6．1． ∠4L1413 91
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92 CHAPTER 6． ANALYSlS AND RES I兀TS
data set． This dif［erence may partly be due to the different backgrounds used． Therefore，
we assigned rather large errors of 10％even in the inner region of r＜2ノ．7 for these data．
We will quantify七he sys七ematic error of the Suzaku ICM temperature in the following sec七ion．
We plot the related quanti七ies， surface brightness，5k， and electron density，ηe， in
丘gures 6．1（b）and（d）． We derived the Chandra surface brightness丘om the emission measures prorvided by A． Vikhlinin（priva七e communication）． The XMM−Ne祖 oηsurface
brightness is f士om Snowden et a1．（2008）． The Suzaku surface brightness comes from theノ
normalization of theαρec model fit． The surface brightness results are consistent with each other within 10ノ． In the outer region， the Suzaku surface brightness is significantly higher than the Chandra values． The cause of this discrepancy could be the different region of the cluster observed． In particular， Suzaku observed mainly along the major axis， while Chandra observed the minor axis， as we show in丘gure 8．4（a）． We obtained the electron density by deprojecting the emission measure with me七hod described Kriss
et aL （1983）．
We show the abundance pro丘le in丘gure 6．1（c）． Our nominal values are higher than the results of Chandra and XMM・1Ve励oη． However， our errors are large and it is di伍cult to draw firm conclusions．
6．1．4 Systematic Errors
Tb estimate the systematic errors on our electron density，七emperature and abundance
pro丘les， we examined the effects of varying七he background spec七ra ffom their nominal levels． We adopted a systematic error for七he NXB intensity of土3％and the level of the CXB fluctuation was scaled from the Ginga result（Hayashida 1989）as shown in table 5．7．We considered a±20％errOr for the contamination thickness on the IR／UV blocking丘lters in front of the XIS sensors． As mentioned earlier， we also looked into the effect of the
difference between the Anders＆Grevesse（1989）and Feldman（1992）abundance models．
We give the outcome of these variations in丘gure 6．1 and table 6．1 for the abundance model comparison， and in figure 6．1 and table 6．2 for the other comparisons． System−
atic variations of七he surface brightness are comparable七〇its statis七ical error for all七he systematics we examined． The same is true of the temperature except for uncertain七ies on七he UV／IR filter contamination， where the maximum possible range allowed is about 40％larger than the nominal sta七istical errors． Systematics on the abUndance pro丘le were less than the statistical uncertainties except for the outer two spa七ial bins with七he Feld−
man（1992）abundance models． We conclude丘orn七his investigation七hat our statistical
errors also encompass most possible systematic effects．6．1．5Search for WHIM Lines
We searched for the warm−hot intracluster medium（WHIM）which could exist in the
filaments of large−scale structures of the universe． The outer regions of clusters may be6．2． A2204 93
（a）FI＋BI．1ぴ一15 （b）FI十BI，15ノー20ノ
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0．5 1 2 5 0．5 1 2 5 Energy〔keV） Energy（keV）
Fig．6．2：0vII（cyan）and OvIII（pink）line spectra in 10 −15 and 15 −20 annuli．
