Tracing the Gas to the Virial Radius (R100) in a Fossil Group

1.7 MB·English

by  Philip J. Humphrey

Accepted for publicationin The Astrophysical Journal
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
TRACING THE GAS TO THE VIRIAL RADIUS (R ) IN A FOSSIL GROUP
100
Philip J. Humphrey1, David A. Buote1, Fabrizio Brighenti2,3, H´el`ene M. L. G. Flohic1,4, Fabio Gastaldello1,5,
William G. Mathews3
Accepted for publication inThe Astrophysical Journal
ABSTRACT
We present a Chandra, Suzaku and Rosat study of the hot Intra Group Medium (IGrM) of the
2
relaxedfossil group/poor cluster RXJ1159+5531. This groupexhibits anadvantageouscombination
1
offlatsurfacebrightnessprofile,highluminosityandoptimaldistance,allowingthegastobedetected
0
outtothe virialradius(R ≡R =1100kpc)inasingleSuzakupointing,while thecomplementary
2 vir 108
ChandradatarevealaroundmorphologyandrelaxedIGrMimagedownto kpcscales. Wemeasurethe
n IGrM entropy profile over ∼3 orders of magnitude in radius, including 3 data bins beyond ∼0.5R
200
a
that have good azimuthal coverage (>30%). We find no evidence that the profile flattens at large
J
scales (>R500), and when corrected for the enclosed gas fraction, the entropy profile is very close to
2 the predictions from self-similar structure formation simulations, as seen in massive clusters. Within
1 R , we measure a baryon fraction of 0.17±0.02, consistent with the Cosmological value. These
vir

results are in sharp contrast to the gas behaviour at large scales recently reported in the Virgo and
]
O Perseus clusters, and indicate that substantial gas clumping cannot be ubiquitous near Rvir, at least
in highly evolved (fossil) groups.
C
Subjectheadings: Cosmology: darkmatter—Xrays: galaxies: clusters—Galaxies: groups: individual:
.
h RXJ1159+5531—Galaxies: ISM
p
-
o 1. INTRODUCTION an entropy profile that rises with radius, r, such that
r S ∝ T r1.1, where T is a characteristic temperature
t Galaxy groups (defined here as bound systems with 0 0
s (Tozzi & Norman 2001; Voit et al. 2005; Kaiser 1986).
a virial masses, Mvir, in the range ∼ 1013–1014M⊙) are Observationsofgalaxyclusters in factreveallower-mass
[ essential ingredients in the assembly of structure within
the Universe. Locally ∼30% of galaxies are found in objects to be systematically offset upwards from this re-
3 groups that are less massive than 1014M (Eke et al. lation, but approaching it by ∼R500 (e.g. Ponman et al.
v ⊙ 2003;Pratt et al. 2010). This indicates nongravitational
2004). Systems of this mass range have been implicated
2 energy injection, likely a consequence of preheating of
as key sites in both efficient star formation (Springel &
2 thegasinfilamentspriortoaccretion,orfeedbackdueto
Hernquist 2003), and the morphological transformation
3 star formation or a central AGN (Voit & Ponman 2003;
of galaxies (Zabludoff & Mulchaey 1998). Typically the
3 Voit & Donahue 2005; Ponman et al. 2003). The fine
dominant baryoniccomponent is, however,an extended,
. balance between these different processes should affect
106 hMo5t00g∼>as5h×al1o0,1t3hMat⊙c(aGniocodnintaiient∼>al7.02%00o9f)6t.heSubcahryaonmsaast- bprootfihlet,hemsahkainpgeiatnadpnootremntailaizllaytipoonwoefrftuhledeiangtrnoopsyticpr(oe.xgy.
sive hot gas halo can make them both luminous X-ray
1 Borgani et al. 2005; McCarthy et al. 2010), especially
sources, and, potentially, targets for detection in large
: at the group scale, where these effects should be com-
v numbers by future Sunyaev-Zeldovich surveys (Haiman
paratively more important. Recent Chandra and XMM
i et al. 2001).
X observationsofrelaxedgroupshaverevealedcomplexen-
r ingX-ermayissoibosnerfvroamtionthsephroovtidgeasthine bgreostupms.eaOnsf fpoarrtsitcuudlayr- tropy profiles that flatten at large(∼>0.1R500) and small
a scales,albeitwithsomescatter(Gastaldelloetal.2007a;
interest is the entropy proxy, S = ne−2/3kT (where ne is Mahdavi et al. 2005; Finoguenov et al. 2007; Humphrey
the electron number density, k is Boltzmann’s constant etal. 2008;Sun etal. 2009;Cavagnoloet al.2009;John-
and T is the temperature), which is related to the spe- son et al. 2009; Flohic et al. 2011), possibly indicating
cific entropy through a logarithm and constant offset. If that both star formation and AGN feedback are impor-
purelygravitationalprocessesshapetheenergeticsofthe tant (Voit & Donahue 2005;McCarthy et al. 2010).
gas, self-similar structure formation simulations predict Feedback also shapes the enclosed gas fraction (f )
gas
profiles of groups and clusters, which are found to rise
1Department of Physics and Astronomy, University of Cali- withradius(Allenetal.2002;Vikhlininetal.2006;G07;
forniaatIrvine,4129FrederickReinesHall,Irvine,CA92697
2Dipartimento di Astronomia, Universit`a di Bologna, via Sun et al. 2009), but with groups containing a system-
Ranzani 1,Bologna40127,Italy atically smaller fraction of their gas at small scales (e.g.
3University of California Observatories/Lick Observatory, Fig 11 of Humphrey et al. 2011, hereafter H11). As-
UniversityofCalifornia,SantaCruz,CA95064,USA suming they can be converted into a reliable estimate
4DepartamentodeAstronom´ıa,UniversidaddeChile,Casilla
for the total (initial) baryon fraction in the cluster (f ),
36DSantiago, Chile b
5INAF,IASF,viaBassini15,20133Milano,Italy fgas measurementsareapowerfulcosmologicaltool,used
6 We define M∆ as the mass within R∆, i.e. the geometrical either directly (White et al. 1993; Allen et al. 2002), or
radius within which the mean mass density of the system is ∆ in employing the gas mass as a virial mass proxy (e.g.
timesthecriticaldensityoftheUniverse.
