On the dust content of galaxy clusters
AAstronomy & Astrophysics manuscript no. dust˙arxiv c (cid:13)
ESO 2018October 7, 2018
On the dust content of galaxy clusters
C. M. Guti´errez , , M. L´opez-Corredoira , Instituto de Astrof´ısica de Canarias, E-38205 La Laguna, Tenerife, Spain Departamento de Astrof´ısica, Universidad de La Laguna, E-38206 La Laguna, Tenerife, SpainReceived xxxx; accepted xxxx
ABSTRACT
Aims.
We present a study to estimate the dust content in galaxy clusters.
Methods.
This was done by using one the most complete existing catalogues of galaxy clusters based on Sloan Digital Sky Survey(SDSS) data and following two methods: the first one compares the colours of samples of galaxies in the background of clusters withthose of galaxies in the field. Using this method, we have explored clustercentric distances up to 6 Mpc. The galaxies used in this firstmethod were selected from the SDSS-DR9, among those having reliable photometry and accurate estimation of photometric redshifts.The results are largely independent of the galactic cut applied. At | b | > ◦ , the sample contains 56 985 clusters in the redshift range0 . < z < .
68 (the mean redshift is 0.30) and ∼ . × galaxies. The second method computes the contribution of dust in clustersof galaxies to the far infrared sky. That is estimated indirectly by measuring the e ff ect of clusters in the E ( B − V ) extinction map. Results.
Using the first method, we did not find any dependence with clustercentric distance in the colours of background galaxies.As representative of the whole results, the surface integral of the excess of colour g − i in three rings centred in the clusters and withradius 0-1, 0-2, and 0-3 Mpc is − . ± . + . ± .
8, and − . ± . , respectively. This allows us to constrain themass of dust in the intracluster media, M dust < . × M (cid:12) (95% C. L.) within a cluster radius of 3 Mpc. With the second method,which averages the extinction of all clusters, we find a surface integral of the excess of colour g − i of 3 . ± . . Fromthe extinction and redshift of each cluster, we obtain 0.13 Jy and (1 . ± . × erg s − for the mean flux and luminosity at100 µ m. This is ∼
60 times the far infrared luminosity of a Milky Way-like galaxy. By assumming similar properties for the dust, wecan estimate a total dust mass per cluster of ∼ × M (cid:12) , which is compatible with the hypothesis that the dust is within the spiralgalaxies of a cluster. Separating the clusters in 5 × Key words. galaxies: clusters: general, galaxies: clusters; intracluster medium
1. Introduction
Intergalactic media in galaxy clusters does not o ff er a comfort-able ambient for dust grains to survive. Dust grains are progres-sively destroyed by the collision of particles (Draine & Salpeter1979). Although this process is relatively fast, the exact sputter-ing time depends on the density and temperature of the media, aswell as on the chemical composition and size of the grains. For awide range in temperature, the growth of dust by accretion is notenough to compensate the sputtering, although several mecha-nisms like mergers, supernova winds, or ram-pressure strippingcan inject dust continuously into intergalactic regions of clusters.Little is known from an observational point of view; several pi-oneer studies (Zwicky 1962; Karanchetsev & Lipovetskii 1969;Bogart & Wagoner 1973; Boyle et al. 1988; Romani & Maoz1992) compared the attenuation of the light as a function ofwavelength in objects situated in the background of clusters withthose of objects in the field. Using single cases or small samplesof clusters, extinctions within the range ∼ . − . ff ects in some of these pre-vious studies and put a constraint < .
05 mag on the excess ofcolour of the light of background galaxies crossing foregroundAbell clusters. Xilouris et al. (2006) discover a systematic shiftin the colour of background galaxies viewed through the inter-
Send o ff print requests to : [email protected] galactic medium of the nearby M81 group. This reddening co-incides with atomic, neutral gas that is previously detected be-tween the group members. Myers et al. (2003) find anticorre-lation between Quasi Stellar Objects (QSOs) and clusters butlittle reddening. They suggest gravitational lensing as a possi-ble explanation of the anticorrelation. In the last decade, sev-eral groups have used large compilations of data that are mostlySloan Digital Sky Survey (SDSS) based to put much tighterconstraints. Essentially, all of them used a common techniquebased on the attenuation and reddening of the light of back-ground objects (galaxies and / or QSOs) when passing througha cluster. This is quantified by comparing the same propertiesof objects in the field. Nollenberg et al. (2003) used nearby,medium, and poor Automated Plate Measuring Machine (APM)galaxy clusters and derived a 99% C.L. upper limit in the red-dening due to dust in crossing clusters A R = .
