Temperature structure of the intergalactic medium within seven nearby and bright clusters of galaxies observed with XMM-Newton
aa r X i v : . [ a s t r o - ph ] F e b Astronomy & Astrophysics manuscript c (cid:13)
ESO 2018November 6, 2018
Temperature structure of the intergalactic medium within sevennearby and bright clusters of galaxies observed withXMM-Newton.
H. Bourdin and P. Mazzotta , Dipartimento di Fisica, Universit`a degli Studi di Roma ”Tor Vergata”,via della Ricerca Scientifica, 1, I-00133 Roma, Italye-mail: [email protected], [email protected] Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USAReceived 5 June 2006 / Accepted 31 October 2007
ABSTRACT
Aims.
Using a newly developed algorithm, we map, to the highest angular resolution allowed by the data, the temperaturestructure of the intra-cluster medium (ICM) within a nearly complete X-ray flux limited sample of galaxy clusters inthe redshift range between z = 0 .
045 and z = 0 . Methods.
We use a multi-scale spectral mapping algorithm especially designed to map spectroscopic observables from X-ray extended emission of the ICM. By means of a wavelet analysis, this algorithm couples spatially resolved spectroscopywith a structure detection approach. Derived from a former algorithm using Haar wavelets, our algorithm is nowimplemented with B-spline wavelets in order to perform a more regular analysis of the signal. Compared to otheradaptive algorithms, our method has the advantage of analysing spatially the gas temperature structure itself, insteadof being primarily driven by the geometry of gas brightness.
Results.
For the four clusters in our sample that are major mergers, we find a rather complex thermal structurewith strong thermal variations consistent with their dynamics. For two of them, A2065 and A2256, we perform a 3-danalysis of cold front-like features evidenced from the gas temperature and brightness maps. Furthermore, we detect asignificant non-radial thermal structure outside the cool core region of the other 3 more “regular” clusters, with relativeamplitudes of about about 10 % and typical sizes ranging between 2 and 3 arcmin. We investigate possible implicationsof this thermal structure on the mass estimates, by extracting the surface brightness and temperature profiles fromcomplementary sectors in the “regular” clusters A1795 and A2029, corresponding to hottest and coldest regions inthe maps. For A2029, the temperature and surface brightness gradients seem to compensate each other, leading toa consistent mass profile. For A1795, however, the temperature structure leads to a significant mass discrepancy inthe innermost cluster region. The third “regular” cluster, A478, is located in a particular sky region characterised bystrong variations of neutral hydrogen column density, Nh, even on angular scales smaller than the cluster itself. Forthis cluster, we derive a spectroscopic Nh map and investigate the origin of Nh structure by discussing its correlationwith galactic emission of dust in the infrared.
Key words.
Galaxies: clusters: general – Galaxies: intergalactic medium – X-rays: galaxies: clusters – Techniques: imageprocessing – Techniques: spectroscopic
1. Introduction
Clusters of galaxies are thought to form by accretion of lessmassive groups and clusters under the influence of grav-ity. Following this scheme, they successively overcome sometransient merging processes that alter their energy contentand some relaxation phases, which lead to the almost viri-alised systems we observe.The thermodynamical state of X-ray emitting intra-cluster medium (ICM) depends on both the cluster mergerhistory and some not yet perfectly understood physicalprocesses that drives its thermalisation, such as heat con-duction or viscosity. Revealed by X-ray observations, thebrightness and temperature structure of the ICM testifiesto this final state. The brightness structure of the ICM hasbeen extensively studied in the past (e.g. Forman & Jones
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H. Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies performing spatially resolved spectroscopy with requiredsignal-to-noise. To do so, the field of view is firstly sam-pled in independent spatial bins following a mesh refine-ment scheme, then spectroscopic estimations are performedwithin each bin. Several binning strategies have been pro-posed in this context: adaptive binning (e.g. Sanders &Fabian 2001), “contour binning” (Sanders 2006), or Voronoitessellation (e.g. Cappellari & Copin 2003). Proposed byBourdin et al. (2004), a third approach consists in usingHaar wavelet coefficients in order to couple a multi-scalespectroscopic analysis with a structure detection scheme.Among these algorithms, only the last one performs adirect investigation of structure for the searched parameteritself –i.e. the ICM projected temperature– while the signalanalysis is essentially driven by the geometry of gas bright-ness in all the other algorithms. Here, we present a newversion of the algorithm of Bourdin et al. (2004), now im-plemented with B-spline wavelets and possibly enabling usto apply a more conservative thresholding strategy. Otherimprovements are related to adaptations to more recent cal-ibration of XMM-Newton instruments, which particularlyallow us to combine data coming from the three EuropeanPhoton Imaging Cameras (EPIC).This algorithm has been used to perform a systematicstudy of a nearly complete X-ray flux selected sample ofseven clusters observed with XMM-Newton. Along this pa-per, we first discuss the sample selection and data prepara-tion in Sects. 2 and 3, then expose our data analysis schemein Sect. 4, and finally give a brief description of the thermalstructure observed in each single cluster in Sect. 5. Beforeproviding general discussions and conclusions in Sect. 9, wediscuss more specific issues related to thermal features ob-served within individual objects: isoradial thermal struc-ture in the relaxed clusters Abell 1795 and Abell 2029(Sect. 4), cold fronts in the merging clusters Abell 2065 andAbell 2256 (Sect. 7). The additional Sect. 8 is related to thehigh neutral hydrogen column density variations observedacross the field of view of Abell 478.The cluster radii are computed as angular diame-ter distances, assuming a λ -CDM cosmology with H =70 km . s − . Mpc − , Ω = 0 .
3, Ω Λ = 0 .
2. The cluster sample
Starting from the X-ray Brightest Cluster Sample (BCS)of Ebeling et al. (1998), we selected a flux limited sam-ple of clusters. In order for the clusters to have an ob-served angular size close to the EPIC cameras field ofview, we limited the cluster redshift selection to the range δ z = [0 . , .
3. Observations and data preparation
All data used for this investigation come from the EPICXMM-Newton database. We use individual observations ofAbell 399, Abell 401, Abell 478, Abell 1795, Abell 2029,and Abell 2065, and a multiple pointing observation ofAbell 2256. For all of these clusters, data sets combineobservations obtained from the three EPIC instruments:MOS1, MOS2 and PN. A summary of data sets is providedin Table 2, with associated exposure times.