Table 6．3：Intensity of redshifted OvII（0．508 keV）and OvIII（0．569 keV）lines in unit of lO 6 photons cm−2 s−1 arc皿il1−2 with 2σupPer limits or 90％confidence errors fbr a single parameter．
Region SovIII sovII
2へ7−7 ．，＿．．．．．＿， ＜0．119 〈0ユ35 7 −10 ．．．．．．，，．．．， ＜0．075 ＜0．091 10 −15 @ ．，．．＿＿．＿． ＜o．085 0．094±8：8き宝 15 −2ぴ ．．，．＿．．．．＿ ＜0．095 0．081±8：呂旨！
connected to these filaments and are considered to be promising regions to search fbr
possible WHIM emission．
We analyzed the regions 2． 7−7 ，7L工0 ．10 −15 ， and 15 −20 ， We丘tted the FI十BI spectra simultaneously We added two gaussian lines to model the oxygen emission lines，
They had fixed redshifted energies of O．508 keV（OvII）and O．569 keV（OvlII）， with a 6xed width ofσニ0．0． The ICM spectra fitted with the additional two gaussian lines are shown in丘gure 6，2， and table 6．1（c）gives the丘t results． The best temperatures are consistent with the results of the previous丘t without the lines． Because redshifted line energies overlapped with those of the Galactic lines， we were unable to distinguish these emission lines directly． Table 6．3 gives our result for the line intensities which are either 2σupPer limits or marginal detections．
62 A2204
We extracted pulse−height spectra in nve annular regions丘om the XIS event丘les． The inner and outer radii of the region8 were O −3 ．5，3 ，5−7 ，7 −1r，5，11 ．5−15 ．5， and
15 ．5−19 ．5respectively measured加m the XルfM／Vεωεoηsurface brightness peak of
94 CHAPTER 6． ANALYS∫S AND RESひL四
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P向edgd r6di嶋（arcmln） Pr司6ctgd信dius（〕
Fig．6．3：Surface brightness profUe of A2204 in O．5−5．O keV energy band in Suzaku（a）
and XMMNeω￡oπin O．35−1．25 keV（b）．
A2204 at（R．A，， Dec．）＝（16h32m45ξ7，05°34 43 ）in J2000． We analyzed the spectra in FI：0．5−10 keV and BI：0．牛10．O keV except fOr FI：0．5−5．0，7．0−10、O keV in 15 ，5−19．5
range， However Below O．7 keV range we think it is contaminated by SWCX． In the
the 15 ，5−19 ，5 annulus， we utilized as a background region． Because positions of the calibration sources themselves were masked out using masked calibration source area for each detector using the cα〜mα5為calibration database（CALDB）file， we included Mn−Kα（5．9keV）energy band from the 55Fe calibration source． Because this region is not large area， we also found out the difference of background area with 11 ．5−19 ．5．
6．2．1 Surface Brightness
There are no references for a surface brightness pro丘le of A2204， We constructedβmodel fit to／Vεω紘oηimage in O，35−L25 keV， first． However， theβmodel is not consistent with the observed data over 10 which the background was subtracted like in figure 6．3（a）．
Then we modeled 2βmodel pro61e froln 5μ批μin O．5−10．O keV． With spectral 6tting of 15 ．5−19 ．50f background region by丘xing 100％CXB intencity by Kushino et aL（2002）
we strained intensity of galactic component． After that， we subtracted 100％CXB， GAL，
and NXB仕om observed image， We show the last result of surface brightness pro丘1e
compared with background intensity in 6gure6．3（b）in O．5−5．O keV． We show the best一丘t parameters in table6．4． Because of Suzaku angular resolution， the peak of the simulated ICM is smoothed in the figure 63〔b）． The best−fit 2βmodel is traced the observedprofile．
6．2． A2204 95
Table 6．4：Bes七一fit parameter of double 5βmode1
β1 0．70±0．03
rc1（arcmin） 1．22±0．006