2
Voevodkin & Vikhlinin 2004). Massive clusters are pre- aticerrorsintheGeorgeetal. backgroundtreatment. In
ferredin this analysis since f measuredat these scales the outermost bins, the deprojection procedure adopted
gas
should be closer to f than in poor clusters or groups. by Urban et al. (2011) and Simionescu et al. (2011) de-
b
Still,systemswithmassesaslowas∼2×1014M (Allen pends sensitively on the correct modelling of projected
⊙
etal.2008),orevenlower(Voevodkin&Vikhlinin2004) emission from regions outside the field of view. Further-
are routinely used. Translating into f the f values more, while Simionescu et al. attempted to mitigate the
b gas
measured at scales far smaller than the virial radius, scattered light contamination from the cluster core, it is
R (typicallyat∼R ), involvesanumberofassump- unclearhowsensitivetheirresultsweretothiscorrection.
vir 2500
tions that have yet to be robustly verified, especially in Similarly,theXMM-NewtonprofilesofUrbanetal. were
lower mass halos (e.g. Arnaud 2005). Intriguingly, for sensitive to the treatment of the background.
most of the group-scale objects studied by Gastaldello In this paper, we present a joint Chandra and Suzaku
et al. (2007b, hereafter G07), extrapolating f outside study (carefully cross-checked with the archival Rosat
gas
the field of view yielded global f constraints consistent data) of the very relaxed galaxy group RXJ1159+5531,
b
with the Universal baryon fraction (0.17: Dunkley et al. allowing, for the first time in a system with a mass as
2009;Komatsuet al.2011),in accordwith the idea that low as ∼ 1014M , the gas to be traced to scales as
⊙
X-ray bright groups are baryonically closed (Mathews large as the virial radius, R . A single, giant ellipti-
108
et al. 2005). Nevertheless, this extrapolation was sub- calgalaxydominatesthe stellarlight,makingitaproto-
ject to significant systematic uncertainty. typical “fossil group” (Vikhlinin et al. 1999) and imply-
To date, most observations of the gas in groups and ing a highly evolved(i.e. relaxed) dynamical state (Pon-
clusters have been restricted to within ∼R , and typ- man et al. 1994). The optimal combination of distance
500
ically much smaller scales are attained. For example, (z = 0.081), mass (R = 12′) and high surface bright-
vir
R was only reached for 11 of the 43 systems studied ness (such that gas is already detected to ∼R with
500 500
in the currentlargestgroupsample (Sun et al.2009). In Chandra: Vikhlinin et al. 2006; G07; Sun et al. 2009),
groupsatthesescales,f isstillonly∼0.07,incontrast make it possible to measure the gas to R in a single,
gas vir
to ∼0.11 for clusters. Given the low, stable background modest (85 ks) Suzaku pointing.
fortheSuzakuXISinstrument,recentworkhasbegunto The group was observed with the X-ray centroid
pushmeasurementsofthe ICMinclustersoutto∼R , slightlyoffset(by5′)fromtheSuzakuopticalaxis,toen-
200
or beyond, but a coherent picture has not yet emerged. able coverageout to ∼12′, while minimizing the compli-
While some studies have found consistency with model cationsofstray-lightfromhavingtheX-raypeakoutside
predictions (Reiprich et al. 2009; Hoshino et al. 2010), thefieldofview. Althoughthisconfigurationlimitedthe
deviations from hydrostatic equilibrium (Bautz et al. number of radial bins we can study, by combining the
2009), temperature asymmetries associated with large- Chandra and Suzaku data, we were able to achieve ∼3
scale structure (Kawaharada et al. 2010) and, in three spatial bins outside ∼ 0.5R200, with ∼>30% azimuthal
systems, an unexpected flattening of the entropy proxy coverage,in comparison with ∼6 bins, and ∼15% cover-
profileoutside∼R (PKS0745-191: Georgeetal.2009; age in the ∼3 times longer Suzaku exposure of Perseus
500
Perseus: Simionescu et al. 2011; Virgo: Urban et al. (Simionescuetal.2011). Inconjunctionwiththearchival
2011), have been seen. Simionescu et al. and Urban Chandradata,wewereabletomeasurethegasproperties
et al. (see also Nagai & Lau 2011) attributed the en- over almost three orders of magnitude in radius.
tropy flattening, and associated over-estimate of f , to Previous studies of RXJ1159+5531, based on the
gas
putative clumpiness of the ICM in the outskirts of the Chandra data (Vikhlinin et al. 2006; G07; Sun et al.
cluster, leading to a systematically biased gas density 2009),havereportedconflictingparameterizationsofthe
measurement. gravitatingmass profile. Adopting the popularNavarro-
Given the lack of a consistent story in the outskirts Frenk-White (NFW: Navarro et al. 1997) profile (plus,
of clusters, the ubiquity of a clumpy ICM remains to in the case of G07, a baryonic component), M in-
500
be determined. The azimuthal temperature variations ferred from these studies has varied significantly from
in Perseus (Simionescu et al. 2011) and the large-scale ∼ 6×1013–1014M , and the corresponding NFW con-
⊙
asymmetries in the X-ray image of Virgo (Bo¨hringer centration parameter from ∼1.7–5.6, which remains a
et al. 1994) indicate that these systems are not relaxed puzzle (see § 4.2). The addition of new data at large
at large scales, consistent with ongoing formation. This scales should help pin down the mass profile more pre-
could give rise to deviations from sphericity (complicat- cisely, particularly if the scale radius were as high as
ing the deprojection) or local hydrostatic equilibrium found by Vikhlinin et al. (400 kpc). In this paper, we
(hence an underestimate of the gravitating mass, and employedthe “forward-fitting”mass analysis techniques
an over-estimate of f ), and local distortions in the en- outlinedinH11,whichenable finer controlofsystematic
gas
tropy profile. On account of the proximity of these clus- uncertainties than more traditional methods (Buote &
ters, only a small fraction of the outer annuli were im- Humphrey 2011a).
aged in these studies, so it is unclear whether such large We assumed a flat cosmology with H = 70km s−1
0
effects would be seen in azimuthally averaged profiles. and Ω = 0.7. We adopted R as the virial radius
Λ 108
An additional concern is the need to minimize sources (R ), based on the approximation of Bryan & Norman
vir
of systematic uncertainty in this background-dominated (1998)for the redshift of RXJ1159+5531. Unless other-
regime(e.g.,Reiprichetal.2009,Bautzetal.2009,H11). wisestated,allerror-barsrepresent1-σ confidencelimits
Eckert et al. (2011) demonstrated that the Rosat PSPC (which, for our Bayesian analysis, implies the marginal-
surface brightness profile of PKS0745-191 disagrees at ized region of parameter space within which the inte-
7.7-σ with the Suzaku density profile inferred by George grated probability is 68%).
etal.(2009). Theyattributedthediscrepancytosystem-
3
2. DATAREDUCTIONANDANALYSIS resulting annuli had widths larger than ∼3′′, which is
2.1. Chandra sufficient to prevent spectral mixing between adjacent
annuli on account of the finite spatial resolution of the
The region of sky containing RXJ1159+5531 was im- mirrors. Data in the vicinity of point sources and chip
aged by the ACIS instrument aboard Chandra on two gaps were excluded. We extracted spectra from all the
separateoccasions. We considerhere only the deep data activechips(excludingS4,whichsuffersfromnoise). Ap-
takenintheACIS-Sconfiguration(ObservationID4964; propriatecount-weightedspectralresponsematriceswere
beginning onFeb 112004). A shallowerACIS-I observa- generatedforeachannuluswiththestandardCIAOtools
tion was also available, but to simplify the analysis (in mkwarfandmkacisrmf. Representativespectra,without
particular, the background modelling), we chose not to backgroundsubtraction, are shown in Fig 2.
