The galaxy cluster outskirts probed by Chandra

0.95 MB·English

by  Andrea Morandi

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed7April2015 (MNLATEXstylefilev2.2)
Chandra
The galaxy cluster outskirts probed by
Andrea Morandi1⋆, Ming Sun1, William Forman2, Christine Jones2
1 PhysicsDepartment, Universityof Alabama inHuntsville, Huntsville, AL 35899, USA
2 Harvard-Smithsonian Centerfor Astrophysics, 60 Garden St., Cambridge, MA 02138, USA
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2 7April2015

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p
A ABSTRACT
We studied the physical properties of the intracluster medium in the virialization re-
3 gion of a sample of 320 clusters (0.056 < z < 1.24, kT ∼> 3 keV) in the Chandra

archive. With the emission measure profiles from this large sample, the typical gas
]
O density,gasslopeandgasfractioncanbeconstrainedouttoandbeyondR200.Weob-
serveasteepeningofthedensityprofilesbeyondR500 withβ ∼0.68atR500 andβ ∼1
C
at R200 and beyond. By tracking the direction of the cosmic filaments approximately
.
h with the ICM eccentricity, we reportthat galaxyclusters deviate from sphericalsym-
p metry, with only small differences between relaxed and disturbed systems. We also
- did not find evolution of the gas density with redshift, confirming its self-similar evo-
o
lution. The value of the baryon fraction reaches the cosmic value at R200: however,
r
t systematics due to non-thermal pressure support and clumpiness might enhance the
s
measured gas fraction, leading to an actual deficit of the baryon budget with respect
a
[ to the primordialvalue. This study has important implications for understanding the
ICM physics in the outskirts.
2
v Key words: cosmology: observations – cosmology: large-scale structure of Universe
5 –galaxies:clusters: general – X-rays: galaxies:clusters
9
0
4
0
. 1 INTRODUCTION (ICM) profiles out to and beyond R , where R is the
1 200 200
radiuswithin which themeantotaldensityis200 timesthe
0 Exploring the virialization region of galaxy clusters is vi-
5 critical density of the Universe. Initial results were surpris-
tal to our understanding of large scale structure formation,
1 ing,revealingsignificantdeparturesfromthetheoreticalpre-
offering a direct view of cluster growth. This topic has re-
: dictions. These observations showed that, at large cluster-
v centlyraisedtheattentionofthescientificcommunity,since
centric radii (R > R ), the observed entropy profiles
i anaccuratemeasurementofthemassandbaryonicfraction ∼ 200
X becomes flatter (e.g., Bautz et al. 2009; Kawaharada et al.
of cluster outskirts can provide constraints on cosmological
2010), and the observed gas fraction exceeded the cosmic
r parameters, and allow us to test the validity of the CDM
a baryon fraction of the universe (Simionescu et al. 2011).
framework (e.g. Reiprich et al. 2013).
Suzakumeasurementscallforappreciablegasclumpinessin
Nevertheless, the outskirts remain a relatively unex-
the outskirts, inferred from its effects on thermodynamic
plored territory, bearing thesignature of a complex physics
profiles (Walker et al. 2013) or from the high values, larger
such as ongoing accretion processes, significant departures
than the cosmic baryon fraction, of the gas mass fraction
from virialization and hydrostatic equilibrium (Lau et al.
towardsthevirialradius.However,difficultiesariseinmod-
2009),clumpingofthegas(Morandi & Cui2014).Theseef-
eling out point sources and/or galactic foreground with
fectsmaybias,inturn,themeasurementsofclustermasses,
the limited angular resolution (∼ 2 arcmin) of Suzaku at
thus limiting the use of galaxy clusters as a high-precision
the level required for measuring the extremely low surface
cosmological proxy. Hence a deeper understanding of the
brightnessintheclusteroutskirts.Inparticular,theSuzaku
state of theintracluster gas in cluster outskirts is required.
point-spread function and the stray light can cause signif-
Observations are very challenging in cluster outskirts,
icant contamination from the brightness in the central re-
since the X-ray surface brightness drops below the back-
gions to large radii. Moreover, Suzaku observations have
ground level at large radii. Thanks to its low particle back-
beenmostlyperformedalongnarrowsarms,whichmightre-
ground from its low orbit, Suzaku observations have ex-
flects preferential directions connected with the large-scale
tended X-ray measurements of the intracluster medium
structure (e.g., in the direction of filaments). Therefore, it
is possible that the aforementioned measurements are not
representativeof thecluster as a whole.
⋆ E-mail:[email protected]
(cid:13)c 0000RAS
2 Morandi et al.
Independent ROSAT PSPC observations (with low kT >3keV,observedwithChandra.Westacked1 theemis-
∼
background and large field of view) have shown the steep- sion measure profiles EM ∝ n2dl of the cluster sam-
e
ening of the gas density profile at large radii, but at the ple to detect a signal out to aRnd beyond R200. We then
levelconsiderablylargerthanthoseinferredfromtheSuzaku measured the average emission measure, gas density and
observations (the ICM slope β = 0.890 ± 0.026 at R200, scatter in cluster outskirts. This pioneering work for the
Eckert et al. 2012). Chandra archive follows the original idea successfully ap-
In this respect, independent measurements with pliedinROSAT(Eckert et al.2012,seealsoDai et al.2007);
Chandra with respect to Suzaku can shed light on and with the Sunyaev Zeldovich maps (Plagge et al. 2010;
systematic uncertainties in the current measurements Planck Collaboration et al. 2013), which allowed to detect
(e.g., Ettori & Balestra 2009b; Ettori & Molendi 2011; thephysical properties beyond R200.
Moretti et al.2011):indeed,despiteitshigherparticleback- The paperis organized as follows. In §2 wepresent the
ground, Chandra provides a superior angular resolution cluster sample, in §4 we describe the X-ray analysis and
which is fundamental in order to: i) remove emission from in §5 we discuss the systematics in the data analysis. The
unrelated sources, e.g. point sources; ii) to constrain the results on the gas density and gas mass fraction are pre-
emission of clusters out to the virial radius, especially for sented in §6 and §7. In §8 we summarize our conclusions.
higher-redshift cool-core clusters, for which there might be Throughout this work we assume the flat ΛCDM model,
a non-negligible contribution from the bright cluster core withmatterdensityparameterΩm =0.3, cosmological con-
to the emission in the outer volumes and from secondary stant density parameter ΩΛ = 0.7, and Hubble constant
scatter by sources outside the field of view. Note that the H0 = 100hkms−1 Mpc−1 where h = 0.7. Unless otherwise
propertiesoftheparticlebackgroundarewellknownviathe stated, we report theerrors at the68.3% confidencelevel.
stowed background observations, with uncertainties in the
background across its spectrum which are within < 2 per-
∼
cent(Hickox& Markevitch(2006)andseealsodiscussionin
Sun et al. (2009)).
