Table Of Content

Astronomy & Astrophysics manuscript no. 1803rsj February 2, 2008 (DOI: will be inserted by hand later) The V-band luminosity function of galaxies in A2151 1 2 1 1 3 R. Sańchez-Janssen , J. Iglesias-Pa´ramo , C. Munõz-Tunõń , J.A.L. Aguerri , and J.M. V´ılchez 1 Institutode Astrof´ısica deCanarias, Calle V´ıa Láctea s/n, E-38205 La Laguna, Tenerife, Spain e-mail: [email protected]; [email protected]; [email protected] 2 Laboratoire d’AstrophysiquedeMarseille, BP8, Traverse du Siphon,F-13376 Marseille, France 5 e-mail: [email protected] 0 3 Institutode Astrof´ısica deAndaluc´ıa, CSIC, Apdo. 3004, E-18080 Granada, Spain 0 e-mail: [email protected] 2 n Received ...; accepted ... a J Abstract. We present a wide field V-band imaging survey of approximately 1 deg2 (∼ 7.2 h−2 Mpc2) in the 9 75 1 direction of the nearby cluster of galaxies Abell 2151 (the Hercules Cluster). The data are used to construct the luminosityfunction(LF)downtoMV ≈−14.85,thusallowingustostudythedwarfgalaxypopulationinA2151 1 for the first time. The obtained global LF is well described by a Schechter function with best-fit parameters v α = −1.29+0.09 and M∗ = −21.41+0.44. The radial dependence of the LF was investigated, with the faint-end −0.08 V −0.41 6 slope tending to be slightly steeper in the outermost regions and farther away than the virial radius. Given the 0 presence of significant substructure within the cluster, we also analysed the LFs in three different regions. We 4 find that the dwarf to giant ratio increases from the northern to the southern subcluster, and from low to high 1 local density environments, although these variations are marginally significant (less than 2σ). 0 5 Key words.galaxies:photometry – galaxies:luminosity function – galaxies:clusters:A2151 0 / h p 1. Introduction ries predict the formation of large numbers of low mass - o halos, the latter observational evidence may indicate the r The luminosity function (LF) of galaxies (that is, the existence of some mechanism that eliminates at least the t s probability density of galaxies in a certain population of visiblecomponentofgalaxiesinlowdensityregions(Tully a a given luminosity) is one of the key observable quan- : et al. 2002). v tities for galaxy evolution theories (Binggeli, Sandage i & Tammann 1988), although the link between the data X and the underlying physics is still not easily understood A2151(theHerculescluster),togetherwithA2147and r a (Benson et al. 2003). Galaxies in high density environ- A2152,formspartoftheHerculesSupercluster,oneofthe ments,suchasrichgalaxyclusters,canevolverapidly(less largest and most massive structures in the local Universe than1Gyr)duetodifferentphysicalprocesses,e.g.harass- (Chincarini, Thompson & Rood 1981; Barmby & Huchra ment (Moore et al. 1996), ram-pressure stripping (Gunn 1998). The kinematical analysis of Barmby & Huchra & Gott 1972; Quilis, Moore & Bower 2000), tidal effects (1998)revealsthatA2151andA2147areprobablybound and mergers (Toomre & Toomre 1972; Bekki, Couch & to each other, and that the supercluster as a whole may Shioya 2001; Aguerri, Balcells & Peletier 2001) or star- also be bound. A2151 (z = 0.0367) is an irregular and vation (Bekki, Couch, & Shioya 2002). The LF should spiral-rich cluster (∼ 50%, Giovanelli & Haynes 1985). reflect this important role of the environment in regulat- There is strong evidence (from optical and X-ray studies) ing galaxy evolution. Recent results from large surveys suggestingthattheclusterisstillintheprocessofcollaps- (De Propris et al. 2003) point towards the composite LF ing: the lack of hydrogen deficiency in the spiral popula- of cluster galaxies having a characteristic magnitude that tion(Giovanelli&Haynes1985;Dickey1997),the bumpy is approximately 0.3 mag brighter and a faint-end slope distribution of the hot intracluster gas and its low X-ray (directly related to the ratio of dwarf to giant galaxies, flux (Magri et al. 1988; Huang & Sarazin 1996), and the D/G) that is approximately 0.1 steeper than those found presenceofatleastthreedistinctsubclusters(Bird,Davis for field galaxies. As hierarchical galaxy formation theo- & Beers1995,BDB hereafter).All this evidence indicates that A2151 is a young and relatively unevolved cluster, Send offprint requests to: R. Sánchez-Janssen thus making it an excellent target for studying the LF e-mail: [email protected] and establishing comparisons with more evolvedsystems. 