1．0，ΩA＝0（Einstein−de−Sitter mode1）．

2．1．2 Hierarchical structure fbrmation

At present， the hierarchical clus七ering scenario is widely supported， because it is naturally expected ffom the cold dark matter modeL Also， the fact七hat the galaxies a七redshifts

〜5have been observed， whereas the most distan七〇bserved clusters is at 2〜1， indicates that small systems have been formed first．

   According to the bottom−up scenario，1arge−scale structures of the universe have formed from infinitesimally small density perturbations at the early universe through the grav−

itational interaction， and we can recognize three fUndamental building blocks：stars，

galaxies， and clusters of galaxies． A number of numerical simulations for the structure formation have shown producing the large−scale structures and clusters of galaxies． This result is recognized as a strong support to the hierarchical clus七ering scenario． Following an early work by White s 700−body simulations（1976）， calculations such as the one by

2，1，STR UCTURE AND EVOLσT∫ON OF THEσMVERSE      7

Eke et al．（1998）inclllde〜V−body／gas−dynamical sin−llatiolls which are designed to in−

vestigate the evolution of clusters． Borgani＆Guzzo（2001）compared the e、・olution of universe in different universe nユodels ofΩm＝0．30f lowΩη、 cosmology andΩm＝10f Einstein−deSitter（EdS）cosmology in figure 2．2． Despite the similar pattern produced at．

the present time（z＝0）， the past pattern of the universe is very different． This evolu−

tionary differellce represents one of the motiva．tions for the deep X−ray searches of clusters down to a very faillt且ux levels， Clusters at z竺0．5 are no longer considered as exceptions，

and even a few examples at z＞1are now known． The main result reached these surveys is the evidence fbr a weak evolution of the bulk of the cluster poplllation out toε＝1，

again consistent with the picture of a low一Ωηヱuniverse．

   Hierarchical clustering for the hot gas and dark matter f士om Inatter aggregates that have reached all approximate dynamical eqllilibrium givillg them their charactelistic shapes， and indicates that the clusters are fOrmed through sub−cluster nlergers and／or absorption of groups of galaxies． Thus， the evolution of the galaxy cluster popu］atioll is tightly connected to the evolution of the large−scale structures and the universe as a whole． It is for this reason that observations of galaxy clusters can be used to trace the evolution of the universe and to test cosmological models．

Fig．2．2：Evolutioll of gravitational clustering silnulated using an N−body code氏）r two differellt models（Borgani＆Guzzo 2001）． Each of the three red shif士snapshots shows a region with sides of 250ノ〜−lMpc and thlckness of 75カー1 Mpc comoving wlth the cosmic expallsion． The upper panels describe a Hat low−density model withΩη，＝0，3 andΩA＝

0．7．and the lower panels show an Einstein−de−Sitter model（EdS）withΩm＝1， In both cases the amplitude of the power spectrum is collsistent with the number dellsity of nearby galaxy clusters and with tlle large−scale CMB anisotropies．＼＞llow circles mark the positiolls of galaxy clusters with履「＞3keV． The size of the circles is proportional to temperature．

8      CHAPTER 2． REVZE W OF（兀｛ZS TER OF GAjLAXZES

2．1．3 Collapse condition

We will brie且y review the collapse scenario according to七he spherical collapse mode1．

First of a11， consider a mass shell designated by 2 with a radius r乞at epoch舌＝ち， which is moving with the general expansion untilτ＝ち（Peebles 1980）． The kinetic energy per unit mass of the shell relative to the center is，

       瓦一1（醐2，    （2・4）

where璃is the Hubble constant at舌＝ち． Suppose that the average density inside the

shell，角， is higher than the homogeneous background，ρb，τ， by a factor 1十δ， i．e．

       ρτ ＝＝  ρ6，τ（1十δ）       （2．5）

      −8…GΩ乞璋（1＋δ），   （2・6）

whereΩz is the density parameter atτ＝ち． Then the potential energy per unit mass of the shell whose mass is嘱is，

   慨一一㍗一一4π磐   （2・7）

      ＝ 一ΩiKi（1十δ）．       （2．8）

Thus， the total energy is

      E  ＝＝  」ぽ十「鵬      （2．9）

      −1乎δ［δ一（よ一・）］・  （2…）

Since隅くOandΩi＜1， the following condi七ion

      1

      δ〉豆一1，     （2・11）

in other words，

       厄二（1十δ）Ω乞ρcrτちi＞ρcrZちτ，       （2．12）

gives the total energy negative and the shell will eventually collapse． Here， we use the critical densityρc弼ちz at the redshift z as，