In addition to the extended and optically thin emissionof ICM, X-ray observations gather photon impact eventsrelated to other sources, such as spatially resolved X-rayemitting galaxies and the cosmic X-ray background (CXB).Moreover, observations may be transiently contaminatedby solar flares. While the extended contributions of ICMand CXB are hardly separable, contributions from point-sources and solar flares can be isolated and removed fromthe observed signal through spatial and temporal waveletanalyses, respectively.In order to detect high solar flares periods and removecorresponding data sets, we analyse light curves with asso-ciated high energy events (10-12 keV) and softer events (1-5keV), respectively. As proposed by Nevalainen et al. (2005),this two-step analysis first enables us to isolate the mostprominent flares at high energy, where ICM brightness isexpected to be negligible, then detect some additional con-tribution of soft flares only. For each of these curves, we usea B3-spline “`a-trous” wavelet algorithm in order to detectdisruptions, and select the positive irregularities with am-plitude overcoming a 2 σ significance threshold with regardto the light-curve fluctuation. This “cleaning” process hassignificantly lowered the effective exposure time of observa-tions, as reported for individual observations and pointingson Table 2.In order to identify point-sources, we analyse EPIC-MOS event-lists which are more suited to imaging, andadopt an object separation algorithm derived from themulti-scale vision model of Bijaoui & Rue (1995). Afterdetecting and imaging point-sources, we associate a maskto regions of the field of view dominated by point-sourcescontribution, and isolate events coming from these regionswhen analysing the signal. XMM-Newton imaging cameras provide photon impactevent lists with associated energy and position on the de-tector planes. In order to analyse our signal using discretewavelet algorithms, we group events coming from variousobservations, if any, and sample them spatially into sky co-ordinate grids, with given angular resolution, a . We also . Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 3 Table 1.
Cluster sample with associated redshift, coordinates, total ICM flux from the BCS survey (Ebeling et al. 1998), andP4/P0 power ratio reported in Buote & Tsai (1996). Last column: average neutral hydrogen column density measured along lineof sight of each cluster (Dickey & Lockman 1990).Cluster Redshift Equatorial coordinates ICM flux Power ratio Neutral hydrogen columnname (J2000) (10 − W.m − / 10 − erg.s − .cm − ) P4/P0 density (10 m − )Relaxed clustersA478 0.088 04 13 25.0 +10 27 54.0 39.9 0.025 15.1A1795 0.062 13 48 53.0 +26 35 32.0 68.1 0.004 1.2A2029 0.077 15 10 56.0 +05 44 42.0 61.3 0.050 3.14Major merger clustersA399 0.072 02 57 53.0 +13 02 00.0 28.8 - 10.9A401 0.074 02 58 58.0 +13 34 00.0 42.8 0.157 10.5A2065 0.072 15 22 42.0 +27 43 00.0 22.2 - 2.95A2256 0.058 17 03 58.3 +78 38 31.0 49.5 0.395 4.1 sample events in energy so as to perform spectral analyses,which leads to 3-D event cubes associated with each EPICinstrument, and sampled in position (k,l) and energy (e).For imaging and spectral-mapping purposes, we asso-ciate to these event cubes a set of local “effective exposure”E( k, l, e ) and “background” cubes, n bck F bck ( k, l, e ), withsimilar position-energy sampling, and use them for mod-elling the bolometric or spectroscopic ICM radiation; wereport details about the background modelling in appendixA. Let us define here the “effective exposure” E( k, l, e ) atpixel [k,l] as the linear combination of CCD exposure times t CCD ( k, l, p ) related to individual observations p , with cor-rection for spatial variations of the mirror effective area orso-called “vignetting factor”, ∆ a mirror ( k, l, e ), transmissionby other focal instrument, –i.e. reflection grating spectrom-eter (RGS)– tr RGS , and detector pixel area with correctionfor gaps and bad pixels, a CCD ( k, l ) . For K observations,we get:E( k, l, e ) = K X p =1 t CCD ( k, l, p ) × ∆ a mirror ( k, l, e, p ) × tr RGS ( k, l, e, p ) × a CCD ( k, l, p ) (1)
4. Data analysis
In order to map the ICM temperature structure, we havebuilt a spectral mapping algorithm coupling a spectroscopicand multi-scale analysis of the X-ray signal, to a waveletmapping of the searched parameter structure.Mainly following the scheme of the Bourdin et al. (2004)algorithm –hereafter the 2004 algorithm– we first samplethe field of view using redundant and square grids withtypical size s j = 2 j a , { j ∈ [0 , j max ] } , according to a dyadicscheme. Then, we locally estimate the gas temperature Tand its fluctuation σ T by fitting a spectral model to the Information about these instrumental effects areprovided in the following XMM-Newton CurrentCalibration Files (CCF), corresponding to each obser-vation epoch: RGS* QUANTUMEF, XRT* XAREAEF,EMOS* LINCOORD, EPN LINCOORD, EMOS* BADPIX,EPN BADPIX data, within each meta-pixel [ k, l, j ] of the different grids.A set of temperature maps T( k, l, j ) is obtained, with as-sociated noise expectation maps σ T ( k, l, j ). Filtering theT( k, l, j ) and σ T ( k, l, j ) maps using high-pass analysis fil-ter enables us to code the temperature variations as waveletcoefficients W T ( k, l, j ) with expected noise σ W T ( k, l, j ), andto detect significant temperature structures as wavelet coef-ficients with amplitude overcoming a significance thresholddepending on σ W T ( k, l, j ). Finally, we map the gas tem-perature using a Tikhonov regularised thresholding of thewavelet transform.More detailed in Bourdin et al. (2004), this general ap-proach has been adapted to the present study. In particular,the local spectral fitting is now implemented using an up-dated plasma emission code and now allows a multiple pa-rameter estimation. Furthermore, a B-spline wavelet trans-form is now used instead of the Haar wavelet transform.Below we describe both of these improvements in detail. The local estimation of ICM temperature is performed byfitting a normalised spectral model, F evt (T , Z , Nh , e ), to thedata set associated with meta-pixel [ k, l, j ]. Combining con-tributions of ICM itself, n ICM ( k, l ) F ICM (T , Z , Nh , e ), and“overall background”, n bck F bck ( k, l, e ), this model is sam-pled in photon energies, e , and depends on the ICM tem-perature T, metal abundances, Z, and neutral hydrogendensity column along the line of sight, Nh:n evt ( k, l ) F evt (T , Z , Nh , e )= E( k, l, e ) × n ICM ( k, l ) F ICM (T , Z , Nh , e )+n bck F bck ( k, l, e ) , (2)The unnormalised ICM contribution F ICM (T , Z , Nh , e )is modelled from plasma radiation flux φ ICM (T , Z , e ), fol-lowing the Astrophysical Plasma Emission Code (APEC,Smith et al. 2001) as a function of the gas temperature Tand heavy elements abundances Z, being set according tothe solar element composition of Grevesse & Sauval (1998).It is obtained by red shifting and distorting φ (T , Z , e ) in or-der to take into account X-ray absorption by the galacticneutral hydrogen h (Nh , e ) with given column density alongthe line of sight, Nh, following absorption parameters ofBalucinska-Church & McCammon (1992). Introducing the H. Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies
Table 2.
Effective exposure time of each EPIC XMM-Newton observation. In brackets: fraction of the useful exposure time aftersolar-flare “cleaning”. Cluster MOS1 effective MOS2 effective PN effectivename exposure time (ks) exposure time (ks) exposure time (ks)A399 8.3 (58.6 %) 4.6 (32.8 %) 4.2 (45.2 %)A401 12.0 (92.5 %) 10.0 (77.4 %) 2.8 (35.1 %)A478 30.3 (44.2 %) 38.0 (30.5 %) 47.0 (43.6 %)A1795 22.5 (45.8 %) 23.5 (47.8 %) 19.3 (45.5 %)A2029 6.5 (37.5 %) 7.7 (44.4 %) 6.4 (50.6 %)A2065 20.4 (61.0 %) 19.9 (60.3 %) 12.2 (55.8 %)A2256 (1) 8.7 (62.1 %) 8.5 (60.3 %) 4.8 (54.8 %)A2256 (2) 7.9 (48.5 %) 8.6 (53.0 %) 5.9 (50.9 %)A2256 (3) 8.6 (47.3 %) 8.9 (48.6 %) 5.3 (26.3 %)A2256 (4) 7.8 (47.8 %) 7.1 (43.3 %) 6.5 (58.0 %)
Fig. 2.
