The gas distribution in the high-redshift cluster MS 1054-0321

5.8 MB·

by  M. S. Mirakhor

Mon.Not.R.Astron.Soc.000,1–12(2016) Printed21January2016 (MNLATEXstylefilev2.2)
The gas distribution in the high-redshift cluster MS
1054-0321
M. S. Mirakhor(cid:63) and M. Birkinshaw
H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL
6
1
0
Accepted2016January18.Received2016January15;inoriginalform2015October06
2

n
a ABSTRACT
J
WeinvestigatethegasmassdistributioninthehighredshiftclusterMS1054-0321us-

0 ingChandra X-rayandOCRASZeffectdata.Weuseasuperpositionofoffsetβ-type
2 models to describe the composite structure of MS 1054-0321. We find gas mass frac-
] tionsfgXa-sray =0.087+−00..000051 andfgSaZs =0.094+−00..000031 forthe(main)easterncomponentof
A MS 1054-0321 using X-ray or SZ data, but fX-ray =0.030+0.010 for the western com-
gas −0.014
ponent. The gas mass fraction for the eastern component is in agreement with some
G
results reported in the literature, but inconsistent with the cosmic baryon fraction.
.
h The low gas mass fraction for the western component is likely to be a consequence of
p gas stripping during the ongoing merger. The gas mass fraction of the integrated sys-
- tem is 0.060+0.004: we suggest that the missing baryons from the western component
o −0.009
are present as hot diffuse gas which is poorly represented in existing X-ray images.
r
t The missing gas could appear in sensitive SZ maps.
s
a
Key words: galaxies: clusters: individual: MS 1054-0321 − galaxies: clusters: intr-
[
acluster medium − galaxies: clusters: general − X-rays: galaxies: clusters − cosmic

1 background radiation − cosmology: observations
v
4
0
3
5 1 INTRODUCTION electrondensityandtemperatureonthelineofsight).This
0 parameter dependence makes the SZ effect a powerful tool
The properties of massive high redshift clusters could place
. to probe lower-density regions of the hot gas, and thus to
1 powerful constraints on the cosmological parameters that
providebetterinsightintogaspropertiesoutsidethecluster
0 govern the physics of the early Universe (Joy et al. 2001;
6 core or in the hottest regions. For reviews of the physics of
Brodwin et al. 2012). Several studies have used clusters at
1 the SZ effect see Rephaeli (1995), Birkinshaw (1999), and
highredshifttoprovidevaluableinformationongalaxyfor-
: Carlstrom,Holder&Reese(2002).Duetothedifferentsen-
v mation and evolution in the richest environments and to
sitivityoftheSZeffectandtheX-rayemissiontoouterand
i probeGaussianityinthedensityfieldthatseededstructure
X inner regions of the cluster, these two independent probes
formation (Foley et al. 2011; Wen & Han 2011; Brodwin et
r al. 2012). Massive clusters, with M ∼1015M , are iden- canbeusedtoprovideamorecompletepictureoftheICM.
a tot (cid:12) By combining X-ray and SZ effect data, the distance of the
tified by their gravitational lensing of background galaxies
cluster can be estimated and hence the Hubble constant or
(Zaritsky&Gonzalez2003;Medezinskietal.2011),andby
other cosmological parameters can be found (e.g. Birkin-
the X-ray emission or Sunyaev-Zel’dovich effect (SZ) from
shaw, Hughes & Arnaud 1991; Worrall & Birkinshaw 2003;
their hot intracluster medium (ICM) (Morandi, Ettori &
Bonamente et al. 2006). Alternatively, tight constraints on
Moscardini 2007; Battaglia et al. 2012).
the gas mass fraction of the cluster can be obtained (see
The X-ray emission from diffuse hot plasma at T >
Grego et al. 2001; LaRoque et al. 2006; Planck Collabora-
5keV is primarily bremsstrahlung from the gas within the
tion 2013, for example).
potential well of the cluster’s dark matter halo. The X-ray
luminosityisproportionaltothesquareoftheelectronden-
ObservationswithX-raysatellitessuchasChandra and
sity, hence is sensitive to the denser regions of the cluster.
XMM–Newton have provided high quality images of the X-
Ontheotherhand,thethermalSZeffect,thechangeinthe
ray emission and detailed structural properties of the ICM
brightness of the cosmic microwave background caused by
(e.g. Vikhlinin et al. 2006; Pratt et al. 2009). In parallel,
hot electrons in the ICM inverse-Compton scattering, de-
many SZ observatories such as the South Pole Telescope
pends on the ICM pressure (the integrated product of the
(SPT, Carlstrom et al. 2011), and the One Centimeter Re-
ceiverarray(OCRA,Lancasteretal.2011)havemadehigh
(cid:63) E-mail:[email protected] signal-to-noiseSZmeasurementstowardclusters.Generally
(cid:13)c 2016RAS
2 M. S. Mirakhor and M. Birkinshaw
themodelsusedtointerpretSZeffecthavebeenrathersim- fits the main cluster component with β = 0.73 ± 0.18,
ple. r = (422±109)h−1kpc and r = (298±65)h−1kpc.
c1 50 c2 50
In this paper we investigate the gas mass distribution Considering only the main component of MS 1054-0321
ofthehighredshiftclusterMS1054-0321,takingadvantage and using the best fit temperature from the ASCA spec-
of a long Chandra observation of MS 1054-0321 and high trum, Neumann & Arnaud (2000) derived gas masses in-
signal/noiseSZeffectdatafromOCRA,todevelopathree- side 1.65h−1Mpc of (1.9±0.3)×1014h−5/2M and 2.5×
50 50 (cid:12)
dimensionalgasdensityprofileoftheβ-modeltype.Weuse 1014h−5/2M from the best fit parameters of the 1D and
50 (cid:12)
this to improve the measurement of the gas mass of MS 2D beta models, respectively. They estimated total masses
1054-0321. The physical properties of the gas of MS 1054- ofMS1054-0321at1.65h−1Mpcof2.0+0.8×1015h−5/2M
50 −0.4 50 (cid:12)
0321 were analysed in previous studies. However in most and 1.6×1015h−5/2M from the 1D and 2D β-models, re-
of these studies, standard isothermal β-models were used 50 (cid:12)
spectively. The gas mass fraction is then about 0.10h−3/2
fortheclusterplasmadistributionalthoughthestructureof 50
theclusterisclearlymorecomplicated.SincetheICMmass or 0.16h−503/2, depending on the choice of model.
and the total mass of cluster are functions of temperature, Jeltemaetal.(2001)analysedaChandra ACIS-Sobser-
we also re-analyse the X-ray temperature structure of MS vationofMS1054-0321.TheyestimatedtheX-raytempera-
1054-0321.Weuseourresultstoestimatethegasandtotal turefortheentireclustertobe10.4+1.7keV,andconfirmed
−1.5
masses of the cluster. the substructure in the ROSAT HRI data. The eastern
In the next Section we review MS 1054-0321. In Sec- clumpisalmostcoincidentwiththemaincomponentofthe
tion 3 we describe the X-ray and radio observations of MS cluster, and has an X-ray temperature of 10.5+−32..41keV. The
1054-0321.Theanalysismethodfor3Dsingle-βanddouble- westernclumpismorecompactanddenserthantheeastern
β models used to describe the plasma distribution is pre- clump, with a temperature of 6.7+−11..72keV. The quoted er-
sented in Section 4. The gas mass content of MS 1054- rorsareat90%confidencerangesforthetwo-parameterfit.