       ρ。晦一霊    （2・13）

where

       Hz＝Ho E（z），       （2．14）

      E2（z）＝Ωo（1十z）3十ΩA，       （2．15）

      Ω・−8：竃゜；ΩA−3嵩・  （2・16）

Hereρo is the non−relativistic matter density， HO is the current Hubble constant， and A is the cosmological constant．

2．ヱ．8TRσCTσRE AND EVOLσTION OF THEσMVER8E      9

If the density parameter，Ωτ， is close to unity， density perturbations wi七h a smal1 ampli七ude can collapse． Thus clusters of galaxies are effectively formed in such epochs．

Figure．2．3 shows the dynamics of over−dense spheres・The larger initial over−densityi the earlier the sphere，s expansion hal七s． A system would expand spherically without self一 gravitation in an acceralating uIliverse， while gravity stops the expansion and collapses it into a virialized system with su伍ciently high density A system with larger initial over−

density collapses earlier into smaller virialized system． The clusters of galaxies， which are the largest virialized systems， haveρ／ρcrit＞2000rδ＞500．

！い1／lt      l   

〃

    ノノ！！

RAαus

Fig．2．3：The dynamics of over−dense spheres in the expanding universe．（Rees 1992）

2．1．4Warm−Hot Inter−cluster Medium

The study of warm−hot intergalactic medium（WHIM）is the remaining frontier of X−ray astronomy The importance of the observational study of WHIM are as follows． First，

WHIM carries about 50％of七he baryonic mat七er in the present universe． Locating WHIM gives us an answer to七he question of missing baryon problem paused by Fukugita et a1．（1998）．WHIM is the best tracer of七he large−scale structure of the universe． Galaxies by optical surveys or clusters of galaxies by X−rays only shows us七he densest part of the丘lamentary structure． WHIM reveals the fainter part of the丘lament and enables us to see the structure of dark matter very clearly WHIM holds the thermal history of the universe． WHIM has been ionized， heated and metal−enriched through the past star，

galaxy structure−formation processes，七herefore thermal and chemical properties of the WHIM would be very useful source to look into the thermal history of the universe．

10       CHAPTER 2． RE VZEW OF CL USTER OF GALAXlES

2．2 Clusters of Galaxies

Clusters of galaxies are the largest wel1−defined structures in the universe， with a typical linear dimension of 1−3 Mpc． A cluster consists of 100−1000 member galaxies， with the size ranging ffom the cD galaxy， which belongs to the most luminous galaxy class in the universe， to dwarf galaxies．

    In the early 1930s， Zwicky measured velocities of member galaxies in the Coma cluster，

and found that they are traveling too fast（〜1000 km s−1 in average）to be gravitationally bound unless the total mass in the clus七er greatly exceeds that corresponding to optical luminosities of member gabxies． This is the丘rst evidence for large−scale dark mat七er．

Subsequent measurements velocity dispersions of rich clusters were found typically to be 700 km s−1， implying mass−to−light ratios of M。tal／Lt。ta1〜150−400 MO／LO（e．g．

Peebles 1993）． Here凪。tal and Lt。tal are the total dynamical mass and the total optical luminosityi respectively In contrast， individual galaxies typically have mass−to−1igh七ratios of 10 M◎／・LO in their luminous central regions．

． With cosmic X−ray observation， witch started in the 1960s， clusters were found to be the mos七luminous class of X−ray sources in the universe after some types of active galac−

tic nuclei（AGNs）． The X−ray emission originates from the intracluster medium（ICM），

namely a ho七（107−108 K）and low density（10−4−10−2 cm−3）plasma in theintracluster space． Extensive observation with previous X−ray satellites provided measurements of densities and temperatures of the ICM． These results implied that the mass if the ICM is greater than that of the stellar component in member galaxies． Characteristic emission lines from ionized heavy elements were detected in the X−ray spectra of clusters． The implied sub−solar metallicity of the ICM indicates that the ICM is a mixture of the pri−

mordial gas and that reprocessed in the stellar interior． Moreover， X−ray observations of the ICM have provided independent and more accurate皿easurements of the七〇tal mass，

and hence of the dark matter， in clusters of galaxies． According七〇acontemporary con−

sensus， about 5−10％of a cluster mass is in the stellar component， another 10−20％

is in the ICM， and the rest is in dark matter．

22．1 Virial radius and the virial density

Let us consider a time variation of a radius r（τ）fixed on a spherical shell． The force on the shell comes from the gravity due to a mass M inside the she11． Since our shell is fixed to matter， the change of r does not affec七M． The， the equation of motion is，

∂2r  αM

d￡2ニー 窒Q      （2・17）

Using a simple relation，

幽2］∂云一2 ；吻  （218）