include it in our study. The data-reduction was carried Spectral-fitting was carried out in the energy band
out as described in H11, using the CIAO4.1 and Hea- 0.5–7.0 keV, using Xspec vers. 12.5.1n, by minimizing
soft6.8 software suites, in conjunction with the Chandra the C-statistic to mitigate biases that arise (even in the
calibration database (Caldb) version 4.1.2. Briefly, the high-count regime) when using the standard χ2 approx-
datawerereprocessedfromthe “level1”eventsfiles,fol-
imations for Poisson-distributed data (Humphrey et al.
lowing the standard data reduction threads7. Periods of
2009b). To aid convergence, we rebinned the spectra
high backgroundwere identified by eye in the lightcurve
to ensure at least 20 photons per bin. The data in all
from a low surface-brightness region of the CCDs and
annuli were fitted simultaneously, to enable the source
data from these intervals were excised, leaving a total
andbackgroundcomponentsto be modelled atthe same
exposureof75ks. Pointsourcesweredetectedinthe0.3–
time. InkeepingwithH11andGastaldelloetal.(2007b),
7.0keVimagewiththewavdetectCIAOtask,whichwas
we modelled the projected (rather than the deprojected)
supplied a 1.7 keV exposure map to minimize spurious
source emission in each annulus as coming from a single
detections at chip boundaries. The detection threshold
APECplasmamodelwithvariableabundances,modified
(10−6) guaranteed∼<1 spurious source per CCD. All de- by foreground Galactic absorption (Dickey & Lockman
tected sources were confirmed visually, and appropriate
1990)9. We allowedthe total abundance of Fe (Z ) and
ellipticalregionscontaining∼99%ofthesourcephotons Fe
the abundance ratios with respect to Fe of the elements
were generated.
O, Ne, Mg, Si and Ni to vary in each annulus. The
InFig1,weshowasmoothed,flat-fieldedChandraim-
abundance of He, and the abundance ratios of the other
age,havingremovedthepointsourceswiththealgorithm
elements were fixed to 1 Solar (Asplund et al. 2004). To
outlined in Fang et al. (2009). The image was smoothed
improve S/N, we tied Z between the outermost two
with a Gaussian kernel, the width of which varied with Fe
annuli, and constrained the abundance ratios to be the
distance from the nominal X-ray centroid according to
same in all annuli.
an arbitrary powerlaw, ranging from ∼1′′ at the centre
To account for emission from undetected LMXBs in
of the image to ∼1′ at its edge. The image is smooth
the central galaxy, we included an additional 7.3 keV
and very round, consistent with the relaxed morphology
bremsstrahlung component. Since the number of X-ray
expected for a fossil system. To search for more subtle
pointsourcesisapproximatelyproportionaltothestellar
structure, we used dedicated software to fit an elliptical
light(e.g.Humphrey&Buote2008),therelativenormal-
beta model (with constant ellipticity) to the central 2′-
izationofthiscomponentbetweeneachannuluswasfixed
wide portionofthe unsmoothed(flat-fielded) image8. In
to match the relative K-band luminosity in the match-
Fig1,weplot(data−model)2/model,corresponding(ap- ing regions,which we measured from the 2MASS image.
proximately) to the χ2 residuals from this fit. To bring This component is only important in the very central
out the structure, we smoothed this image with a Gaus- region (∼<20 kpc) of the system.
sian kernel of width 3 pixels. There is weak evidence of To accommodate the background, we included ad-
a small(∼4′′), coherentstructure in the residualswithin ditional spectral components in our fits. Specifi-
the central (∼10 kpc) region, which may imply a small cally, we included two (unabsorbed) APEC components
depressionin the surface brightness (by ∼20–30%). The (kT=0.07 keV and 0.2 keV) and an (absorbed) power-
formal significance of this feature depends sensitively on law component (Γ = 1.41; De Luca & Molendi 2004).
prior information (in particular, the region of the im- The normalizationofeachcomponentwithin eachannu-
age over which one searches for structures; e.g. Kaastra lus was assumed to scale with the extraction area, but
et al. 2006). Still, even if the feature is real, it should the total normalizations were fitted freely. We discuss
not give rise to a significant error in the recovered, az- the possible impact of an additional, “Solarwind charge
imuthallyaveragedmassprofile(seeBuote&Humphrey exchange”backgroundcomponentin§6.2.1. Toaccount
2011a; Churazov et al. 2008). Aside from this modest for the instrumental background, we included a number
feature, the overalllack of significant, coherentresiduals of Gaussian lines and a broken powerlaw model, which
indicates that the X-ray image is very relaxed. were not folded through the ARF. We included sepa-
Spectra were extracted in a series of contiguous, con- rate instrumental components for the front- and back-
centricannulicentredatthe X-raycentroid. The widths illuminated chips, and assumed that the normalization
of the annuli were chosen to contain approximately the ofeachcomponentscaledwiththe areaofthe extraction
samenumberofbackground-subtractedcounts,whileen- annulus which overlapped the appropriate chips. The
suringsufficientphotonsforusefulspectralanalysis. The normalization of each component, and the shape of the
instrumental components, were allowed to fit freely. We
7 http://cxc.harvard.edu/ciao/threads/index.html
8Weobtainedabest-fittingmajoraxiscoreradiusof2′′,β=0.51
andaxisratioof0.9. 9 Wediscusstheresultsfromadeprojectedanalysisin§6.4.
4
Residuals
45:00.0
55:40:00.0 200kpc
Declination 35:00.0
30:00.0
30.0 XIS 0
25:00.0
34:00.0
01:00.0 30.0 12:00:00.0 30.0 11:59:00.0 58:30.0
Right ascension
30.0
33:00.0
30.0
Declination 32:00.0
30.0
31:00.0
50kpc
30.0
Chandra
55:30:00.0
10.0 05.0 12:00:00.0 55.0 50.0 45.0 11:59:40.0 35.0
Right ascension
Fig.1.—SuzakuXIS0(topright)andChandra(bottom left)imagesofRXJ1159+5531. TheapparentasymmetriesintheXIS0image
are due to the asymmetric point spread function of the telescope, rather than the intrinsicshape of the source. The Chandra image has
beencleanedofpointsourcesandmildlysmoothed. Thesmoothingscalevariedfrom∼1′′ atthesmallestscales,to∼1.1′ (100kpc)atthe
outerpartoftheimage(seetext). Atthetopleft,weshowa“residualsignificance”image(seetext)ofthecentreofthegroup,indicating
deviations froma smooth model fit to the (Chandra) X-rayisophotes. There isno obvious large-scalefeature inthis map, indicating the
systemislargelyrelaxed.
included two Gaussian lines (at 1.77 and ∼2.2 keV), the densitytobeconstrained(thisissimilartotheoutermost
intrinsic widths of which were fixed to zero. The ener- annuli of NGC5044, studied by Buote et al. 2004).