S1（counts s−1 Ms−1 pixel−1） 66．81土0．28 β2 0．71±0．002rc2（arcmin） 777土83
S2（counts s−1 Ms−1 pixel−1） 0．22±0．002
6．2．2 Spectral Fitting
We assumed thermal plasma model for ICM as ρんαb5×αρec and energy range is in
O．7−10．O keV that we excluded七he contaminated energy by SWCX below O．7 keVl First，we fitted the model with observed data using background region in 15 ．5−19 ．5 in which we strain CXB and galac七ic components with fitting． We also found out CXB intensity as fixing七he value subtracted point source flux from 100％CXB by Kushino et a1．（2002）．
Galactic components are LHB and MWH we assumed． Because MWH temperature exists
below the lower limits of spectral energy range，0．7 keV， we丘xed it to O．074 keV（Lumb et al．2002）． when we did no七freeze the power law index of cxB， r＝1．220±1：81；withX2／∂o∫＝3921．27／3517． But we could not strain temperature error enOugh． Then we
丘xed F＝1．41（Kushino et al．2002）． which value is from the averaged CXB． When we looked into the case excluding subs七ructure which exisdn south wes七〇f 11ノ．5−15，．5， we could not detec七the significan七ICM tempera七ure in 11ノ．5−15ノ．5． Reiprich et a1．（2009）ordered in this manner，
6．2．3 Results
We show七he best−fi七parameters and profiles of temperature， abulldance， surface bright−
ness， and electron density in table 6．5 and丘gure 6．4． The temperature in OL 3 ．5region is slight decreasing because of cooling flow mentioned by Sanders et a1．（1999）． Temperature profile is isothermal−like within r200，0ur S批α肋observation result is smoothly connected with XMM−」1Veω oηresult by Snowden e七al．（2008）in figure 6．4（a）． In the 11 ．5−15ノ．5 region， Reiprich et al．（2009）mentioned here is the clus七er free region because of out−
side of r200． We also looked into if there is some cluster component in 11，，5−15，．5． We detected ICM component in 11 ．5−15 ．5 in figureG．7 though the normalization is lower than that of CXB in all energy band．
We looked into spectral丘七ting with abundance model as Anders＆Grevesse（1989）
and Feldman（1992）． We measured about 2 keV higher by Feldman（1992）than that by Anders＆Grevesse（1989）． Because Feldman（1992）de丘ne less Fe amount七han Anders
＆Grevesse（1989）， Feldman（1992）leads higher profile than Anders＆Grevesse（1989）．
96 CHAPTER 6． ANALYS阻AND RE8肌ZS
6．2．4 Systematic Errors
To strain systematic errors， we found out NXB土5％， CXB fluctuations mentioned before
chapter， and contamination of IR／UV blocking丘1ters contamination土20％． The best−
fit parameters of these results are shown in table 6．6． By NXB fluctuation自of−5％，
tempera七ure is varied for 6 keV in 11ノ．5−15，．5． And abundance is varied for O．2 Z（∋in 11ノ．5−15 ．5．We also found out且uctuation of contamination with 20％． It also a丘ected
with measurement of七emperature and abundance．
6．2． A2204 97
Table 6．5：The best fitting parameters of the spectral fits of A2204 with 90％confidence errors for one parameter in O．7−10．O keV．
Nomina1（a）＊ んT Abundance IVorm§ 811 ×2／dof
（keV） （ZO）
o −3ノ．5 7．26±8：65 0．41±8：8》 911．37±§：9… 321．40±｛：II 1835．6／1444 3ノ．5−7／ 7．55±8：19 0．35±8：86・ 36．28±8：ZI 12．38±8：》9 1100．9／ 1124 7 −11，．5 5．94±8：㍑ o．25±8：｝1 8．57±8：§； 2．74±8：｝Z 455．8／480 11 ．5−15，．5 4．32±士8壬 o．52±8：ii； 3．35±8：；き 1．11±8：；箋 318．8／318 15ノ．5−19 ．5 − 一 一 210．8／152
Tot a1 − 一 一 一 3921．9／3518
Nomina1（b）† えT Abundance IVorm§ Sll ＼X2／dof