Thisdataanalysisprojectrepresentsafollow-up ofour 2 CLUSTER SAMPLE
previous works on studying cluster thermodynamic proper-
ties, including emission measure, gas density, and gas frac- The sample we chose for this analysis is composed of 320
tion, out to R (Morandi et al. 2013b; Morandi & Cui clusters from the Chandra archive (Table 1), with redshift
200
2014). Indeed, when data of sufficient depth are avail- rangez=0.056−1.24 (thesamplemedianredshiftis∼0.4)
able, we have shown that Chandra can accurately mea- and temperatures kT ∼>3 keV (thesample median temper-
sure the surface brightness and temperature of clusters ature is ∼ 7 keV). These sources have been observed with
out to R (Bonamente et al. 2013; Morandi et al. 2013b; theACIS-Iimagingarray.Theseclustershavebeenselected
200
Morandi & Cui 2014, e.g., in Abell 1835 and Abell 133). becausetheX-rayobservationsencompassR200ofeachclus-
The Chandra’s superior angular resolution enables robust ter, hence they are suitable for observations of cluster out-
identification and removal of point sources from the X-ray skirts. Moreover, source-free regions of the cluster observa-
images, while minimizing the contribution from the bright tion are always present,allowing measurements of thelocal
cluster core to the emission in the outer volumes – both background (Figure 1). The modeling of the background is
challenging tasks for Suzaku – and to provide an inde- indeed crucial for robust measurements of the physical pa-
pendent confirmation of the Suzaku results. Observational rameters in theouter regions.
constraints on the gas clumping factor inferred from the This sample encompasses most of the clusters
inhomogeneities of the X-ray surface brightness are also from large samples studied in previous works, in-
significantly smaller than those inferred from the Suzaku cluding e.g. Vikhlinin et al. (2006), Maughan et al.
measurements (C ∼ 1.5−2 at R , Eckert et al. 2013a; (2008), Cavagnolo et al. (2009), Ettori et al. (2009a) and
200
Morandi et al. 2013b; Morandi & Cui 2014); the gas den- McDonald et al. (2013).
sity slope reaches β ∼0.9 at R , in good agreement with Although thesample was selected based on thequality
200
the predictions of hydrodynamical simulations, but steeper of the existing observations and hence might be subject to
than the values inferred from recent Suzaku observations selection effects, for the purpose of this work we did not
(Bautz et al. 2009; Kawaharada et al. 2010). requirethatthesample becomplete, giventhehigh levelof
self-similarity of theclusteroutskirts. The X-ray properties
At present, Suzaku has mainly studied high mass clus-
of the galaxy clusters in our sample are presented in Table
ters to the virial radius, primarily at low redshift, given
its large PSF (∼ 2′), which limits the size of the annuli 1, while the number of net counts per bin for each cluster
and the distribution of total net X-ray counts are shown in
usedinthespatiallyresolvedspectralanalysis,reducingthe
Figure A1.
angular resolution of the temperature and entropy profiles
(Bautz et al. 2009; Urban et al. 2013). It is clearly impor-
tant to study clusters at higher redshift to investigate e.g.
theevolutionofthethermalpropertiesoftheICM,andwith
independentX-ray observatories.
1 Wecautionthereaderthat,fromnowon,withtheword“stack-
Inordertostudythephysicalproperties oftheICMin
ing” we do not refer to an actual co-adding of the images, but
thevirialization region weexploitthelargearchivaldataset rather to the median of the distribution of the radial emission
of Chandra clusters. We study the surface brightness pro- measure profiles EM at radii R/R200, once re-scaled according
files of a sample of 320 clusters (0.056 < z < 1.24) with theself-similarmodel(see§3forfurtherdetails).
(cid:13)c 0000RAS,MNRAS000,000–000
The galaxy cluster outskirts probed by Chandra 3
Table1.Table1ispublishedinitsentiretyintheelectroniceditionoftheMonthlyNoticesoftheRoyalAstronomicalSociety.Aportion
isshownhereforguidance regardingitsformandcontent. Inthepresenttable wereporttheX-raypropertiesofthe galaxyclustersin
oursample.Foreachobjectdifferentcolumnsreporttheclustername,theredshiftz,theexposuretimetexp,theidentificationnumber
oftheChandraobservations,thespectroscopictemperatureTew intheradialrange0.15−0.75R500,thecentroidshift(inunitsofR500),
andaflagforthepresenceornotofacoolingcore(labeledCCandNCC,respectively).
Cluster z texp ID Tew w CC/NCC
ks (keV) (×10−2)
A85 0.056 272.4 9044881488248834884488548864887 6.45±0.86 0.49±0.18 CC
488815173162641517416263
A133 0.057 2393.0 1344213443134441344513446134471344813449 3.76±0.25 0.26±0.09 CC
1345013451134521345313454134551345613457
1433314338143431434514346143471435413391
1339213518318337101217712178121799897
A644 0.070 48.9 221110420104211042210423 8.12±1.12 1.56±0.57 CC
A401 0.075 153.9 1041610417104181041914024 5.44±0.86 1.03±0.38 NCC
A2029 0.076 29.2 610110434104351043610437 7.38±0.92 0.21±0.08 CC
A1650 0.084 218.4 769158225823635663576358724210424 5.89±0.86 0.38±0.14 CC
104251042610427
A1068 0.137 19.5 13595135961359713598 6.38±1.26 0.29±0.11 CC
A2276 0.141 39.5 10411 3.40±0.48 0.49±0.18 NCC
A1413 0.143 155.6 50031219412195121961312816615002537 7.78±0.22 0.57±0.21 CC
7696
A3402 0.146 19.8 12267 3.09±0.55 1.39±0.51 NCC
3 THE SELF-SIMILAR MODEL: MEASURING hibitcomplicatedphysicalphenomena,suchasAGNheating
THE PHYSICAL PARAMETERS and cooling flows, theunderlyingphysicsof theoutskirts is
relatively simple, gravity-dominated and hence nearly self-
Stackingtheemissionmeasureofaclusterpopulationispos-
similar.
siblethankstothehigh levelof self-similarity of thecluster
AssumingthesphericalcollapsemodelfortheDMhalo
outskirts.
and the equation of hydrostatic equilibrium to describe the
Inthisrespect,theself-similar model(see,e.g., Kaiser distribution of baryons into the DM potential well, in the
1986) gives a simple picture of the process of cluster for- self-similarmodeltheclustermassatanoverdensity∆(e.g.
