The gas distribution in the outer regions of galaxy clusters
D. Eckert, F. Vazza, S. Ettori, S. Molendi, D. Nagai, E. T. Lau, M. Roncarelli, M. Rossetti, S. L. Snowden, F. Gastaldello
aa r X i v : . [ a s t r o - ph . C O ] O c t Astronomy & Astrophysics manuscript no. outskirts c (cid:13)
ESO 2018May 21, 2018
The gas distribution in the outer regions of galaxy clusters
D. Eckert , , F. Vazza , S. Ettori , , S. Molendi , D. Nagai , E. T. Lau , , M. Roncarelli , M. Rossetti , , S.L. Snowden , and F. Gastaldello , INAF - IASF-Milano, Via E. Bassini 15, 20133 Milano, Italy ISDC Data Centre for Astrophysics, Geneva Observatory, ch. d’Ecogia 16, 1290 Versoix, Switzerlande-mail:
[email protected] Jacobs University Bremen, Campus Ring 1, 28759 Bremen, Germany INAF - Osservatorio Astronomico di Bologna, Via Ranzani 1, 40127 Bologna, Italy INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127 Bologna, Italy Department of Physics, Yale University, New Haven, CT 06520, USA Shanghai Astronomical Observatory, 80 Nandan Road, Shanghai 200030, China Dipartimento di Astronomia, Universit`a di Bologna, via Ranzani 1, 40127 Bologna, Italy Dipartimento di Fisica, Universit`a degli studi di Milano, via Celoria 16, 20133 Milano, Italy NASA/Goddard Space Flight Center, Code 662, Greenbelt, MD 20771, USA University of California at Irvine, 4129, Frederick Reines Hall, Irvine, CA, 92697-4575, USAPreprint online version: May 21, 2018
ABSTRACT
Aims.
We present our analysis of a local ( z = 0 . − .
2) sample of 31 galaxy clusters with the aim of measuringthe density of the X-ray emitting gas in cluster outskirts. We compare our results with numerical simulations to setconstraints on the azimuthal symmetry and gas clumping in the outer regions of galaxy clusters.
Methods.
We have exploited the large field-of-view and low instrumental background of
ROSAT /PSPC to trace thedensity of the intracluster gas out to the virial radius. We stacked the density profiles to detect a signal beyond r andmeasured the typical density and scatter in cluster outskirts. We also computed the azimuthal scatter of the profileswith respect to the mean value to look for deviations from spherical symmetry. Finally, we compared our average densityand scatter profiles with the results of numerical simulations. Results.
As opposed to some recent
Suzaku results, and confirming previous evidence from
ROSAT and
Chandra , weobserve a steepening of the density profiles beyond ∼ r . Comparing our density profiles with simulations, we find thatnon-radiative runs predict density profiles that are too steep, whereas runs including additional physics and/or treatinggas clumping agree better with the observed gas distribution. We report high-confidence detection of a systematicdifference between cool-core and non cool-core clusters beyond ∼ . r , which we explain by a different distributionof the gas in the two classes. Beyond ∼ r , galaxy clusters deviate significantly from spherical symmetry, with onlysmall differences between relaxed and disturbed systems. We find good agreement between the observed and predictedscatter profiles, but only when the 1% densest clumps are filtered out in the ENZO simulations.
Conclusions.
Comparing our results with numerical simulations, we find that non-radiative simulations fail to reproducethe gas distribution, even well outside cluster cores. Although their general behavior agrees more closely with theobservations, simulations including cooling and star formation convert a large amount of gas into stars, which results ina low gas fraction with respect to the observations. Consequently, a detailed treatment of gas cooling, star formation,AGN feedback, and consideration of gas clumping is required to construct realistic models of the outer regions ofclusters.
Key words.
X-rays: galaxies: clusters - Galaxies: clusters: general - Galaxies: clusters: intracluster medium
1. Introduction
The outskirts of galaxy clusters are the regions wherethe transition between the virialized gas of clustersand the accreting matter from large-scale structure oc-curs and where the current activity of structure for-mation takes place. Around the virial radius, the as-sumption of hydrostatic equilibrium, which is a neces-sary assumption for reconstructing cluster masses fromX-ray measurements, might not be valid any more (e.g.,Evrard et al. 1996), which could introduce biases to X-ray mass proxies (Rasia et al. 2004; Piffaretti & Valdarnini2008; Nagai et al. 2007b; Lau et al. 2009; Meneghetti et al.2010; Fabjan et al. 2011). As a result, the characterization of the X-ray emitting gas in the outer regions of galaxy clus-ters is important for mapping the gas throughout the entirecluster volume, studying the formation processes currentlyat work in the Universe, and performing accurate mass es-timates for cosmological purposes (e.g., Allen et al. 2011).Because of the low surface brightness of the X-rayemitting gas and the extended nature of the sources,measuring the state of the intracluster gas around thevirial radius is challenging (Ettori & Molendi 2011).Recently, the
Suzaku satellite has achieved a break-through in this domain, performing measurements of
1. Eckert et al.: The gas distribution in the outer regions of galaxy clusters cluster temperatures out to r (Reiprich et al. 2009;Bautz et al. 2009; Kawaharada et al. 2010; Hoshino et al.2010; Simionescu et al. 2011; Akamatsu et al. 2011;Humphrey et al. 2012), even in one case beyond r (George et al. 2009), although this detection is likelyhampered by systematic effects (Eckert et al. 2011a).Interestingly, some of the Suzaku results indicate verysteep temperature profiles and shallow density profilesin cluster outskirts, at variance with the results from
XMM-Newton (Pratt et al. 2007; Leccardi & Molendi2008; Snowden et al. 2008; Croston et al. 2008),
Chandra (Vikhlinin et al. 2006; Ettori & Balestra 2009),
ROSAT (Vikhlinin et al. 1999; Neumann 2005), and with theresults from numerical simulations (Roncarelli et al. 2006;Tozzi & Norman 2001; Nagai & Lau 2011). Thus, thebehavior of the gas in cluster outskirts is still the subjectof debate. Throughout paper, we refer to cluster outskirtsas the region with r > r .Thanks to its large field of view (FOV, ∼ )and low instrumental background, ROSAT /PSPC is to thepresent day the most sensitive instrument for low surface-brightness emission. Its ability to detect cluster emission atlarge radii has been demonstrated by Vikhlinin et al. (1999)and Neumann (2005) (hereafter, V99 and N05). Becauseof the large FOV, it can perform simultaneous local back-ground measurements, so it is less affected than
Suzaku bysystematic uncertainties. Its main limitation, however, isthe restricted band pass and poor spectral resolution, whichmakes it impossible to measure cluster temperatures.This paper presents the analysis of a sample of 31galaxy clusters observed with
ROSAT /PSPC, with the aimof characterizing the cluster emission at large radii andcomparing the results with three different sets of numer-ical simulations (Roncarelli et al. 2006; Nagai & Lau 2011;Vazza et al. 2010). The paper is organized as follows. InSect. 2, we describe our cluster sample and the availabledata. We present our data analysis technique in Sect. 3 andreport our results in Sect. 4. We compare our results withnumerical simulations in Sect. 5 and discuss them in Sect.6. Throughout the paper, we assume a ΛCDM cosmologywith Ω m = 0 .
3, Ω Λ = 0 .
7, Ω b = 0 . H = 70 km s − Mpc − .
2. The sample
We selected objects in the redshift range 0 . − .
2, suchthat r is easily contained within the FOV of the instru-ment and is large enough to allow for an adequate sam-pling of the density profile. We restricted ourselves to ob-servations with enough statistics to constrain the emissionaround the virial radius. Our final sample comprises 31 clus-ters in the temperature range 2.5-9 keV, with the additionof A2163 ( kT ∼
18 keV). Among our sample, we classified14 clusters as cool core (CC) following the classificationof Cavagnolo et al. (2009) (i.e. they exhibit a central en-tropy K <
30 keV cm ), and 17 as non cool core (NCC, K >
30 keV cm ). We recall that CC clusters exhibit arelaxed morphology, a high central density and a temper-ature decrement in the central regions, while NCCs tracedynamically-disturbed clusters with irregular morphologies We define r ∆ as the radius within which M ( < r ∆ ) / πr =∆ ρ crit and flat temperature and density profiles in their cores (e.g.,Sanderson et al. 2009; Hudson et al. 2010).Our sample of clusters, together with the log of theavailable data and some important quantities, is shown inTable 3. In Fig. 1 we plot the distribution of temperature(left hand panel) and central entropy (right hand panel)for our sample. It should be noted that the sample wasselected based on the quality of the existing observationsand might be subject to selection effects. However, for thepurpose of this work we did not require that the samplebe representative or complete, since we are interested incharacterizing cluster outskirts, which exhibit a high levelof self-similarity.