025 mag on 1.3Mpc scales. Chelouche et al. (2007) compared the photomet-ric and spectroscopic properties of quasars behind clusters withthose in the field. By using the SDSS-DR5 spectroscopic quasarsample (Schneider et al. 2007) and the catalogue of SDSS clus-ters obtained by Koester et al. (2007), they detected an excess ofcolour E ( B − V ) ∼ − mags on Mpc scales. Bovy et al. (2008)used a sample of SDSS luminous, early-type galaxies and theSDSS cluster catalogue obtained by Berlind et al. (2006) andobtained restrictions E ( B − V ) < × − and 8 × − magson scales of 1-2 and < a r X i v : . [ a s t r o - ph . C O ] S e p uti´errez & L´opez-Corredoira: On the dust of galaxy clusters the Red-sequence Cluster Survey (Gladders & Yee 2005) and acatalogue of 90,000 galaxies with photometric redshifts in therange 0.5-0.8, did not find evidence of colour di ff erences withclustercentric distance and put a severe restriction on the aver-age visual extinction of < A v > = . ± .
010 mags within aclustercentric distance R . McGee & Balogh (2010) exploredthe presence of dust on large scales by using 70,000 low redshiftSDSS galaxy groups and clusters. They claim the detection ofdust out to a cluster-centric distance of 30 Mpc h − . Muller et al.(2009) summarized the results of those studies (see their Table1). Other authors had followed a more direct approach search-ing for the contribution of intracluster dust emission to the farinfrared sky maps. Of course, the total IR emission of the clustercontains the contribution from dust within galaxy members andwithin the intracluster media. First claims of direct extended spa-tial detections (Wise et al. 1993) in the infrared using IRAS werecontroversial with several authors (e.g. Stickel et al. 2002) point-ing out that part of these detections could be due to dust withingalaxy members of the clusters, or to Galactic cirrus. The mostcomplete study following this method was conducted by Montier& Giard (2005) and Giard et al. (2008) combining IRAS data ofmore than 10,000 clusters. Those authors obtained a clear sta-tistical detection of emission in the bands at 12, 25, 60, and 100 µ m. According to the estimation of IR emission due to the di ff er-ent galaxy populations in cluster member galaxies, Roncarelli etal. (2010) concluded that most (if not all) of the signal detectedcomes from the emission of dust in cluster members. The MIPS(Multiband Imaging Photometer for Spitzer) o ff ered a significantquantitative improvement that has allowed studies of single clus-ters (Bai et al. 2007 on Abell 2029, and Kitayama et al. 2009 onComa cluster). These last authors put the following constraintson the emission of dust within the central 100 kpc: ∼ × − ,6 × − , and 7 × − MJy s − at 24, 70 and 160 µ m respectively.Following Kitayama et al., this translates to an expected visualextinction A v < .
02 mag and a surface mass density of dust of Σ d < . × M (cid:12) kpc − .The study presented here combines and extends the two ap-proaches outlined above. In both cases, we follow a statisticalapproach averaging the contribution of a large sample of clustersand background galaxies selected from the SDSS survey. Thepaper is structured as follows: After this introduction, Section 2describes the properties of the samples used, the restrictions ap-plied to get the final subsamples, and the methology; Section 3analyzes the main results, estimates the amount of dust per clus-ter, and compares it with the results presented by other authorsand with theoretical expectations; conclusions are presented inSection 4.
2. Samples and methodology
As outlined in the previous section, we follow two methods: inthe first, we study the additional reddening of galaxies in thebackground of clusters as compared with similar galaxies in thefield; in the second, we estimate the contribution of clusters ofgalaxies to the optical extinction maps. The basic ingredientsof our study are a map of extinction and catalogues of clustersand galaxies, respectively. The sample of galaxies was obtainedfrom the SDSS DR9 photometric catalogue (Ahn et al. 2012).Several potential cluster catalogues were considered. On the ba-sis to optimize completitude and sky and redshift coverage, thesample of clusters obtained by Wen et al. (2012) was chosen us-ing the SDSS-III survey. The spatial coverage of that survey is ∼ ,
000 square degrees and contains 132,684 clusters in the redshift range 0 . ≤ z ≤ .