The quadratic B-spline scaling function φ ( x ) and dualwavelet ψ ( x ) in 1D. instrument area A ( e ), and convolving ICM radiation fluxby the detector response in energy R ( e ) , we get the radia-tion power measured by the instrument for a given emittingsource at redshift z :F ICM (T , Z , Nh , e )= R ( e ) (cid:20) A ( e ) × h (Nh , e ) × φ ICM [T , Z , (1 + z ) e ]1 + z (cid:21) , (3)where instrument area A ( e ) takes into account the ef-fective area of mirrors a mirror ( e ), the filter transmission tr filter ( e ) and detector quantum efficiency q CCD ( e ) : A ( e ) = q CCD ( e ) × tr filter ( e ) × a mirror ( e ) . (4)In order to get a robust estimation of ICM tempera-tures, whatever the local statistics are, the spectral fit-ting is performed by maximising the log-likelihood functionlog L(T , Z , Nh , e ) = P i log F evt (T , e i ), where our spectralmodel is summed on all energy channels, e i . In order to map the ICM temperature structure at scale j ,we analyse the spatial correlation of temperature measure-ments using wavelet coefficients W T ,j ( k, l ), computed from Detector responses are tabulated within the XMM-Newtonredistribution matrix files (RMF) Information about these instrumental effects areprovided in the following XMM-Newton current cal-ibration files (CCF), corresponding to each observa-tion epoch: XRT* XAREAEF, EMOS* QUANTUMEF,EPN QUANTUMEF, EMOS* FILTERTRANSX,EPN FILTERTRANSX
Table 3.
The quadratic B-spline analysis filters.-2 -1 0 1 2 3 h .125 .375 .375 .125 g -.5 .5˜ h .125 .375 .375 .125˜ g -.03125 -.21875 -.6875 .6875 .21875 .03125 the temperature maps T j ( k, l ). A trivial solution to thiscomputation has been proposed in the 2004 algorithm: fil-tering the temperature maps T j ( k, l ) using Haar high-passanalysis filters enables one to get a set of Haar wavelet co-efficients W T ,H,j ( k, l ). Indeed, the Haar wavelet is the dualfunction of the top-hat smoothing kernel Π j ( k, l ), whichmay be applied to the searched map T ( k, l ) for comput-ing the maps T j ( k, l ), at scale j . However, thresholdingHaar wavelet transforms usually generates square artifacts,in particular when analysing regular signals.Due to the expected smoothness of our signal, a betteranalysis of its spatial correlations can be provided by themore regular B-spline wavelets; see Curry & Schoenberg(1947) for definition and e.g. Mallat (1998) for applicationto wavelet bases. Indeed, we do not expect any strong dis-continuities in our signal, due to joint effects of both theinstrument PSF and the 2-D projection of the gas tem-perature structure. Since B-spline wavelets are the dualfunctions of the m degree B-spline interpolation functionsobtained by (m+1) self-convolving of a top-hat smooth-ing kernel, they can also be used in our context; start-ing from the temperature maps T j ( k, l ) and convolvingthem (m) times by a top-hat smoothing kernel Π j ( k, l )provides a new set of smoothed maps T S ( m ) ,j ( k, l ), whosedual wavelet coefficients are m degree B-spline wavelet co-efficients W T ,S ( m ) ,j ( k, l ). Introducing the smoothing length a = 2 j at scale j, we get:Π j ( k, l ) = [ k − a ,k + a − ] × [ l − a ,l + a − ] , (5)T S ( m ) ( k, l, j ) = Π j ( k, l ) ( m ) ⋆ T( k, l, j ) . (6)Like the Haar wavelet, the B-spline wavelets can be pro-jected in bi-orthogonal bases. We therefore adopted theshift-invariant Coifman & Donoho (1995) algorithm forcomputing the wavelet coefficients W T ,S ( m ) ,j ( k, l ), follow-ing a similar scheme as for the 2004 algorithm. To do so,the smoothed maps T S ( m ) ( k, l, j ) are convolved with a set . Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 5 Fig. 1.
EPIC-XMM “soft” (0.5-2.5 keV) exposures images of the clusters in our sample. of three high-pass analysis filters h ( k ) g ( l ), g ( k ) h ( l ) and g ( k ) g ( l ), associated with the B-spline wavelet, which leadsto the three sets of wavelet coefficients W T ,S ( m ) ,j,h ( k, l ),W T ,S ( m ) ,j,v ( k, l ) and W T ,S ( m ) ,j,d ( k, l ):W T ,S ( m ) ,j,h ( k, l ) = h ( k ) g ( l ) ⋆ T S ( m ) ( k, l, j ) , W T ,S ( m ) ,j,v ( k, l ) = g ( k ) h ( l ) ⋆ T S ( m ) ( k, l, j ) , W T ,S ( m ) ,j,d ( k, l ) = g ( k ) g ( l ) ⋆ T S ( m ) ( k, l, j ) . (7)In order to re-construct the signal T ( k, l ), the waveletcoefficients are first convolved using the high-pass inversefilters, ˜ h ( k )˜ g ( l ), ˜ g ( k )˜ h ( l ) and ˜ g ( k )˜ g ( l ) associated with thebi-orthogonal wavelet analysis and added to each other,which allows us to average the redundant information.Thus, the risk occurring when re-constructing the signalfrom the thresholded wavelet transform is significantly low-ered.Here we decided to work with the quadratic B-splinewavelet ( m = 2, see Fig. 2), which is regular enough for our purpose but more compact than B-spline wavelets of higherdegree. The quadratic B-spline analysis filters are reportedin Table 3. In order to map the ICM brightness structure, we have builtan imaging algorithm where the local brightness L X ( k, l )is first estimated from a brightness model associated withpixel [k,l], then iteratively de-noised in the scale-space bymeans of a discrete Haar wavelet analysis.We estimate the local ICM brightness L X ( k, l ) for en-ergy band ∆ e , by correcting the number of events n evt ( k, l )detected at pixel (k,l), from the expected “background”contribution, n bck ( k, l ), and exposure weighted instrumentarea, a( k, l ): H. Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies
Fig. 3.