3. Data analysis
We used the
ROSAT
Extended Source Analysis Software(Snowden et al. 1994) for data reduction. We filtered outtime periods when the master veto count rate exceeds 220cts/sec (using valid times ), and extracted light curves forthe whole observation using rate pspc . We used the ao executable to model the atmospheric column density forthe scattering of solar X-rays, and fit the light curves ineach energy band to get the relative contributions of thescattered solar X-rays (SSX) and of the long-term enhance-ments (LTE), using the rate fit executable.We then extracted event images in each energy bandand the corresponding effective exposure maps, taking vi-gnetting effects into account. We computed the contri-bution of the various background components, the LTE( lte pspc ), the particle background ( cast part ), and theSSX ( cast ssx ), and combined them to get a map of allthe non-cosmic background components. The point-spread function (PSF) of
ROSAT /PSPCstrongly depends on angle, and ranges from ∼
15 arcsec on-axis to 2 arcmin in the outer parts of the FOV. Thus, thesensitivity of the instrument to point sources is higher on-axis, and a larger fraction of the cosmic X-ray background(CXB) is resolved. Consequently, when detecting sources inthe image it is important to use a constant flux threshold,such that the same fraction of the CXB is resolved overthe entire FOV and the value measured in the source-freeregions can be used to subtract the background. We detectpoint sources using the program detect with a minimumcount rate of 0.003 cts/sec in the R3-7 band ( ∼ × − ergs cm − s − in the 0.5-2.0 keV band) to resolve the samefraction of the CXB over the FOV, and mask the corre-sponding areas. To compute surface-brightness profiles, weextract count profiles from the event images in the R3-7band (0.42-2.01 keV) with 30 arcsec bins centered on thesurface-brightness peak, out to the radius of 50 arcmin.We divide each pixel by its corresponding exposure to ac-count for the vignetting effects, following the procedure ofEckert et al. (2011b) . We perform the same operation forthe background map and subtract the non-cosmic back-ground profile in each bin. ∼ eckert/newsite/Proffit.html2. Eckert et al.: The gas distribution in the outer regions of galaxy clusters kT [keV]2 3 4 5 6 7 8 9 10 N u m b e r [keV cm K1 10 N u m b e r Fig. 1.
Distribution of temperature (left) and central entropy (right) of the members of our sample (see Table 3). In theleft panel, A2163 ( kT ∼
18 keV) is located outside of the range.We tested this procedure on four different blank fieldsto estimate the accuracy in our determination of the CXB.We extracted the surface-brightness profile for the four ob-servations from the center of the FOV, grouped the binsto ensure a minimum of 100 counts per bin, and fittedthe resulting profiles with a constant (see Fig. 2). Whilethe agreement is qualitatively good, significant deviationsfrom the model are found, leading to an excess scatter of ∼ r islarger than 15 arcmin, our systematic error of 6% is a con-servative estimate of the level of systematic uncertaintiesat the virial radius.For each cluster, we then use temperature pro-files from the literature ( XMM-Newton , Snowden et al.(2008);
Chandra , Cavagnolo et al. (2009);
BeppoSAX ,De Grandi & Molendi (2002)) to estimate the virial tem-perature of the cluster. We approximated T vir as the meantemperature in the 200-500 kpc region, i.e. excluding thecool core and the temperature decline in the outskirts(Leccardi & Molendi 2008). Using this estimate of T vir , wecomputed the value of r from the scaling relations ofArnaud et al. (2005). One might argue that the scaling re-lations of Arnaud et al. (2005) were computed using themean temperature in the 0 . − . r region, which in mostcases extends beyond the available temperature profiles.Using the mean temperature profiles of Leccardi & Molendi(2008), we computed the mean temperature extracted inthe 0 . − . r and 200-500 kpc regions. In the temper-ature range of our sample, we found that the results differat most by 2%, so our values of r are unbiased. We thenused the source-free region of the observation ( r > . r )to fit the surface-brightness profile with a constant and getthe cosmic background level for the observation, with theexception of the Triangulum Australis cluster, for which we ] - a r c m i n - S B [ c oun t s s -4 R a t i o Fig. 2.
Surface-brightness profiles for 4 blank-field PSPCobservations from the center of the FOV, fitted with a con-stant. The dashed line shows the vignetting correction curvefor comparison, in arbitrary units; the bump at ∼
22 ar-cmin is caused by the support structure. The bottom panelshows the ratio between data and model.used the range r > . r because of the high value of r ( ∼
37 arcmin).After having estimated the sky background for our ob-servation, we again extracted the surface-brightness profilein the radial range 0 − . r with logarithmic bin size.The best-fit value for the CXB was subtracted from theprofile and its error was added in quadrature to each bin.The systematic error of 6% on the CXB was also added inquadrature to account for the cosmic variance and system-atic uncertainties. For comparison, we note that in mostcases the statistical uncertainties in the profiles are on theorder of 10% of the CXB value around r .
3. Eckert et al.: The gas distribution in the outer regions of galaxy clusters
To compute the density profiles, we first rebinned ourbackground-subtracted surface-brightness profiles to ensurea minimum of 200 counts per bin and a detection signifi-cance of at least 3 σ , to reach sufficient statistics in each bin.We used the procedure of Kriss et al. (1983) to deprojectthe observed profiles, and the PSPC response to convertthe observed count rates into emission measure, throughthe normalization of the MEKAL model (see Eckert et al.2011a, for details), N orm = 10 − π [ d A (1 + z )] Z n e n H dV, (1)which is proportional to the emission measure. We assumedthat the spectrum of our sources is described by an ab-sorbed MEKAL model with N H fixed to the 21cm value(Kalberla et al. 2005) and abundance fixed to 0 . Z ⊙ . Weused temperature profiles from the literature (see Table 3)and interpolated them onto the same grid as the SB pro-files. The resulting model was then folded with the PSPCresponse, and the conversion from PSPC R3-7 count rateto emission measure was inferred. Beyond the limit of thetemperature profiles, the temperature of the outermost an-nulus was used. We note that the conversion from PSPCcount rate to emission measure is highly insensitive to thetemperature; between 2 and 8 keV, the conversion factorchanges at most by 4%. Once converted into the MEKALnormalization, we inferred the density profiles, assumingspherical symmetry and constant density into each shell.The error bars on the density profiles were estimated us-ing a Monte Carlo approach. In each case, we generated 10 realizations of the surface-brightness profile using Poissonstatistics, and performed the geometrical deprojection fol-lowing the method described above. The 1 σ error bars werethen estimated by computing the root-mean square devia-tion (RMS) of our 10 realizations of the density profile ineach density bin. For the purpose of this work, we are also interested in thedeviations in the X-ray emission from spherical symmetry.We divide our images into N azimuthal sectors with con-stant opening angle, and compute the surface-brightnessprofiles in each sector individually. We then compute thescatter of the various sectors with respect to the meanprofile, following the definition introduced by Vazza et al.(2011b),Σ = 1 N N X i =1 ( SB i − h SB i ) h SB i , (2)where h SB i is the mean surface-brightness and SB i , i =1 ..N denotes the surface-brightness computed in the vari-ous sectors. It must be noted that the statistical fluctua-tions of the SB between the different sectors introduce acertain level of scatter in Eq. 2, which must be taken intoaccount for determining the level of intrinsic scatter. Weused two different methods to disentangle between statis-tical and intrinsic scatter. In the first case, we computedthe level of statistical scatter independently and subtracted it from Eq. 2. In the second case, we used a maximum-likelihood estimator to determine the intrinsic scatter andits uncertainties. The two methods gave consistent resultsand are described in detail in Appendix A. For the remain-der of the paper, we refer to the results obtained using thedirect method (see Sect. A.1).In our analysis, we group the bins of the total surface-brightness profiles to reach a minimum of 8 σ per bin to en-sure adequate statistics in the scatter measurements, andthen divide our images into 12 sectors with an opening of30 ◦ . The result of this analysis is a radial profile describingthe intrinsic azimuthal scatter of the X-ray surface bright-ness, in percent.It must be noted that the method presented here is sen-sitive to all kinds of deviations from spherical symmetry,whether it is induced by the asymmetry of the large-scalestructure (e.g., filaments), by gas clumping or by ellipticity.The cause of the observed asymmetry cannot be determinedfrom the azimuthal scatter alone.