8. According to those authors, thecatalogue is more than 95 % complete for clusters with a massof M > M (cid:12) in the range 0 . ≤ z ≤ .
42 and con-tains a false detection rate less than 6 %. The catalogue presentsphotometric redshifts for all the clusters, whilst only ∼
30 %have determination of redshift based on the spectroscopy of theirbrighter cluster galaxy (an updated version of the catalogue with52,683 spectroscopic redshifts was presented by Wen & Han2013). From these cases, it was estimated for the photometric es-timation of redshifts, a systematic o ff set < .
004 and a standarddeviation < . // heasarc.gsfc.nasa.gov / W3Browse / galaxy-catalog / abellzcat.html).The map for extinction used was the well known and widelyused map by Schlegel et al. (1998). This map covers the full skyand presents an estimation of the E ( B − V ) extinction obtainedfrom the analysis of COBE DIRBE and IRAS data. The pixelsize is 2.37 arcmin with a FWHM = . . According to such au-thors, the maximum level of such possible extragalactic contam-ination is below 0.01 mags and should be nearly uniformly dis-tributed. For each of the galaxies from SDSS-DR9, we downloaded therelevant information for this study: equatorial coordinates, mag-nitudes in the g , r , and i filters, photometric redshifts, and thecorresponding errors as estimated by SDSS pipelines . The num-ber of objects catalogued as galaxies in that survey and having clean photometry is ∼ . × . We selected those galaxieswith photometric errors < . g , r , and i , considered. This dramatically re-duces the sample to 31,182,824 objects. We also removed a fewoutliers ( ∼ .
07 % of the sample) with extreme g − r ( < − . > . g − i ( < . > . | b | <
20 degrees) where any pos-sible e ff ect of reddening by clusters would be largely maskedby the heavy Galactic extinction at low latitudes. The exact cutin latitude is a compromise to select those regions with lowGalactic extinction, whilst at the same time maintaining a sam-ple of clusters large enough. We ran numerous tests changingthe Galactic latitude cut within the range 20-50 degrees, and inaddition, we removed those clusters from the analysis situatedin regions with mean extinctions > .
05 mags as measured incircle with a radius of 6 Mpc projected at the cluster distance.Nevertheless, none of the results presented here is critically de-pendent from those restrictions.The following step was to determine the relative position ofeach galaxy with respect to the sample of clusters. For clusters,we use a conservative error in the photometric redshift of 0.02 Only the contribution from extragalactic objects with flux > . From the various estimations of magnitudes computed by SDSSpipeline, we follow the prescription in SDSS web pages and used themagnitudes called modelmag . SDSS computes photometric redshiftsaccording to several algorithms; we used the one recorded in the table
Photoz (for details see SDSS web pages). See SDSS web pages for an explanation of this concept.2uti´errez & L´opez-Corredoira: On the dust of galaxy clusters
Fig. 1. ( Le f t :) Histogram of number of clusters as a function ofredshift. (
Right :) Mean number of galaxies in the backgroundof clusters.(see Wen et al. 2012), whilst we use the corresponding errorslisted in the SDSS catalogue for galaxies. For each cluster, weselected all galaxies that are projected at clustercentric distancesup to 6 Mpc. This distance is > × R for all the clusters in oursample. The uncertainty in the estimation of such distance due tothe uncertainty in the photometric redshift of the clusters are ∼
30, 20, and 8 % at redshifts 0.05, 0.1 and 0.2, respectively, so thiscould introduce some filtering in the case of a radial dependenceof colours with clustercentric distance.A galaxy was considered to be in the background of a clusterwhen ∆ z ≡ z gal − z cluster > (cid:113) σ z gal − σ z cluster . The relatively largeerror in redshift, due to the photometric technique used for thedetermination of the redshifts in the galaxies and clusters, makesit impossible to know their relative position in the space of red-shift for most ( ∼ /
3) of the galaxies projected along the line ofsight of a given cluster.Using a cut in galactic latitude of 20 degrees, the numberof clusters and background galaxies selected by this method are56,985 and 5,287,825 (the corresponding numbers at | b | > < ∼ .