2 R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 Throughoutthis articlewe assumeavalueofH =75km in the overlapping chips, for which we obtained a maxi- 0 s−1 Mpc−1, which puts A2151 at a distance of 147 Mpc. mum dispersion of 0.18 mag at the faintest magnitudes. TheaimofthispaperistostudytheLFofA2151down On the other hand, the background field was accurately to the dwarf regime,thus extending the previous work of calibrated since several standards from the Landolt 107 Lugger(1986),who computedthe R-bandLF ofthe clus- field (Landolt 1992) show up in the different frames. All ter over a wide area (4.6 × 4.6 Mpc2) but only down to the V magnitudes were corrected for Galactic extinction M =−19.8.The paper isarrangedasfollows:inSection using the Schlegel, Finkbeiner & Davis (1998) dust maps R 2 we describe the observations and data reduction proce- and the Cardelli, Clayton & Mathis (1989) extinction dures. Section 3 gives the details of the source extraction curve. and star/galaxy separation, and the estimate of the limiting magnitudes of the sample. In Section 4 we present 3. Data Analysis the LF inA2151andanalysepossible variationsofits parameters within location in the cluster. Finally, Section 5 3.1. Source extraction discusses the results. Identification and extraction of sources was carried out using the automated code SExtractor (for specific details 2. Observations and data reduction see Bertin & Arnouts 1996). Objects are identified as every detection having a certain minimum area and num- Observations were carried out with the Wide Field ber counts abovea limiting thresholdtakingthe sky local Camera at the 2.5 m Isaac Newton Telescope (INT), lo- backgroundasa reference.These limiting sizes andfluxes cated at the Observatorio del Roque de los Muchachos weresetto36pixels2 andtwicethestandarddeviationof during four different runs in the period 1999–2002. The the sky counts, respectively. More precisely, sources were WFC consists of four thinned AR-coated EEV 4k × 2k extractedusingabackground-weightedmethod,sothatin CCDs and a fifth one acting as an autoguider. The pixel every case the threshold takes a local value. This avoids scale is 0.33 arcsec pixel−1, giving a total field of view a lot of spurious detections in the surroundings of bright of about 34 × 34 arcmin2. A square area of about 11 × galaxyhalosandsaturatedstars,wherethelocalthreshold 11 arcmin2 is lost at the top right corner of the field due is significantly increased. Careful visual inspection of the to the particular arrangement of the detectors. The top frames was carried out and all definitely spurious entries left corner of Detector #3 is also lost because of filter were removed from the catalogues, such as H ii regions vignetting. ofspiralgalaxies,whichfulfilalltheabove-statedrequire- We imageda mosaic offive overlappingpointings cov- ments. ering a total area of about 1.05 deg2 (∼ 7.2 h−2 Mpc2) 75 The separation between stars and galaxies was per- in the directionof the Abell 2151cluster.The totalexpo- formedonthebasisoftheSExtractorstellarityindex(S/G sure time for each field was 2 × 900 s using the Harris V hereafter). The code assigns a numerical value between 0 broad-band filter. A control field outside the Abell 2151 and 1 to all detections accordingto the following criteria: cluster was also observed in order to get the background star-likeobjectshavevaluescloseto1whilegalaxy-likeob- galaxy counts with the same instrumental configuration jects are closer to 0. This S/G classifier behaves correctly as the cluster counts. Two 1000 s exposures were taken forbrightobjectsbutbreaksdownatthelowermagnitude in the direction of the Landolt 107 field. The averagesee- end (especially in bad seeing conditions), where a correct ing of the fields ranged between 1.1 and 1.7 arcsec, with classification remains difficult. a maximumvalue of2 arcsecinone ofthe CCDs. Table 1 In order to test the reliability of the index we sim- shows a detailed log of the observations. ulated artificial isolated 3 stars and recovered them us- Data reductionconsistingofbiassubtractionandflat- ing SExtractor and the same selection criteria as for the fielding was carried out in the usual way using the IRAF Hercules fields. The stars were generated with the art- reduction package.1 The images corresponding to the data.mkobjects package in IRAF and then added into Abell2151fieldwerecalibratedusingaperturemagnitudes frames reproducing the same sky counts and S/N ratio of bright galaxies taken from Takamiya, Kron & Kron as the scientific ones. The PSF profiles were assumed to (1995)since no standard stars were available for the pho- beGaussian4 andFWHMsspannedthevaluesofoursee- tometriccalibration(seeTable1).Thedifferencesbetween ingconditions.Atotalnumberof750starsweresimulated ourcalibratedmagnitudesand thoseof TKK95for galax- in the magnitude range 17 ≤ m ≤ 23 for two different V ies in our central field (computed within an aperture of seeing conditions (1.2 and 2 arcsec FWHMs). 17.5arcsecradius)neverexceeded0.05mag.Photometric zero points for the remaining fields were calculated by 2 this corresponds to an apparent size of 2 arcsec, which is cross-correlatingaperture magnitudes of common objects themaximum seeing disc size in ourframes. 