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Fig． 5．3： The upper panels show the observed spectra fitted with ICM model ℃onstant×（apec） and galactic−2T−III background model
℃onstallt×（apec十gauss十gauss十wabs×（apec十powerlaw）） in FI：0．5−1．O keV， BI：0．4−
1．O keV， after subtracting the NXB fOr the annular regions：（a）3 ．5−7 ，（b）7 −11 ．5，
and（d）11㌧5−15 ．5． Each compollents are BI（red cross）， FI（black crosses）， CXB of BI
（purple）， GALI of BI（grey）， GAL20f BI（sky blue）， ICM of BI（orange）、 total model
spectra of BI（green）and FI（blue）respectively The lower panels show the residuals m
units ofσ・．
78． CHAPTER 5． BACKGROσND ANALYSI8
5．4 Cosmic X−ray Background
An ICM tempera七ure measurement in the ou七er regions of a cluster is very sensitive
to the CXB leve1． We took the 100％CXB surface brightness to be lo＝6．38×10−8
erg cm−2 s−1 sr『1 based on the ASCA−GIS measurements（Kushino et al．2002）． Morettie七al．（2008）summarized measurements（Gruber et al．1999；McCammon e七a1．1983；
Gendreau e七a1．1995；Vecchi et al．1999；Kushino et al．2002；Revnivtsev e七al．2003；
DeLuca et a1．2004；Revnivtsev et a1．2005；Hickox et a1．2006）of the CXB leve1， including
their new result with XMM−Ne耐oη． The measured CXB surface brightnesses show a
significant range from the HEAO l value of（5．41土0．56）x10−8 erg cm−2 s−1 sr−1（Gruber et a1．1999）to（7．71土0．33）x10−8 erg cm−2 s−1 sr−1 with SAX−MECS（Vecchi et al．1999）in the 2−10 keV band． Recent measurements show the且ux to be within about 10％ of the level reported by Kushino et aL（2002）．
We estimated the remaining CXB surface brightness after the above point−source sub−
traction by七he following three methods：（1）sub七rac七ing the summed point source fluxes
measured with Suzaku from the 100％CXB，（2）subtracting the summed point source
fluxes es伍mated using the log IV−log S relation， and（3）fitting a power−law model七〇the dif［use emission in the 20L 26， region after the point sources are excised．
In case（1）， we subtracted contribution of the excised sources of 1．80±8：ll×10二8 erg c皿一2 s−1 sr−1 from the loo％cxB， dividing昂（＝4．83±8：98×10−13 erg cm−2 s−1 0f the Suzaku total by 17ノ．8×17，．8 area of the XIS FOV． In case（2）， we calculated the integrated point source flux per steradian from
∫（S＞So）一 ﾟ竺2Sご7＋2， （5・2）
where k and午are the di任erential log N−10g S normalization and slope， respectively． We take nominal values，んo＝1．58×10−15 sr−1（erg cm−2 s−1）午一1 and午＝2．5， ffom Kushino e七al．（2002）．5b is taken as 2×10−14 erg cm−2 s−1， which is slightly higher than our flux limit， because the assumed log N−log S in equation（5．2）does not take into account the flattening of the rela七ion in the fainter且ux end． In case（3）， we fit the spec七ra from the solid angle in the 20 −26， annulus that remain after the source excision by apower−law model using a uniform且ux ancillary response丘1e（ARF；see section 4．2．1）．
The ARF assumes that X−ray photons comes into七he detectors uniformly仕om the sky．
direction within 20 radius from the optical axes of the respective XRTs， The model fit is αρec十ωα63×（αρec十ρoωerlαω）where the twoαpec components represent the galactic emission． This is the 2T−III model described ill section 5．6． In this case， value of七he 勾一匠xcolumn is de七ermined by the spectral fit， and then lx is calculated assuming lo＝6．38×10−8 erg cm−2 s−1 sr−1 in table 5．5．
We summarize our estimations of the remaining CXB surface brightness，勾一1X， in table 5．5． All three methods give consistent resul七s． Hereafter we will use a nominal
diffuse cosmic X−ray background spectrum（after subtraction of point sources brighter
than〜1×10−14 erg cm−2 s−1 in 2−10 keV band）described by a power−1aw with a photon5．5．NON X−RAY BA CKGROσND 79
index F＝1．37， and surface brightness 4．73 x 10−8 erg cm−2 s−1 sr−1 in the 2−10 keV