gies of the ∼2.2 keV lines were allowed to fit freely, as
were as the normalizations of all the components. To 2.2. Suzaku
verify the fit had not become trapped in a local min- The region of sky containing RXJ1159+5531 was im-
imum, we explored the local parameter space by step- agedbySuzakubeginningonFeb52009(observationID
ping individual parameters over a range centred around 804051010),withthreeoftheXISunitsoperating. Data-
thebest-fittingvalue(analogoustocomputingerror-bars reduction was performed using the Heasoft 6.8 software
withthealgorithmofCash1976). Thecovariancematrix suite, in conjunction with the XIS calibration database
(whichcontainstheerrorbars)wascomputedviatheeffi- (Caldb) version 20090925. To ensure up-to-date cali-
cientMonteCarlotechniqueoutlinedinHumphreyetal. bration, the unscreened data were re-pipelined with the
(2006), and we carried out 250 error simulations. aepipeline task and analysed following the standard
The best-fitting models are shown in Fig 2 for a rep- data-reduction guidelines10. Since the data for each in-
resentative selection of spectra. While the instrumen- strumentweredividedintodifferentlytelemeteredevents
tal background is clearly significant at high energies fileformats,weconvertedthe“5×5”formatteddatainto
(∼>2keV),onlyintheoutermostannulusdoesthesource “3×3”format,andmergedthemwiththe“3×3”events
signal fall below the background level. Nevertheless, files. The lightcurve of each instrument was examined
given the optimal temperature of the gas (≃1 keV), the for periods of anomalously high background, but no sig-
Fe L-shell peak is still visible as a small “bump” in the
spectrumat∼0.9keV,enablingthegastemperatureand 10 http://heasarc.gsfc.nasa.gov/docs/suzaku/analysis/abc/
5
Chandra 0−5 kpc XIS1 180−460 kpc
1
0.
1
Count s keV−1−1 100.01−3 Counts s keV−1−1 00.0−3
1
0.5 1 2 5 0.5 1 2 5
Energy (keV) Energy (keV)
Chandra 57−94 kpc XIS1 460−825 kpc
1
0
0.
keV−1 0.01 keV−1
Count s −1 Counts s −1 0−3
1
0−3
1
0.5 1 2 5 0.5 1 2 5
Energy (keV) Energy (keV)
5 Chandra 415−670 kpc XIS1 825−1200 kpc
0
0.
1
02 0.0
0.
Count s keV−1−1 0.01×10−3 Counts s keV−1−1 10−3
5
0−3
1
×
2
0.5 1 2 5 0.5 1 2 5
Energy (keV) Energy (keV)
Fig.2.— Representative Chandra and Suzaku XIS1 spectra for RXJ1159+5531, shown (Chandra) without background subtraction,
or (Suzaku) with the instrumental background subtracted. In addition to the data, we show the best-fitting model, folded through the
instrumental response (solidblack line), along with the decomposition of this model into its various components. For the Chandra data,
we show the hot gas contribution (solid red line), the composite emission from X-ray binaries (dash-dot magenta line), the instrumental
background(dottedorange)andthecosmicX-raybackground(dashedpurpleline). FortheXIS1data,weshowthehotgasemissionfrom
eachannulusassolidlines(red,green,blueandorangeindicating,respectively,the0–2′,2–5′,5–9′and9–13′ apertures,respectively),sky
background (using the samecolour scheme as for Chandra). For Chandra, the background isdominated by the instrumental component,
whereas for Suzaku, which has a lower instrumental background but is less able to resolve the cosmic component into individual point
sources,thecosmiccomponentdominates.
nificant amount of data was found to be contaminated eliminate ∼>90%ofthe sourcephotons fromcontaminat-
in this way, leaving 85 ks of total “cleaned” exposure ing any spectra).
time. 85 ks total exposure time survived flare cleaning. Since RXJ1159+5531wasslightly offsetfromthe cen-
In Fig 1, we show the 0.5–7.0 keV image for the XIS0 tre of the field ofview, it was possible to extractspectra
detector,excludingdatainthevicinityofthecalibration outtoscalesof∼13′fromthesingle,pointedobservation.
sources. By visual inspection of the images for all three Therefore, spectra were extracted in four concentric an-
activedetectors,wefoundonly1brightpoint-source(co- nuli (0–2′, 2–5′, 5–9′ and 9–13′), centred at the nominal
inciding with one of the calibration sources in the XIS0 position of RXJ1159+5531 in the field of view of each
image). In subsequent analysis, we excluded a circular instrument. Due to the large field of view of Suzaku,
regionof2.5′radius,centredonthissource(whichshould ourspectralextractionregionsactuallyachieve∼55–60%
6
azimuthal coverage in the 5–9′ aperture, and ∼27% in Nevertheless, given the ∼keV temperature of the gas,
the 9–13′ region. Data in the vicinity of the calibration the Fe L-shell peak is still clearly visible over the cos-
sources and the identified point sources were excluded. mic X-ray background component (§ 5), and so the gas
For each spectrum, we generated an associated redistri- properties can be measured with reasonable precision.
bution matrix file (RMF) using the xisrmfgen tool and
an estimate of the instrumental background with the 2.3. Rosat
xisnxbgen task. Ancillary response files (ARFs) were
RXJ1159+5531wasobservedserendipitouslybyRosat
generatedforeachspectrumwiththexissimarfgentool in the outskirts (∼17′ off-axis; ∼2.5′ inside the support-
(Ishisakietal.2007),whichmodelsthetelescope’soptics
ring structure) of a pointed PSPC observation (obser-
through ray-tracing. Since the point-spread function of
vation ID 700055n00). Given its relatively poor spa-
the telescope is very large (∼2′ half power diameter),
tialresolutionandlimited energy pass-band,we only re-
evenwith suchlarge apertures it is necessaryto account
quired to measure the Rosat surface brightness profile,
for spectral mixing between each annulus. We did this
centredat the source (see § 4.5 for more details). We do
by employing the algorithm described in H11.
not expect much extended emission from the principal
We modelledthe spectrumineachannulusas the sum
target of the observation, an unrelated, foreground Sy1
of source plus sky background components. The instru-
galaxy (NGC3998). Therefore, we extracted the surface
mental background (which is not the dominant back- brightnessprofileofRXJ1159+5531outtoscalesof∼25′
ground component; H11) was subtracted directly, us-
(∼2R ). Topreparethedata,wefollowedthestandard
ing the model generated with the xisnxbgen task. For vir
Rosatdata-reductionrecipe(see,forexampleFangetal.
