The Cool-Core Bias in X-ray Galaxy Cluster Samples I: Method And Application To HIFLUGCS
AAstronomy & Astrophysics manuscript no. aa15856 c (cid:13)
ESO 2018October 25, 2018
The Cool-Core Bias in X-ray Galaxy Cluster Samples I: MethodAnd Application To HIFLUGCS
D. Eckert , S. Molendi & S. Paltani INAF/IASF-Milano, Via E. Bassini 15, 20133 Milano, Italy ISDC Data Centre for Astrophysics, University of Geneva, 16, ch. d’Ecogia, 1290 Versoix, SwitzerlandPreprint online version: October 25, 2018
ABSTRACT
Aims.
When selecting flux-limited cluster samples, the detection efficiency of X-ray instruments is not the same forcentrally-peaked and flat objects, which introduces a bias in flux-limited cluster samples. We quantify this effect in thecase of a well-known cluster sample, HIFLUGCS.
Methods.
We simulate a population of X-ray clusters with various surface-brightness profiles, and use the instrumentalcharacteristics of the
ROSAT
All-Sky Survey (RASS) to select flux-limited samples similar to the HIFLUGCS sampleand predict the expected bias. For comparison, we also estimate observationally the bias in the HIFLUGCS sampleusing
XMM-Newton and
ROSAT data.
Results.
We find that the selection of X-ray cluster samples is significantly biased ( ∼ Conclusions.
Observationally, we propose to select the objects according to their flux in a well-defined physical rangeexcluding the cores, 0 . r − r , to get rid of the bias. From the fluxes in this range, we reject 13 clusters out of the64 in the HIFLUGCS sample, none of which appears to be NCC. As a result, we estimate that less than half (35-37%)of the galaxy clusters in the local Universe are strong CC. In the paradigm where the CC objects trace relaxed clustersas opposed to unrelaxed, merging objects, this implies that to the present day the majority of the objects are not in arelaxed state. From this result, we estimate a rate of heating events of ∼ / − per dark-matter halo. Key words.
Galaxies: clusters: general - X-rays: galaxies: clusters - Galaxies: clusters: intracluster medium
1. Introduction
Galaxy clusters are the biggest gravitationally-bound struc-tures in the Universe. They are filled with a hot ( kT ∼ −
10 keV) plasma, the Intra-Cluster Medium (ICM), whichhas been heated to X-ray emitting temperatures by grav-itational collapse. In the original “cooling-flow” scenario(Fabian 1994), all clusters after relaxation from a majormerging event should evolve into the cooling-flow state,where the gas condensates in the central regions and thencools through radiative processes until it eventually formsstars. This paradigm was supported by observations ofprominent surface-brightness peaks and temperature dropsin the cores of clusters, which were supposed to be associ-ated with the central cooling flow. However, this picture wasnot confirmed by the latest generation of X-ray telescopes(
XMM-Newton , Chandra ), which found no spectroscopicevidence for the presence of the cooling gas in the cen-tral regions of clusters predicted by the cooling-flow model(Peterson et al. 2001; Kaastra et al. 2001). These resultslead to the revision of the classification of galaxy clusters,which were thereafter categorized into “cool-core” (CC)and “non-cool-core” (NCC) objects (Molendi & Pizzolato2001). Since in the center of clusters the cooling time can bemuch shorter than the Hubble time, these results imply theexistence of a heating mechanism which is responsible forquenching the cooling flow. Feedback from Active Galactic Nuclei (AGN) in the central galaxies is the most probablesource of heating in the ICM (e.g., McNamara & Nulsen2007).Apart from the nature of the heating source, the fail-ure of the cooling-flow model also has repercussions on theformation scenario of galaxy clusters. Indeed, some numeri-cal studies of cluster mergers have found that cool cores arehardly disrupted by merging events (Poole et al. 2008), andthat the state of a cluster (CC or NCC) is determined oncefor all during the formation process (McCarthy et al. 2008).Recent observational works have shown that the popula-tion of clusters is bimodal (Cavagnolo et al. 2009), whichcould support this scenario because of the lack of inter-mediate objects. However, other studies found no evidencefor bimodality in the distribution of clusters (e.g., Prattet al. 2010), and the recent identification of regions rem-iniscent of cool cores in merging clusters (“cool-core rem-nants”, Rossetti & Molendi (2010)), probably associatedwith ancient cool cores disrupted by merging events, ar-gues against this idea. Thus, the question of the formationprocess of cool cores is still an open one.An important clue to the understanding of the forma-tion process of cool cores is the observed ratio betweenCC and NCC clusters in the local Universe, which dependsstrongly on the different formation scenarios. Indeed, in theold cooling-flow scenario it was believed that the majorityof clusters (70-90%) in the local Universe had a cooling flow a r X i v : . [ a s t r o - ph . C O ] N ov Eckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I (Peres et al. 1998), which is expected if all clusters naturallyevolve into the cooling-flow state. In this case, one mightalso expect a strong dependence of the CC fraction on theredshift. Conversely, if the state of a cluster is determinedonly by an initial entropy injection event as suggested bysome simulations (McCarthy et al. 2004), a very differentbehavior can be expected.Observationally, to measure the fraction of CC objectsit is crucial to use a sample which is as complete and as freeof selection biases as possible. In this respect, the very dif-ferent surface-brightness profiles observed in CC and NCCobjects might introduce a bias in the selection of X-rayflux-limited samples. Indeed, CC systems exhibit a promi-nent surface-brightness peak, as opposed to NCC clusterswhich show flat emission profiles. The diversity of surface-brightness profiles might introduce a bias in favor of CCs inX-ray flux-limited samples. In this paper, we investigate theimpact of such a flux selection on the measurement of theCC over NCC ratio when computed using a well-studied,nearby cluster sample, HIFLUGCS, which was extractedfrom the
ROSAT
All-Sky Survey (RASS).HIFLUGCS (Reiprich & B¨ohringer 2002) is a completeflux-limited sample extracted from RASS data. It comprises64 clusters with a flux higher than 2 . × − ergs cm − s − (0.1-2.4 keV band). According to the authors, it is tothe present day the largest complete X-ray selected sam-ple of galaxy clusters. Additionally, an extended sample of106 objects also exists, which comprises objects which wereoriginally excluded for completeness reasons (in particularbecause of high absorption). The objects of the extendedsample are nearby ( z < .
2) and span a luminosity rangebetween ∼ and ∼ h − ergs s − .From ROSAT and
ASCA data, Chen et al. (2007) es-timated the fraction of CC to be 49% in the HIFLUGCSsample. More recently, studies have been carried out us-ing
Chandra data (Mittal et al. 2009; Hudson et al. 2010),which clearly demonstrate the existence of a class of inter-mediate objects. In particular, Hudson et al. (2010) (here-after, H10) claim a fraction of 44% “strong CC” objectsand 28% “weak CC” clusters, where the classification ofthe objects was performed using the central cooling time(CCT), which was found to be the best indicator of thestate of a cluster. Strong CC objects were defined as ob-jects which exhibit a central cooling time < < CCT < > z > . m = 0 .
27, Ω Λ = 0 .
73 and H = 72 km s − Mpc − .
2. The simulation
To estimate the CC bias introduced into a sample, we use aMonte Carlo approach where clusters are distributed follow-ing the observed luminosity function, with a known inputfraction of CC vs NCC objects, and then selected using thecriteria of the corresponding sample. A realistic descriptionof the survey properties (RASS) and of the instrumentalcharacteristics are implemented to perform the selection.The fraction of CC vs NCC clusters is then computed fromthe selected sample and compared with the input ratio. Thedependence of the bias on several input parameters (lumi-nosity, redshift, absorption) is also analyzed.