mation in which the ICM physics is driven by the infall of ∆=500,200) and temperature are related by:
cosmic baryons into the gravitational potential of the clus-
E ∆1/2M ∝T3/2 ; (1)
terDMhalo.Powerlawscalingrelationsareexpectedunder z z tot
simplified models in which clusters are self-similar objects, where the factor ∆ = ∆ ×
z
having formed in single monolithic gravitational collapses 1+82(Ω −1)/ 18π2 −39(Ω −1)2/ 18π2 , with
z z
andwhoseICMisheatedonlybytheshocksassociatedwith Ω(cid:2)z = Ω0m(1 + z(cid:0))3/E(cid:1)z2, accounts for e(cid:0)voluti(cid:1)o(cid:3)n of clus-
thecollapse. Theunderlyingidea is thatgravity is theonly ters in an adiabatic scenario (Kaiser 1986). So we have
responsible for the observed values of the different physical R ∝ (M/(ρ ∆ ))1/3 ∝ T1/2E−1∆−1/2. By setting
∆z c,z z z z
propertiesofgalaxyclusters;henceclustersareidenticalob- f ≡ E (∆ /∆)1/2 (e.g. Ettori et al. 2004), from the
z z z
jects when scaled by their mass or temperature (Lau et al.
previous equations we can easily obtain the following
2014).
relations:
Numerical simulations confirm that the DM compo-
f R ∝T1/2
nent in clusters of galaxies, which represents the dominant z ∆z gas
fraction of the mass, has a remarkably self-similar behav- f M ∝T3/2 (2)
z gas gas
ior; however the baryonic component does not show the
From the previousequation it follows that:
same level of self-similarity. For instance, deviation of the
L − T relation in clusters with respect to the theoreti- EM ∝ n2 dl∝M2 /R5 ∝f2 f3T1/2 (3)
cal value predicted by the previous scenario suggest that Z e gas ∆z gas z gas
some energetic mechanism, in addition to gravity, such as assuming that all clusters have the same gas mass fraction
(pre)-heatingandcooling(Borgani et al.2005;Bryan 2000; f . Note that our sample is characterized by a relatively
gas
Morandi & Ettori 2007; Sun 2012) intervene to break the narrow temperature range (larger than 3 keV), such that
expected self-similarity of the ICM in the innermost re- thephysicalparametersoftheclustersinoursampleshould
gions.Consequently,thecomparison oftheself-similar scal- showlittledependenceongasfraction.Theelectrondensity
ing relations to observations allows us to evaluate the im- n (r)can befinally inferred bydeprojecting thestacked X-
e
portanceoftheeffectsofnon-gravitationalprocesses onthe ray emission measure profile (Equation 3) via the spherical
ICM physics.Whilethecentralregions of clusters often ex- onion peeling method (Morandi et al. 2013a).
(cid:13)c 0000RAS,MNRAS000,000–000
4 Morandi et al.
InordertoinferR (∆=500,200,100)fromtheknown
∆
value of R , we apply the following statistical method.
500
First, we assumed a NFW distribution with parameters
(c,R );second,weinferredavalueoftheconcentrationpa-
200
rameterviathec−M relationofDuffyet al.(2008)based
vir
ontheresultsfrom numericalsimulations. Thisprovidesan
estimate of R for given value of R . For our sample we
∆ 500
haveR =(0.65±0.01)R andR =(1.36±0.01)R
500 200 100 200
The gas fraction within an overdensity ∆ can be com-
puteddirectly from the gas density profiles:
M 3 1
f = gas,∆ = ρ (x)x2dx. (5)
gas,∆ M∆ ∆ρc,z Z0 gas
with x=R/R .
∆
4 X-RAY ANALYSIS
DescriptionoftheX-rayanalysismethodologycanbefound
in Morandi et al. (2013b). Here we briefly summarize the
most relevant aspects of our data reduction and analysis.
Figure1.Distributionoftheclustersinoursampleinatempera-
tureversusredshiftdiagram.Thedashedlinemarkstheregionof
theplotcorrespondingto10arcmin(the ACIS–IChandra fovis 4.1 X-ray data reduction
16×16arcmin).Notethesomeclusters,e.g.A133,A644,A2029,
All data were reprocessed from the level 1 event files us-
A1650andA85,atlowredshift(∼0.05),arecharacterizedbyval-
uesofR200 largerthanthefovofChandra.Theseclustershavea ing the CIAO data analysis package – version 4.6.1 – and
large number of mosaic observations covering the outskirts. The the calibration database (CALDB 4.6.3) distributed by the
blue and red dots correspond to clusters classified as cool core ChandraX-rayObservatoryCenter.NotethattheACISQE
andnon-coolcore,respectively(see§4.4). contamination model, which has been released in CALDB
and is associated with the deposition of one or more mate-
rialsontheACISdetectorsoropticalblockingfilters,isthe
Inourworkwehaveconsideredallthephysicalquantity latest available (version N0009).
at fixed overdensity (∆ = ∆), i.e. f = E in the above Weanalyzed613datasets,correspondingto320galaxy
z z z
equations. clusters, retrieved from the NASAHEASARCarchive with
In order to infer R from the observables quantities, atotalexposuretime∼20Msforthewholesample.Allthe
500
we rely on the existence of low-scatter scaling relations be- observations are carried out by using theACIS–I CCD.
tween the total thermal energy Y = M T and the to- Wereprocessedthelevel-1eventfilestoincludetheap-
X gas X
tal mass, as predicted by self-similar theory and confirmed propriategainmapsandcalibrationproducts.Aspartofthe
byhigh-resolutioncosmologicalsimulations(Kravtsov et al. datareduction,correctionsweremadeforafterglows,charge
2006).InthisrespectweusedtheY −M relationmeasured transfer inefficiency (CTI), bad pixels and solar flares. We
X
for the Sunet al. (2009) sample of clusters: used the acis process events tool to check for the pres-
ence of cosmic-ray background events, correct for spatial
E2/5M = h 52B1.−613×1014 YX 0.571 gain variations due to charge transfer inefficiency and re-
z 500 (cid:18)0.7(cid:19) (cid:18)3.60×1013M⊙keV(cid:19) compute the event grades. Then we filtered the data to in-
(4) clude the standard events grades 0, 2, 3, 4 and 6 only, and
with B=0.571. Hencewe recovered R . therefore we filtered for the Good Time Intervals (GTIs)
500
WepointoutthatwedeterminedT intheradialrange supplied,which are contained in theflt1.fits file.
X
0.15−0.75R (§4.2),whilethepreviousrelationhasbeen Acarefulscreeningofthebackgroundlightcurveisnec-
500
calibrated in the range 0.15−1 R . Our choice is moti- essarytodiscardcontaminatingflareevents.Acommonway
500
vatedbythefactthatthisisastraightforwardmeasurement of removing these periods of particle background flares is
for our intermediate and high-z clusters because exposures to create a lightcurve of the local background, once point
were designed to provide a sufficient statistical accuracy to sources of high and variable emission are excluded. The
infer the spectral temperature in the aforementioned radial lightcurve is then created by using the tool dmextract. In
range. We correct our T measurements in order to match order to clean the datasets of periods of anomalous back-
X
thedefinitionemployedinEquation4viamocksimulations groundrates, weusedthedeflare script,soas tofilterout
by assuming our average gas density profile (§6) and the the times where the background count rate exceed ±3σ of
averagetemperatureprofileasmeasured byVikhlinin et al. the mean value. Most observations were taken in VFAINT
(2006). This correction is 0.96±0.02. mode,andinthiscaseweappliedVFAINTcleaningtoboth
R and Y were computed iteratively, measuring the the cluster and blank-sky observations. Finally, we filtered
500 X
temperature in the aperture 0.15−0.75 R and the gas the ACIS event files on energy selecting the range 0.3-12
500
masswithinR ,computinganewY ,andhenceestimat- keV,so as to obtain a level-2 event file.