4. Results
In Fig. 3 we show the scaled emission measure profiles (left,following Eq. 1) and the deprojected density profiles (right)for the 31 clusters in our sample. A self-similar scalingwas applied to the emission-measure profiles (Arnaud et al.2002); i.e., each profile was rescaled by the quantity∆
SSC = ∆ / z (1 + z ) / (cid:18) kT
10 keV (cid:19) / . (3)The density profiles were rescaled by E ( z ) = Ω m (1 + z ) + Ω Λ following their expected evolution with redshift(Croston et al. 2008). As already noted by several authors(e.g., Vikhlinin et al. 1999; Neumann 2005; Croston et al.2008; Leccardi et al. 2010), the profiles show a remarkablelevel of self-similarity outside of the core ( r > . r ).On the other hand, the large scatter observed in the cen-tral regions reflects the distinction of the cluster popu-lation into CCs, showing a prominent surface-brightnesspeak, and NCCs, which exhibit a flat surface brightness pro-file in their cores, as expected from the standard β -model(Cavaliere & Fusco-Femiano 1976), SB ( r ) = SB (cid:18) rr c (cid:19) ! − β +0 . . (4)In the radial range 0 . − . r , the scatter of the den-sity profiles is 10%-20%, in excellent agreement with the Chandra (Vikhlinin et al. 2006) and
XMM-Newton re-sults (Croston et al. 2008). However, Croston et al. (2008)needed to rescale the profiles by T − / to account for thelower gas fraction in low-mass objects. In our case, perform-ing such a scaling does not reduce the scatter of the profilesfurther. This is probably explained by the relatively narrowtemperature range spanned in our sample (all but one ob-jects have a temperature higher than 3 keV), such that theclusters in our sample should show little dependence on gasfraction.
4. Eckert et al.: The gas distribution in the outer regions of galaxy clusters r/r -2 -1
10 1 S e l f- s i m il a r sca l e d E M -10 -9 -8 -7 -6 -5 -4 r/r -2 -1
10 1 ] - [ c m - E ( z ) H n -4 -3 -2 Fig. 3.
Scaled emission measure (left, in units of cm − Mpc) and density profiles (right) for the 31 clusters of our sample(see Table 3).
To compute the mean profile of our sample, we interpolatedeach profile following a predefined binning in units of r common to all clusters and performed a weighted mean tocompute stacked profiles. The errors on the interpolatedpoints were propagated to the stacked profiles. We also di-vided our sample into the two classes (CC and NCC) tolook for differences between them.In Fig. 4 we show the stacked emission-measure (EM)profile for the entire sample compared to the profilesstacked for the two populations separately (see alsoAppendix C). Interestingly, we note a clear distinction be-tween the two classes in cluster outskirts (see the bottompanel of the figure). Namely, beyond ∼ . r , NCC pro-files systematically exceed CCs. A similar effect has re-cently been noted by Maughan et al. (2011), who founda crossing of the average density profiles at a similar ra-dius, and also at a lower statistical significance in the worksof Arnaud et al. (2010) and Pratt et al. (2010). We stressthat this effect is really a difference between the two classes;i.e. it is not introduced by a biased distribution of anotherquantity (such as temperature or redshift). Indeed, group-ing the profiles according to the temperature or the redshiftdid not show any particular behavior, which indicates thatwe are really finding an intrinsic difference between the CCand NCC classes. This result could follow from a differentdistribution of the gas in the two populations or from ahigher clumping factor in disturbed objects (see Sect. 6).Alternatively, the observed difference could be explainedby an inaccurate determination of r for NCC clusters.Indeed, the scaling relations of Arnaud et al. (2005) werecomputed under the assumption of hydrostatic equilibrium,which is fulfilled better in CC clusters. This explanationis, however, unlikely. Indeed, to recover self-similarity, ourvalue of r should have been systematically underesti-mated by ∼
10% for NCCs, i.e. since r ∝ T / vir the virialtemperature of the NCC clusters should have been under-estimated by more than 20%. From mock Chandra observa-tions of a sample of simulated galaxy clusters, Nagai et al.(2007b) have determined that the spectroscopic tempera-tures of unrelaxed clusters differs from that of relaxed clus-ters by ∼ S e l f- s i m il a r sca l e d E M -8 -7 -6 -5 -4 r/r0.2 0.4 0.6 0.8 1 1.2 R a t i o Fig. 4.
Stacked emission measure profile (in units of cm − Mpc) for the entire sample (black), and the two populationsindividually (CC, red; NCC, blue). See also Appendix C.The bottom panel shows the ratio between the CC andNCC populations.difference. It is therefore unlikely that such a large error onthe virial temperature would be made.We fit the mean scaled emission-measure profiles fromFig. 4 with the standard β -model (Eq. 4), adding a second β component in the case of the CC clusters to take thecool core into account. The (double) β model gives a goodrepresentation of the data in the radial range 0 − . r ( ∼ r ), but significantly exceeds the observed profilesabove this radius, in agreement with the results of V99,N05, and Ettori & Balestra (2009). For CC clusters, thebest-fit model gives β = 0 . ± . β = 0 . ± . r , we observe a significant steepening,with a slope β = 0 . ± .
054 for CCs and β = 0 . ± .
5. Eckert et al.: The gas distribution in the outer regions of galaxy clusters r/r -1
10 1 ] - [ c m - E ( z ) H n -4 -3 -2 Fig. 5.
Average proton density profile for the entire sample.The dashed lines indicate the positive and negative scatterof the profiles around the mean value.is flatter than that of the CC profile beyond r . The fitsof the profiles in various radial ranges are reported in Table2 to quantify the steepening.Given the limited number of objects in our sample, wehave to verify that this result is not a chance realization.We fit all the emission-measure profiles at r > . r witha β profile, fixing the value of β to 0.7 and r c to 0 . r ,and extracted the best-fit normalization for all profiles. Wethen sorted the normalization values into the CC and NCCclasses, and performed a Kolmogorov-Smirnov test to de-termine the probability that they originate in the same par-ent distribution. Using this procedure, we found that thechance probability for this result is very low, P ∼ × − .Therefore, we can conclude with good confidence that weare indeed finding an intrinsic difference between the twoclasses. We stacked the density profiles shown in the right handpanel of Fig. 3 following the same method as for the EMprofiles. From the different profiles, we also computed thescatter of the profiles around the mean value, following amethod similar to the one presented in Sect. 3.4 for theazimuthal scatter. The statistical scatter was subtractedfrom the total scatter using the same technique. In Fig.5 we show the average density profile of our clusters to-gether with the scatter of the individual profiles aroundthe mean value (see also Table 1). At r , the mean den-sity is n = (3 . ± . × − E ( z ) cm − , with 25%scatter. For comparison, it is interesting to note that thedensity of PKS 0745-191 claimed in the Suzaku analysis ofGeorge et al. (2009) at r deviates from our mean valueby more than 5 σ , which casts even more doubt on this mea-surement (Eckert et al. 2011a).As for the EM, we also extracted mean density profilesindividually for the two classes of clusters in our sample.The same behavior is observed at large radii; i.e., the den-sity of NCC clusters is systematically higher (by ∼ r ∼ . r . A global steepening ofthe density profiles is also observed beyond ∼ r . Table 1.
Mean emission-measure and density profiles com-puted from our sample. R in R out ScEM n H E ( z ) − σ . ± . · − . ± .
033 580.03 0.06 (1 . ± . · − . ± .
018 460.06 0.09 (7 . ± . · − . ± .
012 360.09 0.12 (5 . ± . · − . ± .
010 260.12 0.15 (3 . ± . · − . ± .
009 210.15 0.18 (2 . ± . · − . ± .
008 170.18 0.21 (1 . ± . · − . ± .
007 170.21 0.24 (1 . ± . · − . ± .
007 130.24 0.27 (9 . ± . · − . ± .
006 120.27 0.30 (7 . ± . · − . ± .
006 150.30 0.33 (5 . ± . · − . ± .
005 120.33 0.37 (4 . ± . · − . ± .
005 150.37 0.42 (3 . ± . · − . ± .
005 120.42 0.47 (2 . ± . · − . ± .
004 120.47 0.52 (1 . ± . · − . ± .
004 180.52 0.59 (1 . ± . · − . ± .
004 160.59 0.66 (7 . ± . · − . ± .
004 250.66 0.74 (5 . ± . · − . ± .
003 100.74 0.83 (3 . ± . · − . ± .
003 340.83 0.93 (1 . ± . · − . ± .
002 170.93 1.05 (1 . ± . · − . ± .
002 111.05 1.17 (6 . ± . · − . ± .
002 22Note: Column description. 1 and 2: Inner and outer bin radii inunits of r ; 3: Emission measure rescaled by ∆ SSC in units ofcm − Mpc; 4: Average proton density in units of 10 − cm − ;5: Scatter of the various profiles relative to the mean value inpercent. Our density profiles are in good agreement with the re-sults of V99. However, while V99 estimated the densityfrom β -model fitting, we performed a geometrical depro-jection of the data using temperature profiles to infer themean density profile. This method has the advantage of notdepending on any model. We computed the gas mass from our deprojected densityprofiles and stacked them in the same way as describedabove. In the self-similar model, the gas mass is expectedto follow the relation M ∝ T / (e.g., Bryan & Norman1998). However, observational works indicate that the ac-tual M gas − T relation is steeper than the expected self-similar scaling (Neumann & Arnaud 2001; Arnaud et al.2007; Croston et al. 2008) because of the lower gas fractionin groups and poor clusters. For this work, we use the rela-tion determined from the REXCESS sample (Croston et al.2008) to rescale our gas mass profiles, M gas ∝ E ( z ) − (cid:18) kT
10 keV (cid:19) . . (5)As above, we divided the sample into CC and NCCclasses, and stacked the two classes individually. In Fig. 6we show the mean gas mass profiles for CC and NCC clus-ters. As expected, CCs have a higher gas mass in their innerregions, since their central densities are higher. More inter-estingly, we see that the two profiles converge in cluster
6. Eckert et al.: The gas distribution in the outer regions of galaxy clusters r/r -1
10 1 ] [ M - . k T g as M Fig. 6.