0321 is discussed in Section 5. Finally, in Section 6 we Using the temperature of the whole cluster, Jeltema et al.
summarise our results. Throughout this paper, we use a estimated a virial mass of ∼ 6.2+−11..63×1014h−1010M(cid:12) within
ΛCDM cosmology with Ωm = 0.3, ΩΛ = 0.7, and H0 = r200 = 0.76h−1010Mpc. The authors also estimated the total
100h kmsec−1Mpc−1 with h =0.7. Uncertainties are massusingaβ-model(settingβ =1andfittingfortheclus-
100 100
at the 68% confidence level, unless otherwise stated. ter core radius), and obtained a mass of 7.4×1014h−1010M(cid:12)
within r .
200
An investigation of the temperature structure of MS
1054-0321 using XMM–Newton (Gioia et al. 2004) indi-
2 CLUSTER MS 1054-0321 cated a temperature for the whole cluster of 7.2+0.7keV,
−0.6
The rich cluster MS 1054-0321 is the most distant and lu- lowerthananyofthetemperaturesreportedpreviously.The
minous cluster in the Einstein Extended Medium Sensitiv- twosignificantclumpsalreadyseenbytheROSAT andthe
ity Survey (EMSS, Gioia et al. 1990). Due to its high red- Chandra satelliteswerealsoseenintheXMM–Newton data.
shift (z = 0.83 corresponding to angular diameter distance AsintheresultreportedbyJeltemaetal.(2001),theeast-
DA = 1.57Gpc) and complicated morphology, the ICM ern clump has the higher temperature, 8.1+−11..32keV, consis-
plasma of MS 1054-0321 has been subjected to many stud- tent with the integrated cluster temperature, and the west-
ies.X-rayobservationsofMS1054-0321withtheASCAand ern clump, at 5.6+−00..86keV, is 30% cooler than the eastern
ROSAT satellites were analysed by Donahue et al. (1998). clump.Quotedconfidencelimitsare90%foroneinteresting
The ASCA spectrum showed a high X-ray temperature of parameter.
12.3+3.1keV (90% confidence interval), which should indi- Jee et al. (2005) analysed HST ACS weak-lensing and
−2.2
cate that MS 1054-0321 is a massive cluster. The X-ray Chandra X-ray data of MS 1054-0321. The dark matter
image from the ROSAT HRI identified two or three com- structure mainly consists of three dominant clumps with a
ponents in addition to an extended component, suggesting few minor satellite groups. The eastern weak-lensing clump
that MS 1054-0321 is not in a relaxed state. Based on this fromthemassmapisnotdetectedintheX-raydata,andthe
X-raytemperatureandusingthemass-temperaturerelation twoX-rayclumpsaredisplacedontheapparentmergeraxis
adoptedfromthesimulationsofEvrard,Metzler&Navarro relative to the central and western weak-lensing substruc-
(1996), the virial mass of MS 1054-0321 estimated by Don- tures, probably due to ram pressure. Jee et al. estimated
ahueetal.(1998)was∼7.4×1014h−1010M(cid:12) withinaregion the projected mass to be (7.14±0.11)×1014h−1010M(cid:12) at
of a radius r =1.5h−1 Mpc. r =1Mpc, consistent with previous lensing work (Luppino
200 100
TheROSAT HRI observationofMS1054-0321wasre- &Kaiser1997;Hoekstra,Franx&Kuijken2000).Theyalso
analysedbyNeumann&Arnaud(2000)andnewHRI data fitted the X-ray surface brightness of MS 1054-0321 to an
were included in order to gain better insight into the main isothermal1Dβ-model,excludingthecoreregion(r<45(cid:48)(cid:48))
componentsofMS1054-0321.Theseauthorsfoundevidence fromthefit,tofindβ =0.78±0.08andrc =(16±15)(cid:48)(cid:48),cor-
forasignificantclumptothewestofthemaincomponentof responding to (85±80)h−1 kpc in our adopted cosmology.
100
the cluster. The HRI image was fitted to 1D spherical and UsinganX-raytemperatureof8.9+1.0keV, Jeeetal.found
−0.8
2D elliptical β-models. Excluding the western component, themasswithinradius1Mpcis(8.4±0.14)×1014h−1010M(cid:12),
Neumann & Arnaud found the best fit to the 1D spheri- agreeing with their weak-lensing result.
cal model to have β = 0.96+0.48 and r = 442+184h−1kpc. UsingOVRO/BIMAinterferometricSZeffectdata,Joy
−0.22 c −104 50
However, if the western substructure is included, the best etal.(2001)estimatedthegasmassofMS1054-0321within
spherical model fit gives β = 2 and r = 840h−1kpc aradiusof94(cid:48)(cid:48)(501h−1 kpcinouradoptedcosmology)tobe
c 50 100
with large errors. On the other hand, an elliptical β-model (3.7±0.6)×1013h−2 M foratemperatureof10.4+5.0keV.