The first step for the simulation is to select randomly aluminosity in the 0.1-2.4 keV band ( L X ) and a redshift ( z ),following the observed distribution of clusters, i.e. N cl ( L X , z ) = F ( L X , z ) (cid:18) dVdz (cid:19) dL X dz, (1)where the X-ray Luminosity Function (XLF) F ( L X , z ) hasthe form F ( L X , z ) = C ( z ) L − αX exp( − L X /L (cid:63) ( z )) . (2)The dependence of the luminosity function on the redshiftis given by L (cid:63) ( z ) = L (cid:63) (0)(1+ z ) A and C ( z ) = C (0)(1+ z ) B ,where C (0) is the normalization of the luminosity functionat z = 0 (Mullis et al. 2004). For the parameters of theluminosity function we use the values extracted from theBCS survey: α = 1 . L (cid:63) (0) = 2 . × h − ergs s − (Ebeling et al. 1997). The cosmological evolution of theXLF follows the work of Mullis et al. (2004), A = − . B = 1 . L X > × ergs s − and z < .
25 to cover all theparameter space of the sample. At low redshift, the cosmo-logical dependence of the XLF is negligible, and thereforethe redshift distribution goes like z , given that the numberof objects is proportional to dVdz ∼ z . The luminosity dis-tribution follows approximately a cut-off power law as ex-pected from Eq. 2. From the luminosity, we use the L X − T relation, L X = A (cid:18) kT vir (cid:19) α , (3) ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 3 to get the corresponding temperature. For the parametersof the relation, we use the values derived by Anderssonet al. (2009), A = 1 . × ergs s − (2-10 keV band) and α = 2 .
79. We neglect the scatter of the relation. For galaxygroups, the relation is steeper (Helsdon & Ponman 2000), soat low temperatures ( kT < L X − T relation ( A = 9 . × ergss − , α = 4 . L X and z , we derive the0.1-2.4 keV flux of the corresponding object in the observerframe.In addition to the luminosity and redshift, we also sim-ulated a distribution of galactic hydrogen column density( N H ). For this purpose, we used the 21 cm maps fromKalberla et al. (2005) and computed the distribution of N H , restricting to galactic latitudes | l | > ◦ to match theconsidered samples. Values of N H were then simulated fol-lowing the observed distribution. For the surface-brightness profiles of the simulated clus-ters, we use two different sets of parameters describing dif-ferent physical cases. For simplicity, we divide the popu-lation of clusters strictly into CC and NCC clusters (i.e.we neglect intermediate objects). Namely, for NCC clus-ters we assume a surface-brightness profile described by abeta model (Cavaliere & Fusco-Femiano 1976), S ( r ) = S (cid:2) r/r c ) (cid:3) − β +1 / , (4)while for CC clusters we assume a double-beta model, S ( r ) = S (cid:16)(cid:2) r/r c ) (cid:3) − β +1 / + R (cid:2) r/r c ) (cid:3) − β +1 / (cid:17) , (5)where we use the same value of β for the 2 beta components,and R is the ratio between the two components at r = 0.In the first case, we choose fixed values for the rele-vant parameters, which were estimated by averaging theobserved quantities from the sample of Mohr et al. (1999).In both cases, we use a common β value of 0.64. For NCCclusters, a core radius r c = 230 kpc was chosen. For CCclusters, we use a core radius for the smaller beta compo-nent, r c , of 40 kpc, while the core radius of the broaderbeta component, r c , is set to 170 kpc, a smaller value thanfor NCC clusters. All these parameters show relatively smallscatter in the Mohr et al. (1999) sample. The most uncer-tain parameter of the simulation is the ratio between the 2beta components at r = 0 for CC clusters, namely R . Fromthe Mohr et al. (1999) sample, this quantity has a meanvalue of ∼
15 with large scatter, the values ranging from1.5 up to ∼
100 from an object to another. In the following,we use a constant value R = 15 for CC clusters. Indeed,we found that the results of the simulation do not differsignificantly when a single value or a distribution of valuesis used for the relevant parameters (see Sect. 3). For theremainder of the paper, we refer to this set of parametersas case I.As an alternative approach, we also performed simula-tions in which the various core radii are defined as a fixedfraction of r , hereafter case II. More specifically, for each For a given over-density factor ∆, r ∆ is defined as the radiuswithin which the total mean density is a factor ∆ above thecritical density. simulated cluster we use the scaling relation of Arnaud et al.(2005) to compute the expected value of r , and choosefor the various core radii a fixed fraction of r . In termsof r , for NCC systems we use r c = 0 . r , while forCC objects we choose r c = 0 . r and r c = 0 . r .It is unclear which of the two parameter sets shouldprovide a better description of the data. Indeed, the firstapproach assumes that in cluster cores feedback effects aredominant, thus creating universal core properties which donot depend on cluster mass. Conversely, the second ap-proach neglects the feedback effects and assumes that thecore properties are only determined by gravitational pro-cesses, in which case they should follow a self-similar rela-tion. Since it is known that both effects are important, ourtwo choices of scale radii should provide limiting cases. The
ROSAT all-sky survey (RASS) covered the whole skywith a typical exposure time of a few hundred seconds(Cruddace et al. 2002). The instrument featured an effec-tive area A ∼
400 cm @ 1 keV and a spatial resolution of ∼
20 arcsec FWHM averaged over the FOV. The backgroundcount rate, which we estimated by computing the meannumber of counts in RASS images, is low, ∼ − countss − arcmin − (0.1-2.4 keV). To convert fluxes to RASScount rates, we used the XSPEC package (Arnaud 1996)v12.6.0 and the ROSAT /PSPC response. We assumed thatthe spectrum of each source is described by an absorbedMEKAL model (Kaastra & Mewe 2000) with varying tem-perature and hydrogen column density. The conversion fac-tor from flux to count rate was then computed for a range ofvalues of kT and N H . For any initial value of temperatureand N H , we estimate the conversion factor by interpolatingthe nearest points.In the case of extended sources, the choice of the inte-gration radius from the surface-brightness peak is crucial.Beyond a given radius, the surface brightness of the sourcebecomes smaller than that of the background, and thereforethe observed flux of a cluster in a real observation is alwayssmaller than the total flux of the cluster. For this reason,the fluxes computed as described above cannot reproduceaccurately the RASS.To overcome this difficulty, for each cluster with a giventotal flux F we define a radius r max such that F obs = (cid:90) r max S ( r ) 2 πr dr. (6)Obviously, the surface-brightness profile S ( r ) is normalizedin such a way that (cid:90) ∞ S ( r ) 2 πr dr = F. (7)For a cluster to match the selection criterion of HIFLUGCSwe impose that F obs , not F , be above the flux limit of thesample (i.e. 2 . × − ergs cm − s − ).Clearly, a realistic definition of r max is important to re-produce accurately the observed samples. Given that theoriginal fluxes were computed inside the maximum radiusup to which the source is detected (Reiprich & B¨ohringer2002), we chose to use for r max the radius for which thesurface-brightness of the source is equal to that of the back-ground. This should be regarded as a conservative choice, Eckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I
Radius [arcsec]1 10 D i ff e r e n t i a l nu m b e r o f c oun t s -2 -1 Fig. 1.
Differential number-of-counts profiles (in units ofcounts per arcmin) for a CC (black) and a NCC cluster(blue) with the same redshift ( z = 0 .
05) and luminosity( L X = 10 ergs s − ), compared to the ROSAT /PSPCbackground profile (red).since in most cases the source contribution can be mea-sured up to a somewhat larger radius. In Fig. 1 we showthe differential number-of-counts profiles, i.e. the surfacebrightness times 2 πr , for the ROSAT /PSPC backgroundand two clusters, a CC and a NCC, both at z = 0 .