Enclosed gas mass profiles for CC (red) and NCCsystems (blue). The data were rescaled by E ( z ) kT − . asobserved in the REXCESS sample (Croston et al. 2008).outskirts, and exhibit a gas mass around the virial radiusthat is consistent within the error bars. At r , the univer-sal gas mass is M gas, = (2 . ± . × E ( z ) − (cid:18) kT
10 keV (cid:19) . M ⊙ , (6)with a scatter of 17% around the mean value. This resultfollows from the higher density measured in average beyond ∼ . r in NCC clusters and the steeper slope of CC pro-files in the outskirts (see Sect. 4.2). The lower density ofCC clusters in the outer regions compensates for the well-known excess observed in the cores, such that the total gasmass contained within the dark-matter halo follows a uni-versal relation. We also estimated the average gas fractionby computing the expected value of M using the scalingrelations of Arnaud et al. (2005). For our sample, we finda mean gas fraction within r of f gas, = (0 . ± . (cid:18) kT
10 keV (cid:19) . , (7)in good agreement with previous works (e.g.,Vikhlinin et al. 2006; McCarthy et al. 2007), whichfor the most massive objects corresponds to ∼
89% of thecosmic baryon fraction (Jarosik et al. 2011).
Following the method described in Sect. 3.4, we computedthe azimuthal scatter of the surface-brightness profiles forall the clusters in our sample, and rescaled the scatter pro-files by our estimated value of r . We then stacked theprofiles using the same procedure as described above andcomputed the mean azimuthal scatter. We recall that sincethe surface brightness depends on n e , the variations in den-sity are less important than the ones computed here.In Fig. 7 we plot the average scatter profile, comparedto the mean value for CC and NCC clusters. The increasein the innermost bin is an artifact introduced by the smallnumber of pixels in the center of the images, so it shouldbe neglected. At small radii ( r < . r ) we find a clear r/r0.2 0.4 0.6 0.8 1 A z i m u t h a l sca tt e r Fig. 7.
Stacked azimuthal scatter in surface-brightness forthe entire cluster sample (black). The red and blue datarepresent the mean profile extracted from CC and NCCclusters, respectively.difference between CC and NCC clusters, which is eas-ily explained by the more disturbed morphology of thelatter. In this radial range, CC profiles exhibit a scat-ter of 20-30%, which corresponds to density variations onthe order of 10%, in good agreement with the value pre-dicted by Vazza et al. (2011b) from numerical simulations.Conversely, beyond r ∼ r , the profiles for CC and NCCclusters are similar, and indicate a high scatter value (60-80%).We investigated whether any systematic effect could af-fect our result in cluster outskirts, where the backgroundis dominating with respect to the source. Indeed, in suchconditions, the total scatter is dominated by the statisticalscatter. In case the mean level of systematic uncertainties inthe CXB reconstruction exceeds our adopted value of 6%,Eq. A.2 immediately implies that the intrinsic scatter wouldbe overestimated. The presence of both intrinsic and sta-tistical scatter could also introduce some covariance term,which is not taken into account in Eq. A.2. To test this hy-pothesis, we ran a set of simulations including source andbackground, where we introduced a given level of intrinsicscatter for the source and a systematic error in additionto the Poisson statistics for the background. We then com-puted the intrinsic level of scatter following Eq. A.2. Oursimulations indicate that, even when increasing the level ofsystematic uncertainties to 12% of the CXB value, a signif-icant bias in the measured scatter only appears when thesource-to-background ratio is close to the systematic uncer-tainties. Since, by construction, we never detect any signalwhen the source is less than ∼
15% of the CXB value, ourresults are unaffected by these effects, and we can concludewith good confidence that the high level of scatter mea-sured beyond ∼ r is an intrinsic property of our clustersample.In addition, we also tested whether the scatter for thetwo populations in the outermost regions could be affectedby small-number statistics or driven by some particular ob-jects. Of the 31 objects in our sample, a measurement of thescatter at r could be obtained for 23 of them (12 NCCand 11 CC). We used a jackknife method to test whether asingle object dominates the results for any of the two pop-
7. Eckert et al.: The gas distribution in the outer regions of galaxy clusters ulations; i.e., we randomly exclude one or two profiles fromthe sample, recompute the mean profiles, and examine thedistribution of the mean values. In both cases, the distri-bution of results is regular, which indicates that our resultsare not biased by a particular object.V99 also investigated the deviations from spherical sym-metry by measuring the value of β in six sectors in the ra-dial range r > . r , and concluded that the assumptionof spherical symmetry is relatively well satisfied in clusteroutskirts, at variance with our results (see Fig. 7). However,when fitting a β -model the fit is mostly driven by the shapeof the profile in the innermost region, where the statisticsare higher. Conversely, our method is model-independent,and it directly stacks the data at similar radii. For relaxedobjects, our data also indicate little deviation from spheri-cal symmetry at r < r , and a significant scatter is onlyobserved beyond r , so it is probable that these devi-ations would not be reflected in the β -model fit. For in-stance, the case of A2029 is striking. While, in agreementwith V99, we find little azimuthal variations in β outer , weobserve a high level of scatter in this object beyond r ,which is explained by the presence of a possible filamentconnecting A2029 to its neighbor A2033 in the north (seeGastaldello et al. (2010) and Appendix B). Moreover, V99deliberately excluded a number of systems with obviouslydisturbed morphologies, such as A3558 and A3266, whichwe included in our sample. Therefore, our results do notcontradict those of V99.
5. Comparison with numerical simulations
In this section, we compare our observational re-sults with three different sets of numerical simulations(Roncarelli et al. 2006; Nagai et al. 2007b; Vazza et al.2010). We analyze the results of a composite set of cosmo-logical runs, obtained by the different authors with slightlydifferent cosmological and numerical setups. In addition,the preliminary data reduction was made on each datasetfollowing independent post-processing techniques, aimed atassessing the role of gas clumping on the comparison be-tween simulated mock and real X-ray observations. Ouraim in this project is to test the most general and converg-ing findings of such different runs against our observationswith
ROSAT /PSPC.
ENZO
We use a sample of 20 simulated clusters from the high-resolution and non-radiative (NR) resimulations of massivesystems presented in Vazza et al. (2010). In this set ofsimulations, adaptive mesh refinement in the
ENZO
ART
We analyze a sample of ten simulated clusters with T X > . ART ) N-body+gas-dynamics code(Kravtsov 1999; Kravtsov et al. 2002), which is a Euleriancode that uses adaptive refinement to achieve high spatialresolution (a few kpc) in self-consistent cosmological simu-lations. To assess the impact of cluster physics on the ICMproperties, we compared two sets of clusters simulated withthe same initial conditions but with different prescription ofgas physics. In the first set, we performed hydrodynamicalcluster simulations without gas cooling and star formation.We refer to this set of clusters as NR clusters. In the secondset, we turned on the physics of galaxy formation, such asmetallicity-dependent radiative cooling, star formation, su-pernova feedback, and a uniform UV background. We referto this set of clusters as cooling+star formation (CSF) clus-ters. For detailed descriptions of the gas physics and mockX-ray images we refer the reader to Nagai et al. (2007a,b).Following Nagai & Lau (2011), we also computed theclumping-corrected gas density profiles of X-ray emittinggas with
T > K for comparisons with X-ray observa-tions. Indeed, the formation of dense clumps increases theemissivity of the gas, which leads to an overestimation ofthe measured gas density when the assumption of constantdensity in each shell is made. For these profiles, we com-puted the average squared density from the simulations ineach radial bin and took the square root of the total tomimic the reconstruction of density profiles from real data(see Nagai & Lau 2011, for details).