100 (cid:12) −2.0
(cid:13)c 2016RAS,MNRAS000,1–12
Gas distribution in MS 1054-0321 3
Using the mean gas mass fraction of a sample of galaxy 7.0keV)fromacircularregionofradius90(cid:48)(cid:48)centredat(RA,
clusters reported by Grego et al. (2001), the derived total Dec) = (10h57m00s.02, −03◦37(cid:48)36(cid:48).(cid:48)00). This corresponds to
masswas(4.6±0.8)×1014h−1 M withinthesameradius. the position of the optically brightest galaxy in the clus-
100 (cid:12)
LaRoque et al. (2006) derived the gas mass fraction within ter (Best et al. 2002). We fitted the X-ray spectrum with
r for a sample of massive clusters including MS 1054- a MEKAL model (Mewe, Gronenschild & van den Oord
2500
0321fromChandra togetherwithOVRA/BIMAdatausing 1985) modified by local Galactic absorption after binning
threedifferentmodelsfortheplasmadistribution.Thefirst the counts to at least 30 per energy bin. The iron abun-
model, the isothermal β-model fit to the X-ray data at ra- dance and the temperature were left free to vary, whereas
diusbeyond100kpcandtoalloftheSZeffectdata,yielded the Galactic absorption and the cluster redshift were con-
fX-ray = 0.144+0.014 and fSZ = 0.153+0.034. The second strainedat3.67×1020atomscm−2(Dickey&Lockman1990)
gas −0.013 gas −0.029
model, the nonisothermal double β-model fit to all of the and 0.83 (van Dokkum et al. 2000), respectively. The best
X-ray and SZ effect data, gave fX-ray = 0.106+0.009 and fityieldsatemperatureT =8.5±0.7keVandametalabun-
gas −0.010
fgSaZs =0.102+−00..002108. The third, the isothermal β-model fit to dance Z = 0.33±0.11Z(cid:12) at 68% confidence level, with a
the SZ data with β fixed at 0.7, yielded fSZ =0.187+0.081. reduced χ2 = 0.74 for 215 degrees of freedom. Our tem-
gas −0.054
PerformingajointfitanalysisofthesameX-rayandSZef- perature estimate is in good agreement with the Chandra
fectdata,Bonamenteetal.(2008)determinedthegasmass temperaturereportedbyJeeetal.(2005)(T =8.9+−10..08keV)
fraction of MS 1054-0321 using an isothermal β-model ex- and by Tozzi et al. (2003) (T = 8.0±0.5keV), and also
cluding the central region (100 kpc) from the X-ray data. withtheXMM–Newton temperature,T =7.2+−00..76keV(90%
They found the gas mass fraction within 89(cid:48)(cid:48) (475h−1 kpc confidence limits), presented by Gioia et al. (2004). How-
100
in our adopted cosmology) to be 0.164±0.019. ever,itisslightlylowerthantheJeltemaetal.(2001)value,
In Table 1 we summarize the reported measurements based on the same Chandra data (T =10.4+−11..75keV at 90%
of the physical properties of MS 1054-0321. The numerical confidencelimits),andmuchlowerthantheASCAtempera-
valuesofthesemeasurementsareconvertedtothecosmology ture, T =12.3+−32..12keV (90% confidence limits), determined
adopted by this work. As can be seen, the results are not by Donahue et al. (1998). The metal abundance obtained
entirely consistent. fromourfittingoftheX-rayspectrumagreeswithprevious
results reported by Gioia et al. (2004) (Z = 0.33+0.19Z
−0.18 (cid:12)
at 90% confidence limits) and by Jee et al. (2005) (Z =
0.30±0.12Z ).
(cid:12)
3 DATA
We also investigated the temperatures of the densest
3.1 The X-ray image parts of the eastern and western components by extracting
counts from the regions with size of 48.71(cid:48)(cid:48) ×45.46(cid:48)(cid:48), cen-
We used archival data for MS 1054-0321 from the same tred at RA = 10h56m59s.87, Dec = −03◦37(cid:48)31(cid:48).(cid:48)68, and RA
Chandra ACIS-S observation in April 2000 used by Jel- = 10h56m56s.16, Dec = −03◦37(cid:48)39(cid:48).(cid:48)95 (Fig. 1). There are
tema et al. (2001) and Jee et al. (2005). The total obser-
around 3090 and 2725 counts in the energy range of 0.5-7.0
vation duration was 90 ks. Chandra Interactive Analysis of
keV in the eastern and western components, respectively.
Observations(CIAO)version4.5,withcalibrationdatabase
The X-ray data again were fitted with a MEKAL model,
(CALDB)version4.5.9,wasusedtoreducetheX-raydata. with Galactic absorption frozen at 3.67×1020atomscm−2
The data were reprocessed by running the chandra repro
and the cluster redshift frozen at 0.83. The temperature
script to create a new level = 2 event file, and a new bad
and the metal abundance were left free to vary. The best
pixelfile.Tominimizethehighenergyparticlebackground,
fit for the eastern component gives a temperature T =
countswereconsideredonlyintheenergyrange0.5-7.0keV. 10.7+1.9keVandanabundanceZ =0.11+0.22Z withare-
X-raybackgroundcountswereobtainedfromthelocalback- duce−d1.χ52 =0.71 for 72 degrees of freedom−0..1F1or(cid:12)the western
groundontheChandra ACIS-S3chip.Pointsourcesonthis component,thebestfitgivesatemperatureT =6.8+0.9keV
chip were detected, removed, and replaced by a local esti- and an abundance Z = 0.34+0.20Z with a reduce−d0.8χ2 =
mate of the background emission. Our image of the X-ray −0.19 (cid:12)
0.66 for 67 degrees of freedom. The X-ray spectra with the
surfacebrightnessofMS1054-0321isshowninFig.1.This
best fit models of the full cluster, the eastern and western
image is smoothed by a two-dimensional Gaussian kernel
componentsareshowninFig.2.Allthespectrawerebinned
with σ=3.44(cid:48)(cid:48).
to 30 or more counts per energy bin.
The X-ray structure of the cluster shows an elliptical
Our temperature measurements clearly show that the
shape elongated in the east-west direction with two main
eastern component is hotter than the western component.
components,indicatedbytwogreenboxeslabelledEandW.
Such results are fully consistent with the temperatures of
Theeasterncomponentisrelativelydiffuseandlessbrightat
the eastern and western components reported by Jee et al.
its centre, which lies around 5(cid:48)(cid:48) (40 kpc) from the position (2005) (T = 10.7+2.1and7.5+1.4keV), and by Jeltema et
of the cluster brightest optical galaxy (Best et al. 2002). al. (2001) (T = 10−.51.+73.4and6−.71.+21.7keV at 90% confidence
The western component is more compact, has a higher X- −2.1 −1.2
limits).Gioiaetal.(2004)alsonoticedthesignificantdiffer-
ray surface brightness, and its peak is separated from the
ence of temperature between the eastern and western com-
peak of the eastern component by ∼55(cid:48)(cid:48) (420 kpc). ponents(T =8.1+1.3and5.6+0.8keVat90%confidencelim-
−1.2 −0.6
its), but their temperatures are systematically lower than
ourvalues.Ourresultsfortheabundanceagreewitheastern
3.2 The X-ray spectra
andwesterncomponentvaluesobtainedbyJeeetal.(2005)
Theemissionweightedtemperatureofthewholeclusterwas (Z =0.16+0.19 and0.47+0.24Z ),andbyGioiaetal.(2004)
−0.16 −0.23 (cid:12)
obtained by using counts (∼ 14120 counts between 0.5 and (Z =0.12+0.35 and 0.51+0.36Z at 90% confidence limits).
−0.12 −0.32 (cid:12)
(cid:13)c 2016RAS,MNRAS000,1–12
4 M. S. Mirakhor and M. Birkinshaw
Table 1.ThephysicalpropertiesofMS1054-0321reportedintheliterature.