500 X
ing a new valueof R . Pointsourcesandextendedsubstructuresweredetected
500
(cid:13)c 0000RAS,MNRAS000,000–000
The galaxy cluster outskirts probed by Chandra 5
and removed using the script wavedetect, which provides istodividethecountsimagebyanexposuremap,weighted
candidate point sources, and the result was then checked according to a specific model for the incident spectrum, to
through visual inspection. rescale all partsoftheimage tothesamerelative exposure.
Nevertheless, since the exposure map is both energy and
position dependent, we cannot assume the same exposure
4.2 X-ray surface brightness analysis
map for source and backgroundemission. Ourmodel of the
We produced X-ray images from the level-2 event file. Our desired source surface brightness SX,s breaks down the ob-
goal isindeedtomeasuretheemission measureandthegas served emission SX,obs into four components:
density profile in a non-parametric way from the surface
S (x)∝ S (x)·C (x,E)+S (x)·C (x,E)
X,obs X,s s X,bkg bkg
brightness. Multipleobservations were reduced individually
+S (x,E(t))+S (x,E) (6)
toapplythecorrectcalibration toeachdataset.Thecluster X,pb X,r
surface brightness profileis obtained from merged images. where S (x) is the source surface brightness in the pixel
X,s
TheX-rayimageswereextractedfromthelevel-2event x = (x,y), S is the cosmic X-ray background (CXB)
X,bkg
filesintheenergyrange0.7−2.0keV.Thisenergybandwas
backgroundandS isthe(timedependent)particleback-
X,pb
chosen in order to: i) maximize the S/N in the outskirts of ground.C (x,E)andC (x,E)refertotheexposuremaps
s bkg
the clusters, and ii) minimize the dependency of the cool-
for source and background,respectively.
ing function on the temperature and metallicity. Concern- S (x,E) refers to the readout artifact background.
X,r
ing the latter point, the integrated cooling function in the
We simulated, re-normalized and accounted for this read-
(0.7−2) keV band is approximately given by Λ(T)∝T−α,
out background using the make readout bg routine (see
with −0.02.α.0.2 for T >2 keV (in all the clusters the
∼ Hickox& Markevitch (2006) for furtherdetails).
temperatureisnotexpectedtofallbelow∼2keV),suchthat
Theradialsurfacebrightnessprofileisthusderivedwith
systematicuncertaintiesintheestimatedprojectedtemper-
theexposurecorrectionandparticlebackgroundsubtraction
aturehaveanegligible impactonthegasdensity.Inpartic-
using the scaled stowed background. The region where the
ular, we point out that we inferred the density profiles out
CXBismoredominantthantheclusteremissioncanbede-
to R from the stacked emission measure profiles.
100 termined from the flattened portion at the outer region of
We then corrected the images by the exposure maps
the surface brightness profile. We applied a direct subtrac-
to remove the vignetting effects. We created an exposure-
tionoftheCXB+particlebackgroundbymeansofEquation
corrected image from a set of observations using the 6.InordertocalculateC (x,E),wemodeledthesoftCXB
bkg
merge obs tool to combine the ACIS–I observations. All
component by an absorbed power law with index 1.4 and
mapswerecheckedbyvisualinspection ateachstageofthe
two thermal components at zero redshift, one unabsorbed
process.
componentwithafixedtemperatureof0.1keVandanother
Next,wedeterminedthecentroid(x ,y )ofthesurface
c c absorbedcomponentwithatemperaturederivedfromspec-
brightness image by locating theposition where thederiva- tral fits(∼0.25 keV,Sun et al. 2009).
tivesofthesurfacebrightnessvariationalongtwoorthogonal
The boundary radius of the X-ray and surface bright-
(e.g., X and Y) directions become zero.
nessanalysiscorrespondstoaratioofsourcetobackground
Since for all the clusters the field-of-view encompasses
flux∼15-40percentatR .Thus,acarefulanalysisofthe
200
the X-ray boundary (R ), the emission does not extend
100 systematics and how theseuncertainties propagate into the
across the entire detector, and we have a sufficiently large determination ofthephysicalparametersis required(§5.2).
regiontoobtainalocalbackground.Inalltheclustersthelo-
With robust background subtraction and modeling,
calbackgroundwasmeasuredfromaregionbeyond1.5R ,
200 from the X-ray images we measure the emission measure
where the surface brightness was approximately constant, profileEM ∝ n2dlandcalculatedthemediandistribution
e
i.e. it has reached thebackground level.
to compute stRacked profiles. We then scaled the emission
The local background is a combination of a particle
measureprofilesandthedeprojecteddensityprofilesforthe
componentthatisnotvignetted,andaskycomponentthat
clusters in our sample. A self-similar scaling was applied to
isvignetted.Todeterminethesurfacebrightnessoftheclus-
the emission-measure profiles, i.e. each profile was rescaled
ter and of the local soft X-ray background, an accurate bythequantityE3(kT/10 keV)1/2 (§3),followingtheirevo-
z
procedure consists of subtracting the non-vignetted parti-
lution with redshift and dependency on the cluster mass,
cle component as measured from Chandra observations in
since the profiles is expected to show a remarkable level of
which the ACIS detector was stowed, after rescaling the
self-similarity outside of the core (R > 0.2R ). From the
200
stowed backgroundtomatchthe9.5−12keVclustercount
deprojectionofthemedianemissionmeasureprofilewethen
rateoftheobservations(wheretheChandraeffectiveareais
recover theexpected density profile.
negligible and thusvery little cluster emission is expected).
Indeed,althoughtheparticlebackgroundfluxmayvarywith
time,Hickox & Markevitch(2006)hasshownthatthespec-
4.3 X-ray spectral analysis
tral distribution of the particle background is remarkably
stable, even in the presence of changes in the overall flux, Theglobaltemperatureshavebeenrecoveredbyfittingspec-
and that the ratio of soft-to-hard (2-7 keV to 9.5-12 keV) tra from different observations simultaneously. The spec-
countratesremainsconstanttowithin <2percentintime. tral analysis was performed by extracting the source spec-
∼
Weverifiedthatalloursourcesarecharacterizedbyremark- tra from circular annuli around the centroid of the surface
ablystablebackgroundbycomparingthespectraofthelocal brightness and by using the CIAO specextract tool from
background and of theblank sky fields. each observation. The spectral fit was performed by simul-
In order to correct for vignetting, a common approach taneouslyfittinganabsorbedthermalemissionmodelinthe
(cid:13)c 0000RAS,MNRAS000,000–000
6 Morandi et al.
energy range 0.7-7 keV and in the region 0.15−0.75 R .
