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Register a new userMass Function of Rich Galaxy Clusters and Its Constraint on sigma_8
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The mass function of galaxy clusters is a powerful tool to constrain cosmological parameters, e.g., the mass fluctuation on the scale of 8 h^{-1} Mpc, sigma_8, and the abundance of total matter, Omega_m. We first determine the scaling relations between cluster mass and cluster richness, summed r-band luminosity and the global galaxy number within a cluster radius. These relations are then used to two complete volume-limited rich cluster samples which we obtained from the Sloan Digital Sky Survey (SDSS). We estimate the masses of these clusters and determine the cluster mass function. Fitting the data with a theoretical expression, we get the cosmological parameter constraints in the form of sigma_8(Omega_m/0.3)^{alpha}=beta and find out the parameters of alpha=0.40-0.50 and beta=0.8-0.9, so that sigma_8=0.8-0.9 if Omega_m=0.3. Our sigma_8 value is slightly higher than recent estimates from the mass function of X-ray clusters and the Wilkinson Microwave Anisotropy Probe (WMAP) data, but consistent with the weak lensing statistics.
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We present the analysis of the galaxy stellar mass function in different environments at intermediate redshift (0.3<z<0.8) for two mass-limited galaxy samples. We use the IMACS Cluster Building Survey (ICBS), at masses M_ast >10^(10.5) M_sun, to study cluster, group, and field galaxies at z=0.3-0.45, and the ESO Distant Cluster Survey (EDisCS), at masses M_ast > 10^(10.2) M_sun, to investigate cluster and group galaxies at z=0.4-0.8. Therefore, in our analysis we include galaxies that are slightly less massive than the Milky Way. Having excluded the brightest cluster galaxies, we show thatthe shape of the mass distribution does not seem to depend on global environment. Our two main results are: (1) Galaxies in the virialized regions of clusters, in groups, and in the field follow a similar mass distribution. (2) Comparing both ICBS and EDisCS mass functions to mass functions in the local Universe, we find evolution from z~0.4-0.6 to z~0.07. The population of low-mass galaxies has proportionally grown with time with respect to that of massive galaxies. This evolution is independent of environment -- the same for clusters and the field. Furthermore, considering only clusters, we find that no differences can be detected neither within the virialized regions, nor when we compare galaxies within and outside the virial radius. Subdividing galaxies in terms of color, in clusters, groups, and field red and blue galaxies are regulated by different mass functions, but comparing separately the blue and red mass functions in different environments, no differences are detected in their shape.
We investigate potential systematic effects in constraining the amplitude of primordial fluctuations sigma_8 arising from the choice of halo mass function in the likelihood analysis of current and upcoming galaxy cluster surveys. We study the widely used N-body simulation fit of Tinker et al. (T08) and, as an alternative, the recently proposed analytical model of Excursion Set Peaks (ESP). We first assess the relative bias between these prescriptions when constraining sigma_8 by sampling the ESP mass function to generate mock catalogs and using the T08 fit to analyse them, for various choices of survey selection threshold, mass definition and statistical priors. To assess the level of absolute bias in each prescription, we then repeat the analysis on dark matter halo catalogs in N-body simulations designed to mimic the mass distribution in the current data release of Planck SZ clusters. This N-body analysis shows that using the T08 fit without accounting for the scatter introduced when converting between mass definitions (alternatively, the scatter induced by errors on the parameters of the fit) can systematically over-estimate the value of sigma_8 by as much as 2sigma for current data, while analyses that account for this scatter should be close to unbiased in sigma_8. With an increased number of objects as expected in upcoming data releases, regardless of accounting for scatter, the T08 fit could over-estimate the value of sigma_8 by ~1.5sigma. The ESP mass function leads to systematically more biased but comparable results. A strength of the ESP model is its natural prediction of a weak non-universality in the mass function which closely tracks the one measured in simulations and described by the T08 fit. We suggest that it might now be prudent to build new unbiased ESP-based fitting functions for use with the larger datasets of the near future.