Study Method Radius Mgas Mtot fgas
(h−1010Mpc) (1013h−1010M(cid:12)) (1014h−1010M(cid:12))
Donahueetal.(1998) M-T relation r200=1.50 — 7.4a —
Neumann&Arnaud(2000) β-modelb 1.16 13.30±2.10 14.00+5.60 0.095
−2.80
Ellipticalβ-modelb 1.16 17.50 11.20 0.156
Gregoetal.(2001) β-modelc r500=0.86 — — 0.053±0.028
Joyetal.(2001) β-modelc 0.50 5.29±0.86 4.60±0.80 0.115+0.013
−0.016
Jeltemaetal.(2001) M-T relation r200=0.76 — 6.2a —
β-modeld r200=0.76 — 7.4 —
Jeeetal.(2005) Weak-lensing 0.7 — 7.14±0.11 —
β-modele 0.7 — 8.40±0.14 —
LaRoqueetal.(2006) β-modelf r2500≈0.18g 0.74+−00..3354 0.52+−00..3227 0.144+−00..001143
0.78+0.29 0.52+0.32 0.153+0.034
−0.33 −0.27 −0.029
Doubleβ-modelh r2500≈0.18g 0.74±0.18 0.70+−00..2240 0.106+−00..000190
0.72±0.11 0.70+0.24 0.102+0.020
−0.20 −0.018
β-modeli r2500≈0.18g 0.82±0.11 0.43+−00..1151 0.187+−00..008514
Bonamenteetal.(2008) β-modelf r2500=0.48 5.18+−00..8740 3.15+−00..9780 0.164±0.019
a Virialmass.
b FittedtotheX-raydata.
c FittedtotheSZeffectdata.
d FittedtotheX-raydatawithβ fixedat1.00.
e FittedtotheX-raydatawithexcludingthecentralregion.
f FittedjointlytotheX-raydatabeyondthecentralregionandtotheSZeffectdata.
g Weestimatedther2500radiususingparametersfromthebest-fitmodelfortheSZeffectdataandtheX-raydataoutside
thecentralregion.
h FittedjointlytotheX-rayandSZeffectdata.
i FittedtotheSZeffectdatawithβ fixedat0.70.
Jeltemaetal.(2001)reportedsimilarresults,(Z =0.08+0.23 Theseresultsindicatethatthetemperatureoftheeast-
−0.08
and 0.46+0.27Z at 90% confidence limits), relative to the ern component decreases by a factor ∼ 2 over scale ∼ 50(cid:48)(cid:48)
−0.26 (cid:12)
slightlydifferentsolarironabundanceofAnders&Grevesse (380kpc),excepttothenorth,wherealesser,orno,temper-
(1989). ature change is found. Fixing the metallicity at the cluster
The significant variation in temperature between these central value leads to higher outer temperatures in the east
twocomponentsledustoinvestigatethetemperaturestruc- and south, and lower temperature gradients. If the Galac-
ture for other regions within the cluster atmosphere. Thus, tic hydrogen column is allowed to be free, then we obtain
we extracted counts from three regions to the north, south, fits of equivalent quality to these found with fixed NH, but
and east of the eastern component (see Fig. 1). The size of withbest-fittemperatures∼1keVhigherinallcases.How-
each region was chosen to be equivalent to that of the east- ever, the fitted values of NH are below the known Galactic
ern (or western) component, and their centres are about column, and so we don’t consider these results further.
50(cid:48)(cid:48) (380 kpc) away from the centre of the eastern compo-
nent. There are around 1040, 1430, and 890 counts in the
3.3 The Sunyaev-Zel’dovich effect data
energy range 0.5-7.0 keV in the north, south, and east re-
gions, respectively. The X-ray spectrum in each region was MS 1054-0321 was observed at 30 GHz over the period 28
binned to include at least 50 counts per bin. The X-ray February2006to2June2006usingtheTorun´32mtelescope
datawerethenfittedtoaMEKALmodelmodifiedbyalo- equipped with the prototype One Centimetre Receiver Ar-
calGalacticabsorption.Galacticabsorptionandthecluster ray (OCRA-p) (Lancaster et al. 2007). OCRA-p consists of
redshift were fixed as before, whereas the temperature and two1.2arcminFWHMbeamsseparatedby3.1arcmin,and
the metal abundance were left free to vary. The best fit for can achieve 5 mJy sensitivity in 300 seconds. OCRA-p ob-
theregionnorthoftheeasterncomponentgivesatempera- servedMS1054-0321for∼11hoursusingacombinationof
ture T =11.8+7.0keV and an abundance Z =0.76+1.33Z beam-switchingandposition-switching.Suchatechniqueis
−3.7 −0.76 (cid:12)
with a reduced χ2 = 1.39 for 15 degrees of freedom. For efficientatsubtractingatmosphericandgroundsignals,and
the region to the south, the best fit yields a temperature removes such contaminating signals better than position-
T = 6.5+2.2keV and an abundance Z = 0.38+0.46Z with switchingorbeam-switchingalone(Birkinshaw&Lancaster
−1.3 −0.38 (cid:12)
a reduced χ2 = 0.91 for 22 degrees of freedom. The best 2008). The principles of the beam- and position-switching
fit temperature and abundance for the region to the east technique and the data reduction process are described in
are T = 5.0+1.7keV and Z = 2.20+2.19Z with a reduced detail in Lancaster et al. (2007).
−0.9 −1.21 (cid:12)
χ2 =1.08 for 13 degrees of freedom. The OCRA data were calibrated by reference to two
(cid:13)c 2016RAS,MNRAS000,1–12
Gas distribution in MS 1054-0321 5
11.8+7.0
−3.7
E
W
5.0+1.7 10.7+1.9
−0.9 −1.5 6.8+0.9
−0.8
8.5±0.7
6.5+2.2
−1.3
1"arcmin"="457"kpc
Figure 1.Chandra X-rayimageoftheclusterMS1054-0321inthe0.5-7.0keVenergybandsmoothedbyaGaussianofσ=3.44(cid:48)(cid:48) (26
kpc). The green circle and boxes show the regions in which the X-ray temperatures were extracted. Numerical values are the best-fit
temperaturesinunitsofkeVforgivenregions.TheEandWlettersdenotetheeasternandwesterncomponentsoftheclusterdiscussed
0 0.054 0.11 0.16 0.22 0.27 0.33 0.38 0.44 0.49 0.5
inthemaintext.
object_all.pi object_1.pi object_2.pi
0.1
V V 0.01 V 0.01
ec/ke 0.01 ec/ke ec/ke
nts/s0.001 nts/s0.001 nts/s0.001
u u u
o o o
C C C
0.0001 0.0001
0.0001
als 0.02 als 0.01 als 0.01
u u u
Resid−0.020 Resid−0.010 Resid−0.010
0.5 1 2 4 8 0.5 1 2 4 8 0.5 1 2 4 8
Energy (keV) Energy (keV) Energy (keV)
Figure2.BinnedX-rayspectraforMS1054-0321.Left:Thefullcluster.Centre:theeasterncomponent.Right:thewesterncomponent.