05 andwith a luminosity of 10 ergs s − (total flux F ∼ × − ergs cm − s − ). The value of r max in the two cases is givenby the intersection between the black/blue curve and thered curve. In the specific case shown here, r max = 490 (cid:48)(cid:48) forthe CC case and r max = 640 (cid:48)(cid:48) for the NCC case. In termsof flux, this results in a ∼
25% higher observed flux for theCC cluster compared to the NCC cluster, for the same totalflux.
The critical parameter for the simulation, c , is the fractionof clusters hosting a cool core. Since we expect that the ob-served value of c in the samples is biased, we wish to com-pute the input value of c for which the fraction of CC clus-ters in a simulated sample reproduces the observed valuein a given observed sample. Therefore, for each simulatedcluster we randomly choose whether it is CC or NCC, im-posing a fraction c inp of CC clusters. We then compute thecorresponding integration radius r max as explained aboveand calculate the observed flux using Eq. 6. For a cluster tomatch the selection criterion of a sample, we then imposethe corresponding flux limit. In addition, we also check thedetection level of each source. More specifically, we imposethat the signal-to-noise of a source, defined as S/N = N source (cid:112) N source + N bkg , (8)where N source and N bkg are the total number of countsof the source and the background integrated up to r max ,be above 5.0 to be selected in the sample. In the case ofHIFLUGCS, all the objects are detected with S/N >
Table 1.
Results of different simulations of 10 objects withan input CC fraction c inp = 0 .
38. Left: Surface-brightnessparameters used for the simulation (see Sect. 2.2). Right:Observed fraction of CC clusters in the simulated samples.
Simulation c obs All fixed 0 . ± . β . ± . r c , r c and r c . ± . R . ± . ] -1 [ergs s X L N u m b e r Redshift -3 -2 -1 N u m b e r Fig. 2.
Distribution of luminosities (left) and redshifts(right) of the objects in the simulated flux-limited sample.Once the simulated sample is selected, we infer the frac-tion of CC clusters among the selected objects ( c obs ), andcompare this number with the input fraction c inp .
3. Simulation results
We started by simulating a population according to caseI (see Sect. 2.2). In a simulation of 10 objects, we foundthat ∼
900 match the selection criteria, which allows us tocompute the observed fraction c obs with good accuracy. Wethen performed simulations for a range of values of c andfound that the observed value of 49% (Chen et al. 2007)corresponds to an input ratio c inp = 0 . ± .
02, i.e. to asignificant bias of ∼ c inp = 0 . ± . c inp = 0 . c obs on other quantities, in par-ticular on luminosity, redshift and hydrogen column den-sity. A simulation with a very large number of objects isrequired to study the dependence of c obs on these param-eters. Fixing the value of c inp to 0.38, we then performedlarge simulations of 10 objects for the two parameter sets(case I and case II), where as expected ∼ ,
000 matchthe selection criterion. Figure 2 shows the luminosity andredshift distributions of the selected objects. The distribu-tions peak at a luminosity ∼ × ergs s − and a red-shift ∼ .
05, which matches well the observed quantitiesof the HIFLUGCS sample (Reiprich & B¨ohringer 2002).Moreover, as expected, the log N -log S of the sample is well-represented by a power law with an index − /
2, in agree-ment with the properties of the actual sample.We studied the dependence of c obs on redshift, luminos-ity and absorption. The resulting plots are shown in Fig. 3 ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 5 ] -1 [ergs s X L F r ac t i on o f CC ob j ec t s -2 -1 F r ac t i on o f CC ob j ec t s Fig. 3.
Dependence of the observed fraction of CC objects, c obs , on the 0.1-2.4 keV luminosity (left) and the redshift(right). In both cases, the black or blue data show the simulation results for case I or case II, respectively (see text). Thedashed red lines show the input fraction of CC objects, c inp , which was fixed to 0.38 for the simulations.(black: case I; blue: case II). Since they represent extremecases where the core radii are determined only by gravi-tation (blue) and feedback (black) effects, the two curvesshould give lower and upper bounds to the actual values. Incase I, we observe a strong dependence of c obs on the lumi-nosity. In particular, the low-luminosity objects ( L X < ergs s − ) are very strongly biased towards CC clusters.Since the number of objects in this luminosity range is rela-tively small (see the left panel of Fig. 2), this effect does nothave a big influence on the mean value of c obs . This effectis related to the background level. Indeed, these objects areboth low-luminosity and nearby, so their surface-brightnesspeak is small. In the case of some NCC clusters, it caneven be below the surface brightness of the background, inwhich case r max = 0 and the source is not detected at all.Conversely, because of their peaked profiles CC objects withthe same total luminosity are easily detected. Therefore,CC clusters completely dominate the detected objects atluminosities below 10 ergs s − . In case II, this effect, al-beit present, is much less severe, because low-luminosity(i.e. low-mass) systems have smaller core radii. As a re-sult, they are more concentrated, and the effect becomesless important. It has been claimed (e.g., Chen et al. 2007)that low-mass systems (groups, poor clusters) are predom-inantly CC. If the CC bias is not taken into account, wesee from our simulation that one would immediately reachsuch a conclusion, even if the true fraction of CC objectswould not depend at all on luminosity.From Fig. 3 we also observe a dependence of c obs on theredshift of the object. In particular, we note a significant in-crease in c obs at the highest redshifts. This is a consequenceof the cut-off in the luminosity function. At rather highredshifts, only the most luminous objects are selected, andabove the cut-off luminosity their number decreases quicklywith increasing luminosity. Since, for a given limiting flux,the associated luminosity is smaller for CC than for NCCsystems, the relative number of CC objects will be signifi-cantly larger. We note that unlike the low-luminosity effect,which is due to a combination of the intrinsic properties ofthe different population and of the background level, thiseffect is caused by the flux limit. With a lower flux limit,this effect would not disappear, but would be shifted to higher redshift, where the effect of the cut-off in the lumi-nosity function will start to appear. Unlike the luminositydependence, in case II we find a stronger evolution of c obs .In this case, since we are only selecting high-mass systemsthe core radii are proportionally larger, which increases thebias.As expected, the selected sample shows very little de-pendence on N H . Indeed, the measured value of c obs is con-stant for varying N H , and the total fraction of CC is verysimilar to the one obtained when the effect of absorption iscompletely neglected.To visualize the simulated objects and compare themwith the actual data, we plotted all the detected clustersin the L X − z plane, and added to the plot the data ofthe HIFLUGCS sample from Chen et al. (2007). In thiscase, we classified the clusters as CC/NCC on the basis oftheir classical mass deposition rate, CC clusters being theones showing a non-zero mass deposition rate. The resultingplot for case I can be seen in Fig. 4. Black (NCC) and red(CC) dots each represent a single simulated cluster, whilethe green symbols (NCC) and yellow circles (CC) show theactual data for the objects of the extended HIFLUGCSsample.Interestingly, we see in Fig. 4 that at all redshifts thesimulated CC clusters populate a broader range of lumi-nosities than NCC clusters. In other terms, the total fluxlimit of the sample is different for CC and NCC clusters.At low luminosities (log L X < .
5) CC objects dominatethe observed and simulated data, which again indicates anobservational bias (see the left panel of Fig. 3). All but oneNCC clusters lie in the area populated by the black dots,while the remaining object is found just below the limit.This indicates that our simulation reproduces well the prop-erties of the sample. A similar conclusion is reached for caseII.