band， which comes from七he 2T−III（a）row of the method（3）． We adopt this method
because it directly．measures七he quantity of in七erest in our observations．To estima七e the ampli七ude of the CXB Huctuations， we scaled the measured fluctu−
ations丘om Ginga（Hayashida 1989）to our且ux limit and FOV area． The Huctuation
width is given by the followiIIg relation，
等㌘一；i：r（Ω。，S。。品。Ω。，Gi。g。）一゜5（ご）°25， （5・3）
where（σsuzaku／1cxB）means the fractional CXB fluctua七ion wid七h due to the statistical
fluctuation of discrete source number in the FOV． Here， we adoptσGinga／1cxB＝5％，
with S，（Ginga：6×1『12 erg cm−2 s−1）represen七ing七he upPer cut−off of七he source flux，
andΩe（Ginga：1．2 deg2）representing七he e丑ec七ive beam size（or effective solid angle）of the detector． We show the result，σ／∫cxB， for each spatial region in table 5．7． 1 1n the case of A2204， we also looked into CXB level．
We estimated the remaining CXB surface brightness by the following七hree methods：
100％CXB by Kushino et a1．（2002）with abandunce model Feldman（1992）（2）丘t七ing a
power−1aw model to七he diffuse emission in the 15 ．5−19 ．5 region with ab皿dance model of Anders＆Grevesse（1989）and（3）丘tting a power−1aw mgdel to the diffuse emission in the 15 ．5−19 ．5 region with abundance model of Feldman（1992），In the case of A2204， The CXB flux wi七hin 20 circle is stronger than the value of Kushino et al．（2002）in table 5．5． It is possible that CXB value is also affected with SWCX mentioned before． CXB intensities measured for A2204 are s七ronger than that of A1413． We suspect it because of small background region with 15，．5−19，．5． To give background enough efFective area， we utilized 11，．5−19．5 region which is out of virial radius as background in the test（d）of A2204． However， the background in七ensity is no七considered different result from o七her cases．
5．5 Non X−ray Background
The non X−ray background（NXB）spectra were estimated from the Suzaku database of
dark earth observations using the procedure of Tawa et a1．（2008）． We accumulated data for the same detec七〇r area， for七he same distribution of COR2 as the A14130bservationusing the⑰5η功geπFTOOLS covering 30 days before to 90 days after the observation
period of A1413． To increase the A1413 signal−to−noise ratio by reducing the NXB countrate， we required COR2 to be＞8GV and PINUD七〇be between 100 and 300 cts s−1．
After this screening the exposure time dropped from 108 ks to 72 ks， nevertheless the丘t
residuals were reduced． We also tested other screening criteria， such as COR2＞8GV
and COR2＞5GV， both with no PINUD screening． The former criterion did not affect
七he final spectral results signi丘cantly， but the latter gave different ICM temperatures． To80 CHAPTER 5． BA CKGROσND ANALYSL3
Table 5．5：Estimation of the CXB surface brightness after七he point source excision of
A1413， A2204， and AWM7．
A1413
10−1支＊ 1k† r‡
（1） ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 4．58±8：》… i．80±8：萎i 1．41（fixed）
（2）§ ．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 4．15 2．23 1．41（fixed）
（3）2T−III（a）ll．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 4．73±8：憂 1．65±8：弱 1．37±8：8ξ
（3）2T−III（b）‖．．．．．．．−．．．．．．．．．．．．．．．＿．．．． 4．69±8：趨 1．69±8：｛§ 1．40±8：85
（3）2T−III（c）lL．．．．．．．．．．．．．．．．．．．．．．．．．．．． 5．16±8：鵠 1．22±8：藷 1．44±8：8§
（3）con七ami十20％ll．．．．．．．．．．．．．．．．．．．．．．＿ 5．04±1：；1 1．34±8：ll 1．45±8：8；
（3）contami−20％ll．．．．．．．．．．．．．．．．．．．．．＿． 4．95±8：；1 1．33±8：ll 1．44±1：12
A2204
・ 勾一1x＊ r‡
（3）2T−III（a）ll．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 723±8：§Z 1．41（fixed）
（3）2T−III（b）＃．．．．．．．．．．．．．．．．．．．．．．．．．．＿ 6．67±8：§至 1．41（fixed）
（3）contami十20％ll．．．．．．．．．．．．．．．．．．．．．．＿ 7．10±田1 1．41（fixed）
（3）con七ami−20％ll．．．．．．．．．．．．．．．．．．．．．．．．． 7．29±8：1； 1．41（fixed）