GADGET
This set includes four massive halos simulated with the
GADGET-2
Tree-SPH code (Springel 2005), with M > M ⊙ (for a detailed description see Roncarelli et al.2006, and references therein). Each object was simulatedfollowing two different physical prescriptions: a NR run (re-ferred to as ovisc in Roncarelli et al. 2006) and a run in-cluding cooling, star formation, and supernovae feedback(CSF).To eliminate the dense clumps that dominate the den-sity and surface brightness in the outskirts, when comput-ing the profiles for every radial bin, we excise the one percent of the volume that corresponds to the densest SPHparticles. This empirical method mimics the procedure ofmasking bright isolated regions from the analysis of ob-served clusters. We compared the simulations with our observed mean
ROSAT density profile (see Fig. 5 and Table 1). We presentthe detailed comparison in Fig. 8, with the NR simulations(left hand panel) and with the CSF simulations (right).From the figures, we find relatively good agreement be-tween all the different sets of simulations, especially beyond ∼ . r . The NR GADGET run has a lower normalizationthan the corresponding grid codes, because in
GADGET thefraction of baryons virializing into clusters is less than thecosmic value ( ∼
78% of the cosmic baryon fraction), whilegrid codes predict a baryon fraction in clusters very close
8. Eckert et al.: The gas distribution in the outer regions of galaxy clusters ] - [ c m - E ( z ) H n -5 -4 -3 ] - [ c m - E ( z ) H n -5 -4 -3 NR profilesGADGETARTENZO r/r0.2 0.4 0.6 0.8 1 1.2 R a t i o r/r0.2 0.4 0.6 0.8 1 1.2 R a t i o ] - [ c m - E ( z ) H n -5 -4 -3 ] - [ c m - E ( z ) H n -5 -4 -3 CSF profilesGADGETARTART cl r/r0.2 0.4 0.6 0.8 1 1.2 R a t i o r/r0.2 0.4 0.6 0.8 1 1.2 R a t i o Fig. 8.
Comparison between the mean
ROSAT density profile for our sample and the different sets of numerical simula-tions. The shaded area indicates the data and 1 σ scatter as shown in Fig. 5. The bottom panels show the ratio betweensimulations and data as a function of radius. Left:
Comparison with NR simulations. The dotted red curve represents the
ENZO profile (Vazza et al. 2010), the solid green curve shows the
ART simulations (Nagai et al. 2007b), and the dashedblue curve is the
GADGET profile (Roncarelli et al. 2006).
Right:
Same with CSF simulations. The dashed blue line showsthe
GADGET simulations, while the green curves show the
ART profiles, for the total density (solid) and corrected forclumping (dotted, Nagai & Lau 2011).to the cosmic value. In general, we see that the predicteddensity profiles are too steep compared to the data. Wenote that NR runs predict steeper profiles than the runs in-cluding cooling, star formation, and feedback effects. CSFprofiles also have lower normalizations, since radiative cool-ing transforms a fraction of the gas into stars. The profileincluding the effects of clumping shows the best agreementwith the data.To quantify this effect, we fitted the various profiles inthree different radial ranges (0 . − . r , 0 . − . r ,and 0 . − . r ). In the inner regions, the effects of addi-tional physics are expected to be important, thus highlight-ing the differences between NR and CSF runs. The radialrange 0 . − . r ( ≈ . − r ) is a good range for com-paring with the data, since the effects of radiative coolingshould be small, and data from several different satellitesare available for cross-check. On the observational side, thedensity profiles in this radial range are well-fitted by the β -model (see Eq. 4), and several independent works convergeto the canonical value of β ∼ . β for our averagedensity profile and the various sets of simulations, fixing thecore radius to 0 . r (e.g., Mohr et al. 1999). The resultsof this analysis are shown in Table 2. The fits to the ob-servational data were performed on the emission-measureprofiles (see Sect. 4.2) to take advantage of the larger num-ber of bins and minimize the uncertainties linked to thedeprojection procedure.These numbers confirm the visual impression that thesimulated gas density profiles are steeper than the observedones. In the 0 . − . r range, while all our datasetsconverge to a β value very close to the canonical value,all the simulations lead to significantly steeper gas profiles, Table 2.
Values of the β parameter(Cavaliere & Fusco-Femiano 1976) in several radialranges for the average ROSAT profiles and the varioussets of simulations.
Data set β . − . β . − . β . − . Data, total 0 . ± .
002 0 . ± .
009 0 . ± . . ± .
004 0 . ± .
016 1 . ± . . ± .
003 0 . ± .
011 0 . ± . ENZO
ART , NR 0.801 0.956 0.983
ART , CSF 0.808 0.842 1.005
ART , NR, cl 0.701 0.824 0.854
ART , CSF, cl 0.803 0.718 0.902
GADGET , NR 0.856 0.857 0.971
GADGET , CSF 0.756 0.864 0.944Note: The core radius was fixed to 0 . r in all cases. Thesubscript cl indicates the profiles corrected for the effect ofclumping using the method described in Nagai & Lau (2011). with β values higher than 0.85, with the exception of the ART profile that includes CSF and clumping. Therefore, wecan see that at this level of precision the effects of additionalphysics cannot be neglected, even in regions well outside ofthe cluster core.The results presented in Table 2 also highlight the dif-ferences between NR and CSF runs. Inside r , the sim-ulations including additional physics lead to flatter den-sity profiles compared to the NR runs. In this case, gascooling converts a fraction of the X-ray emitting gas intostars. Since the cooling efficiency decreases with radius,more gas disappears from the X-ray range in the central
9. Eckert et al.: The gas distribution in the outer regions of galaxy clusters r/r0.2 0.4 0.6 0.8 1 1.2 S ca tt e r r/r0.2 0.4 0.6 0.8 1 1.2 S ca tt e r r/r0.2 0.4 0.6 0.8 1 1.2 S ca tt e r r/r0.2 0.4 0.6 0.8 1 1.2 S ca tt e r Fig. 9.
Left:
Comparison between the average observed azimuthal scatter profile from Fig. 7 (black) and the scatter inthe simulations for the
ENZO runs (red), for the total scatter (solid line) and when filtering out the 1% most-luminouscells (dashed curve). The cyan (NR) and magenta (CSF) curves represent the scatter in the
ART simulations.
Right:
Samefor the CC (red) and NCC (blue) observed profiles, compared to the 1%-filtered
ENZO profiles for the morphologicallyrelaxed (red) and disturbed (blue) simulated clusters.regions, which results in flatter density profiles and lowernormalizations. We note, however, that this effect is prob-ably overestimated in the CSF simulations. Indeed, it iswell-known that these simulations predict a stellar fractionthat is well above the observed value (e.g., Kravtsov et al.2005; Borgani & Kravtsov 2009). This effect is particularlystrong in the
ART
CSF simulation, for which nearly onethird of the gas is converted into stars. Beyond r , thereis little difference between NR and CSF runs; i.e., the effectsof additional physics are not important. At large radii, theeffect of gas clumping (Nagai & Lau 2011) dominates andflattens the observed profiles. As we can see in Table 2 andin the right hand panel of Fig. 8, the ART profile includingboth additional physics and a post-processing treatment ofclumping reproduces the behavior of the data more closely,even though it is still slightly too steep.
A study of the azimuthal scatter in the radial profiles ofdensity, temperature, entropy and X-ray brightness of sim-ulated
ENZO clusters has been presented in Vazza et al.(2011b). In this case, we differ from the analysis reportedthere by computing the azimuthal scatter from more an-gular sectors, N=12, than for N=2, 4, and 8 exploredin Vazza et al. (2011b). In the simulations, several denseclumps are present, which may bias the predicted scatter.To overcome this problem, we computed the scatter of thesimulated clusters both for the total gas distribution andby filtering out the 1% most X-ray luminous cells, as inRoncarelli et al. (2006), which removes a large fraction ofthe clumps.We also performed a similar analysis on the set of
ART simulations, both for the NR and CSF runs. In this case, weanalyzed mock X-ray images using the same method as theobservational data (see Sect. 3.4), and applied our point- source detection algorithm to remove the most prominentclumps. In Fig. 9, we show the measured scatter profile fromFig. 7, together with the scatter profiles of X-ray bright-ness from
ENZO and
ART simulations. Interestingly, we notethat NR runs (red and cyan) overestimate the observed az-imuthal scatter, while CSF simulations underestimate it.In the latter case, radiative cooling lowers the entropy ofthe gas, which makes it sink into the cluster’s potentialwell. This effect produces more spherical X-ray morpholo-gies, thus lowering the azimuthal scatter. Conversely, in NRruns, the effects of dynamics are more important, which cre-ate more substructures and increases the azimuthal scatter.Interestingly, the profile that best reproduces the datais the
ENZO profile for which the 1% most-luminous pix-els were filtered out. This may indicate that some clumpsare indeed present in the observations, but were detectedas point sources and were masked for the analysis. We notethat, even if in this case the azimuthal scatter from NR sim-ulation runs is in good agreement with the
ROSAT data,the absolute profiles of density are too steep compared toobservations (see the left hand panel of Fig. 8). However,our definition of the azimuthal scatter (Eq. 2) is normal-ized to the absolute value of the profile at each radii, whichmakes it a rather robust proxy of cluster asymmetries onlarge ∼ Mpc scales.In the right hand panel of Fig. 9, we also show the aver-age radial trends of the azimuthal scatter for the projectedX-ray emission from the
ENZO clusters after dividing thedataset into 11 CC-like and 9 NCC-like objects, comparedto the observed scatter profiles for the CC and NCC classesfrom Fig. 7. This division is of course only qualitative, sinceno radiative cooling is modeled in these runs. However, our Because of how few objects are considered, we ignored the
GADGET simulations for this analysis. For a comparison be-tween
GADGET and
ENZO scatter profiles, we refer the reader toVazza et al. (2011b).10. Eckert et al.: The gas distribution in the outer regions of galaxy clusters sample can be divided into classes that are quite similarto observed CC and NCC properties, based on the anal-ysis of the power ratios P /P and of the centroid shift w , evaluated within r as in Cassano et al. (2010). Weclassify as NCC-like systems those for which the values of P /P > − and w > .