25. This does not exactly reproduce the distri-bution of redshifts in the Wen et al. (2012) catalogue, as clustersat very high redshift have not been considered because they donot have background objects in the galaxy sample. As expected,the number of galaxies projected behind a given cluster dependsstrongly on the redshift of the cluster; this is basically a conse-quence of the cut in magnitude adopted for the galaxy sample.Maps of ( g − r ), ( g − i ) and ( r − i ) colours and the corre-sponding radial profiles are shown in Figs. 2 and 3, respectively. Fig. 2.
Map of colours g − r , g − i , and r − i (from left to rightrespectively) of mean colours of galaxies as a function of theprojected clustercentric distance. The maps have a radius of 6Mpc and a binning of 0.3 x 0.3 Mpc . The mean colour of eachmap has been subtracted. The gray scale is linear and has anamplitude of 0.02 mags. Fig. 3.
Excess of colours as a function of projected clustercentricdistance. The units of the vertical axis are milimags.These maps represent the mean colours of galaxies in the back-ground of clusters as a function of the projected clustercentricdistance. The radius of the maps and the binning are 6 Mpc and0.3 Mpc x 0.3 Mpc, respectively. The mean values of the coloursare 1 . ± . . ± . . ± .
003 for g − r , g − i ,and r − i , respectively. If we select only those objects at | b | > Table 1.
Average excess of colours (in milimags Mpc ) withindi ff erent clustercentric radius. Rad (Mpc) ∆ ( g − r ) ∆ ( g − i ) ∆ ( r − i )0-1 − . ± . − . ± . − . ± . + . ± . + . ± . + . ± . − . ± . − . ± . + . ± . Mpc centred in the clusters of 2 .
69, 3 .
37, and 1 .
63 milimagsMpc in ( g − r ), ( g − i ) and ( r − i ), respectively.The above procedure introduces some degree of filtering inthe reddening by each cluster due to the fact that a given galaxycould be in the background of more than one cluster, and then itslight crosses each foreground cluster at di ff erent clustercentricdistances. The amount of filtering would depend on the unknownspatial distribution of intracluster dust. To avoid this uncertainty,several tests were conducted by modelling the dust spatial dis-tribution. Here, we only give the results of a very conservativeapproach that avoids any a priori dust modelling by consideringonly those galaxies lying in the background of just one cluster. Indoing that, the size of the sample drastically reduces to ∼ , . × galaxies. We also do not detect any excessof signal within any clustercentric distance. The corresponding95% C.L. limits are 120, 39, and 40 milimags Mpc for the ex-cess of colours g − r , g − i and r − i in a projected clustercentricradius of 1 Mpc, respectively. We follow the method first proposed by Kelly & Rieke (1990)and developed by Montier & Giard (2005). As discussed bythese authors (an references therein), the detectability of indi-vidual clusters in IRAS infrared maps is compromised by thelow sensitivity of the maps, as compared to the signal expectedfrom clusters and to the noise confusion level of ∼ / sr dueto extragalactic sources in those maps. Instead of using the in-frared maps as Montier & Giard did, we used the extinction map E ( B − V ) by Schlegel et al. (1998). Both approachs are similaras the extinction E ( B − V ) map is basically the point-source sub-tracted IRAS 100 µ m map, corrected to a reference temperatureof 18.2 K using the DIRBE temperature map, and multiplied bya constant p = . ± . / (MJy sr − ). The estima-tions obtained using this method contain the contribution of dustin the ICM and within galaxy members.We built a 2 × > E ( B − V ) map ingalactic coordinates centred on each cluster, each rotated by arandom angle multiple of π/
2, and averaged all the maps. Giventhe large spatial density of clusters, a given pixel in the extinctionmaps might contribute to several cluster maps. This introducessome degree of correlation between pixels. After many tests, wedecided to limit the analysis to those clusters at a galactic lat-itude | b | >
50 degs. Although the mean galactic extinction is0.024 mags at | b | >
50 degs, we still flagged out all clusterssituated in regions of particularly heavy Galactic extinction, orthose immersed in large gradients, i.e. those with a mean level ofextinction > .
05 mags or a rms > .