（3）NXB十5％ll．．．．．．．．．．．．．．．．．．．．．．．．．．．．． 6．75±；：82 1．41（fixed）
（3）NXB−5％IL．．．．．．．．．．．．．．．．．．．．．．．．．＿ 7．67±8：豊 1．41（fixed）
＊Estimated surface brightness of the CXB after the point source excision in unit of 10−8
erg cm−2 s−1 Sr−1（2−10 keV）．
†Contribution of七he resolved point sources in unit of 10−8 erg cm−2 s−1 sr−1（2−10 keV）．
‡Assumed or estimated photon index of the CXB．
§Surface brightness of 100％of CXB is assu、med as勾＝6．38×10−8 erg cm−2 s−1 sr−1（2−10 keV）．
In七egrated point source contribution，丘， is calculated with equation（5．2）． See section 5．4 fbr details．
ll See section 5．6 fbr de丘nition． Abundance model is by Anders＆Greves白e（1989）．
‖See sec七ion 5．6 for de丘nition． Abundance model is by Fbldman（1992）．
‖はR）ur−regions simoltanious丘tting wi七h 11ノ．5−19 ．5 as background region． Abundance model is by Anders＆Grevesse（1989）．
test a possible NXB uncertainity systematic error， we varied its intensity by土3−75％
as investiga七ed by Tawa et al．（2008）．
5．6 Galactic Components
We fit the data in the 20ノー26， region to constrain the fOreground Galactic emission， using
the same uniform−sky ARF as the CXB componen七． We investigated the best model
5．6．GALACT∫C COMPONENTS 81
Fig．5．4：Rosat ALL Sky Survay map（R45 band：R4＝52−69， R5＝70−90）
to llse and the best−fit model paralneters． Ill all cases， we also included a power−law model to represent the CXB， We tried a sillgle telnperature therlnal pla．sma model，1T：
αρεc＋迎bs×poωεr〜側， a two tenlperature model，2T：ulαb5×（αρεcl十αpεc2十ρouleザ1αω）、
alld a two temperature model following Tawa et aL（2009），2T−III：αpεcl＋・忙・αbs×（αpεc2十 ρoω杉r〜α⇒．In all models、 redshift and abundance of theαρεc components were fixed at O．O and l，0， respectively Tlle two temperature variants try to model the Local Hot
Babble（LHB）and the Milky Way Halo（MWH）．WC tried three types of the 2T model：
both temperatures fixed to O．204 keV and O．074 keV given by Lumb et al．（2002）、 one temperature 6xed to O．074 keV alld the second temperature仕ee、 both temperatures hlee，
We call the first model as 2T−1， and the second model as 2T−II．．The third model did not converge in the fitti119、 so that we do not disα1ss it further．
We fbund tha．t the IT alld 2T−I models gave γorse X2 values compared with the 2T−
II and 2T−III fits． We show the best一丘t parameters in table 5．6 for the 2T−III modeL
which we adopt． wdind that the LHB alld MwH temperatures are oユ12±3．88…kev and
O．278：8：8｝；keV、 respective1｝こ These values are consistent with those obtained by Ta ・a et aL（2009）． We also show in ta．ble 5．6 how the best−fit parameters change as a result of systematic changes ill the CXB and NXB leveIs alld of the abundance 1皿odel used（labeled（a）or（b））． The variations are small：less than±10％for the temperatures alld
士15％允rthe normalizatiolls， Finally， our baseline CXB十GAL model is denoted 2T−III
（a），αρεC1十ωαb5＊（αρεC2十ρOU・er〜αω）With ab−mdanCeS f士Om AnderS＆Gre、−eSSe（1989），
We link all para．meterS Of thiS mOdeL eXCept all Overall 110rlnaliZatiOn， when perfOrnling the 6ts for thp diHセrellt spatia．l regiolls．
In the case of A2204、 the intensity of gala〔・tic compollellts are strollger in order than A2204 case． That is due to the SWCX or the a．ffection of our galactic componellts in real，
However as shown ill figure 5．4， di任use distribution suggests that A2204 is locate Ilot so
82 CHAPTER 5． BACKGROσND ANALYSI正1
speci丘c addreSs． We also thought that this property of galactic and CXB intensi七ies is due to the possibility with the inconsistency ofβmodel and ICM surface brigh七ness pro丘1e．
However， we could not recognized difference of considerable results betweenβprofile and 2βprofile which modeled with S鵬αえμ1．0−10．O keV image． Then we conclude that A2204
is much aHected with SWCX con七amination below l keV．