ICM temperature maps of the clusters in our sample overlaid to the soft (0.5-2.5 keV) X-ray brightness isocontours. Theisocontour levels are logarithmically equispaced by a factor √ a( k, l ) = Z ∆ e E( k, l, e ) F evt (T o , Z o , Nh o , e ) de, (8) c L X ( k, l ) = n evt ( k, l ) − n bck ( k, l )a( k, l ) , (9)where the weighted instrument area a( k, l ) is com-puted for a fixed ICM emission model, F evt (T o , Z o , Nh o , e ).“Corrected” photon maps obtained from local estimator c L X ( k, l ) and for energy band 0 . − . c L X [ k, l ], associated with a multi-scale analysis of c L X ( k, l ) using redundant grids. Driven by asignificance criterion of detected structure, this threshold-ing is set after estimating the probability density function(PDF) of noise wavelet coefficients, P(W c L X [ k, l ]). To do so,we deduce P(W c L X [ k, l ]) from the PDF of noise wavelet co-efficients associated with local event counts, n evt : P(W c L X [ k, l ]) = P(W n evt [ k, l ])a[ k, l ] , (10)which enables us to use an analytical form ofP(W n evt [ k, l ]), first proposed by Bijaoui & Jammal (2001)for Haar wavelet analyses of uniform Poisson noise.Introducing the modified Bessel function of order m, I m (n evt ), we get:P(W n evt ) = ∞ X m = −∞ e − n evt I m (n evt ) δ (W n evt − m ) . (11)
5. 2D temperature structure
The ICM temperature maps of each cluster in our sampleare presented in Fig. 3, overlaid to the relative 0 . − . evt (T o , Z o , Nh o , e )assumed for computing brightness maps has been obtainedby spectral-fitting of an overall cluster spectrum excludingthe core region of relaxed clusters. . Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 7 The temperature maps have been computed fromspectral-fitting within the . − . o have been deduced from the spectral fitting ofF evt (T o , Z o , Nh o , e ). For each cluster except Abell 478, theneutral hydrogen column densities, Nh o , have been esti-mated by spectral fitting, similarly to the metal abun-dances. The values obtained are consistent with measure-ments by Dickey & Lockman (1990), in the 1 degree neigh-bourhood of each cluster centre (see Table 1). For A478, theNh has been left as free parameter, since Dickey & Lockman(1990) measurements were inconsistent with X-ray spectro-scopic estimations (see Sect. 8 for details).The EPIC-XMM field of view has been sampled in 256 ×
256 pixels, and the wavelet analysis has been unfolded oversix spatial resolutions, allowing detection of features withtypical size ranging from about 12 arcsec to 3.5 arcmin. Thethresholding of the wavelet coefficients has been performedfollowing the Donoho (1995) thresholding approach, leadingto threshold levels that are always higher than the noisefluctuation σ (typically from 1 .
75 to 2 . σ with increasinganalysis scales, thresholds lower than 2 σ being related tothe highest resolution details, namely the cool core regionsof relaxed clusters only).In the following we give a short description of each clus-ter separately. For convenience we group the clusters fol-lowing the dynamical classification, used in previous workand based on the X-ray morphology, of relaxed and mergingsystems. As observed in X-rays, Abell 1795 is known as an ellipti-cal and relaxed cluster, as predicted by the relatively lowP4/P0 power ratios (see Table 1). The XMM-Newton ob-servation of Abell 1795 confirms a globally elliptical sym-metry for this cluster. Nevertheless, the XMM-Newton X-ray image in Fig. 1 shows the presence of a sharp surfacebrightness variation, at about 1 arcmin to the south withrespect to the cluster centre. From a Chandra observation,this sharp surface brightness feature has been identified asa cold front and interpreted as the result of the sloshingof core gas within the cluster potential well (Markevitchet al. 2001). This scenario is consistent with what can beobserved on surface brightness contours in Fig. 3, revealingat the same time a strong compression of isophotal linesacross the cold front, and a shift of the cluster brightnesspeak towards the south, with regard to large radii isophotes.The temperature map of Abell 1795 in Fig. 3 shows aglobal elliptical symmetry with a cool core. If we performa radial analysis, it is consistent with temperature profilesderived from XMM-Newton (Tamura et al. 2001; Arnaudet al. 2001; Ikebe et al. 2004) and Chandra observations(Ettori et al. 2002; Markevitch et al. 2001; Vikhlinin et al.2005). We notice, however, some anisotropies with regardto the overall elliptical symmetry of temperature structure.First of all, the cool core appears as being shifted towardsthe south, as coinciding with the cluster brightness peak. Atlarger radii ( r > ≃ ≃ Similarly to Abell 1795, Abell 2029 was also known as a reg-ular and relaxed cluster (see also the P4/P0 power ratiosin Table 1). Except for its very central region where X-rayfilaments have been observed (e.g. Clarke et al. 2004), nobrightness nor temperature anisotropies have been previ-ously detected for this cluster.As already noticed by Vikhlinin et al. (2005), this clus-ter is projected near the galactic region of North Polar Spur,the X-ray spectral contribution of which has been modelledand added to the background model of Eq. (A.1). This con-tribution has been fitted simultaneously with cosmic back-ground, in the same external region of the field-of-view,which led to a two thermal component model (kT1=0.22,kT2=0.49, n K /n J = 2 . .The XMM-Newton image in Fig. 1 confirms thatAbell 2029 is globally regular and elliptically symmetric(see also Fig. 3). The gas temperature map in Fig. 3 showsthe presence of a cooler core (kT ≃ . r <
10 arcsec),where the Chandra data analysis of Lewis et al. (2003) in-dicates lower temperatures decreasing to about 2 keV.Nevertheless, as observed for Abell 1795, even if thetemperature structure is elliptically symmetric in the in-nermost regions, at larger radii the temperature map re-veals some non radial thermal features with typical tem-perature variations of ≃ ≃ Known to be regular and relaxed, Abell 478 has been ob-served recently by the Chandra and XMM-Newton tele-scopes (Sun et al. 2003; Pointecouteau et al. 2004). Whilethe Chandra observation has revealed brightness substruc-ture in the very centre of the cluster (Sun et al. 2003),both of these observations have shown a regular structureat larger radii. The elliptical symmetry and regularity ofthe surface brightness of Abell 478 is also evident from theX-ray cluster image in Fig. 1 and confirmed by the lowvalue of the P4/P0 power ratios in Table 1.The gas temperature map of Abell 478 is shown inFig. 3. Due to the strong hydrogen column density ap-pearing across the field of view (Nh = 15 . × m − ),the gas temperature map of this cluster has been com-puted from a spectral fitting process with a free Nh param-eter. Using this procedure the temperature map appearsremarkably regular with elliptical symmetry. This map re-veals a cool core (kT ≃ Normalisation discrepancies with Vikhlinin et al. (2005) aredue to different modellings of the CXB, our model already in-cluding a thermal component at 0 .