01 mags within a square of2 x 2 degrees centred in the cluster. None of the results presentedin the paper depends on the specific values of such constraints.The final sample contains 52,667 clusters.Figure 4 presents the average extinction map; this shows aclear signal concentric with the position of the clusters. The ra-
Fig. 4. ( Le f t :) Map of extinction (48 x 48 arcmin) obtained byaveraging the maps centred on each cluster. (
Right :) A simu-lated map obtained shifting the position of each cluster an anglerandomly distributed in the range 1-2 degrees.
Fig. 5.
Radial profile of the mean extinction in the stacked mapsshown in previous figure. The contribution of the Galactic ex-tinction has been removed by averaging a ring of inner and outerradius of 24 and 40 arcmin respectively.dial profile of the extinction map is shown in Fig. 5; this indicatesan extinction at the centre of the clusters E ( B − V ) = × − mags. To assess the reliability of the signal and the absence ofsignificant systematics, we have created a new stacked map byrandomly and independently shifting the position of each clus-ter by an angle uniformly distributed in the range 1-2 degreesin galactic longitude. The resulting map is shown in Fig. 4 andis compatible with noise random fluctuations. From the uncer-tainties in the estimation of the extinction from our own Galaxyand from the simulated results, we estimate a conservative uncer-tainty in the central value of ∼ × − mags; the main factorcontributing to that is the absolute level of the residual extinc-tion from the Milky Way. The extinction has a Gaussian profilewidth of FWHM =
12 arcmin. Applying the conversion factorbetween E ( B − V ) extinction and emission at 100 µ m quoted inSchlegel et al., the central emission translates into a mean emis-sion at 100 µ m of (1 . ± . × Jy sr − . As it is demonstratedby separating the clusters in bins of di ff erent richnesss and red-shifts, this profile does not reflect the spatial distribution of thecluster, but it is instead dominated by the instrumental resolutionof the extinction map and possibly additional filtering due to themethod.
3. Analysis
For the case of a Milky Way-like dust, in which A V = . ∆ ( g − i ) at rest in cluster (Schlafly & Finkbeiner 2011), A λ ∝ λ − . ap-proximately in the interval from g to i filters. Hence, ∆ ( g − i ) at rest in cluster ≈ ∆ ( g − i ) obs (1 + z cluster ) − . .Since (cid:90) A V dS = (cid:90) dVa V , (1) a V ( r ) = . κ V ρ dust ( r ) , M dust = (cid:90) dV ρ dust ( r ) , the amount of dust within a given radius can be constrainedusing M dust ( r < R ) M (cid:12) = . × κ v (cid:90) R A v dS , (2)where κ v = . × g cm − (Mathis 1990; Loeb & Haiman1997) and S is the projected area in M pc . From the valuesquoted in Table 1 for the excess ∆ ( g − i ) within clustercentricdistances of 1, 2 and 3 Mpc, we obtained the corresponding (cid:82) R A v dS values (see above) and estimated 95 % C.L. limits onthe mass of intracluster dust of 1 . × , 9 . × , and 8 . × M (cid:12) respectively. This corresponds to a limit on the projecteddensity of dust of Σ < M (cid:12) kpc − within theclustercentric radius of 1, 2, 3 Mpc, respectively.Assuming that our Galaxy has a dust exponential disc withscalelength 2.2 kpc (Drimmel & Spergel 2001), except in theinner 4 kpc to take the inner hole into account (L´opez-Corredoiraet al. 2004), and that the extinction observed in the Galactic polesis A V = .
05 mag (Schlegel et al. 1998), the Milky Way wouldproduce 8 . × − mag Mpc observed from outside, which isaround a dust mass of 2 . × M (cid:12) (from Eq. 1). Davies et al.(1997), who used far-infrared emission, gets a similar number: M dust = × M (cid:12) . This means that we are constrained to haveless than ∼
300 times (95% C.L.) the dust mass of the MilkyWay in the intracluster medium.