In the case of AWM7， we fixed LHB component with O．074 keV which is the aver−
aged LHB temperature by Lumb et al．、（2002）． because its normalization is diverged． we listed the value of galactic components in table？？． The nominal best−fit value of its flux is O．231±8：8；♀erg cm−2 s−1 sr−1in east and O．143±8：1；きerg cm−2 s−1 sr−1in south． Because
MWH components of There are no di丘erent result between Anders＆Grevesse（1989）and
Feldman（1992）． The nominal best一丘t value of MWH且ux are O．728±1：i；lerg cm−2 s−1 sr−1in east and O．503±8：621 erg cm−2 s−1 sr−1in south．When we subtraced simulated stray light spectra from r脚spectra−2T−III（c）， in the south region， LHB and MWH且uxes are about twice stronger than other cases， instead of
zero normalization of ICM component． Then we丘xed all of galactic components七〇the
nominal value−2T−III（a）in the south region．ぷ
5．7 Background Fraction in Each Region
Table 5．7， and table 5．8， present many properties of the spatial regions of A1413， and
A2204， we analyzed． The columns are the annular boundarles；the actual solid angle
of each region observed，Ω．；the coverage丘action of each an皿1us which is the ratio ofΩe to the total solid angle of the a皿ulus， Oouεrαgε；the加ction of the simulated cluster photons which fall in the region compared with the total photons from七he entiresimulated cluster， SOσR（班』Z4冗0−REG；the CXB fluctuations due to unresolved point sources，σμcxB；the observed counts， OBS；the estimated counts for each background componellt， NXB， CXB， and GAL；and the frac七ion of background pho七〇ns given by
∫BGD≡（NXB十CXB十GAL）／OBS．
The NXB co皿t rates are calculated from the dark ear七h data． We simulated the CXB and GAL components spectra usingエ乞55乞7ηwith the flux and spectral parameters given in row 2T−III（a）of table 5．5， table 5．6， and table？？， assuming a uniform surface brightness that丘11s七he 20 arcmin radius of七he assumed field． We plot the NXB and CXB spectra in figures C．2 and figure C．3 for A1413， figure C．5 and figure C．6 for A2204， and figure？？
for AWM7． These spectra gave the count rates in table 5．7， table 5．8， and table？？． In the outermost region of∫BGD is consis七ent with 100％in A1413 and A2204． This confirms the accuracy of our background estimation．
5．7．BACKGROσND FRAC質ON lN EL4CH REG∫ON 83
Table 5．6：Galactic components best丘t parameters and 90％confidence errors，
A1413
ん㍗（keV） 」監111 瓦乃（keV） 1元（211 2T−III（a）＊．．． o．112±8：881 0．685±8：8器 o．278±8：81； o．349±8：8器 2T−III（b）†．．． o．110±8：88蓉 o．702±8：8量I o．314±8：8袈 o．424±8：8§1 2T−III（c）‡．．． o．113±8：88§ o．623±8：8題 o．260±8：8麗 o．352±8：；鵠
contami十20％ o．111±1：1器 o．733±8：1揚 o．269±8：1｝1 − o．396±8：1習 1 contami−20％ o，113±1：811 0．633±8：8認 o．286±8：8i8 0．316±8：巻♀；
A2204
ん71（keV） 1ζ（111 ん乃（keV） 理（211 、 2T−III（a）＊．．．． o．074（fixed） 4．835±量：釜9 0．249±8：819 12．337±；：鵠9 2T−III（b）†．．． o．074（fixed） 11．965± ：器9 0．285±8：⑪8§ 10．838±8：§器 2T−III（d）‖．．． 0．074（丘xed） 4．541±1：§翼 0．250±8：8設 12．278±；：199 cont ami十20％＊ 0．074（fixed） 9．111±1：器； 0．254±1：81ま 12．758±；：1｛l cont ami−20％＊ 0．074（fixed） 1．170±至：｝麗 0．244±8：8｝！ 11．869±；：器I CXBmax＊．．．． 0．074（fixed） 5．657±§：器1 0．248±8：82 12．061±；：61 CXBmin＊．．．．． o．074（fixed） 4．675±夏：器｝ o．249±8：1題 12．381±萎：欝 NXB十5％＊．．． 0．074（fixed） 4．819±1：§日 0．249±8：1霞 12．314±1認I NxB−5％＊．．． o．074（fixed） 4，867±量：舗 o．249±⑪：8器 12．341±；：412
＊Abundance model is by Anders＆Grevesse（1989）．
†Abundance model is by Feldman（1992）．
‡Including two gaussian models of OvlI and OvIII， Abundance model is by Anders＆
Grevesse（1989）．
ll Surface brightness in unit of 10−8 erg cm−2 s−1 str−1（0．5−10 keV）．
＃Abundance model is by Anders＆Grevesse（1989）． And CXB model is且xed to Kushino e七al．（2002）
84 CHAPTER 5． BA CKGROσND ANALYS阻
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