4. XMM-Newton and ROSAT analysis ofsurface-brightness profiles from the HIFLUGCSsample
We analyzed available data for the HIFLUGCS sample,with the aim of providing an alternative estimate of the
Eckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I
Redshift0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 X Log L Fig. 4.
Comparison between simulated objects and observational data in the log L X vs z plane. The black and red dotsrepresent the simulated NCC and CC clusters, respectively. The green symbols (NCC) and yellow circles (CC) showthe data from the extended HIFLUGCS sample (Chen et al. 2007). The dashed blue line shows the flux limit for pointsources.CC bias and of extracting a subsample that is unaffected bythe CC bias. We proceeded with the systematic analysis ofsurface-brightness profiles for all clusters in the HIFLUGCSsample. Since the sample is mostly composed of nearbyobjects, the Field Of View (FOV) of the selected instru-ments is a key feature to observe regions as large as pos-sible. Indeed, we are interested in the extraction of totalfluxes within a given physical radius, so a detailed charac-terization of the central regions is not necessary, but it isimportant to detect the emission to relatively large radii.As a result, we decided to use XMM-Newton /EPIC and
ROSAT /PSPC pointed data to pursue our goals, since theyare the X-ray instruments with the largest FOV. In mostcases, when both
XMM-Newton and
ROSAT pointed datawere available, we combined the surface-brightness profilesfrom the two instruments to take advantage of the better
XMM-Newton point spread function (6 arcsec FWHM) inthe central regions and of the larger FOV (1 square degree)and lower background of
ROSAT in the external regions.For very nearby objects ( z < . ROSAT
PSF issufficient to resolve the cores, and a detection to large radiiis needed to constrain the parameters, so we restricted ouranalysis to
ROSAT . Conversely, for the more distant ob-jects ( z > .
08) the apparent size of the objects is smaller, so a better PSF is necessary to resolve the core. In thesecases, only
XMM-Newton was used.To construct a subsample free of selection bias, we mea-sure fluxes in an annulus around the core to exclude thecore component. We then perform a new selection on thebasis of these fluxes. Generally, the flux of a cluster is not awell-defined quantity, since it is computed as the total fluxwithin the area where the source is detected. However, inthis work we wish to extract fluxes within a well-definedphysical region, which we choose to be r . Since in mostcases we do not detect the sources at this radius, a best-fitsurface-brightness model is used to extrapolate the fluxesto r . We use the scaling relations of Arnaud et al. (2005)and cluster virial temperatures from H10 to estimate r for each object. Overall, this corresponds to a size whichranges from ∼
500 kpc for small, group-like objects up to ∼ r , the redshift and virialtemperatures of all HIFLUGCS objects are summarized inTable 4, together with the log of the available data. ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 7 XMM-Newton /EPIC data analysis was carried out in a sys-tematic way using the standard XMMSAS software v9.0.For each EPIC detector, light curves in the soft (2-5 keV)and hard band (10-12 keV) were extracted, and events werefiltered to exclude flares. To minimize the instrumentalbackground, we extracted images from the cleaned eventlists in a narrow band (0.7-1.2 keV, Ettori et al. 2010),which excludes the prominent Al ( ∼ ∼ When available, we restricted our analysis to
ROSAT /PSPC pointed observations. We used the fil-tered event files available in the HEASARC archive andextracted images using the XSELECT tool available withinthe HEASOFT software package with 15 arcsec bins inthe 0.4-2.0 keV bands. Exposure maps in the same energyband were generated using the PSPC detector maps andthe instrument attitude files through the pcexpmap tool. For every cluster and instrument, we used the outputcount images and corresponding exposure maps to extractsurface-brightness profiles. After the detection of individualpoint sources using a local background method, we excisedfrom the images the corresponding regions. We then ex-tracted total count profiles, centered on the image centroid,defined as( (cid:104) x (cid:105) , (cid:104) y (cid:105) ) = (cid:18) (cid:80) x · I x,y (cid:80) I x,y , (cid:80) y · I x,y (cid:80) I x,y (cid:19) , (9)where I x,y is the count rate in the pixel with image coordi-nates ( x, y ). The minimum bin size of the profile was set to7 arcsec ( XMM-Newton ) and 20 arcsec (
ROSAT ), and thebins were grouped to ensure a minimum of 50 counts perbin and permit the use of χ statistics. The count profileswere then divided by the corresponding exposure to correctfor the instrument vignetting.As a result, we obtained exposure-corrected profiles,which we fitted by a source + background model. A double-beta profile was preferred to the standard beta profile whenthe improvement to the fit was found to be statistically sig-nificant by the F-test. The background-subtracted source http://heasarc.gsfc.nasa.gov/ http://heasarc.nasa.gov/lheasoft/ profile SB ( r ) was then inferred. To ensure that the sourcedominates over the background, this procedure was appliedup to the radius r max where the model source intensity is atleast 2 times that of the background. The best-fit surface-brightness model was then used to extrapolate the fluxesto r . We define the total fluxes within r as: F tot = (cid:88) r XMM-Newton surface-brightness pro-files and fitted them jointly to get better constraints onthe parameters. As an example, Fig. 5 shows the XMM-Newton /MOS2 (blue) and ROSAT /PSPC (red) surface-brightness profiles of the cluster A3571 fitted by a double-beta profile plus a constant for the background. While thephysical parameters of the model where fitted jointly, theindividual normalizations and background levels where ad-justed independently. In the innermost 1 arcmin of the pro-file, ROSAT data were ignored to avoid problems of mixingcaused by the broader PSF.To convert the count rates into physical fluxes, we usedthe XMM-Newton /MOS2 and ROSAT /PSPC redistribu-tion matrices and on-axis effective area, and used XSPECto fold the spectrum of each source, modeled by an ab-sorbed MEKAL model with the appropriate temperatureand N H , with the appropriate instrument response. Thefolded spectra were then used to convert the extractedcount rates into unabsorbed physical fluxes in the 0.5-2.0keV band.As a byproduct of this work, we were able to esti-mate the cross-calibration between the two instruments(see Appendix A for details). Indeed, since they are bright,persistent sources, clusters of galaxies are ideal sources tocross-calibrate between two independent missions. On aver-age, we find that MOS2 gives ∼ 15% higher fluxes comparedto PSPC, and hence there is a clear cross-calibration issuewhich must be taken into account. Since the HIFLUGCSsample was selected using fluxes extracted from ROSAT Eckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I -1 10 1 10 ] S u r f ace b r i gh t n ess [ c oun t s / sec / a r c m i n -3 -2 -1 -1 10 1 10 ] S u r f ace b r i gh t n ess [ c oun t s / sec / a r c m i n -3 -2 -1 Distance [arcmin] -1 10 1 10 c -4-3-2-101234 Distance [arcmin] -1 10 1 10 c -4-3-2-101234 Fig. 5. XMM-Newton /MOS2 (blue) and ROSAT /PSPC(red) surface-brightness profile of the cluster A3571, fittedjointly with a double-beta model. The individual normal-izations and background levels were fitted independently.The higher XMM-Newton data points and model at largeradii are caused by a higher background. The bottom panelshows the