The flux at rest is calculated as F ν, rest = (1 + z ) − − α F ν, observed ,given that the emission I ν ∝ ν α ; we take α = + z ) − stems from the increase of thefrequency range, which gives an observed flux larger by a factor(1 + z ). The mean luminosity at 100 µ m is (1 . ± . × ergs − for the whole sample. The luminosity produced by the colddust component of the Milky Way is 2 . × erg s − (Cox etal. 1986) or 2 . × erg s − , according to Davies et al. (1997).Assuming that the emission at 100 µ m includes most of the dustemission in clusters, the value quoted above would correspondto the emission of ∼
60 Milky Way galaxies which is of theorder of the number of spiral galaxies found in clusters, whichis M dust ∼ × M (cid:12) following the numbers of the previoussubsection.To compare the results of method 1 given in Table 1, we canconvert the luminosity into the equivalent surface integral of theassociated absorption by dust: (cid:90) dS A V = . π R E ( B − V ) , (3) E ( B − V ) = . / (MJy / sr) = F , rest πα , α = Rd A ,ν F , rest = L , rest π d L , where d A is the angular distance, d L is the luminosity distance,which are related by d A = d L (1 + z ) . Hence, (cid:90) dS A V = . × − L , rest (erg / s) (cid:104) (1 + z ) (cid:105) , (4)which gives us (cid:82) dS A V = (5 . ± .
1) millimag Mpc , or (cid:82) dS ∆ ( g − i ) = (3 . ± .
1) millimag Mpc with the above num-ber of L , rest ( erg / s ) = (1 . ± . × and a value for oursample of clusters of (cid:104) (1 + z ) (cid:105) = .
87. Using Eq. (2), we getagain a dust mass of 2 × M (cid:12) .According to the discussion by Roncarelli et al. (2010),the infrared emission at 100 µ m from galaxies in clusters isdominated by the emission of late-type spiral galaxies. Thoseauthors estimated a flux of 1904 . + . − . Jy in a sample of7476 MaxcBCG clusters (Koester et al. 2007), or the value of0 . + . − . Jy per cluster (we estimate a mean flux per clusterof 0 . ± .
005 Jy), and concluded that the values detected byGiard et al. (2008) are roughly compatible with their estimationsand leave little chance for any component associated to intraclus-ter dust. Our estimations agree with those by Giard et al. (seesection 3.4) and then reinforces that scenario. The limit foundby estimating the possible reddening galaxies behind clusters(Method 1), although not very tight, are compatible with this.The detection of intracluster dust using this method would re-quire a larger sample of background objects.
As a test of the consistency of our results and to studythe range in redshift z < .
05 that is uncovered bythe Wen et al. (2012) sample, we do a similar analy-sis for the sample of 1,059 Abell clusters with measuredredshifts (see http: // heasarc.gsfc.nasa.gov / W3Browse / galaxy-catalog / abellzcat.html). Considering the whole sample and ap-plying similar restrictions in galactic latitude and extinctions asto the Wen et al. sample, we selected 485 clusters. The averageextinction map (Fig. 6) centred on each cluster shows a clearexcess of signal with a central peak amplitude of E ( B − V ) = (1 . ± . × − mags that corresponds to a density of flux ∼ (6 . ± . × Jy sr − . The radial profile has a FWHM ∼ µ m luminosity of (0 . ± . × erg s − . Ifwe restrict the analysis to those clusters at redshift z < .
05, thenumber of clusters selected is small (86 clusters). The stackedmap (Fig. 6) shows a central excess of extinction E ( B − V ) = (1 . ± . × − mags, and then a flux density and luminosityof (6 . ± . × Jy sr − and (0 . ± . × erg s − , respec-tively. For the sample at z < .
05, the profile has a
FWHM ∼ FWHM ∼
12 arcmin, see next section), this gives a meanangular extension of the dust emission in Abell clusters at red-shifts < .
