CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server CLUSTERS OF GALAXIES IN THE LOCAL UNIVERSE C.S. Kochanek1, Martin White2,J.Huchra1,L.Macri1,T.H.Jarrett3, S.E. Schneider4 & J. Mader5 1 Harvard-Smithsonian Center for Astrophysics, 60 Garden St., Cambridge, MA 02138 2 Departments of Physics and Astronomy, University of California, Berkeley, CA 94720 3 Infrared Processing and Analysis Center, MS 100-22, Caltech, Pasadena, CA 91125 4 Department of Astronomy, University of Massachusetts, Amherst, MA, 01003 5 McDonald Observatory Austin, TX, 78712 email: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Draft version August 9, 2002 ABSTRACT We use a matched filter algorithm to find and study clusters in both N-body simulations artificially populated with galaxies and the 2MASS survey. In addition to numerous checks of the matched filter algorithm, we present results on the halo multiplicity function and the cluster number function. For a subset of our identified clusters we have information on X-ray temperatures and luminosities which we cross-correlate with optical richness and galaxy velocity dispersions. With all quantities normalized by the spherical radius corresponding to a mass overdensity of ∆M = 200 or the equivalent galaxy number 1 overdensity of ∆N = 200ΩM− 666, we find that the number of L>L galaxies in a cluster of mass ' ∗ M200 is 15 log N 666 =(1:44 0:17) + (1:10 0:09) log(M200h=10 M ) ∗ ± ± where the uncertainties are dominated by the scatter created by three choices for relating the observed quantities to the cluster mass. The region inside the virial radius has a K-band cluster mass-to-light ratio of (M=L)K = (116 46)h which is essentially independent of cluster mass. Integrating over all clusters ± 14 1 more massive than M200 =10 h− M , the virialized regions of clusters contain 7% of the local stellar luminosity, quite comparable to the mass fraction in such objects in currently' popular ΛCDM models. Subject headings: cosmology: theory – large-scale structure of Universe 1. INTRODUCTION function. In 5 we apply the algorithm to the 2MASS sam- ple. Finally,§ in 6 we discuss the steps which can improve Clusters of galaxies have become one of our most impor- § tant cosmological probes because they are relatively easy both the synthetic catalog and the algorithm. to discover yet have physical properties and abundances 2. DATA: REAL AND SYNTHETIC that are very sensitive to our model for the formation and evolution of structure in the universe. Of particular inter- We searched for clusters using galaxies in the 2MASS est to us, a cluster sample provides the means to study the survey (Skrutskie et al. 1997) and in simulations of the high-mass end of the halo multiplicity function, the aver- 2MASS survey. We have chosen the 2MASS survey be- age number of galaxies in a halo of mass M, which provides cause of its uniform photometry and large areal coverage, important insight into the process of galaxy formation. which makes it ideal for finding the relatively rare rich clus- In this paper we have two objectives. First, we will ters in the local neighborhood where a wealth of auxiliary demonstrate the use of a matched filter approach to find- information is available. ing clusters in a redshift survey using both synthetic cata- logs and a large sample of galaxies from the 2MASS survey 2.1. 2MASS Galaxies (Skrutskie et al. 1997, Jarrett et al. 2000). With the syn- The 2MASS survey provides J, H, K photometry of thetic data we can test the algorithm and our ability to ex- galaxies over the full sky to a limiting magnitude of tract the input halo multiplicity function from the output K < 13:75 mag (Jarrett et al. 2000). Based on the cluster catalog. Second, we will determine the halo mul- Schlegel,∼ Finkbeiner & Davis (1998) Galactic extinction tiplicity function, N(M), from the 2MASS survey. This model and the available 2MASS catalogs, we selected all study is the first phase in a bootstrapping process – based galaxies with Galactic extinction-corrected magnitudes of 1 on a synthetic catalog known to have problems matching K 12:25 mag and Galactic latitude b > 5◦. The final reality in detail we can calibrate an algorithm which when sample≤ contains a total of 90989 galaxies| | distributed over applied to the real data can supply the parameters for an 91% of the sky. The redshift measurements are 89% com- improved model of the data. Then the improved model plete for K 11:25 mag but only 36% complete between can be used to improve the algorithm and so on. 11:25 < K ≤12:25. The galaxies with redshifts are not a In 2 we describe the synthetic and real 2MASS data. random sample≤ of all of the galaxies – redshifts are more In 3§ we describe our version of the matched filter algo- likely to be of cluster than field galaxies. § rithm. In 4 we test the algorithm on the synthetic catalog, 1 2 § We use the 20 mag/arcsec circular isophotal magnitudes focusing on our ability to determine the halo multiplicity throughout the paper. 