deviations (in σ ) from the surface-brightnessmodel.only, we decided to use the ROSAT normalization to ex-tract fluxes, and apply a 15% cross-calibration factor tothe XMM-Newton fluxes. After applying such a renormal-ization, XMM-Newton and ROSAT fluxes agree with ∼ σ errors, as well as thetotal fluxes from XMM-Newton and ROSAT are summa-rized in Table 5. The flux limit of the HIFLUGCS sample(2 . × − ergs cm − s − in the 0.1-2.4 keV band) trans-lates into a total flux of 1 . × − ergs cm − s − in the0.5-2.0 keV band for a typical temperature of 4 keV. All XMM-Newton fluxes should be rescaled by 15% when com-pared to ROSAT to account for the systematic calibrationdifference. Figure 6 shows the distribution of ratio betweenthe ROSAT fluxes extracted following Eq. 10 and the orig-inal fluxes quoted by Reiprich & B¨ohringer (2002). In thevast majority of cases, we can see that the fluxes estimatedusing Eq. 10 agree very well with the original fluxes. In threecases, our fluxes differ from the original fluxes by a fac-tor ∼ 2, either higher (Fornax and A1367) or lower (NGC4636). All of these are nearby, very extended objects. Thedifference can be explained by the low surface brightness ofthe outer regions, which prevents the detection of a largepart of the flux, and by the instability of the extrapola-tion over a large radial range. Overall, this is however nota problem, given that our definition of cluster fluxes differsfrom the original method, where the fluxes were measuredby integrating the flux within the area where the clustersare detected.According to our analysis, one cluster (Zw III 54) doesnot have a sufficient total flux to match the selection crite-rion of the sample. This cluster is the weakest of the sampleand was at the extreme limit of the original selection, andtherefore, even though our redetermined flux does not dif- Redetermined Flux / Original Flux0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 N u m b e r Fo r n ax A N G C Fig. 6. Distribution of the ratio between our redeterminedfluxes and the original fluxes from Reiprich & B¨ohringer(2002). Since the original fluxes were computed in the 0.1-2.4 keV band, they were rescaled to match our choice ofenergy band (0.5-2.0 keV). The most prominent outliersare highlighted.fer significantly from the original one, we find its flux to bebelow the flux cut. 5. The unbiased subsample To measure the CC fraction, we wish to extract a sub-sample of HIFLUGCS which should be free of the CCbias. The fraction of CC objects would then be computedfrom the subsample and not from HIFLUGCS. At variancewith the cores, it has been found that in cluster outskirtsthe surface-brightness profiles are essentially self-similar(Neumann 2005; Croston et al. 2008; Leccardi et al. 2010),so the selection based on the fluxes in the outer regionsshould be unbiased. We define a new sample by selectingthose objects for which the flux in an annulus excludingthe core, and not the total flux, is above a given flux limit.While the choice of the outer radius is straightforward (weselect r ), the same is not true for the inner radius, r in .Here we require a value such that the core emission wouldbe excluded as much as possible, but that would still allowa statistically accurate determination of the fluxes. To thisend, we analyzed the distributions of the best-fit parame-ters from Table 5. In the cases where a double-beta modelwas required by the fit, we searched for a typical radiusat which the contribution of the core can be considered tobe negligible. To do this, we looked for the radius abovewhich the flux can be attributed mostly to the outer betacomponent. All in all, we find that r in = 0 . r is a reason-able choice. With such a choice, in average 97% of the fluxis attributed to the main beta component, and the fluxescan still be computed with good accuracy. For comparison,this radius is larger than or comparable to the cooling ra-dius r cool for which the cooling time exceeds 7.7 Gyr (H10).Maughan (2007) excised the region within 0 . r to ex-clude the effects of the core. In this case, in average ∼ . r − r radial range. ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 9 To select the corresponding flux limit in this radialrange, we considered a beta profile with the mean parame-ters from our analysis and computed the fraction of the fluxintegrated in this range. From Table 5, we find β ∼ . r c ∼ . r with a scatter of0 . r . Integrating a surface-brightness profile with suchparameters, we estimate that 59% of the flux originatesfrom the 0 . r − r , and therefore the HIFLUGCS fluxlimit translates into a minimum flux of 7 . × − ergscm − s − (0.5-2.0 keV band, 0 . r − r ). Because ofthe 15% normalization difference, this corresponds to a fluxlimit of 8 . × − ergs cm − s − for XMM-Newton fluxes. Since our sample is selected as a subset of HIFLUGCS andnot directly from RASS data, there may be objects thatare not in the HIFLUGCS sample but should be in ours.In other terms, there could be some objects with a flatprofile, for which the total flux would be slightly below theHIFLUGCS limit but the flux in the 0 . r − r radialrange would be above our new limit. This effect could havean influence on our measurement of the CC fraction usingour subsample, and it must be quantified.To estimate the number of objects which might bemissed in our subsample, we computed the distribution ofthe ratio between our fluxes in the 0 . r − r and theoriginal survey fluxes, excluding the most prominent out-liers from Fig. 6 and rescaling the distribution by the ratioof the two flux limits. This defines a probability distribution P DF ( x ) for the probability that the flux of a cluster wouldbe increased or decreased with respect to the flux limitwhen going from the original selection in the HIFLUGCSsample to the one we apply. In the probability distribution,the peaked objects are the ones with a ratio much below 1,while the flat systems have a ratio larger than 1. In Fig. 7we show the resulting probability distribution.For an object with a given total flux F < F lim , theprobability to have a 0 . r − r flux greater than ourflux limit is given by P ( F ) = (cid:90) ∞ F lim /F P DF ( x ) dx, (11)We can then estimate the number of missed objects by inte-grating the probability distribution weighted by the numberof objects at a given flux, i.e. N missed = (cid:88) F 89. Given that the objects which might bemissed are the ones with a high flux outside the core, theirsurface-brightness profile should be very flat, so we expectthem to be mostly NCC. In conclusion, we expect that sta-tistically between 3 and 4 NCC clusters are missed fromour selection. x0.4 0.6 0.8 1 1.2 P D F ( x ) Fig. 7. Normalized distribution of the quantity x = f annulus /f old , where f annulus is the ratio between the fluxcomputed in the 0 . r − r radial range and the cor-responding flux limit (7 . × − ergs cm − s − , 0.5-2.0keV), and f old is the original flux from Reiprich & B¨ohringer(2002) rescaled by the corresponding flux limit (2 . × − ergs cm − s − , 0.1-2.4 keV). This defines a probability dis-tribution P DF ( x ) for the probability that the flux of acluster is increased or decreased when performing our newselection. After the selection of the clusters based on their flux inthe 0 . r − r radial range, we reject 13 clusters fromthe original sample. Table 2 shows the corresponding ob-jects and fluxes, along with their classification by H10.Interestingly, all the rejected objects were classified as CC: 9of the clusters were classified as strong CC clusters (i.e. clus-ters with a central cooling time < z > . . r − r annulus,central cooling time and classification from the work of H10.Four clusters (MKW 