500
WeusedtheXSPECpackage(Arnaud1996,version12.8.2)
to perform the spectral fit. We adopted the APEC emis-
sivity model (Foster et al. 2012) and the AtomDB (version
2.0.2) database of atomic data, and we employed the so-
lar abundance ratios from Asplundet al. (2009). We also
used the Tuebingen-Boulder absorption model (tbabs) for
X-rayabsorptionbytheISM.FreeparametersintheAPEC
model are temperature, metal abundance, normalization.
We fixed the hydrogen column density N to the Galactic
H
valuebyusingtheLeiden/Argentine/Bonn(LAB)HI-survey
(Kalberla et al. 2005). The redshift to the value obtained
from optical spectroscopy. We also group photons into bins
of at least 20 counts per energy channel and applying the
χ2-statistics. We analyzed the observations individually to
checkforconsistencybeforejointlyfittingmultipledatasets
referring to a single cluster. The background spectra have
been extracted from regions of the same exposure for the
ACIS–I observations, for which we always have some areas
(>R ) free from source emission.
∼ 100
We also checked for systematic errors due to possible
source contamination of the background regions, which has Figure 2. Plot of centroid shifts versus electron density at
been estimated by considering the predictions of the sur- 0.03R500 forthewholesample.
face brightnessfrom hydrodynamicalnumericalsimulations
including cooling, star formation and supernovae feedback
(Roncarelli et al. 2006).Thecontamination isalways ofthe masked out point sources, chip gaps and all the substruc-
orderafewpercent,andthistranslatesintoanegligiblebias tures which have been similarly excluded in recovering the
of the determination of the spectral global temperature. emission measure profile. This generates a 2D mask I(x−
We finally validated the method to recover the global x ,y−y ), with x ,y being the centroid as determined in
c c c c
temperature for each cluster by creating a mock spectrum §4.2.Wethensymmetrizedthismask,i.e.I(x−x ,y−y )=
c c
via a single-temperature absorbed thermal model with pa- I(−x+x ,−y+y ),inordertoremoveanyspuriousdepen-
c c
rameters fixed to those from the aforementioned spectral dency of the centroid shifts on the adopted masking, i.e. a
analysis, and then adding a background spectrum from a perfect azimuthally symmetric source must generate a zero
region free of the source emission. We thus repeated the centroidshiftregardlessoftheadoptedmask.Thisdefinition
spectralanalysis on themockdatasets andwefoundavery addsthebenefitsto robustly relate w to theglobal dynam-
good agreement between input and recovered spectral pa- ical state of clusters, while eliminating the impact of point
rameters. sources, chip gaps and substructures similarity masked in
In the appendix we present a comparison between theemission measure profiles.
spectral temperatures and metallicities recovered via the The measured centroid shifts are summarized in Table
AtomDB databases 2.0.2 and 1.3.1, via different models of 1. The errors quoted for the w are the statistical uncer-
X-ray absorption by the ISM, and by accounting also for taintiesonastandarddeviationcalculatedfromnmeasure-
themolecularandionizedhydrogeninthehydrogencolumn ments (w 2/(n−1)). Objects with center shift parameter
densities. w>0.01Rp are classified as morphologically disturbed.
500
Next, systems are classified as cool cores (CC) or
non-cool cores (NCC) on the basis of density E−2n at
4.4 Morphological type classification z e,0
0.03R .Thethresholdweusetodefineacoolcoresystems
500
In this section we describe how the clusters were classified isE−2n >1.5×10−2cm−3.Wecomparedourdefinitionof
z e,0
basedontheirmorphologicaltype,i.e.basedonthepresence CCsystemswithCavagnolo et al.(2009)in§C,whosesam-
of a cool core and/or dynamical state of clusters. Dividing ple shares 93 objects in common with ours. They use the
the data into these subsamples allows us to investigate the entropy threshold K = 30−50keV cm2 to approximately
0
effectofcoolcoresandmorphologicaldisturbanceonaclus- demarcate thedivision between CC and NCC.
ters position with respect tothe mean relation. Notethatcentroidshiftsandcentraldensityarebroadly
We adopted the centroid shift method as our method anti-correlated(Figure2),beingbothaproxyofthedynami-
to infer to the dynamical state of clusters (Maughan et al. calstateofacluster,i.e.cool-coresystemhavelargercentral
2008). Centroid shifts have been measured from the vari- density and overall more relaxed dynamical state.
ation of the centroid of cluster emission within apertures We finally measured the flattening and orientation of
of increasing radii R , which have similarly been previously the X-ray surface brightness. We computed the moments
i
used to infer the emission measure. The centroid shift, w, of the surface brightness within a circular region of ra-
was defined as the standard deviation of these centroids in dius R centered on the centroid of the X-ray image (see
500
unitsof R . Morandi et al. (2010) for further details on this method).
500
Centroid shiftsweremeasuredfrom exposure-corrected ThisallowsustoestimatetheICMeccentricityontheplane
images in order to eliminate the effects of vignetting. We oftheskyandtheorientation(positionangle)ofanelliptical
(cid:13)c 0000RAS,MNRAS000,000–000
The galaxy cluster outskirts probed by Chandra 7
X-ray surface brightness distribution. We use this position threshold flux S is:
thres
angle as a proxy of the direction of the large-scale filament
Sthres dN
(see discussion in §6.3). σ2 =(1/Ω) ×S2 dS (7)
CXB Z0 (cid:16)dS(cid:17)
where dN/dS is the cumulative flux distribution of point
sourcesasemployedbyMoretti et al.(2003).Thethreshold
fluxS hasbeencalculatedbydeterminationofthelocal
5 ANALYSIS OF THE SYSTEMATICS IN THE thres
flux limit to which we can robustly identify a point source,
DATA ANALYSIS
commonly known as sensitivity map (see, e.g., Ehlert et al.