1 2 With the data corrected for Galactic extinction, the re- were ‘assigned’ to halos based on the multiplicity function. lation between apparent and absolute magnitudes is The average number of galaxies assigned to a cluster halo with a FoF mass MFoF is MK = K 5 log(DL(z)=r0) k(z)=K (z)(1) − − −D M M 0:9 where r =10pc,D (z) is the luminosity distance to N (M)= FoF +0:7max 1; FoF (4) 0 L FoF M M redshift z and k(z)= 6 log(1 + z)isthek-correction. R " B # The k-correction is negative,− independent of galaxy type, 12 1 and valid for z < 0:25 (based on the Worthey (1994) galaxies where MR =2:5 10 h− M and MB = 12 1 × models). To simplify∼ our later notation, we introduce 4:0 10 h− M based on the halo occupancy models × (z)=5log(DL(z)=r0)+k(z) as the effective distance of Scoccimarro et al. (2001) which we have modified to D modulus to the galaxy. We use an Ωmat = 1 cosmological better match the observed number densities of galaxies model for the distances and assume a Hubble constant of and the expectation that 2MASS galaxies will trace the H0 = 100h km/s Mpc. For our local sample the particular mass more faithfully than a blue selected sample. We cosmological model is unimportant. sometimes used the virial mass M200 defined as the mass Kochanek et al. (2001) derived the K-band luminosity interior to a radius r200 within which the mean density function for a subset of the 2MASS sample at comparable exceeds 200 times the critical density. The virial radius, 15 1=3 1 magnitudes. The luminosity function is described by a which scales as r200 =1:6(M200h=10 M ) h− Mpc, is Schechter function, slightly smaller than the average radius of the FoF cluster with b =0:2, so that on average M200 =0:66MFoF (me- 1+α dn L dian M200 =0:71MFoF). For massive halos the number of φ(M)= =0:4ln10 n exp( L=L )(2) galaxies actually assigned to a halo is Poisson distributed dM ∗ L − ∗ ∗ for an expectation value of NFoF. Each halo hosts a ‘cen- where MK = MK 2:5log(L=L ) and the integrated lu- tral’ galaxy which inherits the halo center of mass posi- minosity function∗ is− ∗ tion and velocity. Any additional galaxies are randomly assigned the positions and velocities of the dark matter M particles identified with the cluster by the FoF algorithm. Φ(M)= φ(M)dM = n Γ[1 + α; L=L ]: (3) ∗ ∗ In this way the satellite galaxies trace the density and ve- Z−∞ locity field of the dark matter. The parameters for the global luminosity function are n = One problem with standard halo multiplicity functions 2 3 3 ∗ (1:16 0:10) 10− h /Mpc , α = 1:09 0:06 and MK = is that they are one-dimensional functions, N(M), nor- 23:39± 0:05× using the 2MASS 20− mag/arcsec± 2 isophotal∗ malized to match a specific sample (but see Yang, Mo magnitudes.− ± This luminosity function is consistent with & van den Bosch 2002 for improvements in this regard). that derived by Cole et al. (2001). The total luminosity of Even for galaxy mass scales, current models of the halo a galaxy is approximately 1:20 0:04 times the isophotal multiplicity function lead to too few galaxies to match luminosity. ± the luminosity or velocity functions of galaxies over broad We should keep in mind that the early-type and late- ranges (see Kochanek 2001; Scoccimarro et al. 2001; Chiu, type galaxies have different luminosity functions, with the Gnedin & Ostriker 2001). For general theoretical use, early-type galaxies being brighter but less common than we need the luminosity-dependent multiplicity function, the late-type galaxies. The algorithm for finding clusters N(>LM), for the average number of galaxies more lu- | requires both a field luminosity function φf (M) and a clus- minous than L in a halo of mass M. For clusters, we ter luminosity function φc(M) which will be different be- might expect a halo multiplicity function to factor as cause of the morphology-density relation (e.g. Dressler 1980). N (M)Φc(>L)=Φc(>L)whereΦc(>L) is the inte- ∗ ∗ In our present study we assume that we can model both grated cluster luminosity function and N (M) is the mass- ∗ using the global luminosity function, φ (M)=φ (M)= dependent number of galaxies more luminous than L .In f c ∗ φ(M).