05 of ∼ ∼ . Fig. 6. ( Le f t :) Maps of extinction (48 x 48 arcmin) obtainedby averaging the maps centred on each cluster from the Abellsample. (
Right :) The same restricted to those clusters at redshift z < . Comparison between our results and those found by other au-thors are not straightforward, due to the di ff erent methods andsamples used and the di ff erent spatial scales proved. In gen-eral, all the modern works pointed out to a reddenig e ff ect < f ew − mag of extinction per cluster. Our method relies onthe hypothesis that the dust does not extend to distances largerthan 6 Mpc (or at least that it is not distributed uniformly on suchscales). With all these cautions, our results are compatible withthose previous works by Nollenberg et al. (2003), Cheloucheet al. 2007, Bovy et al. (2008), and Muller et al. (2008), whopresent upper limits or marginal detections of excess at the levelof 10 − mag. However, the work by McGee & Balogh (2010)explores the presence of dust on very large scales by measur-ing colour excess of QSOs behind 70,000 low redshift SDSSgalaxy groups and clusters. They claim the detection of dust outto a clustercentric distance of 30 Mpc h − . Although those au-thors measured the excess of colours in very large scales (tens ofMpc), their results (see Fig. 4 in their paper) indicate an excessof colour in g − i ∼ × − mags, which is di ffi cult to reconcilewith the radial profile of that excess, as it is shown in Fig. 3. Wedo not have an explanation for that inconsistency. As mentioned earlier, the only previous statistical work usinga similar method was conducted by Montier & Giard (2005).These authors found an average central emission at 100 µ m of(3 . ± . × Jy / sr, whilst we obtained (1 . ± . × Jy / sr. A direct comparison between both amplitudes is not pos-sible because we need to take into account the di ff erent angu-lar width of both dust profiles. The FWHM of their distributionat 100 µ m has a FWHM ∼ FWHM ∼
12 arcmin. Byassuming two dimensional Gaussian profiles, the dilution fac-tor, (12 / = .
25, between both angular distributions and theratio of the peak amplitudes (1.8) translates into a flux density ∼
25% in our case. This relative agreement is quite remarkableconsidering the di ff erent samples of clusters used. The reasonsfor our comparatively wider profile must come from the use ofthe Schlegel et al. maps with a FWHM ∼ . FWHM ∼ . Fig. 7.
Map of extinction (48 x 48 arcmin) obtained averagingthe maps centred on each cluster. Each map corresponds to agiven range in richness and redshift. Richness increases from topto bottom, while redshift increases from left to right. The meanvalues of richness and redshift in each bin are those quoted inTable 2.
Fig. 8.
Estimated mean cluster luminosity at 100 µ m versus red-shift. The dotted line corresponds to a fit L = L o (1 + z ) α with α = . To determine the origin and possible evolution of dust in clus-ters, it is interesting to study the possible dependence of the dustemission with respect to mass and / or redshift. This was done bysplitting the clusters in 5 × Table 2.
Cluster Luminosities at 100 µ m as a function of redshiftand mass. N clust Mass (10 M (cid:12) ) z L(10 erg s − )1773 0.633 0.189 0 . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . . ± . Table 3.
Cluster luminosities at 100 µ m as a function of redshift. N clust Mass (10 M (cid:12) ) z L(10 erg s − )9944 1.246 0.178 0 . ± . . ± . . ± . . ± . . ± . roughly the same number ( ∼ × ) clusters in each bin. Themasses, M , were obtained from the relation between richnessand mass given by Wen et al. (their equation 2). Although theresulting maps (Fig. 7) are relatively noisy as compared to thestacked map of the full sample presented in Fig. 4, all the mapsshow a clear detection of signal with the maximum at the centreof the maps. The main problem having a low number of clus-ters is the existence of gradients or systematics in the extinctionmap that prevents for a good estimation of the level of Galacticextinction. The analysis of the beam profiles indicate that theyare dominated by the instrumental resolution and that the di ff er-ences between them can be adscribed to the e ff ect of noise andin particular to the uncertainties in estimating the backgroundlevel. After doing many tests, we conclude that the best estima-tion of the luminosities in this case is obtained from the ampli-tude of the central peak when a Gaussian profile is assummed.This width was obtained from the mean value and rms of the dis-tribution of the 5 x 5 profiles. We obtain FWHM = . ± . × M (cid:12) , respectively. There is a clear tendency to increase luminos- ity with redshift and richness. This was quantified by fitting afunction L = L × (1 + z ) α × ( M cluster / M (cid:12) ) β erg s − . The bestfit corresponds to values log( L ) = . ± . α = . ± . β = . ± .
17. The evolution found with redshift agreeswith the models by Le Floch’h et al. (2005) ( α = . ± .
6) andBay et al. (2007) ( α = . + . − . ). Binning the maps in five binsin redshift and computing the luminosities in a similar way, weobtained the results presented in Table 3. As the five bins in red-shift have roughly similar mean masses, we can ignore that de-pendence and fit a function L = L × (1 + z ) α . The results are pre-sented in Table 3 and Fig. 8. The luminosity found for the Abellclusters (see section 3.3) at redshift < .