204 keV (see Eq. (A.1)). H. Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies arcmin from the cluster centre (kT ≃ . Although, independently selected in our cluster sample,Abell 399 and Abell 401 form a close pair separated, inprojected distance, by 3 Mpc (36 arcmin). The brightnesscontours of both Abell 399 and Abell 401 (Fig. 3) areelongated along a N-N-E / S-S-W axis, which is the majordirection of the pair. The Abell 401 brightness contours ap-pear mildly disturbed with a centroid shift to the northeast.Consistent with the expectation of the P4/P0 power ratiosreported in Table 1, they are less regular than the contoursof Abell 1795, Abell 2029 and Abell 478. Abell 399 lookseven more irregular; in particular a sharp edge can be ob-served to the southeast of the cluster core.Using the same data set as used in this work, Sakelliou& Ponman (2004) studied the gas brightness and temper-ature in specific angular sectors of both clusters and alongthe major direction of the pair. From this analysis, theyconclude that, currently, the clusters are just starting tomildly interact and that the sub-features found in their in-ner regions are related to the individual merging historiesof each cluster separately, rather than to the remnant of aprevious merger of the two systems.The temperature maps of Abell 399 and Abell 401 arereported in Fig. 3 to the same spatial scale. We notice ahigher average temperature for Abell 401 (kT ≃ ≃ Abell 2065 has been previously studied by Markevitch et al.(1999) using ROSAT and ASCA data, and by Chatzikoset al. (2006) using Chandra data. These observations re-vealed the asymmetric morphology of this cluster charac-terised by a highly elongated inner region that seems to linktogether the two cD galaxies located in the cluster centre.The temperature structure is also highly asymmetric witha hotter region to the southeast. Furthermore, the Chandraobservation revealed two cold cores coinciding with the clus-ter central cD galaxies.The XMM-Newton temperature map of Abell 2065 inFig. 3 shows the presence of a hot (kT ≃ . ≃ . ≃ . ≃ The X-ray image of Abell 2256 in Fig. 1 shows a complexstructure with two X-ray peaks, one of which is coincidentwith the cluster central dominant galaxy, while the otheris located at 2 arcmin to the northwest. This cluster hasbeen observed with ROSAT and ASCA (e.g. Briel et al.1991; Markevitch 1996) and more recently with Chandra.This latter observation revealed an even more irregular X-ray morphology, the presence of a third subgroup to theeast, and a sharp edge to the southeast of the northwestpeak that has been identified with a “cold front”(Sun et al.2002).The XMM-Newton temperature map of Abell 2256 inFig. 3 shows a bimodal temperature structure along thecluster major elongation axes. Consistent with Sun et al.(2002), we find that the gas in the northwest peak, is thecoldest of the cluster with a temperature of kT ≃ . ≃
6. Radial temperature structure and cluster mass
X-ray emission from round relaxed clusters of galaxies is of-ten used to estimate the cluster mass, assuming hydrostaticequilibrium and spherical symmetry. Using hydro N-bodysimulations, Rasia et al. (2006) investigated the accuracy . Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 9
Fig. 4.
Spectroscopic temperature (top), brightness (middle) and derived mass profiles (bottom) corresponding to the selected redand blue sectors of Abell 1795 (left) and Abell 2029 (right), respectively. Dashed lines on temperature and brightness profiles cor-respond to fits of the projected functions { T x ( r ) , Σ x ( r ) } used for deriving masses, see Eq. (18) and (15). Error bars on temperatureprofiles are 68 % confidence levels. Dispersions of brightness and mass profiles are distribution variances. of the mass estimate and found that, in the best of cases,there is at least a 10% discrepancy between the true andthe estimated mass. They claimed that one of the reasonsfor such a discrepancy is related to small, non radial ther-mal substructure, which seems to be always present, evenin the most relaxed systems produced by any hydro N-bodysimulation.To test whether this problem may also be present inreal clusters, we used our temperature maps and selected specific cluster sectors in which the gas temperature is ei-ther hotter or colder than the gas mean temperature. Fromthese sectors, we extracted temperature and brightness pro-files, then used these profiles to estimate the relative clustermass profiles.For this test we consider only two of the three morerelaxed clusters in our cluster sample: Abell 2029 andAbell 1795. Abell 478, the third round cluster in our sam-ple, was not considered for such a test because, as explained in Sect. 8, it is located in a particular sky region charac-terised by strong angular variations of the neutral hydrogencolumn density, Nh, across the cluster field of view. If nottreated properly, these strong Nh variations may introducespurious thermal features that cannot be easily disentan-gled from the real ones. ICM surface brightness and temperature profiles
Brightness and temperature profiles associated with hotand cold regions of temperature maps for Abell 2029 andAbell 1795 are shown in Fig. 4 with different colours.The brightness profiles Σ x ( r ) have been obtained by av-eraging the brightness estimator of Eq. (9) within logarith-mically equispaced elliptical annuli of N pixels { k, l } r , withnormalisation by the exposure weighted instrument areaa( k, l ) of Eq. (8): c Σ x ( r ) = 1N X { k,l } r c L X ( k, l ) , = 1N X { k,l } r n evt ( k, l ) − n bck ( k, l )a( k, l ) , (12)We then estimated the brightness variance by consider-ing uncertainties to be only related to the Poisson fluctua-tion of n evt ( k, l ): d σ Σ x ( r ) ≃ vuut X { k,l } r d σ evt ( k, l )a ( k, l ) = 1N vuut X { k,l } r n evt ( k, l )a ( k, l ) , (13)The spectroscopic temperature profiles c T x ( r ) have beenestimated by fitting the spectral model F evt k,l (T , Z , Nh , e )of Eq. (2) to the data associated with a set of logarith-mically equispaced sector annuli. Given the high statisticsavailable for each annulus, we were able to perform spec-tral estimations following a χ minimisation process, andget straightforward estimations of confidence intervals. Cluster mass profiles
The surface brightness and temperature profiles extractedfrom the hottest and coldest sectors of A1795 and A2029(see Fig. 4) have been used to estimate the cluster mass pro-file. To do so, we adopt the approach proposed by Vikhlininet al. (2006), that consists in modelling the 3-d density and3-d temperature profiles and fitting the projected quantitiesto the corresponding data set.The 3-d gas density is modelled by a double and modi-fied β -model with 9 parameters. Introducing n p and n e , theproton and electronic density, respectively, we get:[ n p n e ]( r ) = n ( r/r c ) − α [1 + ( r/r c ) ] β − α/ r/r s ) ] ǫ/ + n [1 + ( r/r c ) ] β . (14)The projected surface brightness profile, Σ( r ), as ob-served within a given energy band ∆ E (here 0.7-2.5 keV), is then obtained by integrating the ICM brightness, ǫ ICM (T),along the line of sight:Σ x ( r ) = 1 d (1 + z ) Z ǫ ICM [T( r l )] [ n p n e ]( r l ) dl, (15)where z is the redshift of the source located at distance d , where r l = √ r + l , and where ǫ ICM (T) can be modelledfrom the source radiation power of Eq. (3), so as to accountfor instrument response and effective area. Normalisingwith the same average quantities, T o , Z o , Nh o , as used forcomputing the weighted instrument area in Eq. (8), we get: ǫ ICM (T) = R ∆ E F ICM (T , Z , Nh , e ) de R ∆ E F ICM (T o , Z o , Nh o , e ) de . (16)The 3-d temperature profile