the source, we included an APEC component, for which 2009). A full field of view image with 15′′ pixel size was
the Fe abundance and abundance ratios of other species
generatedinthe0.42–2.0keVband,andthecorrespond-
were allowed to vary (as for the Chandra data). The
ing exposure maps were generated with the pcexpmap
abundance ratios were tied between all annuli, and Z
Fe task. Point sources were detected with the wavdetect
was tied between the outermost two annuli. In the
CIAOtasktosearchforstructureatscalesof1,2,4and
central bin, we also included a 7.3 keV bremsstrahlung
8 pixels, and supplied with the exposure map to mini-
component, to account for possible LMXBs in the cen-
mize spurious detections at the image boundaries. The
tral galaxy. For this component, we obtained a to- detection threshold was set to 10−6, implying ∼<0.1 spu-
tal X-ray luminosity per unit K-band optical light of
rious detections per image, and all point sources were
L /L = 2.7±3.9×1029erg s−1L−1, in good
X,LMXB K ⊙ visually confirmed. We used the ao and castpart Hea-
agreement with the Chandra result of 6.0 ± 1.9 ×
soft tasks to generate, respectively, the scattered Solar
1029erg s−1L−⊙1. This self-consistency gives us confi- X-raybackgroundandtheparticlebackgroundcontribu-
dence in our treatment of the background (described tion, which were then subtracted from the image. The
below), and the lack of bright source contamination in surfacebrightnessprofilewasgeneratedinconcentrican-
the Suzaku field. This ratio is also marginally consis- nuli fromthe flat-fielded image, excluding data from the
tent with the mean scaling determined from local galax- vicinity of any detected point source and, to maximize
ies (Humphrey et al. 2008). theabilitytoidentifyandexcludepointsources,allpho-
The Chandra data revealsa strong temperature gradi- tons not inside the shadow of the inner PSPC support
ent within the central ∼2′. Since we can generally ap- ring. We discuss the surfacebrightnessanalysisindetail
proximate the integrated spectrum of a region in which in § 4.5.
thereisatemperaturegradientbythesumoftwoAPEC
components (Buote 1999; Buote et al. 2003), we added 3. SPECTRALFITTINGRESULTS
a secondAPEC componentin the centralbin. Although 3.1. Metal abundances
we did not consider the fitted temperature or density in
In Fig 3, we show the projected abundance pro-
this binin our subsequentanalysis,it wasstill necessary
file, which is centrally peaked, as expected for a re-
to fit a reasonably accurate model to the data, as some
laxed galaxy group and consistent with a picture in
fraction of the photons from this region are scattered
which metal enrichment is facilitated by mass-loss from
into the surrounding annuli. The spectra from all in-
stars and supernovae in the central galaxy (Mathews &
strumentswerefittedsimultaneously,allowingadditional
Brighenti 2003). There is good agreement between the
multiplicative constants in the fit to enable the relative
profiles measured outside ∼100 kpc with Chandra and
normalization of the model for each instrument to vary
Suzaku, supporting our treatment of these data. To ef-
with respect to the XIS 0.
fect a comparison within the central 2′, where there is a
We found that this model was able to fit the data
well11. We show in Fig 2 representative spectra for the strongabundancegradientrevealedbyChandra,butonly
a single Suzaku data-bin, we extracted a single Chan-
XIS1 instrument, showing various model components.
dra spectrum for this region,and fitted it with the same
As is immediately clear, mixing between annuli is sig-
model as the Suzaku data. The best-fitting Z (shown
nificant. Furthermore, the data are clearly background- Fe
onFig3)wasconsistent(within∼1.5-σ)withtheSuzaku
dominated in the outermost annulus (while the source
and background are comparable in the 6–10′ region). measurement. Thegoodagreementovertheentireradial
rangeisencouraging,andsuggeststhatourtreatmentof
thespectralmixingbetweentheSuzakuannuliisapprox-
11 SincetheC-statisticisnoteasilyinterpretableasagoodness- imately correct.
of-fit,wealsoperformedaχ2fit. Although,ingeneral,suchfitsare
WenotetheslightdipinthecentralChandrabin,sim-
morebiased(Humphreyet al.2009b), thebest-fitting parameters
werevery close to those obtained withthe C-statistic, and the fit ilar to features that have been reported in some other
wasformallyverygood(χ2/dof=1787/1811). galaxy groups and clusters. Still, if hot gas components
7
5 ∼400 kpc to 0.2 Solar (consistent with the projected re-
sults). Wefoundthatthesecondhotgascomponentwas
formallyrequiredinthe centralbin(the improvementin
2 the C-statistic was 13.7 for a difference of 2 degrees of
freedom when it was added); the two temperatures in
this binwere1.29±0.23keVand0.72±0.17keV,consis-
Z.O 1 tentwithacontinuingtemperaturedeclineinthegroup’s
Z/Fe 0.5 cpernotjreec,tiaolnthporuogchediturme.ayalsoreflectdeficienciesinthede-
The deprojected Z profile is shown in Fig 3, and it
Fe
also exhibits a centrally-peaked shape and, significantly,
2
0. no evidence of a central abundance dip. This strongly
suggests that the feature seen in the central bin of the
projected data is simply an artefact of the Fe bias.
10 100 1000
Inadditiontotheabundanceprofile,thedataalsopro-
Radius (kpc) videinterestingconstraintsontheabundanceratioswith
respect to Fe of various species. These are summarized
Fig.3.—ProjectedFeabundanceprofile,measuredwithChandra
in Fig 4; we find excellent agreement between Chandra
(triangles)andSuzaku(stars). ThedashedlineindicatestheChan-
draabundancemeasuredinsameregionasthecentralSuzakubin. and Suzaku. Overlaid on this figure, we show the best-
Note the overall good agreement between Chandra and Suzaku. fitting abundance ratio patterns predicted by combin-
We also overlay (crosses) the deprojected abundance profile mea- ing the metal yields for type Ia and type II supernovae,
suredwithChandra,includingasecondtemperaturecomponentin
through which Fe and the α elements are primarily pro-
theinnermostbin. Notethatthecentraldipseenintheprojected
profileisabsentinthiscase. cessed. We adopted the SNII yields from Nomoto et al.
(1997a), and explored three different theoretical SNIa
yields from Nomoto et al. (1997a), specifically the so-
called“W7”, “WDD1” and “WDD2” models. We found
the WDD2 model fits the data well, provided 82±5%
of the Fe was synthesized in type Ia supernovae. This
2 is consistent with measurements in the central parts of
other galaxy groups and clusters (Humphrey & Buote
2006, and references therein; Werner et al. 2008, for a
olar) review).
S
Z (Fe 3.2. Temperature and density profiles
Z/ 1 The projected gas temperature and density12 profiles
are shown in Fig 5 for Chandra and Suzaku. These pro-
files span almost 3 orders of magnitude in radius. The
outermost Suzaku data-bin reaches ∼1200 kpc, which is
∼R , as found by Gastaldello et al. (2007b); see also
vir
0 O Ne Mg Si Ni § 4.2. There is excellent agreement between the results
Element for the two satellites, giving us confidence in our treat-
Fig.4.—AbundanceratioswithrespecttoFe,expressedrelative mentofthemixingbetweenSuzakuannuli,andourtreat-
totheSolarratios(Asplundetal.2004). Chandradataaremarked mentofthebackgroundcomponents,whichdifferslightly
with triangles, and Suzaku data with stars. The solid line is the
between both satellites. Since two APEC components
best-fit model (χ2/dof=5.7/8) where the enrichment comes from
SNIa and SNII, assuming the WDD2 SNIa yields from Nomoto wereemployedinthecentralSuzakubin,wedonotshow
et al. (1997b) and the SNII yields from Nomoto et al. (1997a). the gas density or temperature for that bin. The Chan-
TheSNIaenrichmentfractionis0.82±0.05. Forreference,wealso dra temperature profile agrees well with that found by
showthebestfitswiththeW7(greendashedline)andWDD1(blue
Vikhlininetal.(2006). InFig5,wealsoshowthedepro-
dottedline)SNIayields,neitherofwhichareformallyacceptable.
jected temperature profile (see § 6.4 for a description of
howthiswasobtained),whichisingoodagreementwith
with a range of different temperatures are found along thedeprojectedprofilereportedfortheChandra databy
the line-of-sight to the central annulus, the measured Gastaldello et al. (2007b).