We present a full description of the N-probability density function of the galaxy number density fluctuations. This N-pdf is given in terms, on the one hand, of the cold dark matter correlations and, on the other hand, of the galaxy bias parameter. The method relies on the assumption commonly adopted that the dark matter density fluctuations follow a local non-linear transformation of the initial energy density perturbations. The N-pdf of the galaxy number density fluctuations allows for an optimal estimation of the bias parameter (e.g., via maximum-likelihood estimation, or Bayesian inference if there exists any a priori information on the bias parameter), and of those parameters defining the dark matter correlations, in particular its amplitude ($sigma_8$). It also provides the proper framework to perform model selection between two competitive hypotheses. The parameters estimation capabilities of the N-pdf are proved by SDSS-like simulations (both ideal log-normal simulations and mocks obtained from Las Damas simulations), showing that our estimator is unbiased. We apply our formalism to the 7th release of the SDSS main sample (for a volume-limited subset with absolute magnitudes $M_r leq -20$). We obtain $hat{b} = 1.193 pm 0.074$ and $hat{sigma_8} = 0.862 pm 0.080$, for galaxy number density fluctuations in cells of a size of $30h^{-1}$Mpc. Different model selection criteria show that galaxy biasing is clearly favoured.
We derive cosmological constraints on the matter density, om, and the amplitude of fluctuations, sig, using $mathtt{GalWCat19}$, a catalog of 1800 galaxy clusters we identified in the Sloan Digital Sky Survey-DR13 spectroscopic data set using our GalWeight technique to determine cluster membership citep{Abdullah18,Abdullah19}. By analyzing a subsample of 756 clusters in a redshift range of $0.045leq z leq 0.125$ and virial masses of $Mgeq 0.8times10^{14}$ hm ~with mean redshift of $z = 0.085$, we obtain om ~$=0.310^{+0.023}_{-0.027} pm 0.041$ (systematic) and sig ~$=0.810^{+0.031}_{-0.036}pm 0.035$ (systematic), with a cluster normalization relation of $sigma_8= 0.43 Omega_m^{-0.55}$. There are several unique aspects to our approach: we use the largest spectroscopic data set currently available, and we assign membership using the GalWeight technique which we have shown to be very effective at simultaneously maximizing the number of {it{bona fide}} cluster members while minimizing the number of contaminating interlopers. Moreover, rather than employing scaling relations, we calculate cluster masses individually using the virial mass estimator. Since $mathtt{GalWCat19}$ is a low-redshift cluster catalog we do not need to make any assumptions about evolution either in cosmological parameters or in the properties of the clusters themselves. Our constraints on om ~and sig ~are consistent and very competitive with those obtained from non-cluster abundance cosmological probes such as Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillation (BAO), and supernovae (SNe). The joint analysis of our cluster data with Planck18+BAO+Pantheon gives om ~$=0.315^{+0.013}_{-0.011}$ and sig ~$=0.810^{+0.011}_{-0.010}$.
The dependence of the luminosity function of cluster galaxies on the evolutionary state of the parent cluster is still an open issue, in particular as concern the formation/evolution of the brightest cluster galaxies. We plan to study the bright part of the LFs of a sample of very unrelaxed clusters (DARC clusters showing evidence of major, recent mergers) and compare them to a reference sample of relaxed clusters spanning a comparable mass and redshift range. Our analysis is based on the SDSS DR7 photometric data of ten, massive, and X-ray luminous clusters (0.2<z<0.3), always considering physical radii (R_200 or its fractions). We consider r band LFs and use the color-magnitude diagrams (r-i,r) to clean our samples as well to consider separately red and blue galaxies. We find that DARC and relaxed clusters give similar LF parameters and blue fractions. The two samples differ for their content of bright galaxies BGs, M_r<-22.5, since relaxed clusters have fewer BGs, in particular when considering the outer cluster region 0.5R_200<R<R_200 (by a factor two). However, the cumulative light in BGs is similar for relaxed and DARC samples. We conclude that BGs grow in luminosity and decrease in number as the parent clusters grow hierarchically in agreement with the BG formation by merging with other luminous galaxies.
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