3 westressthisfactbecausetheS/Gclassifierhasmoreprob- 1 IRAF is distributed by the National Optical Astronomy lems when classifying stars overlapping with other objects or Observatories, operated by the Association of Universities for lying in galactic halos. Research in Astronomy, Inc., under cooperative agreement 4 wealsotriedwithamorerealisticMoffatfunction,butdif- with theNational Science Foundation. ferencesinlimitingmagnitudeandS/Gvalueswerenegligible. R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 3 Table 1. Log of the observations. Seeing values are averagedfrom the four chips in each of the fields. Field R.A.a Dec.a Date texp Seeing (J2000) (J2000) (sec) (arcsec) Ce1 16:05:36.00 +17:43:59.97 1999 June 06 2×900 1.2 Ce2 16:05:23.99 +17:27:59.97 1999 June 06 2×900 1.5 #2 16:06:12.56 +18:10:56.15 2001 April 17 2×900 1.1 #4a 16:02:00.00 +17:55:43.11 2002 May 19 2×900 1.7 #4b 16:04:00.00 +17:50:42.97 2002 May 19 2×900 1.6 Back 15:39:13.99 −00:13:01.07 2002 July 11 2×1000 1.7 a Coordinates correspond to the centre of the WFC. See http://www.ing.iac.es/Astronomy/instruments/wfc/index.html for a detailed description of thespatial arrangement of themosaic. Fig.2. Structural parameters of dE and dSph galaxies in the Virgo Cluster. The data are taken from Binggeli Fig.1. The aperture central surface brightness of all our & Jerjen (1998) (open circles) and Barazza, Binggeli & detected objects as a function of apparent magnitude. Jerjen (2003) (open triangles) while filled squares corre- Note the different location in the plot of stars and ex- spondtooursimulatedgalaxies.Theobjectatthetopleft tendedobjects.Thehorizontaldashedline correspondsto representsade BlokLSB galaxywith anexponentialdisc the2σisophotaldetectionlimitusedinSExtractor,which profile and a scale-length of 3 kpc. cuts the objects’ distribution at V ∼ 21 (vertical dashed line), thus setting the limiting magnitude of the sample (see text for details). exercisewe expect the lowestcontaminationby stars possible,althoughperfectcleaning isalmostunachievablefor the faintest magnitudes.There is a further concernabout The classificationof star-like objects is easily done for losing compact dwarf galaxies as so-called ultra compact good seeing frames (S/G ≥ 0.95), whilst the S/G values dwarfs(UCDs;Drinkwateretal.2000),whichcanassume span a wider range in worse conditions (S/G ≥ 0.85 for a stellar appearance in ground-based images. However, simulated point-like sources brighter than m = 22.0). V these galaxies typically have intrinsic magnitudes much Photometry in all the cases was almost perfect, with dif- fainter (M ∼−11) than our limiting magnitude and the B ferences between input and recovered magnitudes of less dwarfsweareable todetect havelowprobabilityofbeing than0.05magevenforthefainteststars.Aswillbeshown misclassified (see Sect. 3.2.1). inSect.3.2.1,ourlimitingmagnitudeforclustergalaxiesis m ∼21.Thus,wecautiouslysetavalueofS/G≥0.85for V the star-like objects in all the frames, which corresponds 3.2. Photometry tothe S/Gvalueofsimulatedstarsonemagnitudefainter 3.2.1. Sample completeness than our limiting magnitude. All the detections having 0.8 ≤ S/G < 0.85 were carefully inspected by means of One of the key problems in the study of LFs is knowl- IMEXAM, along with bright saturated stars that tend edge of detection limits and completeness of the data. In to have lower S/G values. Those detections with obvious order to make this estimation we followed two different stellaroriginwereremovedfromthecatalogues.Afterthis approaches. 4 R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 Fig.3.Detectionefficiency (solid line) foreachofoursimulatedgalaxymodels.Fromleft to rightandtopto bottom: n =1 with r = 0.75, 1.5, and 3 kpc, and the n = 2 with r = 0.5 kpc model. The shaded regions in the lower panels e e indicate differences between recovered and input magnitudes, which never exceed 0.3 mag. First, for all our detected objects we computed the r = 0.5 kpc) in the magnitude range 17 ≤ m ≤ 23 e V mean central surface brightness (µ ) measured in a cir- (−18.85 ≤ M ≤ −12.85) and with three different axial app V cular aperture of area equal to the minimum detection ratios (0.3, 0.6, and 0.9). A total number of 1500 galaxies areausedinSExtractor.Figure1showsµ asafunction were generated for each of the morphologies in order to app of apparent magnitude for all the detected sources (stars get enoughstatistics. The choiceof these models was mo- andgalaxies).Starsoccupytheupperdiagonallocus,with tivated by the quantitative morphological studies of the saturated objects defining the flat region of the distribu- populations that are supposed to dominate the faint-end tion.Galaxiesarelocatedinthelower-mostbroaderregion oftheLFinnearbyclusters(dEanddSphmainly),which of the plot. showthatthesegalaxieslieinawelldefinedregiononar e vs.nplot.Figure2showsstructuralparametersofdEand The different locations of point-like and extended ob- dSph galaxies in the Virgo Cluster taken from