arXiv subjects

Jeremy L. Tinker

Publications and source records attributed to Jeremy L. Tinker.

At least 109 records · Page 6Linked to original sources

arXiv2010

The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests

We measure the clustering of dark matter halos in a large set of collisionless cosmological simulations of the flat LCDM cosmology. Halos are identified using the spherical overdensity algorithm, which finds the mass around isolated peaks in the density field such that the mean density is Delta times the background. We calibrate fitting functions for the large scale bias that are adaptable to any value of Delta we examine. We find a ~6% scatter about our best fit bias relation. Our fitting functions couple to the halo mass functions of Tinker et. al. (2008) such that bias of all dark matter is normalized to unity. We demonstrate that the bias of massive, rare halos is higher than that predicted in the modified ellipsoidal collapse model of Sheth, Mo, & Tormen (2001), and approaches the predictions of the spherical collapse model for the rarest halos. Halo bias results based on friends-of-friends halos identified with linking length 0.2 are systematically lower than for halos with the canonical Delta=200 overdensity by ~10%. In contrast to our previous results on the mass function, we find that the universal bias function evolves very weakly with redshift, if at all. We use our numerical results, both for the mass function and the bias relation, to test the peak-background split model for halo bias. We find that the peak-background split achieves a reasonable agreement with the numerical results, but ~20% residuals remain, both at high and low masses.

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arXiv2010

An Empirical Characterization of Extended Cool Gas Around Galaxies Using MgII Absorption Features

We report results from a survey of MgII absorbers in the spectra of background QSOs that are within close angular distances to a foreground galaxy at z<0.5, using the Magellan Echellette Spectrograph. We have established a spectroscopic sample of 94 galaxies at a median redshift of = 0.24 in fields around 70 distant background QSOs (z_QSO>0.6), 71 of which are in an 'isolated' environment with no known companions and located at rho <~ 120 h^-1 kpc from the line of sight of a background QSO. The rest-frame absolute B-band magnitudes span a range from M_B-5log h=-16.4 to M_B-5log h=-21.4 and rest-frame B_AB-R_AB colors range from B_AB-R_AB~0 to B_AB-R_AB~1.5. Of these 'isolated' galaxies, we find that 47 have corresponding MgII absorbers in the spectra of background QSOs and rest-frame absorption equivalent width W_r(2796)=0.1-2.34 A, and 24 do not give rise to MgII absorption to sensitive upper limits. Our analysis shows that (1) Wr(2796) declines with increasing distance from 'isolated' galaxies but shows no clear trend in 'group' environments; (2) more luminous galaxies possess more extended MgII absorbing halos with the gaseous radius scaled by B-band luminosity according to R_gas=75x(L_B/L_B*)^(0.35+/-0.03) h^{-1} kpc; (3) there is little dependence between the observed absorber strength and galaxy intrinsic colors; and (4) within R_gas, we find a mean covering fraction of ~70% for absorbers of Wr(2796)>=0.3 A and ~80% for absorbers of Wr(2796)>=0.1 A. The lack of correlation between Wr(2796) and galaxy colors suggests a lack of physical connection between the origin of extended MgII halos and recent star formation history of the galaxies. Finally, we discuss the total gas mass in galactic halos as traced by MgII absorbers. We also compare our results with previous studies.