（keV） （ZG））
0 −3 ．5 7．27±8：；亨 0．41±8：8》 912．03±1：28 321．65±｝：1§ 1736．0／1444 3 ．5−7 7．63±8：§量 0．35±8：86 36．68±8：61 12．52±8：；日 1101．6／1124 7ノー11，．5 6．26±8：6至 o．24±8：拷 9．02±8：§§ 2．90±8：翌 456．5／480 11ノ．5−15 ．5 4．96±；：6！ 0．52±8：1｛ 3．85±8：器 1．30±8：子9 318．6／318 15 ．5−19ノ．5 − 一 一 211．6／153 Total − 一 一 3924．3／3519
Nominal（c）‡ えT Abundance IVorm§ SII X2／dof
（keV） （ZO）
0 −3 ．5 7．30±8：鵠 0．61±8：器 885．76±§：詣 321．62±；：8ii 1818．4／1444 3，．5−7／ 7．80±8：§§ o．52±8：8； 35．38±8：5！ 12．41±8：；9 1088．2／1124 7 −11，．5 6．90±；：毘 o．31±8：｝§ 8．36±8：器 2．77±8：H 441．o／480 11 ．5−15 ．5 6．49±i：9； 0．64±8：6！ 3．18±8：駕 1．13±8：▲！ 324．2／318 15ノ．5−19ノ．5 − 一 一 一 213．3／152 Tot a1 − 一 一 一 3885．0／3518
＊Abundance model is Anders＆Grevesse（1989）．
†Abundance model is Anders＆Grevesse（1989）． CXB parame七ers is f［xed with Kushino et al．（2002）．
‡Abundance model is Feldman（1992）．
§Normalization of the apec component scaled with a factor of SO乙硯αE」Z．4π0」認G／Ωe in table 5．7，
NoアmニSOσR C弼』、4冗0．REθ／Ωe∫ηeηH∂γ／（4π（1十z）2D』）×10−20 cm−5 arcmin−2， where DA is七he angular diameter dis七ance七〇the source．
ll Surface brightness in unit of 10−6 photons cm−2 s−1 arcmin−2（0．7−10 keV）．
98 CHAP皿DR 6． ANALYSlS AND RE8 ULTS
Table 6．6：Same as table 6．5． Abundance model is Anders＆Grevesse（1989）． Energy
band is in O．7−10．O keV，
NXB十5％， CXBMAx たT Abundance Norm§ Sll ）（2／dof
（keV） （ZG））
0ノー3，．5 ．．．．． 7．22±8：；5 0．41±8：8菱 909．15：［4：9舌 320．14±｛：亨§ 1832．9／1444 3 ．5−7 ．．．．． 7．17±8：19 0．35：［8：89 35．21±8：麗 11．93±8：…1 1100．8／1124 7ノー11，．5 ．．．．． 4．78±8：99 0．26±8：｝il 7．77±8』9 2．38±8：｝； 457．1／480 11ノ．5−15，．5 ．．．．． 1．59±8：2今 0．05±8：3ξ 3．56±ii：》ξ 0．63±8：》； 322．8／318 ト 15ノ．5−19ノ．5 ．．．．． 一 一 209．0／151 Tbt a1 ．．．．． 一 一 一 一 3922．4／3517
NXB−5％， CXBMIN んT Abundance Norlm§ Sll ）（2／dof
（keV） （Z㊦）
o，−3，．5 ．．．．． 7．30±8：鵠 o．41±8：8》 914．34±ξ：9客 322．97±▲：82 1835．7／1444 3，．577ノ ．．．．． 7．92±8：ll O．35±8：86 37．67±8：69 12．93±8：》； 1101．7／1124 7，−11 ．5 ．．．．． 7．19±8：9… o．25±8：｝》 9．73±8：18 3．20±8：1； 456．3／480 11，．5−15 ．5 ．．．．． 7．12±i：き2 0．58±8： i｝ 4．89±8：書1 1．77±8：｝1 321．6／318 15ノ．5−19ノ．5 ．．．．． 一 一 一 一 222．2／151 Tbt al ．．．．． 一 一 一 一 3937．5／3517
con七ami十20％ んT Abundance Noηη§ Sll ）（2／dof
（keV） （ZG））
0，−3 ．5 ．．．．． 7．04±8：品 0．40±8：8； 926．20± ：認 325．77±｝：塁 1842．9／1444 3，．5−7， ．．．．． 7．30±8：器 0．34±8：8言 36．89±8：6！ 12．56±8：菱呈 1099．0／1124 7 −11 ．5 ．．．．． 5．93±8：きI o．24±8：！8 8．75±8：4§ 2．78±8：｝書 453．5／480 11，．5−15，．5 ．．．．． 4．82±；：器 o．52±8：§2 3．36±8：認 1．11±8：碧 322．7／318 15ノ．5−19，．5 ．．．．． 一 一 一 212．3／151 Tot al ．．．．． 一 一 一 一 3930．5／3517
contami−20％ 瓦T Abundance Norm§ Sll ）（2／dof
（keV） （ZO）
0，−3ノ．5 ．．．．． 7．55±8：志； 0．42±8：8； 896．19±6：；量 317．08±｝：§§ 1887．34／1444 3 ．5−7， ．、．．． 7．81±8：§； 0．36±8：88 35．67±8：Z； 12．20±8：》9 1100．58／1124 7，−11，．5 ．．．．． 5．97±8：召 o．26±8：｝； 8．42±8：9； 2．70±8：圭8 453．02／480 11，．5−15，．5 ．．．．． 3ト97±｝：》8 0．52±8：量§ 3．38±8：Zき 1．12±8：》言 324．42／318 15，．5−19ノ．5 ．．．．． 一 一 221．12／151 Tot al ．．．．． 一 一 3986．48／3517
＊Normalizatioll of the apec component scaled with a factor of SOL硯OE．孔4冗0．REG／Ωe in table 5．7，
ハτom＝50乙硯CE．孔4刀 0．REG／Ωe∫ηeηH∂γ／（4π（1十z）2Z）麦）×10−20 cm−5 arcmin−2， where Z）A is the angular diameter distance to the source．
†Surface brightness in unit of 10−6 photons cm−2 s−1 arcmin−2（0．7−10 keV）．
6，2． A2204 99
（a） （b）
Prqiected radius（kpc） Prqlected radius（kpc）
10 1000 2000 3000 1 1000 2000 3000
8