Binggeli jects is evident at bright magnitudes (m ≤ 18), while V & Jerjen (1998) and Barazza, Binggeli & Jerjen (2003) the effects of seeing make this distinction at fainter mag- (opencirclesandopentriangles,respectively),whilefilled nitudes difficult. We have computed the 2σ isophotal de- squarescorrespondto ourartificialgalaxies.Objectswith tection limit used in SExtractor, which corresponds to µ=26.15magarcsec−2 (horizontaldashedlineinFig.1). larger effective radii are known to present fainter surface brightness,whichrenderstheirdetectiondifficult.Forthis Given the distribution of the objects in Fig. 1, m ∼ 21 V reasonwe modelled one object with n = 2 and r slightly appears to be the appropriate limiting magnitude of our e larger than those observed and another galaxy with n = sample, as we do not lose objects because of their low 1 and r = 3 kpc; the latter are typical parameters of surface brightness. e the low surface brightness (LSB) galaxies studied by de Secondly,wesimulatedartificialgalaxiesand,aswedid Blok et al. (1995). Note (see Fig. 2) the apparent lack withstars,placedtheminframeswithconditions(seeing, of this kind of galaxy in this Virgo sample. LSB galaxies S/N) identical to the scientific ones, in order to recover areknownto be the mostunstablesystemsduringcluster them with SExtractor. We generated galaxies with two evolution,sufferingfromrapidencountersandstrongtidal different morphological types and different intrinsic half- shocks(harassment,seeMooreetal.1999),thereforerare lightradii(oneexponentialprofilewithre =0.75,1.5and in relaxed clusters. However, as mentioned, the Hercules 3 kpc, andone Sérsicprofile(Sérsic1968)with n = 2 and R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 5 clusterisstillinprocessofcollapseandharassmentmight have produced little effect on such a kind of LSB. On the otherhandAndreon&Cuillandre(2002)showthatalarge populationoflowsurfacebrightnessgalaxiesdominatethe LF in Coma, representing the main contribution at faint magnitudes. As it is not obvious which kind of galaxy is the predominant one in the cluster environment, we cau- tiously set the limiting magnitude of the lowest surface brightness model as our sample limit. The results of our simulations are summarized in Fig. 3, where we plot the fraction of recovered galaxies (N /N ) vs. input apparent magnitude (as given by r i MAG BEST) for each galaxy type (solid lines); shaded regions correspond to recovered magnitude differences, which are always below 0.3 mag. We find that the detection and estimate of magnitudes are less accurate for Fig.4. Backgroundgalaxiesnumber counts in the SA107 galaxies with larger effective radii than smaller ones. field (filled circles), compared with other sources in the Within each of the morphological types, edge-on galaxies literature. The limiting magnitude of LSB galaxies in the aremoreeasilydetected thanface-onones,but the differ- A2151 sample is marked with the dotted vertical line. ences are small enough that we could focus our analysis on averagednumbers. All these results were expected, for it is widely known that detection limits strongly depend onthe interplaybetweenmagnitudes,effective radiusand the population of objects in the background and in our inclination. The recovered S/G parameters for the simu- clusterfieldsweresimilar.Thenumbercountsinthisfield lated sample were always smaller than 0.75. From Fig. 3 are plotted in Fig. 4, together with other V-band counts it is apparent that detection efficiencies strongly depend taken from different sources in the literature.6 The fair on the structural parameters of galaxies. agreementbetweenthesecounts,eachtakenwithdifferent Ourlimitingmagnitude,asderivedfromtheµ −m instrumentation under distinct conditions, makes us con- app V relation, is m ∼ 21 (M ∼ −14.85 at A2151 distance). fident that the resulting LF derived by subtracting our V V control field counts is significant, with the advantage of From the simulations, this value ensures that our sam- havingbeenobtainedunderthe sameinstrumentalset-up ple is at least 80% complete, with the worst case that as the cluster counts. of LSB galaxies. In order to construct the LF of A2151, only objects brighter than this limiting magnitude were considered. 4. The Luminosity Function The luminosity function of galaxies in A2151 was com- 3.3. The control field puted as the statistical difference between the counts in ThemostreliablemethodforcomputingdeepLFsofclus- theclusterandcontrolfieldsamples.Onceagainwestress tergalaxiesinourtypeofsurveyisbymeansofastatisti- thatfinalresultsobtainedforthe LFwillstronglydepend cal subtraction of background/foregroundnumber counts on the galaxycounts used for foreground/backgroundde- from a control field, since the spectroscopic information contamination. Thus, in order to minimize this influence, is usually limited to the brightest galaxies. 