Z may be systematically under-estimated due to the As discussed in § 3.1, there is evidence that the gas
Fe
“Fe bias” (Buote & Fabian 1998; Buote 2000b). Such temperaturemay continueto fallin the centralbin, pos-
a situation could arise either due to projection effects, sibly requiring a second APEC component to be added
or if there is a strong temperature gradient within that to the spectrum in this region. Nevertheless, the results
annulus. To investigate this, we carried out a depro- for the single temperature fit can still be interpreted in
jection analysis (see H11, or § 6.4 of this paper, for a our mass-fitting analysis, provided care is taken to com-
detaileddescriptionofthe deprojectionprocedure),and, pute an appropriately weighted average gas density and
furthermore, included an additional APEC component
within the cental bin, with abundances tied to those of 12 We define the projected density in any given annulus as the
meangasdensityifalltheemissionmeasuredintheannulusorigi-
the other component. Since the deprojection procedure
natesfromaregiondefinedbytheintersectionofacylindricalshell
tends to increase the error-barson the measuredquanti- anda(concentric)sphericalshell,bothofwhichhavethesamein-
ties, we found it necessary to fix the abundance outside nerandouter radiiastheannulus.
8
3 3
Chandra Suzaku
V) V)
T (ke 2 kT (ke 2
ed k cted
Project 1 deproje 1
Chandra Suzaku
ρProjected (10 g cm)−25−3 100.010.11−3 ρdeprojected (10 g cm)−25−3 100.010.11−3 10 100 1000
0 500 1000 0 500 1000 Radius (kpc)
Radius (kpc) Radius (kpc)
Fig.5.— Radial temperature (top panels) and density (bottom panels) profiles for RXJ1159+5531. We show the projected Chandra
profiles in the left column (triangles), the projected Suzaku profiles in the right column (stars), and the deprojected profiles in the right
column. Overlaid are the best hydrostatic model fits to each dataset, which match the data very well and, for the deprojected profiles,
we show in grey the 1-σ confidence region for the model. We exclude the central Suzaku bin from the fitting (although it was used for
abundancedetermination)sincetwotemperaturecomponentswererequired,toaccountforthestrongtemperaturegradient. Intheupper
leftpanel,weshowtheprojectedtemperatureprofilemeasuredbyVikhlininetal.(2006)fromtheChandradata(lightbluecrosses),which
agrees well withour data. Inthe bottom rightpanel, we show (lightbluedashed line)the deprojected density profilefoundbyVikhlinin
etal.(2006), whichisalsoinreasonableagreementwithourdata.
temperature in that region (see H11 for more details). tion of Prugniel & Simien (1997). We fixed the effec-
Inany case,we found that our results wererelativelyin- tive radius and luminosity of this component to the K-
sensitive to the inclusion or omission of that particular band values (9.8 kpc, and 1.0×1012L at the distance
⊙
annulus (§ 6.6). to RXJ1159+5531), inferred from 2MASS (Gastaldello
et al. 2007b), and allowed the K-band M/L ratio to be
4. MASSMODELLING
fitted freely. We additionally included a supermassive
4.1. Method blackhole,withmassfixedat2.4×109M ,basedonthe
⊙
We translated the density and temperature profiles LK ofthe galaxyand the black-holemass versus V-band
into mass constraints using the entropy-based “forward- bulge luminosity relation of (Gultekin et al. 2009), as-
fitting” technique developed in our recent papers sumingLV/LK =0.24,whichistypicalforanoldstellar
(Humphrey et al. 2008,2009a;H11; Buote & Humphrey population with Solar abundances13.
2011a, for a review). Briefly, given parametrized pro- Tofitthethree-dimensionalentropyprofileweassumed
files of “entropy” (S=kTn−2/3, where n is the electron a model comprising a broken powerlaw,plus a constant;
e e sucha modelis reasonablysuccessfulatreproducing the
density) and gravitating mass (excluding the gas mass,
entropy profiles of galaxies and galaxy groups over a
whichiscomputedself-consistently),plusthegasdensity
wide radial range (Humphrey et al. 2009a; Jetha et al.
atsomecanonicalradius(forwhichweused10kpc), the
2007; Finoguenov et al. 2007; Gastaldello et al. 2007a;
three-dimensional temperature and density profiles can
Sun et al. 2009). In order to provide more flexibility
becalculated,underthehydrostaticequilibriumapproxi-
in fitting the data (and weight more heavily the outer
mationandfittedtothedata. Thismodelassumesspher-
data-points in the fit), we also allow an additionalbreak
ical symmetry, which is a standard assumption in X-ray
inthe entropyprofile at largeradius. The normalization
hydrostatic modelling, even when the X-ray isophotes
of the powerlaw and constant components, the radius of
are not perfectly round, since deviations from spheric-
the breaks and the slopes above and below them were
ity likely only contribute a very small error (∼few per-
allowed to fit freely.
cent)intothe recoveredmassprofileandbaryonfraction
FollowingHumphreyetal.(2008),wesolvedthe equa-
(Buote&Humphrey2011b;seealsoPiffarettietal.2003;
tionofhydrostaticequilibriumtodeterminethegasprop-
Gavazzi 2005).
ertiesasafunctionofradius,from10pctoalargeradius
For the gravitating mass model, we assumed an NFW
outsidethefieldofview. Forthelatter,weadoptedtwice
(Navarro et al. 1997) dark matter halo, the virial mass
andconcentrationofwhichwerefreefitparameters,plus
a model for the stellar mass. Since the projected stel- 13 We note that the updated black hole mass versus K-band
luminosityrelationofGraham(2007,theireqn14)givesaslightly
lar light of the central galaxy is known to be well-fitted
smaller mass for the black hole (1.8×109M⊙). Small differences
by a de Vaucouleurs model (Vikhlinin et al. 1999), for
in the black hole mass will not affect our results, however, as the
the stellar mass component, we adopted a deprojected blackholemassisonly∼2%ofthetotalmassattheeffectivecentre
de Vaucouleurs model, using the analytical approxima- oftheinnermostChandra bin.