4, MKW 3S, A2163 and A2589) showa flux below the limit, but consistent with it within 1 σ , sowe included them in our selection. Table 2. HIFLUGCS clusters rejected for the present work.Column description: 1: Cluster name; 2 and 3: 0.5-2.0keV fluxes in the radial range 0 . r − r from XMM-Newton /MOS2 (2) and ROSAT /PSPC (3), in units of10 − ergs cm − s − ; 4: central cooling time in units of h − / Gyr, from H10; 5: cluster classification from H10(SCC = strong cool-core, WCC = weak cool-core). Cluster F XMM F ROSAT CCT ClassA133 6.88 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Of the 51 objects in our subsample, 19 (37%) are clas-sified as strong CC, 18 (35%) as NCC, and 14 (27%) areWCC. When taking into account the clusters which mightbe missed in our subsample (see Sect. 5.2) and assumingthat all of them are NCC, the fraction of SCC is reduced to35% and that of NCC increased to 40%. Compared to theanalysis of Mittal et al. (2009), which found 44% SCC clus-ters, our value of 35% corresponds to a bias of 26% in theoriginal sample. This result is in excellent agreement withthe bias estimated from our simulation (29%, see Sect. 3). F annulus /F core as a cool-core indicator Given that all the clusters excluded by our analysis presentCC characteristics, it is clear that the ratio between theflux in the core, from 0 to 0 . r (hereafter F core ) andthe flux in the annulus 0 . r − r ( F annulus ) stronglydepends on the state of the cluster. In other terms, theratio F annulus /F core could be used as an indicator of theCC state. To investigate this possibility, we checked for apositive correlation between this quantity and the centralcooling time (CCT) as found by H10. In Fig. 8 we showthe ratio F annulus /F core as a function of the CCT for all64 HIFLUGCS clusters, fitted by a simple power law. Apositive correlation is indeed observed, with the best-fit pa-rameters given by F annulus F core = (0 . ± . × (cid:18) CCT (cid:19) . ± . . (13)The correlation between the two quantities is significant:Spearman’s correlation factor for the relation is ρ =0 . +0 . − . . The corresponding likelihood of the correlationoccurring by chance is < − . The scatter of the rela-tion is ∼ F annulus /F core can indeed be used as an indicator ofCC type, and thus Eq. 13 can be used to estimate the cen-tral cooling time. This indicator is robust, since it doesnot depend on any deprojected quantity (similar to the“cuspiness” indicator, Vikhlinin et al. (2007)). However, Table 3. Unbiased HIFLUGCS subsample used in thepresent work. Column description: 1: Cluster name; 2 and3: 0.5-2.0 keV fluxes in the radial range 0 . r − r from XMM-Newton /MOS2 (2) and ROSAT /PSPC (3), in unitsof 10 − ergs cm − s − ; 4: central cooling time in unitsof h − / Gyr, from H10; 5: cluster classification from H10(SCC = strong cool-core, WCC = weak cool-core, NCC =non cool-core). Cluster F XMM F ROSAT CCT ClassA85 23.45 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± tight constraints on the surface-brightness profile parame-ters are necessary, since the fluxes need to be extrapolatedto r . This is a problem for very extended, nearby objects,for which the uncertainties when extrapolating to r arequite large. Indeed, all of the outliers in Fig. 8 are nearby ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 11 Central Cooling Time [Gyr] -1 10 1 10 c o r e / F a nnu l u s F Fig. 8. Ratio between the flux in the 0 . r − r radialrange and the flux in the core integrated up to 0 . r , F annulus /F core (this work), as a function of the central cool-ing time in units of Gyr (H10). The red solid line shows afit to the data with a power law. Spearman’s correlationcoefficient for the relation is ρ = 0 . +0 . − . .( z < . β tend to be flatter thanthe real value (Gastaldello et al. 2007), which probably re-sults in an over-estimation of F annulus . On the other hand,this indicator is excellent for intermediate-redshift objects( z ∼ . XMM-Newton diffi-cult. 6. Discussion Expanding on the work of H10, our analysis reveals thatthe flux-limited samples of galaxy clusters, and in partic-ular the HIFLUGCS complete sample, are significantly bi-ased in favor of CC objects, and hence this effect must betaken into account when estimating the fraction of CC ob-jects from a flux-limited sample. Our assessments of thebias through observations and simulations agree very wellwith each other, which strengthens our point. Overall, wefind that ∼ 29% of the objects should be removed from theoriginal HIFLUGCS sample if one wishes to estimate theCC fraction, and we extracted a subsample as free as pos-sible of the bias, which can also be used for other purposes(see Table 3).Once the appropriate corrections have been applied, wefind that considerably less than half of the objects (38% inour subsample, 35% when taking incompleteness into ac-count; see Sect. 5.3) are classified as strong CC clusters,i.e. exhibit a central cooling time below 1 Gyr. This re-sult has important repercussions on the structure formationscenarios. At variance with the original predictions of thecooling-flow model (Peres et al. 1998), in the scenario whereCC clusters trace relaxed objects our result implies that amajority of clusters has not reached a stable state. In otherterms, in the majority of objects injection of entropy in the ICM by merging events or giant AGN outbursts preventsthe formation of cool cores (McNamara & Nulsen 2007).Obviously, if cool cores cannot be destroyed efficientlyby merging events and the state of a cluster is defined onceand for all during the cluster formation process, as sug-gested by some numerical simulations (Poole et al. 2008;McCarthy et al. 2008), the fraction of CC can only be pre-dicted through large cosmological simulations. Conversely,assuming that clusters evolve through time, the CC frac-tion can be used to estimate roughly the rate of entropyinjection events in the local Universe.Assuming that the NCC fraction evolves through time,the evolution of the fraction of NCC objects can be de-scribed asd f NCC d t = r he f CC − r cool f NCC , (14)where r he is the rate of heating events per dark matterhalo, r cool is the cooling rate, f NCC is the fraction of bothNCC and WCC clusters and f CC is the fraction of SCCclusters. This equation simply reflects the idea that heat-ing events will transform CC clusters into NCC (or WCC),while cooling will do the opposite. The cooling rate is givenby r cool = 1 /τ R , where the relaxation timescale τ R is thetime needed for a cluster to relax from a major heatingevent. In this framework, SCC clusters are the ones whichhave not experienced any major entropy injection eventduring the relaxation timescale, while NCC and WCC haveexperienced or are currently experiencing an entropy injec-tion phase.If we assume that the evolution of f NCC is slow, we areclose to a stationary situation, and Eq. 14 reads r he ∼ r cool f NCC f CC = 1 τ R f NCC f CC . (15)From the simulations of Poole et al. (2006), it appears thatclusters require in average a timescale of ∼ τ R = 5Gyr for our calculation. In the ΛCDM cosmology, a look-back time of 5 Gyr corresponds to a redshift of 0.4, so weare probing the rate of entropy injection events integratedup to redshift 0.4. As a result, we find that the rate of majorheating events per cluster is roughly r he ∼ / − . (16)This number can be compared with the predictionsfrom full cosmological simulations (see e.g., Fakhouri &Ma 2008). Obviously, this estimate relies on several strongassumptions, in particular on the estimate of the relax-ation timescale and on the approximation of equilibrium.From a statistical analysis of cold fronts in galaxy clusters,Ghizzardi et al. (2010) estimate a