5 It should we used largebin widths (1 mag) comparedto photomet- be noted that the selection of the control field is critical, ricuncertainties(seeSect.2andSect.3.2.1),andchecked for the final results derived from the LF strongly depend thatgalaxycountsintheSA107fieldremainedstablefrom on this choice. The selected field must fulfil the require- chip to chip. ment that the area is largeenoughso the cosmic variance Following Huang et al. (1997), errors from both and number count statistics, the main error sources in Poissonianandnon-Poissonianfluctuationsofcountshave LF determination, are minimized. We imaged the SA107 been taken into account. Inclusion of this cosmic vari- (α=15h39m12s, δ =−00o19′60′′) flanking field for these ance points to the fact that background counts in the purposes, where the presence of photometric standards cluster line of sight are not exactly those in our control providedus with highphotometric precisionforthe back- field. This error source affects both the cluster and con- groundcounts.Inordertoensurereliablesubtraction,the trolfield samples (Andreon & Cuillandre 2002).Our final background field should contain a population of objects error bars include this latter term, along with both the similar to that of the cluster. We checked this by con- contribution of photometric error of the zero point and structinga plotlikethe oneinFig.1,withthe resultthat the Poissonianuncertaintiesofbothsamples.Forsimplic- 5 Redshift data in the Supercluster are only complete down 6 The data from the MGC of Liske et al. (2003) were trans- to 15.1 mag, see Barmby & Huchra(1998). formed from theB-band using theiraverage B−V = 0.94. 6 R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 Table 2. Best-fit values for the radial LF of A2151. The quantities denoted by k are derived from an exponential fit to the faint-end of each LF. The columns correspond to the values derived for the three Schechter parameters, those obtained for the exponential parameters, the number of galaxies (N ) used in the computation of each LF and its gal D/G ratio. Region α M* φ∗ χ2 α χ2 N D/G ν k k gal r ≤ rc −1.22±0.12 −22.29±2.09 149±149 0.77 −1.18±0.06 1.25 735 3.54 ± 0.76 rc < r ≤ (rc+rv −1.26±0.09 −21.82±0.49 42±18 0.53 −1.26±0.11 0.96 5575 3.91 ± 0.78 (rc+rv)/2 < r ≤ rv −1.27±0.12 −20.63±0.50 65±33 0.59 −1.21±0.05 0.29 4248 7.05 ± 1.58 r > rv −1.47±0.26 −21.63±4.40 13±39 0.76 −1.32±0.13 0.41 2466 12.09 ± 5.11 Table 3. Best-fit values for the LF of A2151 and the three studied subclusters. Region α M* φ∗ χ2 α χ2 N D/G ν k k gal Global −1.29+0.09 −21.41+0.44 47±14 0.78 −1.24±0.09 0.54 13024 5.13 ± 0.82 −0.08 −0.41 A2151C −1.26±0.08 −21.78±0.51 70±29 0.66 −1.17±0.04 1.54 3380 3.95 ± 0.69 A2151N −1.16±0.17 −22.37±2.23 54±55 0.21 −1.15±0.08 0.26 1880 2.63 ± 0.75 A2151S −1.59±0.10 −23.05±2.01 8±11 0.43 −1.65±0.19 0.55 687 9.38 ± 3.21 Our fitting algorithm minimizes the χ2 by taking errors intoaccountandassignsastatisticalweighttoeachofthe points (1/σ2, where σ corresponds to its error term). i i In Fig. 5 we plot our LF for the total area covered in this study down to m = 21 mag. We find V that the Schechter function is a good representation of the LF in A2151 (χ2 = 0.69) with best-fit parameters ν α=−1.29+0.09 , M∗ =−21.41+0.44 and φ∗ =47±14. −0.08 V −0.41 In order to make a better estimate of the faint-end slopeoftheLF,wefittedourdatatoanexponentialfunc- tion of the type ∼ 10km where m are magnitudes and k is relatedto the αparameterofthe Schechterfunctionby the following expression: α=−(k/0.4+1). (2) Fig.5. Total luminosity function of A2151 down to mV Wederiveabest-fitvalueofk =0.095±0.036(χ2ν =0.54) in the magnitude range −18.85 < M < −14.85, which = 21 (asterisks), with best-fit Schechter function (solid V line) alsooverplotted.The dashedline correspondstothe corresponds to αk = −1.24±0.09 and is thus consistent with the value derived from the Schechter function. best fitto anexponentialfunction for the faint-endofthe LF (−18.85 < M < −14.85). Error bars include both Lugger (1986) computes the R-band LF of A2151 in V a region 4.6 Mpc a side, but only down to M ∼ −19.8, Poissonianandnon-Poissonianfluctuationsofcounts.The R which is approximatelyfive magnitudes brighterthan our inset shows the 1, 2 and 3σ contour levels for the best-fit limit. She derived a value of α=−1.26±0.13, similar to Schechter parameters (indicated by the cross). oursdespite ofotherbigdifferencesbetweenbothstudies: photographic plates vs. CCD images, different surveyed areas and limiting magnitudes, different bands. ity, all these sources were added in quadrature despite of ∗ It is well known that the α and M parameters of their different nature. the Schechter function show a high degree of correla- After background galaxy counts subtraction, the data tion (Schechter 1976), so that their values and errors are were fitted to a Schechter function (Schechter 1976): coupled. In order to