9
the virial radius of the system defined by ignoring the
baryonic components (which is slightly smaller than the 1014
true virial radius of the system), but explore alternative
choices in § 6.4. For any arbitrary set of mass and en-
tropy modelparameters,it is not alwayspossible to find 013
1
a physical solution to this equation over the full radial
range. Suchmodelswerethereforerejectedasunphysical )M.O
dtourtihnegopbasrearmveetderprsopjaecceteedxpdleonrsaittiyona.nIdntoermdeprertaotcuormepparroe- ass(<R) ( 1012
files,we projectedthe three-dimensionalgasdensityand M
temperature,usingaproceduresimilartothatdescribed
in Gastaldello et al. (2007b)14. This involves computing 011
1
an emission-weighted projected mean temperature and
densityineachradialbin,thatcanbecompareddirectly
toTtohecdomatpaa15r.e the model to the data, we used the χ2 1010 10 100 1000
R (kpc)
statistic, fitting simultaneously the Chandra and Suzaku
temperature and density profiles, with the central bin Fig. 6.— Radial mass profile of RXJ1159+5531. The solid
(black)lineindicatesthetotalenclosedmass(andthegreyshaded
of the Suzaku data excluded from our fits. Correlations
region indicates the 1-σ error in the total mass distribution), the
between the density errors were simply implemented by dashed(red)lineindicates thestellarmass,thedotted (blue) line
adopting a form for the χ2 statistic which incorporates isthedarkmatter,andthedash-dot(magenta)lineisthegasmass
the covariance matrix (e.g. Gould 2003)16. Parame- contribution. Overlaidareasetofdata-pointsderivedfromamore
traditionalanalysismethoddescribedinHumphreyetal.(2009a).
ter space was explored with a Bayesian Monte Carlo Westressthatthemodelisnotfittedtothesedata,butisderived
method. Specifically, we used version 2.7 of the Multi- independently from the temperature and density data; neverthe-
Nest code17 (Feroz & Hobson 2008; Feroz et al. 2009). less, the agreement between the different approaches is good. We
alsoshowthemassprofilefoundbyVikhlininetal.(2006)fromthe
Since the choice of priors is nontrivial, we followed con-
Chandra data (light blue dash-dot-dot line), which overall agrees
vention in cycling through a selection of different priors withourresults,althoughishigheratbothlargeandsmallradii.
andassessingtheirimpactonourresults(wediscussthis
in detail in § 6.5). Initially, however, we adopted flat for each mass parameter of interest. The best-fitting
priors on the logarithm of the dark matter mass (over radial mass distribution is shown in Fig 6, along with
the range 1012 < M < 1016M ), the logarithm of the the relative contributions of each of the different mass
⊙
dark matter halo concentration, c (over the range model components. Overlaid are a series of mass data
DM
1<c <100), the logarithmof the gas density at the pointsderivedfromfittingthedeprojecteddatausingthe
DM
canonicalradius,the stellarM/L ratio,andthevarious “traditionalsmoothedinversion”massmodellingmethod
K
entropy parameters. For a more detailed description of (Buote & Humphrey 2011a), which is more subject to
the modelling procedure, see Humphrey et al. (2009a); systematic uncertainties (for more details see § 6.4 and
Buote & Humphrey (2011a). Humphrey et al. 2009a). The agreement is very good,
indicating that the resulting mass profile is not overly
4.2. Mass profile sensitive to the analysis method.
We found the model could fit the density and tem- We obtain a marginalized Rvir=1100 ± 31 kpc,
perature data well, with a best-fitting χ2/dof=14.4/15, which compares to an outer Suzaku annulus spanning
even when taking into account the covariance between 820–1190 kpc (thus having an “effective centre” at
adjacent density data-points (see H11). The best-fitting ∼1000 kpc). Therefore, we confirm that we are able
models are overlaid in Fig 5. In Fig 5, we also show the to reach Rvir with these data. In Fig 7, we show
rangeofpossiblethree-dimensionaltemperatureandden- therelationbetweentheconcentrationofthegravitating
sity profiles predicted by our model that are consistent mass, cvir, and the virial mass, Mvir. To be consistent
with the projected data. In Table 1, we tabulate the withourpastwork(Buoteetal.2007),theMvir andRvir
best-fitting values and marginalized confidence regions are derived from the distribution of the total gravitating
mass, not just the dark matter, and the concentration,
14 In computing the plasma emissivity term, we approximated c is defined as the ratio of R to the characteristic
vir vir
the true three dimensional abundance profile with the projected scale of the DM halo. We compare our results with con-
abundance profile (Fig 5); since the projected and deprojected
centration and mass constraints for RXJ1159+5531 re-
profiles do not differ significantly, this should be sufficient forour
present purposes, but we explore this question in more detail in ported in the literature (and based only on the Chandra
§6.7 data) at different overdensities. We find excellent agree-
15Wenotethat,forsystemswithastrongtemperaturegradient ment with the M -c results from Gastaldello et al.
andkT∼>3keVtheemission-weightedtemperaturemaybebiased (2007b);inparticuvliarrtvhireagreementwiththevirialmass
low (Mazzotta et al. 2004). Nevertheless, we find little evidence
and concentration obtained from that paper is interest-
of any strong bias when we fit the deprojected temperature and
density data, which should be much less sensitive to this effect. ing, given that the Gastaldello et al. (2007b) results at
This suggests that the impact of this effect is not significant here this overdensity were significantly extrapolated. We do,
(§6.4). however, find a systematic offset at R from the work
16 Bydefaultweonlyconsidercorrelationsbetween thedensity 500
ofSun et al.(2009)andVikhlinin et al.(2006),who em-
data, but we investigate introducing a more complete covariance
computationin§6.9andfindthattheresultsarenotsignificantly ployed essentially the same “smoothed inversion” mass
affected. modelling approach(Buote & Humphrey 2011a)in each
17 http://www.mrao.cam.ac.uk/software/multinest/ work,andobtainedslightlyhighermassesandlowercon-
10
TABLE 1
Massresults anderror budget
Test M∗/LK logM2500 logc2500 logM500 logc500 logMvir logcvir
M⊙L⊙−1 [M⊙] [M⊙] [M⊙]
Marginalized 0.54±0.10 13.49+0.03 0.44±0.07 13.77±0.04 0.76±0.06 13.97+0.05 1.05±0.06
−0.02 −0.04
Best-fit (0.51) (13.49) (0.48) (13.75) (0.80) (13.95) (1.09)
∆DMprofile +0.19 +0.08 −0.024 +0.02 ... +0.06 +0.02 ... +0.21(±0.02) ...