02 were found in at least two ofthe three projected maps along the coordinate axes, or asCC-like otherwise, identical to what was done for the samesample in Vazza et al. (2011a).In this figure, we can clearly see that the radial trendof the difference between the two populations disagrees.While in simulations the two trends detach as we movefarther out in the cluster atmospheres, in the observed pro-files the most prominent differences are found in the range0 . ≤ r/r ≤ .
8. In the CC case, we find better qualita-tive agreement in the outskirts than in the central regions.This is not surprising, given that radiative cooling and en-ergy feedback from central AGNs are missing in these runs.Indeed, as we can see in the left hand panel of Fig. 9, radia-tive cooling has a strong impact on the general morphologyof clusters (Fang et al. 2009; Lau et al. 2011). On the otherhand, the simulated disturbed systems have a larger scatterin the outskirts than the observed NCC clusters. However,we observe large differences in the scatter between the var-ious NCC profiles, such that the result may be affectedby small-number statistics. In any case, since the selectioncriteria are very different, we do not expect a one-to-onecorrelation between the various classes.
6. Discussion
In agreement with earlier works using
ROSAT (V99, N05)and
Chandra (Ettori & Balestra 2009), but at variancewith some recent results from
Suzaku (Bautz et al. 2009;Simionescu et al. 2011; George et al. 2009) and
XMM-Newton (Urban et al. 2011), our analysis reveals that onaverage the slope of the density profiles steepens beyond r (see Table 2). This result indicates that the latter re-sults may have been performed along preferential directionsconnected with the large-scale structure (e.g., in the di-rection of filaments). Indeed, the narrow FOV of Suzaku only allowed sparse coverage of the outskirts of nearbyclusters, so that these measurements might be the resultof azimuthal variations. In the case of A1795, Bautz et al.(2009) detected a significant signal only in the northern di-rection, while the Perseus result (Simionescu et al. 2011)was obtained along two narrow arms, covering less than10% of the cluster’s extent at r . Moreover, using sev-eral offset ROSAT /PSPC pointings of the Perseus cluster,Ettori et al. (1998) observed clear azimuthal variations inthe density and gas fraction. Therefore, it is likely that theaforementioned measurements are not representative of thecluster as a whole. This picture is supported by our analysisof azimuthal variations in cluster outskirts, which suggeststhat even CC clusters exhibit significant departures fromspherical symmetry around r . Consequently, a full az-imuthal coverage is required to study the global behaviorof cluster outer regions.An important result of this work is the systematic dif-ference between CC and NCC cluster populations observedbeyond ∼ . r (see Fig. 4). As explained in Sect. 4, thiseffect seems to be an intrinsic difference between the two classes, since it is does not correspond to a biased distribu-tion of our sample in temperature or redshift. Our scaledgas mass profiles provide a natural explanation for this re-sult (see Fig. 6). Indeed, when the appropriate scaling isapplied, the steeper density profiles of CCs in the outskirtscompensate exactly for the excess density in the central re-gions, such that clusters with the same virial mass have thesame gas mass enclosed within r , albeit distributed ina different way for relaxed and disturbed objects. This re-sult was expected in the old cooling-flow scenario (Fabian1994), in which radiative cooling causes the gas to flow in-wards and accumulate in the central regions. While in thecentral regions AGN feedback prevents the gas from coolingbelow a certain level (e.g., McNamara & Nulsen 2007), theentropy injected by the central AGN is not strong enoughto balance the flow in the outer regions of clusters, whichexplains the steep density profiles seen in Fig. 4. Conversely,merging events are capable of injecting a very large amountof energy in the ICM, which results in an efficient redistri-bution of the gas between the core and the outer regionsand creates the flatter density profiles measured for NCCclusters.We also determined the typical scatter in surface-brightness as a function of radius (see Fig. 7) and split thedata into the CC and NCC classes. In the central regions,we observe a systematic difference between CC and NCCclusters, with NCC clusters showing a higher level of scat-ter than CC. This result is easily explained by the largernumber of substructures generally observed in NCC clusters(e.g., Sanderson et al. 2009). For CC clusters, we measurea scatter of 20% −
30% below 0 . r , which correspondsto small variations ( ∼ r < . r )can be used to estimate the X-ray state of clusters, as sug-gested by Vazza et al. (2011b). Conversely, the scatter ofCC profiles increases in cluster outskirts, and there is noobserved difference between the two classes. Interestingly,we note that for CC clusters the turnover in Fig. 7 occursaround r , which coincides with the radius beyond whichlarge scale infall motions and filamentary accretions aregenerally non-negligible (e.g., Evrard et al. 1996). Inside r , the gas is virialized in the cluster’s potential well,and it shows only little deviations from spherical symme-try. Beyond r , accretion processes are important, andthe gas is located mostly along preferential directions (i.e.,filaments). As a result, the distribution of the gas becomesstrongly anisotropic, even for clusters that exhibit a relaxedmorphology in their inner regions. Comparing our density profiles with numerical simulations,we find that all NR simulations predict very steep profilesalready starting from ∼ . r , with values of the β param-eter greater than 0.85 in the 0 . − . r range (see theleft hand panel of Fig. 8 and Table 2). This indicates thatincluding non-gravitational effects is needed to reproducethe observed slope, even well outside of cluster cores. Theruns including additional physics are in better qualitativeagreement with the observations (see the right hand panelof Fig. 8), although their gas fraction is too low becauseof overcooling ( ∼
10% compared to ∼
11. Eckert et al.: The gas distribution in the outer regions of galaxy clusters anisms needed to reproduce observed clusters. Indeed, sim-ple feedback models still face severe problems in matchingthe properties of the stellar components inside galaxy clus-ters, as well as the properties of galaxies within them (e.g.,Borgani & Kravtsov 2009, for a recent review).As illustrated in Table 2, gas clumping may also playa role in reconciling simulations with observations. Indeed,if an important fraction of the gas in cluster outskirts isin the form of dense gas clumps, as suggested in simula-tions (Nagai & Lau 2011), the emissivity of the gas wouldbe significantly increased, thus leading to an overestima-tion of the gas density when the assumption of constantdensity in each shell is made. Our results show that thetreatment of gas clumping slightly improves the agreementbetween data and simulations (see the right hand panel ofFig. 8). In addition, gas clumping also provides an alterna-tive interpretation for our observed difference between theCC and NCC populations beyond 0 . r . Indeed, simula-tions predict a larger clumping factor in unrelaxed clusterscompared to relaxed systems for the same average density,which would result in a higher observed density in the for-mer. At the moment, it is not clear whether this differenceis caused by gas redistribution or clumping, or if both ofthese effects play a role to some extent.On the other hand, we find that numerical simulationscan reproduce qualitatively the observed azimuthal scatterin the galaxy cluster gas density profiles (see Fig. 9), al-though they fail to reproduce the trends observed for theCC and NCC populations separately. Interestingly, we findthat the observed azimuthal scatter is reproduced with rea-sonable accuracy when the 1% most luminous clumps arefiltered out, whereas the NR simulations with no filteringoverestimate the observed level of azimuthal scatter at allradii. Two possible interpretations can be put forward tointerpret this result. Observationally, it is possible that thedense clumps were detected as point sources and were fil-tered out of our observations. If this is the case, long ex-posures with high-resolution X-ray telescopes ( Chandra or XMM-Newton ) should allow us to characterize the pointsources and distinguish between dense clumps and back-ground AGN, possibly unveiling the population of accretingclumps in cluster outskirts. Conversely, if such observationsdo not confirm the existence of the clumps, it would implythat NR simulations significantly overestimate the amountof clumping in cluster outskirts, which would weaken thecase for the interpretation recently put forward to explainthe flattening of the entropy profiles observed in a few cases(Simionescu et al. 2011; Urban et al. 2011).As shown in Fig. 9, radiative cooling may also help rec-oncile the NR simulations with the data. Indeed, radiativecooling lowers the entropy of the gas and makes it sinkinto the potential well, which produces clusters with morespherical morphologies (Lau et al. 2011) and thus reducesthe azimuthal scatter. Since we know that this effect is over-estimated in our CSF simulations, radiative cooling likelyreduces the azimuthal scatter with respect to NR simula-tions, although not as much as what is predicted here. Thiseffect may also explain why NR simulations fail to repro-duce the average scatter profiles of CC clusters (see theright hand panel of Fig. 9).Alternatively, AGN feedback may be an important in-gredient that is rarely taken into account in numerical sim-ulations. Recently, Pratt et al. (2010) observed an anti-correlation between entropy and gas fraction, such that multiplying cluster entropy profiles by the local gas frac-tion allows recovery of the entropy profiles predicted fromadiabatic compression; i.e., the excess entropy observed incluster cores is balanced by a lower gas fraction, and the to-tal entropy follows the predictions of gravitational collapse.Mathews & Guo (2011) interpret this result in terms of thetotal feedback energy injected in the ICM through variousgiant AGN outbursts, which they estimate to be as largeas 10 ergs. In this scenario, feedback mechanisms are pre-venting the gas from collapsing into the potential well, caus-ing a deficit of baryons in the inner regions of clusters, henceflattening the observed density profiles. Moreover, it is wellknown that this mechanism also takes place on group andgalaxy scales, leading to shallower density profiles in theaccreting clumps. As a result, the gas distribution in clus-ter outskirts would be more homogeneous than predicted inNR simulations, in agreement with our observed azimuthalscatter profiles. Therefore, although its implementation intonumerical simulations is challenging (Sijacki et al. 2008),AGN feedback could be an important effect for reconcilingsimulations with observations. A more complex picture ofthe ICM, possibly including the detailed treatment of mag-netic fields, cosmic rays, and thermal conductions (and ofthe instabilities arising from these ingredients), would stillrepresent a challenge for current cosmological simulations.