avoid this effect, we computed the φ(mV)=φ∗×[100.4(m∗−mV)]α+1e−100.4(m∗−mV). (1) dDwwaarrfftgoalgaixainetsrwaetiroe (dDefi/nGe)dinasAt2h1o5se1 hfraovmingthmeaLgFniittusdelefs. R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 7 −18 < M < −14.15, while giants were those brighter B than M = −18. The transformation to B-band magni- B tudes was carried out using the average B−V = 0.7 for galaxies in nearby clusters in the GOLDMine database (Gavazzietal.2003).We obtaineda value of D/G= 5.13 ± 0.82 over the whole surveyed area. Errors were computed using a Monte Carlo method, generating 100 LFs uniformly distributed within the 1σ uncertainty region, and then computing the D/G for all of them. The final error was taken as the dispersion of this distribution. In the following subsections we investigate the dependence of the LF on environment within the cluster. 4.1. Radial Analysis of the LF The dependence of the LF on the cluster region has been Fig.6.Top:dwarftogiantratio(D/G)vs.projectedclus- studiedbyseveralauthors,mainlyfornearbyclusters(but tercentric distance. Errors were computed by a Monte see Andreon 2001 and Pracy et al. 2004 for this kind of Carlo method. Bottom: Radial surface density of dwarf study at intermediate redshift clusters). The pioneering (solid + diamonds) and giant galaxies (dotted + trian- work of Lugger (1989) shows that the faint-end of the gles). Note that the increasingD/Gas we move outwards LF tends to be flatter in high-density regions than in in the cluster is due to a more rapid decreasein the giant low-density regions. More recently, various authors have population, while dwarf galaxies show a more extended claimed the faint-end slope is steeper as we move out- distribution. wards within the cluster than in the inner regions (e.g. Sabatini et al. 2003 for Virgo, Beijersbergen et al. 2002 and Iglesias-Páramo et al. 2003 for Coma). Independent theupperpanelofFig.6,wheretheaforementionedtrend studies (Aguerri et al. 2004) have shown that the core of increasing D/G ratio as we move outwards within the of the Coma Cluster is indeed dwarf-depleted when com- cluster is apparent. In order to determine the origin of pared with the outer regions, giving rise to the observed this increase, we analysed the radial density profiles of steepening. the dwarf andgiantpopulations within A2151.The lower We therefore wanted to explore this trend in A2151. panelofFig.6showsthatthe variationismainlydue toa For this purpose,we dividedour areainfour differentan- morerapidradialdecreaseinthegiantpopulation(dotted nuli from inside the core radius, r , to outside the virial line + triangles),while dwarfgalaxies(solid+ diamonds) c radius,r (0.24h−1 Mpcand1.5h−1 Mpc respectively,see present a more extended distribution (flatter profile). It v Girardi et al. 1998) and computed their LFs. As the X- is also clear from Fig. 6 that in the core of A2151, dwarf ray emission from the cluster shows a very irregular and galaxies follow the same behaviour as the giant popula- bumpy structure, the cluster centre was assumed coinci- tion so that it appears not to be dwarf-depleted. Lugger dent with the optical centre of mass (α = 16h05m26s, (1989) studies the radial dependence of the LF in A2151 δ =17o47′50′′) derived by Tarenghi et al. (1980). A sum- by computing it in different annuli out to 1.2 Mpc from maryoftheresultsislistedinTable2,whereitcanbeseen the cluster centre. She finds that all LFs were consistent thatthereisatendencyofincreasingfaint-endslopeaswe withthatoftheglobalcluster,sothatnosignificantvaria- move outwards in the cluster. However, the large uncer- tionwasevident.Herresultiseasilyunderstoodifwetake tainties in the α parameter do not allow us to claim this into account that we are only able to establish a trend of trend with significance. It is worth noticing that the M∗ increasing D/G despite of reaching much deeper magni- parameter is highly unconstrained in both the innermost tudes. and outermost annuli, showing that these LFs are better described with an exponential function rather than with 4.2. D/G ratio as a function of local galaxy density a Schechter one. Because of the limited statistics (small area covered), the number counts of background objects Phillipsetal.