The solid line is the best fit thermal plasma model. It is clear that the emission line of iron is more evident in the wastern component
thantheeasterncomponent.Lowerpanels:theresidualsfromthebestfitmodel.
bright radio sources NGC7027 and 3C286, with flux densi- 3.4 The radio environment
ties of 5.64 and 2.51 Jy. By reprocessing the OCRA data
for the MS 1054-0321 cluster, we estimated the SZ effect Point source contamination is a major problem in low-
towardtheclustercentretobe−2.18±0.33mJywithstan- resolution observations of the SZ effect. For the two-beam
darddeviationofindividual1-minuterecordsσ=5.16mJy. receiver, OCRA-p, radio sources could lead to an overesti-
ThiscentralmeasuredSZfluxdensitycouldbeincreasedor mate of the SZ effect if they are located in the reference
decreasedbytheemissionofradiosources.Aninvestigation background regions of the observation. Radio sources lead
of radio point sources in the MS 1054-0321 field and their toanunderestimateoftheSZsignalwhentheyliealongthe
impact on the SZ effect measurement is presented below. lineofthesighttothecluster.Byknowingthefluxdensities
and locations of radio point sources near our pointing cen-
treatourobservingfrequency,wecancorrectforthemand
improve our estimate of the SZ effect of the cluster. Cur-
(cid:13)c 2016RAS,MNRAS000,1–12
6 M. S. Mirakhor and M. Birkinshaw
rently, a sensitive survey of the radio sky at 30 GHz does tions of the electron density, n , and electron temperature,
e
not exist, but the radio field of the cluster MS 1054-0321 T , of the intracluster plasma integrated along the line of
e
hasbeenobservedatmultiplebands.Henceweestimatethe sight
flux densities at 30 GHz of the radio sources in the field of (cid:90)
1
MS 1054-0321 by extrapolating from lower frequency mea- S = D n2Λ dθ , (1)
X 4π(1+z)4 A e ee z
surements. We use flux densities from the NRAO VLA Sky
Survey(NVSS)(1.4GHz,Condonetal.1998),andthe28.5 and
GHz flux densities for sources near the cluster centre re- (cid:90)
k σ
portedinCobleetal.(2007).Wealsousefluxdensitymea- ∆T =f(x)T B TD n T dθ . (2)
rm c2 A e e z
surements at 4.85 GHz by reprocessing archival VLA data. e
In all fields, only the radio sources within a radius of 4.5 D istheangulardiameterdistance,z(=0.83)isthecluster
A
arcminfromthecentreoftheclusterareconsidered,andwe redshift, Λ is the X-ray spectral emissivity of the cluster
ee
neglect possible radio source variability. plasma, f(x) describes the frequency dependence of the SZ
We find four significant radio point sources in the field effect and has value −1.91 at our observing frequency. T
r
oftheMS1054-0321cluster.Oneislocatedclosetotheclus- (= 2.725 K, Fixsen 2009) is the temperature of the cos-
tercentre,andanotherisfoundoutsidethereferencearcof mic microwave background radiation, k is the Boltzmann
B
the beam-switched observation. The two remaining sources constant, σ is the Thomson scattering cross section, m
T e
are found in the reference arc, and they could produce a is the electron mass, c is the speed of light, and the in-
negative signal that boosts the apparent SZ effect. All four tegration is taken over the line of sight expressed in an-
pointsourceshave1.4GHzfluxdensitymeasurements.Mea- gular terms, dθ . In order to take into account the cluster
z
surementsat28.5GHzareavailableonlyfortheinnerthree plasma distribution in both components of the MS 1054-
sources. 0321cluster,wedevelopanoffset-centredversionofathree-
The archival VLA data were taken at 4835 and 4885 dimensional double β-model. A centred double β-model is
MHz with 50 MHz bandwidth. We reduced the data us- often used to fit the X-ray surface brightness for clusters
ingtheAstronomicalImageProcessingSystem(AIPS).The that show centrally-enhanced density profiles. One compo-
source3C286=1331+305wasusedastheprimarycalibra- nent describes the cluster-centred density peak, while the
tor to calibrate the flux density, with flux densities of 7.51 second component is flatter and describes the outer part
and7.46Jy.Source1058+015wasthephasecalibrator,and of the cluster. Bonamente et al. (2006) and LaRoque et al.
was observed at around 30 minute intervals throughout the (2006) used a spherical double β-model to describe density
observation.Afterthenormalcalibrationandimagingsteps, profilesofcoolcoreclusters.Inthisworkweuseadoubleβ-
theposition,peakintensity,andtotalfluxdensityofthede- modeltofittheeasternandwesterncomponentsoftheMS
tected radio sources were estimated using the IMFIT task, 1054-0321 cluster which are centred at positions separated
after correction for the VLA primary beam. by ∼55(cid:48)(cid:48).
We estimated the flux densities of the radio sources at Our three dimensional double β-model of the electron
30 GHz by fitting a power law to the measurements and density is of the form
extrapolating to 30 GHz. The flux densities and positions
n =n +n
of the four radio sources within 4.5 arcmin of the pointing e e1 e2
centre of the MS 1054-0321 cluster are given in Table 2. =n (cid:16)1+ θx21 + θy21 + (θz−δ)2(cid:17)−3β1/2
ThesevaluesareessentiallythesameasthosegivenbyCoble e01 θ2 θ2 θ2
cx1 cy1 cz1
eint tahl.ei(r20li0st7.) at 28.5 GHz, except for source 4 which is not +ne02(cid:16)1+ θθ2x22 + θθ2y22 + θθ2z2 (cid:17)−3β2/2, (3)
cx2 cy2 cz2
and
3.5 Radio source corrections (cid:18) (cid:19) (cid:18) (cid:19)(cid:18) (cid:19)
θ cosα sinα Θ −Θ
xn = n n x x0n , (4)
WecorrectourcentralSZeffectmeasurementusingtheflux θ −sinα cosα Θ −Θ
yn n n y y0n
densities and positions of the point sources. The greatest
wherentakesvaluesof1and2,correspondingtotheeastern
contamination comes from source 3, which is observed in
the reference arc at parallactic angle ∼ 5◦. Source 1 is un- orwesterncomponent.ne01andne02arethecentralelectron
densitiesoftheeasternandwesterncomponents,β andβ
modulated by the changing parallactic angle during beam- 1 2
describetheshapesoftheplasmadistributionsoftheeastern
switching,whilesource4haslittleeffectsinceitliesfarfrom
and western components, (θ , θ , θ ) and (θ , θ ,
thesampledreferencearc.Thecorrectedvalueofthecentral cx1 cy1 cz1 cx2 cy2
θ ) are the angular core radii of the eastern and western
SZeffectfluxdensityofMS1054-0321is−2.55±0.33mJy, cz2
components. δ is the offset between the two components
indicating an effect about 1σ greater than our uncorrected
alongthelineofsight,α describestherotationangleofthe
value, and consistent with a massive hot atmosphere. n
xy-plane of each component relative to an observer frame,
(Θ ,Θ )areangularcoordinates,and(Θ ,Θ )arethe
x y x0n y0n
component centre coordinates.