7. Conclusion
In this paper, we have presented our analysis of a sam-ple of local ( z = 0 . − .
2) clusters with
ROSAT /PSPC,focusing on the properties of the gas in cluster outskirts.We then compared our observational results with numeri-cal simulations (Roncarelli et al. 2006; Nagai & Lau 2011;Vazza et al. 2011b). Our main results can be summarizedas follows. – We observed a general trend of steepening in the ra-dial profiles of emission-measure and gas density be-yond ∼ r , in good agreement with earlier worksfrom Vikhlinin et al. (1999), Neumann (2005), andEttori & Balestra (2009). As a result, the shallow den-sity profiles observed in several clusters by Suzaku (Bautz et al. 2009; Simionescu et al. 2011) are proba-bly induced by observations in preferential directions(e.g., filaments) and do not reflect the typical behaviorof cluster outer regions. – We found that NCC clusters have in average a higherdensity than CC systems beyond ∼ . r , which can-not be easily explained by any selection effect. We in-terpreted this result by a different distribution of thegas in the two populations: the well-known density ex-cess in the core of CC clusters is balanced by a slightlysteeper profile in the outskirts, which leads to the samegas mass enclosed within r in the two populations(see Fig. 6). Alternatively, this result could be causedby a larger clumping factor in disturbed objects, leadingto an overestimate of the gas density of NCC clustersin the external regions. – We also observed that NCC systems have higher az-imuthal scatter than CCs in the central regions, whichis easily explained by the more disturbed morphologyof NCC clusters. Conversely, beyond ∼ r both pop-ulations show a similar level of asymmetry (60-80%),which suggests that a significant fraction of the gas is
12. Eckert et al.: The gas distribution in the outer regions of galaxy clusters in the form of accreting material from the large-scalestructures. – Comparing our
ROSAT density profile with numericalsimulations, we found that all NR numerical simula-tions fail to reproduce the observed shape of the den-sity profile, predicting density profiles that are signif-icantly too steep compared to the data (see Table 2and Fig. 8). This implies that nongravitational effectsare important well outside the core region. The runs in-cluding additional physics (cooling, star formation, SNfeedback) predict flatter profiles, although still too steepcompared to the observations. Besides, it is well knownthat these simulations overpredict the stellar fraction inclusters (Borgani & Kravtsov 2009). A slightly betteragreement is found when a treatment of the observa-tional effects of gas clumping is adopted (Nagai & Lau2011). – NR simulations are able to predict the observed az-imuthal scatter profile with reasonable accuracy, butonly when the 1% most luminous cells are filtered out(see Fig. 9). This result implies that either (i) the clumpsare quite bright and were masked as point sources in ouranalysis pipeline, in which case offset
XMM-Newton and
Chandra observations will be able to characterize themspatially and spectrally, or (ii) the non-radiative simu-lations significantly overestimate the effects of clumpingon the observable X-ray properties. Because of the ab-sence of cooling, it is however hard for these simulationsto reproduce the observed trends of azimuthal scatterfor the two populations (CC and NCC) separately.As an alternative explanation, we suggest that AGNfeedback might be important even at large radii, and couldhelp to reconcile observations and simulations. Indeed, re-cent works (Pratt et al. 2010; Mathews & Guo 2011) indi-cate that feedback mechanisms may be responsible for thewell-known deficit of baryons in cluster cores, thus leadingto flatter gas distributions out to large radii. Moreover, theexistence of such mechanisms on group and galaxy scalescould also dilute the accreting material at large radii, lead-ing to a smaller azimuthal scatter.
Acknowledgements.
We thank Klaus Dolag for kindly prodiving thedata of his
GADGET runs. SE, SM, and DN acknowledge the sup-port from the National Science Foundation under Grant No. NSFPHY05-51164 for attending the workshop on “Galaxy Clusters: TheCrossroads of Astrophysics and Cosmology”, where part of thisproject has been discussed. DE was supported by the Occhialinifellowship of IASF Milano. MR and FG acknowledge the financialcontribution from contracts ASI-INAF I/023/05/0, I/009/10/0 andI/088/06/0. FV acknowledges the collaboration of G.Brunetti, C.Gheller, and R.Brunino in the production of
ENZO runs studied in thiswork. DN was supported in part by the NSF AST-1009811, by NASANNX11AE07G, and by the facilities and staff of the Yale UniversityFaculty of Arts and Sciences High Performance Computing Center.
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13. Eckert et al.: The gas distribution in the outer regions of galaxy clusters
Vazza, F., Brunetti, G., Gheller, C., & Brunino, R. 2010, New A, 15,695Vazza, F., Brunetti, G., Gheller, C., Brunino, R., & Br¨uggen, M.2011a, A&A, 529, A17+Vazza, F., Roncarelli, M., Ettori, S., & Dolag, K. 2011b, MNRAS,413, 2305Vikhlinin, A., Forman, W., & Jones, C. 1999, ApJ, 525, 47Vikhlinin, A., Kravtsov, A., Forman, W., et al. 2006, ApJ, 640, 691 . E c k e r t e t a l.: T h e ga s d i s t r i bu t i o n i n t h e o u t e rr e g i o n s o f ga l a xy c l u s t e r s Table 3.
Master table of the cluster sample. Column description: 1. Cluster name; 2. Effective exposure of the PSPC observation; 3. Redshift (from NED); 4.Hydrogen column density, N H , along the line of sight (Kalberla et al. 2005); 5. Mean temperature in the 200-500 kpc radial range; 6. r from Arnaud et al.(2005) scaling relations, in physical units; 7. Same as 6, in apparent units; 8. Central density n (this work); 9. Central entropy K , from Cavagnolo et al. (2009);10. Reference for the temperature profile (1=Snowden et al. (2008); 2=Cavagnolo et al. (2009); 3=De Grandi & Molendi (2002)). Cluster Exposure [ks] z N H [10 cm − ] kT − [keV] r [kpc] r [arcmin] n [10 − cm − ] K [keV cm ] ReferenceA85 10.065 0.05506 0.028 6 . ± . . ± .
25 12.5 1A119 14.758 0.0442 0.037 5 . ± . . ± .
34 233.9 2A133 19.429 0.0566 0.0164 4 . ± .
09 1494 22.68 14 . ± .
18 17.3 1A401 7.519 0.07366 0.0995 7 . ± .
15 2077 24.72 5 . ± .
66 166.9 2A478 23.019 0.0881 0.131 6 . ± .
08 1883 19.05 18 . ± .
19 7.8 1A644 10.310 0.0704 0.0750 7 . ± . . ± .
29 132.4 2A665 37.066 0.1819 0.0431 8 . ± . . ± .
18 134.6 1A1068 10.822 0.1375 0.0173 4 . ± .
17 1587 10.89 15 . ± .
24 9.1 1A1651 7.630 0.084945 0.0156 6 . ± . . ± .
50 89.5 2A1689 14.291 0.1832 0.0186 9 . ± . . ± .
22 78.4 1A1795 35.494 0.06248 0.0121 6 . ± .
08 1828 25.31 20 . ± .
12 19.0 1A1991 21.956 0.0586 0.0248 2 . ± . . ± .
22 1.5 1A2029 13.089 0.07728 0.0323 7 . ± . . ± .
20 10.5 1A2142 19.410 0.0909 0.0383 9 . ± . . ± .
17 68.1 3A2163 7.267 0.203 0.109 18 . ± . . ± .
92 438.0 2A2204 5.346 0.1526 0.0561 8 . ± . . ± .
76 9.7 1A2218 43.179 0.1756 0.0266 6 . ± . . ± .
10 288.6 1A2255 13.676 0.0806 0.0250 6 . ± . . ± .
32 529.1 2A2256 17.000 0.0581 0.0418 6 . ± . . ± .