5.1 Validation of the stacking method 2013,forfurtherdetailsonthemethod).OurjointChandra
observations of the outskirts allow the CXB to be resolved
We validated our stacking method via simulations of mock toathresholdfluxS ∼10−15 ergcm−2 s−1deg−2 inthe
thres
datasets including systematics. From the rescaled emission
soft band. Solving Equation 7, this translates into an error
measure, averaged on the whole sample, we created mock
in the range <3% on the surface brightness in the outer
∼
azimuthally-averaged source brightness images S (r) for
X,s volumesfortheaverageemission measure,whileitbecomes
each observation, according to the observation aspect in-
negligibleintheinnervolumes.Ifweconsiderthesubsample
formation. We then used blank-sky fields to produce realis-
of clusters at higher redshift (z > 0.3), this error becomes
ticbackgroundsSbkg(x)foreach observation.Weextracted
X appreciable (∼<10 percent in the outervolumes).
background images from the blank-field background data
We point out that the previous analysis does not take
provided by the ACIS calibration team in the same chip
intoaccountthepossiblesystematicsduetovariationofthe
regions as in the observed cluster. The blank-sky observa-
PSF across the ACIS-I detector, the PSF being about one
tionseventfilesunderwentareductionprocedureconsistent order to magnitude larger (∼ 10−20 arcsec) at the edges
withthatappliedtotheclusterdata,afterbeingreprojected of the CCD with respect to the aimpoints (∼ 1 arcsec);
onto the sky according to the observation aspect informa-
neither it accounts for the different contamination of the
tion by using the reproject events tool. We then added
galaxy cluster signal in detecting point sources across the
these background images to the source brightness. In or-
CCD. Indeed, the signal of point sources near the edge of
dertoestimatethecontributionoftheparticlebackground,
the field would be diluted on larger angular scales due to
we used stowed background observations, renormalized to thelargerChandraPSF,butatthesametimewouldbeless
matchtheblank-skycountrateathighenergy(9.5-12keV).
contaminated by the cluster signal, the cluster center be-
We point out that in this way we capture biases due both
ing observed customarily near the center of the CCD. The
possible spatial variation of the CXB and temporal varia-
first(second)effectwouldmakemoredifficult(easier)tode-
tions of the particle background spectrum. We finally ap-
tect point sources with respect to the CCD center via the
pliedthewholeproceduredescribedin§4.1(Equation6)on waveletdecomposition algorithm describedin§4.1.Inorder
themock observations. A comparison between thetrueand
togaugetheimpactofthesesystematicsweperform Monte
measured emission measure profile reveals that the distri-
Carlo (MC) simulations of the point sources as employed
bution of the residual (normalized by themeasurement un-
by Moretti et al. (2003), which should account for most of
certainties) follows theexpectedGaussian distributionwith
the CXB background. We then added particle and galactic
zero mean, with reduced χ2 of the order of the unity. This background, which has been convolved with the Chandra
indicates that the measurement errors fairly represent the
PSF at the position (x,y) of the CCD. We finally added
errorbudgetandourrecoveredphysicalparametersare not mock cluster signal (see §3 for details on the mocks). For
significantly biased.
each MC simulation we extracted point source by mimick-
ingtheprocedureofwaveletdetectionalgorithm.Thisallow
us to estimate the bias (downwards) due to the aforemen-
tioned systematics, which is < 3%(4%) on the gas density
5.2 Systematics in background modelling ∼
at R (R ).
200 100
Accurate measurements of the ICM in the cluster outskirts Wethenestimatedfurthersystematicsinthedataanal-
require an accurate knowledge of the components of theX- ysisduetobackgroundsubtraction.Forthispurpose,weuse
ray background, and an accurate understanding of how the stowedbackgroundandlocalbackgroundtakenfromsource-
uncertainties of thebackground modeling propagate on the free regions of the cluster observations in order to model
desired physical parameters. the contribution of the CXB and particle background, re-
For more details and a thorough validation of the spectively. The two major sources of systematic uncertain-
method to gauge statistical and systematic errors, we refer ties are: i) the renormalizion of the stowed background to
thereadertoMorandi & Cui(2014).Herewebrieflyoutline match the cluster count rate at high energy (9.5-12 keV)
thekey aspects. due to Poisson errors; and ii) uncertainties in the parti-
ThecosmicX-raybackground(CXB)consistsofthelo- cle background across its spectrum. Note that the prop-
cal hot bubble emission, the thermal emission of the galac- erties of the particle background are well known via the
tic halo and the contribution of unresolved point sources stowed background observations, with uncertainties in the
(mostlyAGNs).Thelattercomponentismodeledasapower background across its spectrum which are within < 2 per-
∼
law with index 1.4. When analyzing regions of finite size cent(Hickox & Markevitch(2006)andseealsodiscussionin
we must account for Poisson fluctuations of these unre- Sunet al. (2009)).
solved point sources. The expected deviation from the av- Finally, we estimated the uncertainty in our measure-
erage value for a given observed solid angle Ω resolved to a ments due to soft X-ray background variations across the
(cid:13)c 0000RAS,MNRAS000,000–000
8 Morandi et al.
field of view. We divided the regions used to obtain the
background model into independent subregions with differ-
ent azimuthal direction with respect to the cluster center.
Weimplementedabootstrapapproach,wherewerandomly
picked these background subregions, allowing repetitions,
andre-determinedthebackgroundlevelviaEquation6.We
repeated this procedure 105 times, and determined the dis-
tribution of the average background. The uncertainties due
to CXB fluctuations are always smaller than the statisti-
cal error bars determined by assuming that the soft X-ray
background is spatially constant.
Alltheaforementioneduncertaintiesonthebackground
modelling (cosmic X-ray background, particle background,
soft X-ray background variations and unresolved point
sources) have been propagated in recovering the desired
physicalparameters,bymeansofMCrandomizationsofthe
backgroundincludingbothstatisticalandsystematicuncer-
tainties.
5.3 The impact of undetected clumps, gas
inhomogeneities and multi-temperature Figure 3.Bias(upwards)onthegasdensityatR500 duetoun-
distribution detectedsubstructuresatsubvirialtemperaturesT∼0.4keVand
0.6keV.Theplottedredshiftcorrespondstotherangewherethe
TheCDM scenario predictsa picturewhereclumps at sub-
subclumps fall below the detection threshold of the observation
virial temperature are infalling along filaments and accret-
(§5.2), i.e. they are undetected. We assumed a background level
ingontotheclusteroutskirts.Giventhelowsignal-to-noise, of2×10−11 ergcm−2s−1deg−2 inthesoftband,afillingfactor
low sensitivity/integration time and/or poor spatial resolu- of 1% for these subclumps, a cluster temperature of 4 keV and
tionoftheX-raytelescopes,itmightbeimpossibletomask self-similar gas density profile for both cluster and subclumps.
out cold substructures e.g. in the X-ray analysis, and they Thesolid(dashed) linerefersto anobservation timeof100 (10)
might remain undetected. A cold phase (T <1 keV) of the ks.