4 MODELING This is not a general triaxial β-type model, but is ade-
quatetodescribetheX-rayandSunyaev-Zel’dovichsurface
4.1 Cluster atmosphere
brightnessesoftheMS1054-0321cluster.Undertheassump-
The X-ray surface brightness, S , and the Sunyaev- tionofanisothermalintraclustermedium,withtheelectron
X
Zel’dovicheffect,∆T,ofaclustercanbeexpressedasfunc- temperatureequaltothecentraltemperature(T =T ),
en e0n
(cid:13)c 2016RAS,MNRAS000,1–12
Gas distribution in MS 1054-0321 7
Table 2. The radio source fluxes within 4.5 arcmin from the pointing centre of the cluster MS
1054-0321.Fromlefttorightthecolumnsgivethesourceidentificationnumber,therightascension
anddeclinationoftheradiosource,thefluxdensityat1.4GHz(fromCondonetal.1998),theflux
densityat4.8GHzafterprimarybeamcorrection,thefluxdensityat28.5GHz(fromCobleetal.
2007),theexpectedfluxdensityat30GHz.
SourceID RA Dec S1.4 S4.85 S28.5 S30
(J2000) (J2000) (mJy) (mJy) (mJy) (mJy)
1 105659.59 -033727.7 14.10±0.90 7.28±0.10 0.94±0.06 0.87±0.06
2 105657.94 -033858.3 3.10±0.40 1.29±0.12 0.54±0.08 0.48±0.07
3 105648.85 -033728.8 18.20±1.00 4.41±0.20 1.79±0.19 1.75±0.19
4 105648.59 -034007.1 4.64±0.40 2.79±0.22 — 1.36±0.31
the X-ray spectral emissivity becomes a constant over each The total mass of the cluster, which is dominated by dark
component(Λ =Λ ).Fornon-overlappingatmospheres, matter, can be deduced from the cluster gas structure. Its
ee een
the angular structures of the X-ray surface brightness and distributionrelatestotheelectrondensityandtemperature
Sunyaev-Zel’dovicheffectprofileforeachcomponentcanbe profiles of the plasma. We assume that the cluster gas is in
expressed as hydrostatic equilibrium in the gravitational potential well
of the cluster with no significant flow of matter. With the
√ Γ(3β − 1)
S ∝ π n 2 θ further assumption of an isothermal plasma, the total mass
Xn Γ(3βn) czn in each cluster component
×(cid:16)1+ θx2n + θy2n (cid:17)(1/2)−3βn, (5) −k T (cid:90)(cid:90)(cid:90) (cid:16) ∂2 ∂2
θc2xn θc2yn Mtot(θxn,θyn,θz)= 4πGBµme0nDA ∂θ2 + ∂θ2
p xn yn
and
∂2 (cid:17)
∆T ∝√πΓ(32βn− 12)θ +∂θz2 lnnendθxndθyndθz, (10)
n Γ(3β ) czn
2 n where G is the Newtonian gravitational constant, and µ is
×(cid:16)1+ θx2n + θy2n (cid:17)(1/2)−(3/2)βn, (6) the mean mass per particle in unit of mp.
θ2 θ2
cxn cyn
respectively. Any overlap between the atmospheres of the
two components will produce a further X-ray emission con-
(cid:82)
tribution ∝ ne1ne2dθz. 4.3 Fit model to the X-ray image
Accordingly, if we can approximate the structure in
terms of two distinct components (i.e., if the clusters are The X-ray surface brightness image of the MS 1054-0321
separated significantly beyond the largest core radius), the cluster in the 0.5-7.0 keV energy band was fitted to our 3D
X-ray and SZ effect central densities for each cluster com- β-model.Inordertousetheχ2statisticonX-rayeventdata,
ponent can be obtained using were-binnedthedatasothateverybincontainsatleast20
counts. Below we summarise the data gridding and fitting
nX-ray =(cid:104)SX0n√4π(1+z)4 Γ(3βn) (cid:105)1/2, (7) processes, and their implications.
e0n Λeen πDAθczn Γ(3βn− 12) First we identified the location of each event in the 2D
surfacebrightnessimage.Wedividedthe2Dimagevertically
and
intosliceswithequalwidths,andthenwedividedeachslice
nSZ = ∆T0nme√c2 Γ(32βn) , (8) horizontallyintobinsinsuchawaythateverybincontains
e0n T f(x)k T σ πD θ Γ(3β − 1) atleast20counts.Thismeanthatbinshaveareaswithequal
r B e0n T A czn 2 n 2
widthbutdifferentheightbasedonthedensityofeventsina
respectively.IntheseequationsS and∆T arethecen-
X0n 0n givenlocationofthe2Dimage.Inadditiontocalculatingthe
tral X-ray surface brightness and SZ effect signal of each
numberofcountsineachbin,wealsocalculatedthelocation
cluster component.
of the count centroid and the bin area. As a result of the
binning process, the X-ray data roughly became normally
distributed,andthisallowsustoapplytheχ2 statisticand
4.2 Cluster gas and total masses deal with fewer data events, therefore making the fitting
process faster, without losing much detail of features of the
The total number of electrons in the cluster can be calcu-
X-ray surface brightness image.
latedbyintegratingtheelectrondensityprofileoveragiven
Typically, the X-ray surface brightness images contain
volume. The cluster gas mass can be obtained by multiply-
someregionswithfewcounts.FortheMS1054-0321cluster,
ing the total number of electrons by the mean mass per
we noticed some bins with very small values of the number
electron,µ m ,sothatthegasmassforeachcomponentof
e p of counts per unit area. In order to get a better fit to the
the cluster in some volume takes the form
X-ray data, we excluded bins with values smaller than 0.03
(cid:90)(cid:90)(cid:90) countspixel−1fromourdataanalysis.WechosetouseLmfit
M (θ ,θ ,θ )=µ m D3 n dθ dθ dθ . (9)
gas xn yn z e p A en xn yn z version0.7.4asanoptimizerandtheLevenberg-Marquardt
(cid:13)c 2016RAS,MNRAS000,1–12
8 M. S. Mirakhor and M. Birkinshaw
Table 3.Three-dimensionalsingleβ-modelfit. Table 4. Three-dimensional double β-model fit with
δ=0.