is modelled by a 5-parameter broken power-law, with transition region:T( r ) = T o ( r/r t ) − a [1 + ( r/r t ) b ] c/b , (17)then integrated along the line of sight to get a projectedprofile of “spectroscopic-like” temperatures, as defined inEqs. (14) and (15) of Mazzotta et al. (2004):T x ( r ) = 1 R w ( r l ) dl Z w ( r l )T( r l ) dl, (18)with weighting factor w ( l ) = n ( l )T / ( l ) .After fitting the projected ICM brightness Σ x ( r ),and temperature profile T s ( r ) to the observable set { c Σ x ( r ) , c T x ( r ) } , and estimating the related 3-d density ρ ( r ),and temperature T( r ), we use hydrostatic equilibrium ofthe ICM to derive mass profiles (see e.g. Sarazin (1988):M( r ) = − . × M ⊙ T ( r ) r (cid:20) d log ρd log r + d log T d log r (cid:21) (19)Best fits of the projected ICM brightness and tempera-ture profiles with associated cluster mass profiles M( r ), areshown in Fig. 4. The confidence intervals on mass profileshave been estimated by minimising the distance betweenthe projected models and a set of random realisations of ob-served profiles. These profiles have been obtained assumingGaussian statistics around observed values { c Σ x ( r ) , c T x ( r ) } ,with the constraint of rejecting realisations leading to thenon-physical solution of non-monotonically increasing massprofiles. The Abell 1795 ICM temperature map reveals a cold re-gion to the north of the cluster, while the gas temperatureis observed as hotter elsewhere in the 2 to 5.5 arcmin rangeof cluster radii. We selected two complementary “cold” and“hot” cluster sectors in order to compute surface brightnessand temperature profiles in Fig. 4. As we want to ignore ef-fects of gas thermal variations near the cluster core, we ex-cluded this region from our analysis and computed profileswithin a radii range of 1 . − . Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 11 radii, therefore the cool core appears as being shifted withregard to our sectors in Fig. 4.Consistent with what is observed on the temperaturemap, we notice that the absolute temperatures in the twosectors are significantly different. Furthermore, we observethat the two temperature profiles show different shapes:the profile corresponding to the coldest sector peaks at ap-prox 4 arcmin, while the complementary hottest profile ismuch flatter. The two complementary brightness profilesalso show different shapes.It is worth noticing that the resulting mass profiles showsignificantly different shapes (see Fig. 4). In particular, asfor the temperature profiles, the mass profile of the coldestsector shows stronger gradient variation than the hottestone. These different shapes result in the observation thatwhile the relative mass estimates are consistent with eachother at large radii ( r >
250 kpc) –and also consistent withpreviously published profiles of e.g. Ikebe et al. (2004) orVikhlinin et al. (2006)– they become significantly differenttowards the innermost part of the cluster ( r <
250 kpc).We should conclude that, within the radii range inves-tigated, the assumption of hydrostatic equilibrium for thiscluster may be not valid.
The Abell 2029 ICM temperature map reveals a non sym-metric temperature structure within a region ranging from2 to 5 arcmin cluster radii. We selected the coldest regionto the southeast for computing a first set of brightness andtemperature profiles, and a complementary hot sector forcomputing the second set.As with Abell 1795, the discrepancy observed betweentemperature values on profiles in Fig. 4 is consistent withthe radial thermal structure of the temperature map. Inparticular, the profile corresponding to the cold sector isalmost flat (kT ≃ . ≃ . ≃ r ∈ [200 ,
7. Cold fronts
The temperature maps of both merging clusters Abell 2065and Abell 2256 show two hot bow-like regions to the south- east of each cluster centre, which seem to be located nextto abrupt variations of the gas surface brightness, as visibleon photon maps in Fig. 1 or isocontour levels in Fig. 3. Forthis reason, they are likely to be related to cold fronts sep-arating the dense and moving cluster cores from the hotterICM of the cluster outskirts.In order to investigate this hypothesis, for clustersAbell 2065 and Abell 2256 we extracted the ICM surfacebrightness and temperature profiles corresponding to sec-tors shown in Fig. 5. Located across the brightness frontregions, these sectors follow the brightness isophotes andmatch regions with almost uniform isoradial thermal struc-ture.As expected from temperature and brightness maps, weclearly see two temperature jumps on the profiles located ata jump radius r j , also corresponding to a change of slope insurface brightness profiles. In order to check whether thesefeatures can be related to jumps in the 3-d distributions ofthe gas density and temperature, we modelled these distri-butions by two disrupted functions.The gas density profile is modelled by two independent β -models corresponding to regions located inside and out-side the jump radius r j , respectively:[ n p n e ] cf ( r ) = D j n o ( r/r j ) − η h r j /r c ) r/r c ) i β , ∀ r ∈ [0 , r j [ n o ( r/r j ) − η h r j /r c ) r/r c ) i β , ∀ r ∈ [ r j , ∞ [ , (20)while the gas temperature is modelled by a step func-tion: T cf ( r ) = (cid:26) T o , ∀ r ∈ [0 , r j [ D T T o , ∀ r ∈ [ r j , ∞ [ . (21)The 3-d distributions [ n p n e ] cf ( r ) and T cf ( r ) are pro-jected according to Eq. (15) and (18) in order to deriveX-ray brightness and “spectroscopic-like” temperature pro-files, Σ x ( r ) and T x ( r ), which enables us to estimate all freeparameters of Eq. (20) and (21), including r j , by fitting theprojected models to the data. Best fits of X-ray brightnessand “spectroscopic-like” temperature profiles are shown inFig. 5, with associated 3-d distributions of gas density andtemperature. Similarly to the derivation of mass profiles inSect. 6, the confidence intervals on 3-d profiles have been es-timated by minimising the distance between the projectedmodels and a set of random realisations of the observedprofiles. The Abell 2065 sector is located within 5 arcminutes to thesoutheast of the cool elongated central cluster region visiblein Fig. 1.Fitting the disrupted density and temperature profile ofEqs. (20) and (21) for the southeastern sector of Abell 2065leads to a jump radius of r j ≃ . +0 . − . Mpc, a densityjump factor between regions located immediately above andbelow r j , of D j ≃ . +0 . − . , and a temperature jump factorof D T ≃ . +0 . − . . These values yield an almost continuousgas pressure across the front. Interestingly, we notice thatthe value of r j is consistent with the location of a densityjump already reported by Chatzikos et al. (2006), who per-formed a sector analysis of the same cluster region using Fig. 5.
From top to bottom: gas brightness, spectroscopic temperature, and derived density and temperature profiles correspondingto sectors shown on the top maps for Abell 2065 (left) and Abell 2256 (right), respectively. Dashed lines on temperature andbrightness profiles corresponds to fits of the projected functions { T x ( r ) , Σ x ( r ) } (see Sect. 7). The front modelling and fitting regionis bounded by vertical dashed lines on the gas brightness and spectroscopic temperature profiles, while the fitted front position r j is reported by a vertical dot-dashed line. Error bars on the temperature profiles are 68 % confidence levels. Dispersions reportedon the 3d profiles correspond to variances on each distribution.. Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 13 Chandra data. The additional detection of a temperaturejump using XMM-Newton enables us to identify the featureas a cold front.