(1998)pointedouttheexistenceofarelation becomealmostequaltoA2151countsinthemostexternal between the population of dwarf galaxies in a cluster and region,sothattheLFsintheoutermostannulisufferfrom the local density, analogous to the morphology–density smallnumberstatistics,leadingtolargeerrorsinslopede- relationestablishedforbrightgalaxiesbyDressler(1981). termination.Thesecasesarewherenon-parametricalesti- Thisrelationimpliesthatdwarfgalaxiesaremorecommon mation of the D/G ratio provides a more robust study of in lower density environments, and is valid for both local luminosity segregation. and medium redshift galaxy clusters (Pracy et al. 2004). We computed the radial dependence of the D/G ratio We computed the D/G ratio as a function of the pro- inthesefourannuliasinSection4.Theresultisplottedin jected local density (ρ) for A2151 (see Fig. 7). The D/G 8 R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 Fig.7.Dwarftogiantratioasafunctionoftheprojected local bright galaxy density. The data were binned in ρ to show the relation more clearly. werecalculatedby computing the numberofdwarfgalax- ies within a circle of radius equal to the distance to the 10thnearestgiant(bright)galaxy.Giantanddwarfgalax- ies were defined as in Section4. The areasfor the compu- tationofρwerecalculatednumericallyinordertotakethe gaps and overlapping regions in the mosaic into account. Field subtraction was performed using the counts in the SA107 backgroundfield. It is to be noted from Fig. 7 that the projected local density in A2151 is not as large as in other nearby rich clusters suchas Coma (Trujillo etal. 2002).However,our data cover a wide local density range,reaching the outermost regions of the cluster where densities are very low. Figure7alsoshowsthatthedwarfgalaxydensityrelation is only marginal in A2151, with dwarf galaxies slightly more numerous at lower densities. This relation is as significant as that derived by Phillips et al. (1998), but not ascleanasthe onerecentlyderivedbyPracyetal.(2004) for A2218. 4.3. Subclustering In Fig. 9 we show the X-ray map of the central part of A2151as observedwith ROSAT(grey-scaledistribution), togetherwiththeluminosity-weightedgalaxydensitycon- Fig.8. LF of galaxies in each of the subclusters (North tours(figuretakenfromHuang &Sarazin1996).Thisfig- to south from top to bottom). Solid lines are best-fit ureclearlyshowsthatA2151exhibitssubstantialsubclus- Schechter functions, while the faint-end slope has also tering with at least three distinct subclusters identified beenfitted toanexponentialfunction(dashed lines).The in the dynamical analysis of BDB. In our mapping, we insets show the 1, 2 and 3σ contour levels for the best- covertwoofthem(A2151NandA2151C,seeFig.9)while fitting Schechter parameters. A2151Eisoutofoursurvey.However,ascanbeseenfrom the luminosity-weightedgalaxydensitycontours,a fourth overdensity(namely A2151S)seems to exist in the south- the small squares (dashed and dotted lines) in Fig. 9 in ernmostregionofthe cluster,thoughitwasnotidentified order to look for variations among the subclusters. as a distinct entity by the KMM algorithm of BDB. The results of such analysis are shown in Table 3 and As we haveshownthatthe radialLF steepens slightly in Figure 8. We find that there is a tendency towards in the outer regions, we computed the LFs of A2151N, α increasing from the northern to the southern subclus- A2151C and (partly) A2151S in the areas delimited by ter, although this difference is less significant than 2σ R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 9 Fig.9.X-rayemissionfromA2151(grey-scaledistribution)plottedtogetherwithgalaxydensitycontours(takenfrom Huang& Sarazin1996),showingthe significantsubstructurepresentinthis cluster.The LFpresentedinthis paperis computed in the region within the solid lines, while the smaller squares (dashed and dotted lines) indicate the areas where subclusters’ LF were computed. ∗ (see Fig. 10). From this figure it is also evident that M TheglobalLFofgalaxiesintheclusterexhibitsanon- is highly unconstrained in A2151N and A2151S, which flat faint-end slope (α = −1.29). This is not in line with means that an exponential law provides a better descrip- recent results by Valotto et al. (2004), who claim that tion of their LFs. With respect to the central subcluster, clusters with significant X-ray emission (that of A2151 or its LF presents parameters similar to those of the global greater) present flat LFs (α ≃ −1) while steeper slopes LF,revealingthatA2151Cmightbeitsmajorcontributor. are due to projection effects in non X-ray emitting clus- As for the radial LFs, we computed the D/G ratio in ters. In the literature there are few measurements of the the three subclusters to confirm that A2151S shows the LF of cluster galaxies in the V-band. It is important to largestratio of all of them (see Table 3). A more detailed compare results from the same bandpass,because the pa- inspection of its LF points out that the cause of this en- rameters of the LF are known to change with wavelength hancementisanincreaseinthepopulationoffaintgalaxies (Beijersbergen et al. 2002). Considering clusters in the inthesouthernmostsubclusterwithrespecttotheothers. nearby Universe, Lobo et al. (1997) study the V-band LF in the central part of Coma, and find a faint-end slope α =−1.59,significantlysteeper thanour value for V A2151. However, this result has been challenged recently 5. Discussion and conclusions by other authors (Beijersbergen et al. 2002 ; Iglesias- Pa´ramo et al. 2003; Mobasher et al. 2003). At interme- We studied the LF of galaxies in A2151 following four diate redshift, Mercurio et al. (2003) analyse the LF of different approaches:the analysis of the globalLF, its ra- ABCG209 at z = 0.21 and find α = −1.20, which is R dialvariation,andthedependencewithsubclusteringand local density. 