Parameter Fittedvaluea Unit
Parameter Fittedvaluea Unit
SX01 (6.01±0.06)×10−2 countss−1 arcmin−2
α1 6.76±0.07 degrees SX01 (6.22±0.17)×10−2 countss−1 arcmin−2
θcx1 0.90±0.08 arcmin Θx01 105659.64±0.08 hr,min,sec
θcz1=θcy1 1.09±0.05 arcmin Θy01 -033736.75±0.56 deg,arcmin,arcsec
β1 1.26±0.09 — α1 12.62±0.39 degrees
Cb (6.22±0.08)×10−3 countss−1 arcmin−2 θcx1 1.41±0.19 arcmin
θcz1=θcy1 1.51±0.21 arcmin
β1 2.13±0.43 —
a Best-fitvalueswith68%errorbounds. ΘSXx0022 (1100.8556±550..8928)±×01.00−82 counthsr,s−m1ina,rscemcin−2
b ThelocalX-raybackground. Θy02 -033739.72±0.70 deg,arcmin,arcsec
α2 40.03±2.89 degrees
algorithmastheoptimizationmethodinPython.1 Wemea- θcx2 0.23±0.05 arcmin
sure the goodness of the fit using the χ2 statistic, in this θcz2=θcy2 0.38±0.08 arcmin
β2 1.10±0.24 —
case given as Cb (6.24±0.07)×10−3 countss−1 arcmin−2
(cid:88)(cid:16)D −M (cid:17)2
χ2 = i i , (11)
(cid:15)
i
i a Best-fitvalueswith68%errorbounds.
where Di is the number of counts detected per unit area in b ThelocalX-raybackground.
bin i, M is the number of counts predicted by the model
i
per unit area in bin i, and (cid:15) is Poisson error on D .
i i component is less than 6(cid:48)(cid:48) away from the position of the
We first fit a single β-model plus a background com-
brightestgalaxyinthecluster,andthecentreofthewestern
ponent to the eastern component of the cluster, i.e. exclud-
component is consistent with the position of the brightest
ing the X-ray data of the western component and setting
pixel in the X-ray image. The best fit value of the shape
n = 0 in equation (3). Because the X-ray data cannot
e02 parameterobtainedfromthisfitisparticularlyhighforthe
constrain all the parameters in the 3D model, we took the
eastern component, β =2.1±0.4 and a value of β <1 is
core radius along the line of sight, θ , to equal θ or 1 1
cz1 cx1 excludedathighsignificance(∆χ2 >39).Thischaracteristic
θ . The centre of the eastern component was fixed to the
cy1 haspreviouslybeenreported(seeNeumann&Arnaud2000;
position of the brightest cluster galaxy, whereas the other
Jeltema et al. 2001; Jee et al. 2005, for example). Fig. 3
parameters were left free to vary. Values of the best fit pa-
shows the confidence intervals for key shape parameters of
rameters for the single β-model are shown in Table 3. We
the eastern and western components. This figure shows the
present only the results with the assumption of θ =θ
cz1 cy1 usualstrongcorrelationbetweenβ andθ .Fig.4illustrates
since it provided slightly the better fit. The value of the re- c
theX-raysurfacebrightnessoftheclusterMS1054-0321,the
duced χ2 associated with this fit is 1.40 with 1041 degrees
best double β-model fit to the X-ray data, and the residual
offreedom.Hencethisfitcanberejectedatthe99.9%con-
image from the best fit.
fidence level.
A better fit for the X-ray surface brightness image of
MS1054-0321isprovidedbythe3Ddoubleβ-model.Here,
5 RESULTS AND DISCUSSION
the X-ray data were fitted to the model with δ set to three
differentvalues:0,1,and3Mpc.Thecomponentcentresand 5.1 Central electron density
other parameters in equation (3) were left free to vary. The
fit qualities are nearly equivalent in all cases, but a slightly For our single β-model fit, the estimated central densi-
better fit is obtained with δ=0. For both components, the ties of the eastern component are 4.96+−00..0191 × 10−3cm−3
optimisedvaluesobtainedforthecentralsurfacebrightness and 5.06+−00..0096 × 10−3cm−3 from the X-ray and SZ effect
from all fits differ by less than 3%. The shape parameters data, respectively. For the double β-model with zero off-
(β,θ )oftheeasternandwesterncomponentsatδ=1Mpc set between the two components along the line of sight,
c
differ from those obtained at δ = 3Mpc, and from those the corresponding values are 5.00+−00..0013 × 10−3cm−3 and
obtained at our adopted offset δ=0, but the differences do 5.35+−00..0115 × 10−3cm−3. The estimated X-ray central den-
not exceed the errors. sity of the western component is 10.38+−00..3092 ×10−3cm−3.
Thebestfitparametersandsingleparameter68%errors SZ effect data are not available for the western component.
forthedoubleβ-modelincaseofδ=0aregiveninTable4. Fortheeasternandwesterncomponents,thederivedcentral
Asbefore,wepresentonlytheresultswiththeassumptions densities from the X-ray and SZ effect data at the 1 and 3
of θ = θ and θ = θ . We found the reduced χ2 Mpcoffsetsdifferbylessthanabout3%fromthosederived
cz1 cy1 cz2 cy2
associatedwiththisfitis1.06with1423degreesoffreedom. at δ=0.
Clearly, the X-ray data are better described by this model As clearly indicated by these results, the X-ray central
thanthesingleβ-model.Theestimatedcentreoftheeastern densitiesobtainedfortheeasterncomponentusingthesingle
and double β-models are consistent with each other, and
with the central density values derived from the SZ effect
1 Seehttp://lmfit.github.io/lmfit-py. data. They are also in good agreement with those found
(cid:13)c 2016RAS,MNRAS000,1–12
Gas distribution in MS 1054-0321 9
Figure 3. Confidence interval contours for the double β-model fit to the X-ray data of the MS 1054-0321 cluster, superposed with
contoursofthevaluesofthegasmassfractionsfromtheX-rayandSZeffectdata.Thebestfitoftheparametersaremarkedascrosses,
while the blue and red solid contours correspond, respectively, the 68% and 90% confidence intervals. The dashed and dotted contours
define, respectively, the gas mass fractions derived from the X-ray and SZ effect data.Upper and lower panels represent the confidence
levelcontoursoftheshapeparametersfortheeasternandwesterncomponents,respectively.
0 0.1 0.2 0.3 0.4 0.5 .050.10.150.20.250.30.350.40.450.5 -0.1 -0.05 0 0.05 0.1
Figure 4.Left:Chandra X-rayimageoftheclusterMS1054-0321inthe0.5-7.0keVband.Centre:thesourcemodel,madeupoftwo
elliptical β models. Right: the residual image from the best-fit model. The colour scales at the bottom of each image are in units of
countspixel−1,whereapixelhasside0.492(cid:48)(cid:48).
(cid:13)c 2016RAS,MNRAS000,1–12
10 M. S. Mirakhor and M. Birkinshaw
from a nonisothermal centred double β-model (LaRoque et ∼60%largerthanthemassof3.15+0.98×1014h−1 M given
−0.70 100 (cid:12)
al. 2006). The central density of the western component is by Bonamente et al. (2008). The estimated total masses
more than twice that of the eastern component. fallto4.48+0.54×1014h−1 M and6.12+0.73×1014h−1 M
−0.34 100 (cid:12) −0.80 100 (cid:12)
from the single and double β-models if we adopt the lower
temperatureof8.5±0.7keV measuredforthetotalcluster.