The profiles shown in Fig. 5 correspond to a sector locatedwithin 8 arcminutes to the southeast of the eastern clusterpeak. As with Abell 2065, we detect a cold front feature onthe profiles. The front is located at r j ≃ . +0 . − . Mpcfrom the sector centre, with density and temperature jumpfactor of D j = 1 . +0 . − . and D T = 1 . +0 . − . , respectively.Also here, the values of jump factors are consistent withcontinuous gas pressure across the front. As shown by Chatzikos et al. (2006) using Chandra data,the cold front feature seen in Abell 2065 is located to thesoutheast of a dual cluster core, which is likely the remnantof a binary interacting system, now merged. Following thisscheme, the cold front may be related to the motion of theresidual cool core of one of the former interacting clusters,with regard to the hot shocked and mixed gas of the presentcluster.In the same way, it is worth noticing that the front inAbell 2256 is located around a complex –at least dual– clus-ter core, as revealed by wavelet analyses of ROSAT PSPC(Slezak et al. 1994) and Chandra (Sun et al. 2002) images.Also in this case, we may infer that the cold front indicatesthe accretion of a subgroup, the core of which is now partof the eastern complex system in the cluster.
8. Neutral hydrogen column density variationsacross the Abell 478 field of view
The X-ray emission spectra of extragalactic sources are dis-torted by the neutral hydrogen absorption along the line ofsight, whose origin is mostly galactic. We modelled this ef-fect by introducing an absorption law which is a function ofthe neutral hydrogen column density, Nh, to the ICM emis-sion models n evt ( k, l )F evt (T , Nh , [ e ]), of Eq. (2). Dependingon the knowledge of the average Nh value in the direction ofthe source observed, and on the spatial variation across thesource field of view, this parameter may be fixed a priorior locally estimated from the observed ICM emission spec-tra. The average Nh across the field of view of each clusterin our sample was first estimated by fitting Nh absorbedemission models to the overall ICM emission spectra. Forall clusters except Abell 478, these overall spectroscopicmeasurements were consistent with Nh values measured byDickey & Lockman (1990); for A478, the spectroscopic Nhwas found to be about twice as high. Due to the inconsis-tency seen between both of these values, we left the Nh asa free parameter for X-ray spectroscopy. This T − Nh dualparameter spectral-fitting process has enabled us to mapthe estimated Nh across the field of view of A478, using asimilar wavelet algorithm to the ICM temperature mappingalgorithm described in Sect. 4.1.2.A map of the spatial distribution of Nh measured by X-ray spectroscopy across the field of view of A478 is shownby white isocontours on the left panel of Fig. 6. In orderto reduce a possible spectroscopic bias with brightness gra- dient, the map has been obtained from a wavelet analysislimited to scales smaller than 2 arcmin. Significant waveletcoefficients have been selected according to a hard thresh-olding at 2 × σ . The Nh distribution appears irregular withan east-west elongation, an extended excess to the centre ofthe field of view, and a peak to the to the east. Starting fromthe central excess (Nh ≃ × m − ), the Nh decreasesstrongly to the north and south of the field of view, up tovalues consistent with the average galactic value of Dickey& Lockman (1990) (Nh < × m − ) at a distance of 5arcmin from the centre.The Nh central excess shown on the map of Fig. 6has already been reported by Pointecouteau et al. (2004),who performed a spectroscopic analysis within sectorsof the same data set as here. As already proposed byPointecouteau et al. (2004), its origin can be investigatedusing the IRAS far-infrared survey of galactic dust emis-sion at 100 µm , with angular resolution of about 4 ar-cmin. Indeed, the far-infrared galactic dust emission canbe used as a tracer of the galactic neutral hydrogen columndensity, since dust emission is expected to be correlatedto the galactic neutral hydrogen at high galactic latitude( | b | >
10 deg), as shown by e.g. Boulanger et al. (1996) andSchlegel et al. (1998). Notice however that this correlationis expected to be better constrained within low-Nh regionsof the sky (Nh < × m − ) than within high-Nh re-gions like the Abell 478 neighbourhood, since the scatterof the IR/Nh correlation is higher in such regions, possiblydue to the presence of molecular hydrogen, as discussedby Boulanger et al. (1996). A galactic dust emission mapat 100 µm of the 2 degree neighbourhood of Abell 478 isshown in the right panel of Fig. 6. Coming from the lastgeneration of IRAS maps obtained from the IRIS process-ing (Miville-Deschˆenes & Lagache 2005), this map revealsthe structure of the galactic filament where Abell 478 is lo-cated, to a resolution that cannot be reached by the radiosurvey of Dickey & Lockman (1990), with angular resolu-tion of 1 degree. The IR brightness of this map appears tobe strongly structured in this sky region, with relative fluxvariations of more than 100 %. Within a 5 arcmin regioncentred on the brightness peak of A478, the IR emissiv-ity is of about 18 Mjy/sr. This value corresponds to a Nhdensity column of 33 × m − following the IR/Nh cor-relation factor of Boulanger et al. (1996). It is consistentwith density column estimations obtained by X-ray spec-troscopy, and encourages us to use the dust emission at 100 µm as a tracer of the galactic neutral hydrogen distributionwithin this region of the sky.We investigated the accuracy of this tracer by superim-posing our Nh map to a portion of the IRAS map in theleft panel of Fig. 6. Interestingly, we notice some spatialcorrelation between the IR and X-ray estimated Nh map.Indeed, both the central extended excess and the easternpeak shown on the Nh map correspond to similar structuresin IR. However, both maps are not fully correlated in flux,since the maximum of the Nh map is located to the centreof the field of view, while the maximum of the IR map islocated at the eastern peak. Observations of this sky regionusing infrared data of higher resolution may help to showconclusively whether the Nh excess detected near the cen-tre of Abell 478 corresponds to a real feature, or if it is dueto a bias of X-ray spectroscopic estimations.
16. 17. 18. 19. 20. 20. I R e m i ss i v i t y ( M j y / s r ) Abell 478
10 5 0 -5 -10Arc Minutes-10 -5 0 5 10 A rc M i nu t e s Abell 478
Center: R.A. 04 13 30.74 Dec +10 28 01.6 8.0 11. 14. 18. 21. 24. I R e m i ss i v i t y ( M j y / s r ) Abell 478 neighborhood
45 30 15 0 -15 -30 -45Arc Minutes-45-30-15 0 15 30 45 A rc M i nu t e s Abell 478 neighborhood
Center: R.A. 04 13 23.33 Dec +10 27 32.2
Fig. 6.
Left image: IRAS/IRIS 100 µm galactic dust emission map across the field of view of Abell 478 overlaid to the neutralhydrogen column density estimated by X-ray spectroscopy (Nh isocontours are equispaced by 2 × m − and decrease from acentral value of 30 × m − ). Right image: IRAS/IRIS 100 µm galactic dust emission map of the 2 degree neighbourhood ofA478, with A478 ICM brightness contours overlaid. The IR emissivity of the black region to the south of the cluster is of about50 Mjy/sr.