∼
ICM would also coexist in the outskirts with the hot ICM
at virial temperatures (> 2−4 keV), leading to a multi-
∼
phase structure of the ICM. The presence of a multiphase the whole sample, respectively, and repeating our stacking
structure of the ICM will bias the spectroscopic tempera- procedure, we do not find any significant difference in the
tures and gas density. Spectral temperature measurements recovered physical parameters, which might arise given the
indeed customarily hinge on a single-temperature absorbed differentimpactofsubstructuresupontheobservationtime.
thermal model, since the data quality is in general not suf- While thesuperb angular resolution of Chandra is essential
ficient to constrain a multitemperaturemodel, especially in for detecting small-scale clumps and distinguishing the X-
theoutskirts where thesignal is overwhelmed bythe noise. ray emissions arising from clumps and diffuse components,
The presence of undetected dense and cold clumps at we caution the reader that it possible we might actually
temperatures 0.5 < kT < 2 keV in the ICM will typi- missingsomesubstructuresevenindeepobservations,given
∼ ∼
cally enhance the X-ray emission, since the instrument is their low signal-to-noise in the outskirts, which could en-
very sensitive to the low energy features of these clumps hancethe X-rayemission and hencethegas density.
whoseexponentialbremsstrahlungcutoffwill beatenergies Moreover, inhomogeneities in the gas distribution can
∼kT/(1+z). Therefore, besides upon the dynamical state also lead to the overestimate of the observed gas density
of the cluster, the impact of dense clumps will also depend (Nagai & Lau2011;Zhuravlevaet al.2013;Roncarelli et al.
ontheredshiftoftheobservation,theChandraeffectivearea 2013),whichinturnintroducesbiasesinglobalclusterprop-
beingsmallforphotonenergiessmallerthan0.7keV.Thus, erties, such as the gas mass fraction (Battaglia et al. 2013)
if thisdenseclumpsat subvirial temperaturesare verycold andthelow-scatterX-raymassproxy,suchasY ≡M T
X gas X
(<1 keV),high-zclusters might beless biased by thepres- (Khedekaret al. 2013). At R hydrodynamical simula-
∼ 200
ence of a gas at low temperatures, but at the same time it tions predict a gas clumping factor in the range ∼ 1.3−2
willbemoredifficulttodetectthesesubstructuresgiventhe (Nagai & Lau 2011; Zhuravlevaet al. 2013; Battaglia et al.
cosmological dimming. Shallow observations are also more 2013). Gas clumping factor inferred from these simulations
prone to be biased by undetected clumps. In Figure 3 we isinreasonableagreementwithobservations(Morandi et al.
present the bias on the gas density due to undetected sub- 2013b; Morandi & Cui 2014). If they are not properly un-
structures at subvirial temperatures. derstood and modeled, thesenon-equilibrium processes can
The qualitative picture emerging by this toy model is limit theuse of galaxy clusters as cosmological probes.
that the presence of undetected substructures might bias Finally,inordertounderstandhowamultiphasestruc-
upwardsthemeasuredgas density,with amagnitudelarger ture of the ICM can bias X-ray observations, we present
for shallow observations and low redshifts. Nevertheless, by a simple toy problem and we analyze the effect of multi-
dividing our sample into two subsamples, clusters with to- temperature distribution on the physical observables (i.e.
tal net counts smaller and larger than the median value of X-ray spectroscopic temperature and gas density). A cold
(cid:13)c 0000RAS,MNRAS000,000–000
The galaxy cluster outskirts probed by Chandra 9
Figure 4. Bias on the gas density due to a multi-temperature gas distribution of the ICM. We fitted an absorbed thermal emission
model at a single emission temperature Tspec on mock spectra of a two-phase plasma at temperatures Thot and Tcold and in pressure
equilibrium,withgasmassfractionofthecoldgascomponent µ.Weassumethatthegasmass-weightedtemperatureofthistwo-phase
plasma(as measurede.g.bySZ)isconstant, i.e.Tmw=4keV.Theleft(right)panel referstoanobservationredshiftof0.05(1).
phase of the ICM would systematically bias down X-ray We can observe that the gas density on the two-phase
spectroscopictemperatureswithrespecttotheaverage(gas plasma is biased with respect to the true density.Since the
mass-weighted) temperature e.g. probed through SZ. We primary emission mechanism in X-ray clusters is thermal
consider a two-phase gas at temperatures T and T , bremsstrahlungandemission lines,thespectralfitisindeed
cold hot
with gas masses m and m , respectively, and in pres- guided, primarily, by the exponential bremsstrahlung cut-
cold hot
sureequilibrium.Hencethegasmass-weightedtemperature off at high energies, the iron line at energies ∼ 7/(1+z)
T reads: keV, and the lower energy (< 2 keV) emission lines. Com-
mw ∼
plications arise sincethetruespectrumof theastrophysical
Tmw =(1−µ)Thot+µTcold, µ=mcold/(mcold+mhot) (8) sourcemustbeconvolvedwiththeinstrumentalresponseof
the X-ray telescope. Chandra effective area, for example, is
with T =T (T ,T ,µ), T <T <T .
mw mw hot cold cold ∼ mw ∼ hot small for photon energies smaller than 0.6 keV or greater
We generated mock spectra of the previous plasma by
than 7 keV.Hence, thepresence of a cool phase at temper-
means of absorbed APEC emission models at temperatures
ature 0.5<T <2 keV in the ICM will typically bias down
∼ ∼
T and T , and under the boundary condition that gas
hot cold thespectroscopictemperature(single-temperatureabsorbed
mass-weighted temperature (Equation 8) is constant, i.e.
thermalmodel),sincetheinstrumentisverysensitivetothe
T = 4 keV. The hydrogen column density N is fixed
mw H low energy features, such as low energy emission lines. In
to 1020 cm−2. The current emission model is then folded
Figure 4 we can see that the gas density is biased upwards
through response curves(ARFand RMF) of Chandra. aslongas∼T /(1+z)>0.25 keV,awithnon-negligible
cold ∼
SinceTmw isconstant,theproblemtorecoverthespec- dependencyon theobservation redshift,µ andT .Coun-
cold
tral temperature Tspec of the two-phase plasma is fully de- terintuitively, for low temperatures ∼ T /(1+z) < 0.25
cold ∼
scribedviatwoindependentvariables,e.g.Tcoldandµ,while keVandlargervaluesofthecoldphasefractionµ>0.2,the
∼
Thot isadependentvariablewhichcanbeinferredviaEqua- measuredgasdensityisbiaseddownwardsof∼0−20%.This
tion8.Thus,Tspec=Tspec(Tcold,µ),wherewemeasuredthe isduetothefact thatmost oftheemission capturedbythe
spectral temperature by fitting an absorbed APEC emis- X-ray telescope arises from the hot phase of the ICM, with
sionmodelsatasingle-temperatureTspec onthemockspec- temperature Thot ∼>Tmw for Tcold/(1+z)∼<1 keV. On the
tra of the two-phase plasma. The final goal is to infer the contrary, most the emission of the cold phase would be at
biason thegasdensity,which arises sincethespectroscopic verylowenergies,wheretheChandraeffectiveareaissmall,
temperature Tspec is then used to convert observed X-ray and related to emission lines rather than bremsstrahlung.