5.2 Gas mass fraction
The former value is more consistent with that reported by
Thegasmassfraction,f ,canbecomputedbydividingthe Bonamente et al. (2008) than the total mass derived from
gas
gasmassbythetotalmassofthecluster.Todeterminethe the double β-model. The high total mass that we derived
clustermassesasdiscussedinsection4.2,weneedtodefine from the double β-model, relative to that derived from the
a limiting radius within which the masses are measured. singleβ-model,mightsuggestthatthetotalmassisoveres-
DuetosignificantAGNactivityinMS1054-0321relativeto timatedasaresultofoverlapsbetweenthetwocomponents.
lower redshift clusters, particularly at distances between 1 The gas mass fractions obtained within 89(cid:48)(cid:48) for the eastern
and2Mpc(Bestetal.2002;Johnson,Best&Almaini2003), component are fgXa-sray =0.102+−00..000191 and fgSaZs =0.127+−00..001103
wecarriedoutourmeasurementswithintherelativelysmall from the single β-model analysis, and fX-ray = 0.074+0.015
gas −0.006
angular radius θ2500, corresponding to a density 2500 times and fgSaZs = 0.096+−00..001077 from the double β-model analysis.
the critical density of the Universe at the redshift of the Theaveragevalueofthesegasmassfractionsis0.100+0.013,
−0.009
cluster. The θ2500 radius of each cluster component can be about 40% lower than the gas mass fraction estimated by
obtained from Bonamente et al. (2008).
M (θ )=D3θ3 ∆ρ (z), (12) For the eastern component, the estimated X-ray and
tot 2500 A 2500 c
SZ gas mass fractions within θ using the 1 Mpc offset
2500
where the left-hand side is the total mass within angular parameters are consistent with those estimated using the
radius (θ2500) given by equation (10), ρc(z) is the critical 3 Mpc offset parameters, and only about 5% higher than
density of the Universe, and ∆=2500. those derived at δ = 0. These results imply an systematic
In Table 5, we show the gas and total masses, and the errorof∼0.002intheX-rayandSZgasmassfractionsdue
gas mass fractions, of the eastern and western components touncertaintyinthevalueofδ.TheX-raygasmassfractions
using the best fit parameters from our models with δ = 0. for the western component derived within θ for 1 and 3
2500
The 68% confidence interval errors associated with these Mpcoffsetsagree,butareabout10%higherthanthevalue
are given for variations of the fitting parameters. For both for δ = 0, suggesting an systematic error of ∼ 0.001 in the
models, the gas mass fractions derived from the X-ray and gasmassfraction.Theseresultsindicatethattheoffsetissue
SZ effect data for the eastern component are consistent. It isnotresponsibleforthelowgasmassfractionintheeastern
canbeseenfromthedoubleβ-modelanalysisthattheX-ray and western components.
gas mass fraction of the western component within θ is
2500 The gas mass fraction of the eastern and western com-
about one third of that derived for the eastern component.
ponentstogether,withinangularradiusθ ,is0.060+0.004.
Although the values ofthe shapeparameters extracted 2500 −0.009
Thisfractionissmall,andabouttwothirdsofthegasmass
from the models are significantly different, we find that the
fractiondeducedfromtheeasterncomponent.However,the
gas and total masses, and thus the gas mass fraction, for
value is in agreement with that reported by Grego et al.
the eastern component obtained from the single β-model
(2001)withinθ ,and∼40%lowerthantheX-rayandSZ
are consistent with those derived from the double β-model 500
effect gas mass fractions measured from the nonisothermal
over the same angular radius. The X-ray and SZ effect gas
double β-model (LaRoque et al. 2006).
massfractionsfrombothmodelsareingoodagreementwith
To examine the effect of the isothermal assumption
those derived from a nonisothermal double β-model within
on the gas mass fraction measurements, we estimated the
θ (LaRoque et al. 2006), and ∼ 70% higher than that
2500
gas and total masses for both cluster components in the
derivedbyGregoetal.(2001)withinalargerangularradius.
presence of the maximum temperature gradient (Section
However,ourgasmassfractionsare∼40%lowerthanthose
3.2). For the eastern component, the estimated X-ray and
derived from an isothermal β-model fit that excluded the
SZ gas masses are higher by about 3% and 20% than
central region from the X-ray data (LaRoque et al. 2006).
those derived under the isothermal assumption, respec-
To compare our results with those derived by Bona-
tively. The total mass could be as much as 50% lower
mente et al. (2008), we estimate the gas and total masses
withintheirangularradiusθ=89(cid:48)(cid:48).Withinthisradius,the than that derived from the isothermal assumption. The
upper limits on the gas mass fractions are ∼ 0.140 from
derivedX-rayandSZeffectgasmassesfortheeasterncom-
the X-ray data, and ∼ 0.180 from the SZ effect data.
ponent from the single β-model analysis are, respectively,
4.40+0.02×1013h−1 M and4.51+0.06×1013h−1 M .From The estimated X-ray and SZ gas mass fractions there-
the −d0o.u01ble β-mo1d0e0l fi(cid:12)t, these ga−s0.m01asses are1004.36(cid:12)+0.20 × fore are fgXa-sray = 0.087+−00..000051(random)+−00..005031(systematic)
1013h−1010M(cid:12) and 4.67+−00..1068 × 1013h−1010M(cid:12). These−v0.a0l4ues andfgSaZs =0.094+−00..000031(random)+−00..008061(systematic).Forthe
are consistent with each other and with the gas mass of western component, the X-ray gas mass fraction is affected
5.18+0.84×1013h−1 M derivedbyBonamenteetal.(2008) by less than 10% by the isothermal assumption. Thus the
−0.70 100 (cid:12)
withinthesameangularradiusfromanisothermalβ-model gas mass fraction in the eastern component could approach
fittotheX-raydata(excludingthecentralregion)andtoSZ the cosmic value, while the western component is gas-poor.
effectdata.Usingthetemperatureoftheeasterncomponent, Anycontributionfromthenon-thermalpressurewouldtend
10.7+1.9keV,ourestimatesofthetotalmassinside89(cid:48)(cid:48)from to reinforce our conclusion of low gas mass fraction.
−1.5
thesingleanddoubleβ-modelsare5.64+0.68×1014h−1 M Such a low gas mass fraction could suggest that the
−0.43 100 (cid:12)
and 7.70+0.91×1014h−1 M , respectively. Such masses are gas content of the cluster, particularly the western compo-
−1.00 100 (cid:12)
(cid:13)c 2016RAS,MNRAS000,1–12