05 is (0 . ± . × erg s − (not included in the plot) which follows the general ten-dency to decline luminosity at lower redshifts. The ratio from themean luminosity at redshift 0.57 (last bin in Table 3) to the meanluminosty of the Abell clusters is a factor ∼
17. Assuming thatthis ratio is entirely due to evolution in redshift (there could besome e ff ect due to di ff erences in richness), this confirms the highevolution in redshift found by other authors using large samples(e. g. Giard et al. 2008) or single clusters (Bay et al. 2007). Theseauthors found a ratio ∼
17 between the luminosities at 24 µ m ofComa ( z = .
02) and MS1054-0321 ( z = .
4. Conclusions
The main conclussions of our work are – We have conducted a study to estimate the amount and dis-tribution of dust within galaxy clusters. This has been donefollowing two methods: ( i ) analyzing the e ff ect that such dustproduces on the light of objects in their background, and ( ii )analyzing the contribution of clusters to the E ( B − V ) extinc-tion map by Schlegel et al. (1998). – We did not find evidence of additional reddening of back-ground galaxies with respect to galaxies in the field. Ouranalysis imposes maximum limits in the excess of colour dueto intracluster dust extinction (cid:82) R ∆ ( g − i ) dS = − . ± . + . ± .
77 and − . ± .
10 milimags Mpc within clus-tercentric distances of 1, 2 and 3 Mpc respectively. – Using the second method, we clearly detect the far infraredemission produced by the clusters. The corresponding ex-tinction profile can be characterized by a Gaussian functionwith a peak amplitude of 346 × − mags and a FWHM ∼
12 arcmin. The angular profile is dominated by instrumentale ff ects due to the resolution of the extinction map and themethod used and does not reflect the spatial distribution ofthe dust within the clusters. Averaging the extinction of allclusters, we find a surface integral of the excess of colour g − i of 3.4 millimag Mpc . – The above extinction corresponds to an average flux and lu-minosties at 100 µ m per cluster of 0.21 Jy and (1 . ± . × erg s − , respectively. This signal can be explained as dueto emission of 2 × M (cid:12) of dust with temperature of 20 K. – Our results do not allow us to exclude the existence of someintracluster dust, but we constrain the maximum amount ofdust to be a few tens the dust in Milky Way-like galaxies – Separating the clusters in 5 × L = L × (1 + z ) α × ( M / M (cid:12) ) β ergs − erg s − . The best fit corresponds to values log( L ) = . ± . α = . ± .
8, and β = . ± .
17. The depen-dence in redshift agrees with previous studies.
Despite the results of previous studies and the work pre-sented here, new techniques exploring the dust content in galaxyclusters for di ff erent subsamples of objects covering di ff erentranges in mass and redshift are needed. Among the tools thatcan provide a deeper insight in the topic we would like to men-tion those allowing a whole treatment of dust and gas and the useof the recent maps obtained by the Planck / Herschel mission. Aswe have shown, the extinction due to dust in the intracluster me-dia is too small to be measured with current datasets of galaxiesbut can potentially be of interest once new dataset are available.
Acknowledgements.
Thanks are given to the anonymous referee for helpfulcomments. Thanks are given to C.-J. Lin (language editor of A&A) for proofreading of the text.Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation,the Participating Institutions, the National Science Foundation, and theU.S. Department of Energy O ffi ce of Science. The SDSS-III web site ishttp: // / . SDSS-III is managed by the Astrophysical ResearchConsortium for the Participating Institutions of the SDSS-III Collaborationincluding the University of Arizona, the Brazilian Participation Group,Brookhaven National Laboratory, Carnegie Mellon University, University ofFlorida, the French Participation Group, the German Participation Group,Harvard University, the Instituto de Astrofisica de Canarias, the MichiganState / Notre Dame / JINA Participation Group, Johns Hopkins University,Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics,Max Planck Institute for Extraterrestrial Physics, New Mexico State University,New York University, Ohio State University, Pennsylvania State University,University of Portsmouth, Princeton University, the Spanish Participation Group,University of Tokyo, University of Utah, Vanderbilt University, University ofVirginia, University of Washington, and Yale University. We have used also theNED (NASA Extragalactic Database, http: // / ) References
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