(cid:16)−0.11(cid:17) (cid:16)−0.03(cid:17) (cid:16)−0.03(cid:17)
∆AC −0.209 +0.10 +0.003(±0.03) −0.015 +0.07 +0.008(±0.04) −0.013 +0.06 +0.02 +0.04 −0.017(±0.07)
(cid:16)−0.06(cid:17) (cid:16)−0.08(cid:17) (cid:16)−0.08(cid:17) (cid:16)−0.05(cid:17)
∆Background +0.02 +0.10 +0.01 (±0.03) +0.02 (±0.07) +0.01 (±0.04) +0.02 (±0.07) +0.02 (±0.04) +0.03 (±0.07)
−0.06 (cid:16)−0.13(cid:17) −0.02 −0.01 −0.03 −0.01 −0.02 −0.01
∆SWCX −0.193 +0.11 −0.027(±0.04) +0.10 +0.07 −0.052(±0.05) +0.09 +0.06 −0.047(±0.05) +0.09 +0.06
(cid:16)−0.14(cid:17) (cid:16)−0.09(cid:17) (cid:16)−0.08(cid:17) (cid:16)−0.08(cid:17)
∆Straylight −0.005(±0.10) +0.01 +0.02 −0.006(±0.07) +0.003(±0.04) −0.006(±0.06) +0.006(±0.04) −0.007(±0.06)
(cid:16)−0.03(cid:17)
∆Rmax +0.02 (±0.10) +0.01 (±0.03) +0.01 (±0.07) −0.018 +0.05 ±0.01(±0.06) ±0.01(±0.04) ±0.01(±0.06)
−0.01 −0.00 −0.00 (cid:16)−0.03(cid:17)
∆3d +0.05(±0.09) −0.049(±0.04) +0.02(±0.08) −0.053(±0.05) +0.02(±0.07) −0.040(±0.05) +0.02(±0.07)
∆Fitpriors +0.03 (±0.11) +0.01(±0.03) +0.01 (±0.08) ±0.01(±0.04) +0.01 (±0.07) +0.02 (±0.05) +0.01 (±0.07)
−0.01 −0.03 −0.03 −0.00 −0.03
∆Stars −0.031 +0.00 ±0 +0.02 +0.08(±0.10) −0.020 +0.03 +0.07(±0.09) −0.022 +0.04 +0.05 +0.10
(cid:16)0.00 (cid:17) (cid:16)−0.03(cid:17) (cid:16)−0.05(cid:17) (cid:16)−0.06(cid:17) (cid:16)−0.07(cid:17)
∆Weighting +0.09 +0.06 +0.03(±0.03) −0.082(±0.07) +0.04(±0.04) −0.074(±0.06) +0.05(±0.04) −0.069(±0.06)
(cid:16)−0.09(cid:17)
∆PSF ±0.01(±0.11) +0.01 +0.02 −0.012(±0.07) +0.01(±0.05) −0.011(±0.06) +0.02(±0.05) −0.012(±0.06)
(cid:16)−0.03(cid:17)
∆Instrument +0.02 (±0.11) +0.03(±0.03) +0.02 (±0.08) +0.04 (±0.05) +0.02 (±0.07) +0.04 (±0.05) +0.02 (±0.07)
−0.03 −0.05 −0.01 −0.05 −0.01 −0.05
∆Spectral +0.05(±0.10) +0.03 +0.02 −0.019(±0.07) +0.02(±0.04) −0.018(±0.06) +0.02(±0.04) −0.016(±0.06)
(cid:16)−0.03(cid:17)
∆Distance +0.15 (±0.13) +0.01 +0.04 ±0.11(±0.07) +0.03 +0.05 ±0.10(±0.07) +0.07 (±0.04) ±0.09(±0.06)
−0.12 −0.03 (cid:16)−0.02(cid:17) −0.08 (cid:16)−0.03(cid:17) −0.08
∆Entropy +0.01 +0.08 +0.005(±0.03) −0.007(±0.07) −0.003(±0.04) −0.007(±0.06) +0.006(±0.04) −0.006(±0.06)
(cid:16)−0.12(cid:17)
∆Covariance +0.02 +0.08 +0.00 (±0.03) +0.04 +0.06 −0.028(±0.04) +0.03 +0.06 −0.017(±0.04) +0.03(±0.06)
−0.03 (cid:16)−0.15(cid:17) −0.01 (cid:16)−0.08(cid:17) (cid:16)−0.08(cid:17)
Note. —Marginalizedvaluesand1-σconfidenceregionsforthestellarmass-to-light(M∗/LK)ratioandtheenclosedmassandconcentrationmeasured
at various overdensities. Sincethebest-fittingparametersneednot beidenticalto the marginalizedvalues, we also list the best-fittingvaluesfor each
parameter (in parentheses). In addition to the statistical errors, we also show estimates of the error budget from possible sources of systematic
uncertainty. We considera rangeof differentsystematiceffects, whichare describedindetailin § 6; specificallywe evaluatethe effectofthe choiceof
darkmatterhalomodel(∆DM),adiabaticcontraction(∆AC),treatmentofthebackground(∆Background)andtheSolarwindchargeexchangeX-ray
component(∆SWCX),straylight(∆Straylight)maximumradiususedintheprojectioncalculation(∆Rmax),deprojection(∆3d),priorsonthemodel
parameters(∆Fitpriors),treatmentofthestellarlight(∆Stars),removingtheemissivitycorrection(∆Weighting),theeffectoferrorsinourtreatmentof
spectralmixingduetothePSFofSuzaku(∆PSF),theX-ray detectorsused(∆Instrument),spectralfittingchoices(∆Spectral),distanceuncertainties
(∆Distance),the parameterizationof the entropy model(∆Entropy), and covariancebetween thetemperatureand density data-points(∆Covariance).
Welistthechangeinthemarginalizedvalueofeachparameterforeverytestand,inparentheses,thestatisticaluncertaintyontheparameterdetermined
fromthetest. Notethatthesystematicerrorestimatesshouldnotingeneralbeaddedinquadraturewiththestatisticalerror.
4.3. Gas and baryon fraction constraints
∆=vir
Gastaldello In Table 2, we tabulate the best-fitting values and
10 marginalized confidence regions for the gas and baryon
fractionsof the systemat differentoverdensities. Inper-
∆=500 formingthiscalculation,weincludedthemassinbaryons
Gastaldello of the central galaxy and the hot gas (inferred from our
fit), and also folded in two additional, uncounted reser-
c∆ 5 voirsofbaryons,intra-clusterlightandadditionalgalax-
iesinthegroup. Vikhlininetal.(1999)foundthat∼25%
∆=2500 of the V-band stellar light associated with galaxies was
Sun
innon-centralgalaxies. We assumedthat this alsoholds
inthe K-band,andadoptedaK-bandM/Lratioof1for
these galaxies. Furthermore, for the virial mass of the
2
Vikhlinin system, we expect as much as ∼2 times the stellar mass
of the central galaxy will be bound up in intra-cluster
2×1013 5×1013 1014
light(Purcell et al. 2007). If we make the reasonableas-
M∆ (MO.) sumption that these uncounted baryons are distributed
Fig.7.— Derived relation between mass and concentration for inthesamewayasthedarkmatter(thisisapproximately
RXJ1159+5531 (contours). We show the results for several over-
true of the additional galaxylight reported by Vikhlinin
densities (virial≡108, in black; 500 in red; 2500 in blue). We
also compare our results to constraints reported in the literature etal.),thetotalmassinferredfromourmodelling(which
(Gastaldelloetal.2007b;Vikhlininetal.2006; Sunetal.2009). did not explicitly include these components) will be cor-
rect. Wediscussthesensitivityofourresultstoourtreat-
mentofthese components in§ 6.6. Inpractice,however,
centrations than our best-fitting values. We discuss the these uncounted components account for only ∼10% of
possible origin of these discrepancies in § 7.2. thebaryonbudget,sincemostofthe baryonsaretiedup