counts into an emission measure (and thusgas density) via This bias is increasing for higher observation redshifts.
a single-temperature absorbed thermal model. In Figure 4
we present the results of the bias on the gas density for a A multiphase structureof theICM would retain signa-
grid of values of T and µ. tures of the ’melting pot’ in the virialization region, where
cold
(cid:13)c 0000RAS,MNRAS000,000–000
10 Morandi et al.
infalling clumps of matter and gas are predicted to have, profiles. Hereafter, we will refer to the results recovered via
typically, higher density and cooler temperature than their themedian of the emission measure profiles.
surroundings. Current measurements via X-ray telescopes, Finally, we estimated the bias due to uncertainty in
which customarily hinge on a single-temperature absorbed the M −Y relation (Sun et al. 2009) on the desired
500 X,500
thermalmodel,canbethusbiased.Futureinstruments(e.g., physical parameters due to the presence of non-thermal
the upcoming Astro-H and an envisaged Athena-like mis- pressure. The latter can indeed bias downwards the hy-
sion) will have enough collecting area and spectral resolu- drostatic masses through which the M −Y relation
500 X,500
tiontobetterdistinguishmulti-temperaturestructuresspec- has been calibrated. We define the mass bias b between
trally. Moreover, more detailed simulations (e.g. hydrody- the true and hydrostatic mass M , with both masses
hydro
namicalsimulations)includingtheseeffectsmightbeneeded defined at a fixed density contrast of 500. Hence we have
to address theimpact of thesebiases. thatM =M /(1−b).Wefurtherassumeanuniver-
true hydro
sal gas density profile as determined in our work (§6), and
the expression for the self-similar temperature profile from
5.4 Other sources of systematics
Vikhlinin et al. (2006). Thus, by changing the bias param-
Wecheckedtheeffect ofthepresenceofatemperaturepro- eter b and correcting accordingly the normalization of the
fileonthemeasuredemissionmeasures.Theconversionfrom M500−YX,500 relation, we can infer the R500 = R500(T,b)
ACIS-Icountratetoemissionmeasurehasbeendetermined relation from Equation 4, which can adequately described
via an absorbed thermal emission model folded with the bythe following expression:
AICS-Iresponse.Thisconversionfactorwasinferredforeach
T 0.44
clusterbyusingtheglobalspectroscopictemperatureinthe R =E−11095 X 100.37b kpc (9)
500 z (cid:18)6keV(cid:19)
range 0.15−0.75R rather than the temperature profile.
200
As we previously (§4.2) pointed out, the conversion from Thebiasonthetruegasdensitybecomesn /n ≃
e,true e,meas
ACIS-I count rate to emission measure is highly insensi- (R (b)/R )−α. Note that the bias parameter b
500 500,meas
tive to the temperature (for T > 2 keV). The conversion
refers to the non-thermal pressure support at R , since
500
factor changes at most by 8% for low-temperature (T ∼ 3 theM −Y relation has been calibrated at this over-
500 X,500
keV) clusters, which translates into a bias <4% on thegas
∼ densities. For larger radii we do not expect a larger impact
density, while it is negligible (< 1%) for hot (T > 6 keV)
∼ ∼ of the non-thermal pressure, since we used the YX,500 es-
systems. To further check the effect of the presence of a
timator in order to infer R ; hence R and R have
500 200 100
temperatureprofileonthemeasuredstackedemissivity and
been statistically determined by assuming an NFW distri-
hence gas density, we generated mock event files for each bution for the total matter (§3). From Equation 9 and for
clusterundertheseassumptions:i)thegasdensitydistribu- b∼0.1 (see, e.g. Mahdavi et al. 2008; Morandi & Limousin
tion for each cluster is self-similar and fixed to that mea-
2012;Morandi et al.2012)thepresenceofnon-thermalpres-
sured via our stacking method as described in §4.2; ii) we sure can bias upwards the gas density of ∼ 15(25)% at
assume the expression for the self-similar temperature pro-
R (R ).
500 200
filethatVikhlinin et al.(2006)showedtoreproducewellthe
temperaturegradients in nearby relaxed systems, with nor-
malization fixedtothespectraltemperatureofeachsource.
Werepeatedthestackingproceduredescribedin§4.2byas-
6 THE OUTSKIRTS OF CLUSTER: GAS
suming first isothermality and then by accounting for the
DENSITY
temperatureprofile.Weverifiedthattherecoveredphysical
parametersarebiaseddownwardsinanegligiblyway(<2% Results for the gas density, gas density slope β =
∼
for the emission measure) by ourmethod. −1/3dlog(n )/dlog(r) and gas fraction f (< R) =
e gas
As a further test, we compared our gas mass at R500 Mgas(< R)/Mtot(< R) for our sample are presented in Ta-
(recovered via deprojection of individual emission measure ble 2. We divided the data into subsamples to investigate
profiles) with the results of Maughan et al. (2008), whose the dependency on the redshift z, cluster temperature T,
sampleshares95objectsincommonwithours.Wealsocom- clustermorphologicaltype(relaxed/unrelaxed).Weconven-
paredwithMartino et al.(2014),whosesamplecontains32 tionally defined relaxed (unrelaxed) system with w < 10−2
objects in common with us. We found no significant differ- (w > 10−2). We remember that the centroid shifts and
ences between the recovered gas masses (Appendix D). We central density are anti-correlated (Figure 2), being both a
pointoutthattheseindividualgasmassesprofileshavebeen proxyofthepresenceofacool-core:thusthechosenthresh-
recovered only for thepurpose of this comparison, since we oldofwroughlydemarcatesthedivisionbetweenCC/NCC.
actually use stacked profiles across thepaper. The quoted uncertainties reflect the total error budget
Next, we compared the stacked emission measure pro- (measurement error + intrinsic scatter) by means of MC
file by using median and weighted average of the emission randomizations.
measureprofiles,andwedidnotfindanystatisticallysignif- Inordertogaugethebiasimplicitinoursphericalmod-
icant difference for R > 0.05R . Similar conclusions hold eling, we further repeated the X-ray analysis by restricting
∼ 200
for the gas density (Figure 5). This is a consequence of the the stacking procedure (§4.2) in two sectors (f and f in
1 2
factthattheerrors(measurementandsystematic)aresym- Table 2). The sector f has position angle fixed to the ma-
2
metric.However,aweighted-averagewouldsignificantlyun- jor axis of the X-ray brightness distribution and with an
derestimate the final uncertainties on the stacked emission aperture of 60 degrees, i.e. encompassing the cosmic fila-
measure, since it accounts only for the measurement errors ment (see §4.4 for further discussion), while the other (f )
1
but it neglects the intrinsic scatter of the emission measure characterizes theremaining volumes of thecluster.
(cid:13)c 0000RAS,MNRAS000,000–000