47 349.6 1A2597 7.426 0.0852 0.0246 3 . ± .
06 1405 14.65 18 . ± .
22 10.6 1A3112 7.829 0.07525 0.0137 4 . ± . . ± .
26 11.4 1A3158 3.123 0.0597 0.0138 5 . ± . . ± .
20 166.0 1A3266 13.967 0.0589 0.0158 9 . ± . . ± .
49 72.5 3A3558 28.751 0.048 0.0402 5 . ± .
05 1687 29.89 7 . ± .
23 126.2 1A3562 20.518 0.049 0.0376 4 . ± . . ± .
26 77.4 3A3667 12.462 0.0556 0.0452 5 . ± .
05 1721 26.56 4 . ± .
36 160.4 2A4059 5.684 0.0475 0.0122 4 . ± .
08 1513 27.08 4 . ± .
33 7.1 1Hydra A 18.541 0.0539 0.0468 4 . ± .
06 1495 23.75 22 . ± .
17 13.3 1MKW 3s 9.781 0.045 0.0272 3 . ± .
06 1409 26.54 13 . ± .
22 23.9 1PKS 0745-191 9.627 0.1028 0.405 8 . ± . . ± .
45 12.4 1Triangulum 7.343 0.051 0.114 8 . ± . . ± .
79 313.0 1 . Eckert et al.: The gas distribution in the outer regions of galaxy clusters Appendix A: Determination of azimuthal scatterprofiles
The azimuthal scatter (Vazza et al. 2011b) is defined asthe relative scatter in surface brightness between varioussectors (see Sect. 3.4),Σ = 1 N N X i =1 ( SB i − h SB i ) h SB i . (A.1)In practice, computing this quantity is difficult, since thestatistical fluctuations of the surface brightness introduce acontribution to the scatter that is actually dominant in theouter regions. To estimate the intrinsic level of azimuthalscatter, we used two different complementary methods,which we describe in more detail here. A.1. Subtraction of the statistical scatter
Since the statistical fluctuations of the data also introducea certain level of scatter, it must be noted that the quantitycomputed through Eq. A.1 gives the sum of the statisticaland intrinsic scatter,Σ = Σ int + Σ stat . (A.2)The statistical scatter Σ stat is given by the mean of theindividual relative errors,Σ stat = 1 N N X i =1 σ i h SB i , (A.3)and must be subtracted from Eq. 2 to estimate the level ofintrinsic scatter. The validity of Eq. A.3 for the statisticalscatter was verified through a set of simulations of a sourcewith no intrinsic scatter.The uncertainties in the scatter are then estimatedthrough Monte Carlo simulations. Namely, the surface-brightness values in the N sectors are randomized, and thescatter is recomputed each time. This procedure is applied10 times, and the error on the scatter is defined as theRMS of the distribution around the mean value. A.2. Maximum likelihood estimation
To check the validity of our approach we performed an inde-pendent analysis of the scatter. We model the intrinsic scat-ter in the form of a Gaussian. We use a maximum likelihoodalgorithm (Maccacaro et al. 1988) to fit the data, where thefree parameters are the mean and the intrinsic scatter (i.e.the standard deviation of the Gaussian). The methods de-scribed in both Sect. A.1 and this appendix were appliedto the surface brightness distribution within the annuli ofeach cluster (see Sect 3.4 for details). Intrinsic scatter pro-files from different objects were rebinned onto a commongrid in units of r and stacked. In Fig. A.1 we comparethe intrinsic scatters measured with the two methods. Theprofiles are very similar, the general trend towards increas-ing scatter with radius is recovered with both methods. Theonly bin where a significant difference is observed is around0 . r . This comparison therefore provides a confirmationof our scatter analysis using two very different methods. Fig. A.1.
Comparison between the mean azimuthal scat-ter profiles computed using the direct method (black, seeSect. A.1) and the alternative method using a maximumlikelihood estimator (red, see Sect. A.2).
Appendix B: Notes on individual objects – A85:
A subcluster located ∼ ′ south of the cluster center iscurrently merging with the main cluster. This substruc-ture was masked for the analysis. – A401:
The cluster is connected through a filament to its neigh-bor A399, located ∼ ′ south-west of the center ofA401. We extracted the surface-brightness profile in asector of position angle 340-250 ◦ to avoid any contami-nation of A399 to our measurement of the CXB. – A478:
The combination of a favorable temperature/redshiftand a good-quality
ROSAT observation allows us toreach the highest signal-to-noise ratio in the sample at r for this strong CC cluster. As a result, the data fromthis cluster may contribute strongly when a weightedmean is performed. – A644:
This NCC cluster exhibits an unusual decreasing az-imuthal scatter profile, showing large (close to 100%)scatter in its central regions, but no significant scatteraround r . – A2029:
A probable filament connects A2029 to A2033, located ∼ ′ north of the center of A2029. The surface-brightness profile was extracted in a sector with positionangle 140-80 ◦ to measure the CXB level. – A2142:
Several PSPC observations of this famous cold-frontcluster exist. For this work, we used the longest avail-able observation, which was pointed 16 ′ south of thecenter of A2142. This is the only case in the sample forwhich the observation was not pointed on the target. – A3558 and A3562:
These two clusters are located in the Shapley super-cluster and connected by a filament. Consequently, theyshow an unusually high azimuthal scatter in the out-
16. Eckert et al.: The gas distribution in the outer regions of galaxy clusters skirts. The CXB level was estimated by excluding thedirection of the filament. – A3667:
This very disturbed cluster shows the highest emission-measure and density in the sample beyond ∼ . r ,and hence it could bias our average profiles, in particu-lar when computing the difference between the CC andNCC classes. However, removing it from the sample didnot lead to any significant difference, either quantitativeor qualitative. – A4059:
This is the most azimuthally-symmetric cluster in thesample. The azimuthal scatter for this cluster is consis-tent with 0 at all radii. – Hydra A:
A tail of emission (filament?) extends out to ∼ ′ south-east of the cluster core. This leads to a very highazimuthal scatter ( > r . Appendix C: Mean emission-measure profiles
In Table C.1 we give the mean self-similar scaled emission-measure profiles for the CC and NCC classes and the wholesample, as shown in Fig. 4.
Appendix D: Computing the gas fraction fromdensity profiles
The gas fraction in the observations and in the simulatedclusters within an overdensity ∆ can be computed directlyfrom the profiles presented in Fig. 8. Indeed, by definition, M ∆ = ∆ ρ crit πr , (D.1)where ρ crit = H πG = 9 . × − g cm − . Then, f gas, ∆ = M gas, ∆ M ∆ = 3∆ ρ crit r Z r ∆ ρ gas ( r ) r dr (D.2)Making the substitution x = rr ∆ , we find the convenientformula f gas, ∆ = 3∆ ρ crit Z ρ gas ( x ) x dx. (D.3)
17. Eckert et al.: The gas distribution in the outer regions of galaxy clusters
Table C.1.
Data of Fig. 4: mean self-similar scaled emission-measure profiles for the whole sample and for the CC andNCC classes, in units of cm − Mpc R in R out Total CC NCC0 0.02 (1 . ± . · − (9 . ± . · − (1 . ± . · − . ± . · − (4 . ± . · − (8 . ± . · − . ± . · − (2 . ± . · − (6 . ± . · − . ± . · − (1 . ± . · − (5 . ± . · − . ± . · − (7 . ± . · − (4 . ± . · − . ± . · − (5 . ± . · − (3 . ± . · − . ± . · − (3 . ± . · − (2 . ± . · − . ± . · − (2 . ± . · − (2 . ± . · − . ± . · − (1 . ± . · − (1 . ± . · − . ± . · − (1 . ± . · − (1 . ± . · − . ± . · − (1 . ± . · − (1 . ± . · − . ± . · − (9 . ± . · − (1 . ± . · − . ± . · − (7 . ± . · − (8 . ± . · − . ± . · − (6 . ± . · − (7 . ± . · − . ± . · − (4 . ± . · − (5 . ± . · − . ± . · − (3 . ± . · − (4 . ± . · − . ± . · − (2 . ± . · − (3 . ± . · − . ± . · − (2 . ± . · − (2 . ± . · − . ± . · − (1 . ± . · − (2 . ± . · − . ± . · − (1 . ± . · − (1 . ± . · − . ± . · − (9 . ± . · − (1 . ± . · − . ± . · − (6 . ± . · − (8 . ± . · − . ± . · − (4 . ± . · − (6 . ± . · − . ± . · − (3 . ± . · − (4 . ± . · − . ± . · − (2 . ± . · − (3 . ± . · − . ± . · − (1 . ± . · − (2 . ± . · − . ± . · − (8 . ± . · − (1 . ± . · − . ± . · − (5 . ± . · − (8 . ± . · − . ± . · − (4 . ± . · − (5 . ± . · − . ± . · − (3 . ± . · − (5 . ± . · − r/r0.2 0.4 0.6 0.8 1 ] - [ c m - E ( z ) H n -4 -3 -2-2