merger rate of ∼ / − , similar to ours. These numbers can however not bedirectly compared, since most of the merging events respon-sible for producing cold fronts are minor mergers which arenot capable of disrupting a cool core. On the other hand,our calculation gives an estimate of the rate of major en-tropy injection events, whether they are mergers or AGNoutbursts, which are capable of transforming a CC clusterinto NCC or WCC.An interesting result of our simulation is the strong de-pendence of the CC bias on luminosity (see the left panel of Fig. 3). While for clusters ( L X (cid:38) × ergs s − )the bias is modest in HIFLUGCS, groups and poor clus-ters appear to be very strongly affected by this effect. Ouranalysis of the sample qualitatively confirms this result.While only 12 objects (18%) exhibit a temperature be-low 3 keV in the complete sample, almost half (5 out of11) of the objects which were rejected based on our fluxcut in the 0 . r − r annulus fall into this category.As a result, an artificial over-representation of cool coresamong low-luminosity objects might be observed when an-alyzing such a sample. Such a dependence of the CC frac-tion was indeed observed in HIFLUGCS (Chen et al. 2007).Recently, Johnson et al. (2009) claimed to have identified apopulation of merging, NCC galaxy groups, which presentvery shallow surface-brightness profiles, and hence wouldbe difficult to detect in the RASS. This population of NCCgroups could have been missed when selecting the sample,thus influencing the observed CC fraction.A similar, albeit more modest effect impacts on thehigh-redshift clusters ( z > . . r − r radial range, the remaining one (A2163) beinga very disturbed merging object (Markevitch & Vikhlinin2001). While this result is not statistically significant giventhe very small number of objects in this category, it agreeswith the predictions of our simulation. This implies thatthe CC bias should be taken properly into account whenstudying the cosmological evolution of the CC fraction.In addition, we have shown that our fluxes in the0 . r − r radial range can be used as a tracer of thestate of a cluster when compared to the core flux integratedup to 0 . r (see Sect. 5.4), since the ratio F annulus /F core correlates with the central cooling time. This relation canbe interpreted as the fact that, while the profiles are verydifferent in the cores, they are essentially self-similar inthe outer regions of clusters (Neumann & Arnaud 2001;Leccardi et al. 2010). Indeed, while in the central regionsnon-gravitational effects (radiative cooling, AGN feedback,...) are important, in cluster outskirts the profiles are mostlydetermined by gravitational processes. Highlighting the im-portance of excluding the cores when analyzing gravita-tional effects, Maughan (2007) observed that the M − T relation tightens when these quantities are measured be-yond 0 . r . The ratio F annulus /F core therefore traces thedeviations from the expectations of the self-similar model,and thus can be used to trace the state of a cluster. Thissuggests that for the extraction of quantities depending ongravitational processes only, such as the M − T and L X − T relations, the use of a sample selected using fluxes in a well-defined radial range excluding the cores is important (seee.g., Ota et al. 2006). 7. Conclusion In this paper, we presented an analysis of the effect of thedifferent surface-brightness profiles for CC and NCC clus-ters on the selection of X-ray flux-limited samples, basedon both numerical and observational approaches, and esti- mated the fraction of CC objects in the nearby Universe.Our results can be summarized as follows: – Performing realistic simulations of a population of clus-ters and of the selection process of the HIFLUGCS sam-ple, we estimate that ∼ 29% of the strong CC objectspresent in the sample should be removed if one wishesto measure the fraction of CC vs NCC objects using thissample. – Analyzing the populations of simulated CC and NCCclusters in the L X − z plane, we see that CC clusterspopulate a broader range in the diagram. In other terms,the flux limit is actually different for CC and NCC ob-jects when selecting the clusters based on their observedflux only. – In all cases, we find that low-luminosity objects (groups,poor clusters) are much more affected than more lu-minous objects. This effect might explain the lack ofNCC objects in group samples extracted from RASSdata noted by several authors (e.g., Chen et al. 2007).This illustrates the importance of taking into accountthis bias when computing the CC fraction. We also finda trend of increasing bias with redshift. – From our analysis of the surface-brightness profiles ofall HIFLUGCS clusters, we propose to select clustersaccording to their flux in a well-defined physical radialrange excluding the core (0 . r − r ). Performing anew selection according to the flux in this radial range,we exclude 13 objects from the original sample, all ofwhich present CC characteristics, and extract a subsam-ple of HIFLUGCS as free as possible of the CC bias. – Less than half (35 − ∼ . − for the rate of heating events per dark-matter halo and per Gyr. – In addition, we find that the ratio F annulus /F core be-tween the fluxes in the radial range 0 . r − r and0 − . r strongly correlates with the central cool-ing time, and therefore can be used as a CC indicator.We expect this indicator to be particularly effective forintermediate-redshift objects ( z ∼ . Acknowledgements. We thank Thomas Reiprich and FabioGastaldello for their useful comments. DE is supported by theOcchialini post-doc fellowship grant of IASF Milano. For thepresent work, we made extensive use of the XMM-Newton ScienceArchive (XSA) and of the High-Energy Astrophysics Science Archive(HEASARC). References Andersson, K., Peterson, J. R., Madejski, G., & Goobar, A. 2009,ApJ, 696, 1029Arnaud, K. A. 1996, in Astronomical Society of the Pacific ConferenceSeries, Vol. 101, Astronomical Data Analysis Software and SystemsV, ed. G. H. Jacoby & J. Barnes, 17–+Arnaud, M., Pointecouteau, E., & Pratt, G. W. 2005, A&A, 441, 893Bagchi, J., Durret, F., Neto, G. B. L., & Paul, S. 2006, Science, 314,791B¨ohringer, H., Schuecker, P., Guzzo, L., et al. 2004, A&A, 425, 367B¨ohringer, H., Voges, W., Huchra, J. P., et al. 2000, ApJS, 129, 435Cavagnolo, K. W., Donahue, M., Voit, G. M., & Sun, M. 2009, ApJS,182, 12Cavaliere, A. & Fusco-Femiano, R. 1976, A&A, 49, 137Chen, Y., Reiprich, T. H., B¨ohringer, H., Ikebe, Y., & Zhang, Y. 2007,A&A, 466, 805 ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 13 Table 4. Basic properties of HIFLUGCS clusters. Column description: 1: Cluster name; 2: instrument used (1= ROSAT ;2= XMM-Newton ; 3=combination of the two); 3: redshift, from Reiprich & B¨ohringer (2002) and references therein; 4:virial temperature in keV, from H10; 5 and 6: r from the scaling relations of Arnaud et al. (2005) in kpc (5), and thesubtended angle θ in arcmin (6). Cluster Instrument Redshift kT vir [kev] r [kpc] θ [arcmin]A85 3 0.0556 6 1208 19.2A119 3 0.044 5.73 1187 23.5A133 3 0.0569 3.96 981 15.2NGC 507 3 0.0165 1.44 539 27.5A262 3 0.0161 2.44 729 38.1A400 3 0.024 2.26 695 24.6A399 2 0.0715 6.7 1268 15.9A401 3 0.0748 8.51 1427 17.2A3112 3 0.075 4.73 1064 12.8Fornax 1 0.0046 1.34 520 93.92A 0335 3 0.0349 3.53 935 23.1Zw III 54 2 0.0311 2.5 734 20.2A3158 3 0.059 4.99 1100 16.5A478 3 0.09 7.34 1316 13.4NGC 1550 2 0.0123 1.34 519 35.3EXO 0422 2 0.039 2.93 801 17.8A3266 3 0.0594 9.45 1514 22.6A496 3 0.0328 4.86 1098 28.7A3376 3 0.0455 3.8 966 18.5A3391 1 0.0531 5.77 1186 19.6A3395S 3 0.0498 4.82 1086 19.1A576 2 0.0381 4.09 1005 22.8A754 3 0.0528 11.13 1648 27.4Hydra A 3 0.0538 3.45 874 14.3A1060 