9. Discussions and Conclusions
We present a multi-scale algorithm based on wavelets formapping the ICM temperature structure within clusters ofgalaxies. Following the approach proposed by Bourdin et al.(2004), the basic scheme of this algorithm is i) estimate thesearched parameter within square resolution elements, sam-pling the field of view at different scales, ii) filter the anal-ysed signal in order to get wavelet coefficients, iii) thresh-old the wavelet transform obtained, in order to de-noisethe signal and map its 2-D structure. In order to performa more regular reconstruction of structures and to reducethresholding artifacts, we improved the algorithm so that,to filter the signal, we use a B2-spline wavelet instead of theHaar wavelet used in Bourdin et al. (2004) (see paragraph4.1.2 for details). This algorithm was used to map the X-rayand temperature structure of a nearly complete X-ray fluxlimited cluster sample containing the eight clusters that,to date, have useful XMM-Newton observations. For self-consistency of the results, a similar thresholding approachwas adopted for each target.From previous work, three of the clusters in our sample–namely A2029, A1795, and A478– have been identifiedas relaxed systems, while the remaining clusters have beenidentified as major mergers. This classification is supportedby the power ratios analysis of the surface brightness ofthese clusters, obtained from ROSAT observations (Buote& Tsai 1996). The XMM-Newton photon images in Fig. 1and the surface brightness contours in Fig. 3 confirm thisprevious classification: the X-ray morphology of the relaxedsystems is quite regular and elliptical symmetric while themorphology of the merging systems is more complex withthe presence of multiple X-ray peaks.In Fig. 3 we show the temperature maps for all clus-ters in our sample overlaid to the soft (0.3-2.5 keV) X-raybrightness isocontours. Even if with a very different degreeof complexity, we notice that all clusters, including the most relaxed ones, show non radial thermal structure. Let us re-call that, since for this work we are only interested in de-tecting highly significant thermal structure, we adopted aquite conservative approach which is based on the Donoho(1995) wavelet shrinkage. For this reason the angular res-olution of the detected structure appears to be lower thanthe angular resolution expected from EPIC XMM-Newtondata. A wavelet shrinkage with constant threshold, as testedin Bourdin et al. (2004) on simulated observations, or usedin Belsole et al. (2004, 2005) and Sauvageot et al. (2005) onreal data, would reveal non radial thermal structure evenon smaller angular scales.Despite the relatively low angular resolution we findthat, consistent with predictions from numerical hydro N-body simulations, the complexity of the thermal structureof clusters strongly depends on the dynamical status of clus-ters themselves. From Fig. 3 we can see that the temper-ature maps of the clusters in our sample may be classifiedinto three different types, characterised by an increasingregularity of the thermal structure: – “irregular”, as for A399 and A401. While selected inde-pendently in our sample, these clusters actually forma binary and mildly interacting system. It has beenproposed that the strong irregularity of their tempera-ture structure is the result of previous merger activitieswithin each cluster of the system, independently fromthe present interaction (Sakelliou & Ponman 2004). – “bimodal temperature”, as for A2065 and A2256. Theseclusters are known to show some strong temperatureanisotropies and to be presently overcoming a late stageof merging. They show an elongated geometry of surfacebrightness, with temperature maps characterised by acolder and hotter regions on opposite sides along themajor direction of elongation. This thermal structure isdominated by the contrast between cool features to theone side, probably associated with accreted material,and a hotter region to the other side, possibly associated . Bourdin and P. Mazzotta: ICM temperature structure within seven nearby and bright clusters of galaxies 15 with shocked gas –see e.g. Markevitch et al. (1999) andSun et al. (2002), for A2065 and A2256, respectively–and separated from the cluster core by a cold front. – “regular”, as for the relaxed clusters, A2029, A1795, andA478. These clusters have a characteristic cool core re-gion surrounded by a hotter gas annulus region peakingat about 300-400 kpc from the cluster centre. As withthe surface brightness, the temperature map of theseclusters is almost regular and elliptically symmetric, in-dicating a good relaxed status for these systems. It isworth noting, however, that beyond the overall ellip-tical symmetry, we also detect a number of significantnon radial thermal structures outside their cores. Thisresult seems to be consistent with what is predicted byhydro N-body simulations of cluster formation, whereclusters continuously accrete small galaxy groups duringand between major mergers, which lead to temperatureirregularities near the region where groups are accreted.To conclude, we would like to stress that, despite thelarge dispersion of intrinsic brightness and exposure timesof the clusters in our sample, the multi-scale algorithm pre-sented here enabled us to reveal the thermal structure ofthe ICM of each cluster. Apart the detection of strong fea-tures mainly present in merging systems –e.g. cold fronts–,we were also able to detect some mild non-radial tempera-ture structure outside the core of relaxed clusters. We no-tice that the relative temperature variation associated withthese irregularities at fixed radii is about 10 %. We showthat these non radial thermal variations affect the measuredradial temperature profiles (see paragraph 4), and lead, atleast for one of our clusters –A1795–, to an inconsistencyof mass derivations obtained using hydrostatic equilibriumassumption. Nevertheless, for another cluster, A2029, thehydrostatic equilibrium assumption appears to be valid de-spite the presence of temperature irregularities.These results enlighten the possibility of constrainingthe thermalisation status of the ICM and the departurefrom gas hydrostatic equilibrium within bright clusters,using data obtained with current X-ray observatories. Itinvites us to further investigations of ICM temperatureanisotropies within larger samples of relaxed clusters –possibly at even larger cluster radii than here by assumingspecifically an elliptical geometry of the wavelet analysis–and to a more accurate evaluation of the dispersions impliedby these anisotropies on cluster mass estimations. Acknowledgements.
We thank Albert Bijaoui and Eric Slezak fortheir contribution to the conception of the wavelet imaging andspectral-mapping algorithms, and Jean-Luc Sauvageot for his help inreducing XMM-Newton data. We further thank the anonymous refereefor suggestions and comments that improved the paper significantly.H.B. acknowledges the financial support from contract ASI–INAFI/023/05/0. This work is based on observations obtained with XMM-Newton, and ESA science mission funded by ESA Member States andthe USA (NASA).
Appendix A: Background modelling for the EPICcameras on board of the XMM-Newtonsatellite
A typical list of photon impact detection provided by theEPIC CCD cameras gathers events associated with variousprocesses that have to be taken into account for modellingthe observed spectra of extended sources. In the case of ICM observations, the detected photons are at least relatedto two extended contributions: the observed source itselfand the cosmic X-ray background (CXB). Furthermore, asignificant fraction of the events-list is actually associatedwith false detections due to cosmic-ray induced particlesinteracting with the detector. Eventually, a known fractionof events is registered during readout periods of detectors,which leads to an additive noise due to wrong position reg-istration of these so-called “out-of-time” events.We model, as an overall “background contribution” tothe event spectrum n evt ( k, l ) F evt (T , Z , Nh , e ) of Eq. (2),a combination of normalised spectral contributions asso-ciated with CXB, F CXB ( e ), induced particles, F p ( e ), andreadout noise, F oot ( k, l, e ):n bck F bck ( k, l, e ) = E( k, l, e ) × n CXB F CXB ( e )+n oot ( k, l ) F oot ( k, l, e )+n p F p ( e ) , (A.1)where n CXB , n p and n oot are normalisation terms, andwhere F CXB ( e ) is corrected for spatially variable exposureE( k, l, e ) (see equation 1), as it is related to a physical ob-servation. The CXB spectrum F CXB ( e ) is modelled as thecombination of a soft radiation associated with foregroundgalactic gas and a broad band contribution accounting forextragalactic background of unresolved AGNs. FollowingLumb et al. (2002) and Kuntz & Snowden (2000), we usea two temperature thermal radiation ( k T1 = 0 .
074 keV, k T2 = 0 .
204 keV) and a power-law ( γ = 1 .