10 R. Sánchez-Janssen et al.: The V-bandluminosity function of galaxies in A2151 The LFs of the three studied subclusters present dissimilar values of α. Although this difference is only marginally significant (less than 2σ), there is a trend of the faint-end slope to increase from the northern to the southern subcluster, where faint galaxies are more abun- dant than in the other two subclusters. Weplantoextendthisstudyinthefuturetotherestof the Hercules Supercluster, where the environment should clearly reveal its influence. The combination of this data with morphologiesand velocities for cluster members will helpustoshedlightontheevolutionarystatusofgalaxies within the Supercluster. Acknowledgements. This work has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Fig.10. 68%and95%confidencecontoursforthebest-fit Institute of Technology, under contract with the National SchechterparametersofA2151N(dotted),A2151C(solid) Aeronautics and Space Administration. The INT is operated andA2151S(dashed). It canbe seenthatthe characteris- on the island of La Palma by the ING group, in the Spanish ∗ Observatorio del Roque de Los Muchachos of the Instituto de ticmagnitudeM ishighlyunconstrainedinthenorthern Astrof´ısica de Canarias. This work has made use of the ING and southern subclusters. The crosses mark the best-fit dataarchiveinCambridge andoftheINGserviceprogramme values in each region. at ORM. This paper has been funded by the Spanish DGES, grant AYA2001-3939. RSJ acknowledges support from the Academia Canaria deCiencias. consistent with the value presented in this paper.7 In an- otherrecentpaper,Pracyetal.(2004)computethe LFof References the z = 0.18 cluster A2218, finding a somewhat steeper slope of α = −1.38, still compatible with ours within the Aguerri, J. A. L., Balcells, M., & Peletier, R. F. 2001, A&A, errors.Indeed, comparisons of LFs of clusters at different 367, 428 redshifts and distinct evolutionary states raise the prob- Aguerri,J.A.L.,Iglesias-Paramo,J.,Vilchez,J.M.,&Munõz- lem of the possible evolution in time of galaxies in the Tun˜ón, C. 2004, AJ, 127, 1344 cluster, but we simply intend to point out that the val- Andreon,S. & Cuillandre, J.-C. 2002, ApJ, 569, 144= ues presented in this paper are similar, within the errors, Andreon,S. 2001, ApJ, 547, 623 Arnouts,S.,deLapparent,V.,Mathez,G.,Mazure,A.,Mellier, to those found for other clusters in different globalcondi- Y., Bertin, E., & Kruszewski, A. 1997, A&AS,124, 163 tions. Barazza,F.D.,Binggeli,B.,&Jerjen,H.2003,A&A,407,121 The radial LF of A2151 shows a trend of increasing Barmby,P. & Huchra,J. P. 1998, ApJ,115, 6B faint-endslopeaswemoveoutwardsinthecluster.Similar Beijersbergen, M., Hoekstra, H., van Dokkum, P. G., & van results were obtained in other clusters, where the slope derHulst, T. 2002, MNRAS,329, 385 increases even more significantly towards the outermost Bekki, K., Couch, W. J., & Shioya, Y.2001, PASJ,53, 395 regions (Sabatini et al. 2003; Andreon 2001; Mercurio et Bekki, K., Couch, W. J., & Shioya, Y.2002, ApJ,577, 651 al.2003;Beijersbergenet al.2002).This has usuallybeen Benson,A.J.,Bower,R.G.,Frenk,C.S.,Lacey,C.G.,Baugh, explained as dwarf galaxies being destroyed in the inner C. M., & Cole, S. 2003, ApJ, 599, 38 partsoftheclusters,thoughitisimportanttonoticethat Bertin, E. & Arnouts,S. 1996, A&A,117, 393 α (or the D/G ratio)can vary due to changes both in the Binggeli, B. & Jerjen, H.1998, A&A,333, 17 dwarf or/and giant population. We have therefore com- Binggeli, B., Sandage, A.,&Tammann, G.A.1988, ARA&A, putedthenumberofdwarfandgiantgalaxiesasafunction 26, 509 Bird, C. M., Davis, D.S., & Beers, T. C. 1995, AJ, 109, 920 of the projected radial distance to the centre of A2151. Cardelli,J.A.,Clayton,G.C.,&Mathis,J.S.1989,ApJ,345, The dwarf galaxy population in A2151 has a more ex- 245 tended distribution than giant galaxies, resulting in an Casertano, S., Ratnatunga, K. U., Griffiths, R. E., Im, M., increase of the D/G ratio as we move outwards. Neuschaefer, L. W., Ostrander, E. J., & Windhorst, R. A. Alternatively,weinvestigatedtherelationbetweenthe 1995, ApJ, 453, 599 D/Gratioandtheprojectedlocalgiantgalaxydensity.As Chincarini, G., Thompson, L. A., & Rood, H. J. 1981, ApJ, expected,wefoundthatA2151hasmoredwarfgalaxiesin 249, L47 the lower density environments,but this relation is found deBlok,W.J.G.,vanderHulst,J.M.,&Bothun,G.D.1995, to be only marginal. MNRAS,274, 235 De Propris, R.,et al. 2003, MNRAS,342, 725 7 Itshouldbenoticedthatatz∼0.2therest-frameV-band Dickey,J. M. 1997, AJ, 113, 1939 is redshifted almost to R. Dressler, A. 1980, ApJ, 236, 351