1 0.0114 3.16 846 62.1A1367 1 0.0216 3.58 947 37.1MKW 4 1 0.02 2.01 651 27.5Zw Cl 1215 2 0.075 6.27 1225 14.7NGC 4636 3 0.0037 0.9 415 93.0A3526 1 0.0103 3.92 996 80.8A1644 2 0.0474 5.09 1117 20.6A1650 2 0.0845 5.81 1174 12.7A1651 3 0.086 6.34 1226 13.0Coma 1 0.0232 9.15 1513 55.3NGC 5044 1 0.009 1.22 492 45.6A1736 2 0.0461 3.12 828 15.7A3558 3 0.048 4.95 1101 20.0A3562 3 0.0499 4.43 1041 18.3A3571 3 0.0397 7 1314 28.6A1795 3 0.0616 6.08 1213 17.5A3581 2 0.0214 1.97 644 25.5MKW 8 2 0.027 3 816 26.0RX J1504 2 0.2153 9.53 1414 6.9A2029 3 0.0767 8.26 1405 16.5A2052 3 0.0348 3.35 866 21.4MKW 3 3 0.045 3.9 979 18.9A2065 2 0.0721 5.4 1138 14.2A2063 3 0.0354 3.77 966 23.5A2142 1 0.0899 8.4 1408 14.4A2147 1 0.0351 4.07 1004 24.6A2163 2 0.201 15.91 1840 9.5A2199 3 0.0302 4.37 1042 29.5A2204 2 0.152 8.92 1411 9.1A2244 1 0.097 5.78 1165 11.1A2256 3 0.0601 7.61 1358 20.0A2255 3 0.08 5.81 1176 13.3A3667 3 0.056 6.39 1247 19.6Sersic 159-03 3 0.058 2.57 737 11.2A2589 3 0.0416 3.89 979 20.4A2597 3 0.0852 4.05 980 10.5A2634 1 0.0312 3.19 844 23.2A2657 3 0.0404 3.52 932 20.0A4038 3 0.0283 3.14 837 25.3A4059 3 0.046 4.22 1018 19.34 Eckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I Table 5. Results of surface-brightness profile fitting. Column description: 1: Cluster name; 2: β ; 3: outer core radius r c (in kpc); 4: inner core radius r c (in kpc); 5: ratio between the two beta components at r = 0, R ; 6 and 7: estimatedtotal fluxes from 0 to r in the 0.5-2.0 keV band, in units of 10 − ergs cm − s − , from XMM-Newton /MOS2 (6) and ROSAT /PSPC (7); NB: a cross-calibration factor of 0.85 must be applied to the XMM-Newton fluxes (see Appendix A); 8: minimum χ of the fit versus number of degrees of freedom. Cluster β r c r c R F XMM F ROSAT χ /d.o.f.A85 0.638 ± ± ± ± ± ± ± ± 11 2.834 ± ± ± ± 11 30 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 14 2.111 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 31 1.344 ± ± ± ± 10 1.371 ± ± ± 14 1.465 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 10 5.077 ± ± ± 25 41 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 23 17 ± ± ± ± ± 20 83 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 13 1.362 ± ± ± 12 53 ± ± ± ± ± 17 43 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 50 93 ± 13 4.4 ± ± ± ± 13 54 ± ± ± ± ± ± 28 140 ± ± ± ± ± ± ± ± 12 1.465 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 13 1.264 ± ± ± ± ± ± ± ± 13 40 ± ± ± ± ± ± ± ± ± ± ± ± 11 41 ± ± ± ± ± ± 21 1.398 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± See Appendix B.ckert, D. et al.: The Cool-Core Bias in X-ray Galaxy Cluster Samples I 15 Croston, J. H., Pratt, G. 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B¨ohringer,G. W. Pratt, A. Finoguenov, & P. Schuecker , 48–+ Appendix A: XMM-Newton/MOS2 vsROSAT/PSPC cross-calibration The present work offers an excellent opportunity to studythe flux cross-calibration between the instruments used( XMM-Newton /MOS2 and ROSAT /PSPC). Indeed, theHIFLUGCS sample contains bright objects which are in-trinsically persistent over very long timescales, unlike themajority of X-ray emitting sources. In this appendix, wepresent a comparison between the unabsorbed fluxes in the 0 − r radial range for 37 of the 64 HIFLUGCS clusters,for which we performed the analysis by combining bothinstruments. The surface-brightness profiles were fitted si-multaneously with the same physical parameters for bothinstruments, while only the normalizations and backgroundlevels were adjusted individually. For the details of the fluxreconstruction procedure, see Sect. 4.2.Figure A.1 shows the comparison between PSPC andMOS2 fluxes in the 0.5-2.0 keV band. The left panel showsthe PSPC fluxes as a function of the MOS2 fluxes, fitted bya simple linear relationship. The right panel shows the dis-tribution of the ratio between the MOS2 and PSPC fluxes.The best-fit relation gives F ROSAT = (0 . ± . F XMM +(2 . ± . × − , (A.1)where the fluxes are expressed in units of ergs cm − s − .The scatter of the relation is 5%.In conclusion, we can see that a systematic difference inabsolute calibration is clearly present, XMM-Newton giving15% higher fluxes with respect to ROSAT . Appendix B: Notes on individual clusters – A85 : This cluster is categorized as SCC but appearsto be merging with at least one group South of the core(Kempner et al. 2002). This substructure was excisedwhen extracting the surface-brightness profile. – NGC 507 : The surface-brightness profile of this nearbygroup ( z = 0 . χ = 784 . – A399/A401 : These two clusters appear to be con-nected (Sakelliou & Ponman 2004). The ROSAT /PSPCpointed observation was pointed on the centre of A401.The surface-brightness profile for A401 was thereforeextracted in a sector excluding A399. – Fornax : This nearby poor cluster shows a main peakon the BCG NGC 1399 and a secondary peak onNGC 1404. NGC 1399 was chosen as the center ofthe cluster and the area surrounding NGC 1404 wasignored when extracting the surface-brightness profile.Overall, even when using the large ROSAT FOV onlya small fraction of r is observed, hence the errorswhen extrapolating the fluxes can be large. Moreover,the surface-brightness profile of the source is not wellfitted by any simple model, so the results of the fittingprocedure might be unstable. We consider this objectas a very peculiar case. – NGC 1550 : This very nearby group ( z = 0 . XMM-Newton . As a result, lessthan half of r was observed within the FOV ofthe instrument, so the extrapolated fluxes are ratheruncertain. – A3376 : A very disturbed cluster which shows anelongated, cometary shape, and two bow-shock-likegiant radio relics (Bagchi et al. 2006); no obviouscenter can be defined. Using the emission centroid asthe center, this cluster shows an anomalously high core ] -1 s -2 XMM-Newton/MOS2 flux [ergs cm0 10 20 30 40 50 60 70 80 90 -12 · ] - s - R O S A T / PSP C f l u x [ e r g s c m -12 · ROSAT / F XMM F1 1.05 1.1 1.15 1.2 1.25 N u m b e r Fig. A.1. Comparison between XMM-Newton /MOS2 and ROSAT /PSPC unabsorbed fluxes in the 0.5-2.0 keV band.Left: PSPC fluxes vs MOS2 fluxes fitted by a simple linear relationship. Right: Ratio between the MOS2 and PSPCfluxes.radius ( r c = 625 ± 31 kpc) and an extremely steepdecline ( β = 1 . ± . – A3395s : This cluster appears to be merging with asmaller structure in the East (A3395e, Donnelly et al.2001). The surface-brightness profile was extracted ina sector excluding the secondary structure. – A754 : The morphology of this well-known mergingcluster is very disturbed (see Henry et al. 2004, fora detailed analysis of the XMM-Newton data), so noobvious center can be defined. We used the emissioncentroid as the center. – NGC 4636 : The surface-brightness profile of thisnearby elliptical in the outskirts of the Virgo cluster isnot well represented by any simple model ( χ = 1951 . – A1644 : This cluster shows a double-peak structure(Reiprich et al. 2004). We extracted the surface-brightness profile in a sector avoiding the Northsubstructure. – A1736 : This is a difficut case, since no ROSAT /PSPCobservation exists and the available XMM-Newton observation was affected by a high background level. Asa result, the β value could not be constrained, and wasfixed to the standard value of 0 . 67 while fitting. We notehowever that our output fluxes are in good agreementwith the original flux from (Reiprich & B¨ohringer 2002). – MKW 8 : This cluster extends well beyond the FOVof XMM-Newton , which introduces rather large errorswhen extrapolating the fluxes to r . – A2634 : The ROSAT /PSPC image shows a secondarypeak North-West of the main cluster. This structurewas excised for the extraction of the surface-brightness profile. – A4038 ::