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arXiv2009

On the Redshift Evolution of MgII Absorption Systems

We use a halo occupation approach to connect MgII absorbers to dark matter halos as a function of redshift. Using the model constructed in Tinker & Chen (2008), we parameterize the conditional probability of an absorber of equivalent width Wr being produced by a halo of mass M_h at a given redshift, P(Wr|M_h,z). We constrain the free parameters of the model by matching the observed statistics of MgII absorbers: the frequency function f(Wr), the redshift evolution n(z), and the clustering bias b(Wr). The redshift evolution of Wr>1 A absorbers increases from z=0.4 to z=2, while the total halo cross section decreases monotonically with redshift. This discrepancy can only be explained if the gaseous halos evolve with respect to their host halos. We make predictions for the clustering bias of absorbers as a function of redshift under different evolutionary scenarios, eg, the gas cross section per halo evolves or the halo mass scale of absorbers changes. We demonstrate that the relative contribution of these scenarios may be constrained by measurements of absorber clustering at z>1 and z~0.1. If we further assume a redshift-independent mass scale for efficient shock heating of halo gas of Mcrit = 10^{11.5} Msol/h, absorber evolution is predominantly caused by a changing halo mass scale of absorbers. Our model predicts that strong absorbers always arise in ~Mcrit halos, independent of redshift, but the mass scale of weak absorbers decreases by 2 dex from 0<z<2. Thus, the measured anti-correlation of clustering bias and Wr should flatten by z~1.5.

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arXiv2009

What Does Clustering Tell Us About the Buildup of the Red Sequence?

We analyze the clustering of red and blue galaxies from four samples spanning a redshift range of 0.4<z<2.0 to test the various scenarios by which galaxies evolve onto the red sequence. The data are taken from the UKIDSS Ultra Deep Survey, DEEP2, and COMBO-17. The use of clustering allows us to determine what fraction of the red sequence is made up of central galaxies and satellite galaxies. At all redshifts, including z=0, the data are consistent with ~60% of satellite galaxies being red or quenched, implying that ~1/3 of the red sequence is comprised of satellite galaxies. More than three-fourths of red satellite galaxies were moved to the red sequence after they were accreted onto a larger halo. The constant fraction of satellite galaxies that are red yields a quenching time for satellite galaxies that depends on redshift in the same way as halo dynamical times; t_Q ~ (1+z)^{-1.5}. In three of the four samples, the data favor a model in which red central galaxies are a random sample of all central galaxies; there is no preferred halo mass scale at which galaxies make the transition from star-forming to red and dead. The large errors on the fourth sample inhibit any conclusions. Theoretical models in which star formation is quenched above a critical halo mass are excluded by these data. A scenario in which mergers create red central galaxies imparts a weaker correlation between halo mass and central galaxy color, but even the merger scenario creates tension with red galaxy clustering at redshifts above 0.5. These results suggest that the mechanism by which central galaxies become red evolves from z=0.5 to z=0.

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arXiv2009

The Clustering of MgII Absorption Systems at z=0.5 and Detection of Cold Gas in Massive Halos

We measure the large-scale clustering of MgII λλ2796,2803 absorbers with respect to a population of luminous red galaxies (LRGs) at z \sim 0.5. From the cross-correlation measurements between MgII absorbers and LRGs, we calculate the mean bias of the dark matter halos in which the absorbers reside. We investigate systematic uncertainties in the clustering measurements due to the sample selection of LRGs and due to uncertainties in photometric redshifts. First, we compare the cross-correlation amplitudes determined using a it flux-limited LRG sample and a volume-limited one. The comparison shows that the relative halo bias of MgII absorbers using a flux-limited LRG sample can be overestimated by as much as \approx 20%. Next, we assess the systematic uncertainty due to photometric redshift errors using a mock galaxy catalog with added redshift uncertainties comparable to the data. We show that the relative clustering amplitude measured without accounting for photometric redshift uncertainties is overestimated by \approx 10%. After accounting for these two main uncertainties, we find a 1-σanti-correlation between mean halo bias and absorber strength that translates into a 1-σanti-correlation between mean galaxy mass and W_r(2796). The results indicate that a significant fraction of the MgII absorber population of W_r(2796)=1-1.5 Åare found in group-size dark matter halos of log M_h < 13.4, whereas absorbers of W_r(2796)>1.5 Åare seen in halos of log M_h <12.7. A larger dataset would improve the precision of the clustering measurements and the relationship between W_r and halo mass. Finally, the strong clustering of MgII absorbers down to \sim 0.3 h^{-1} Mpc indicates the presence of cool gas inside the virial radii of the halos hosting the LRGs.

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arXiv2009

Interpreting the Clustering of Distant Red Galaxies

We analyze the angular clustering of z~2.3 distant red galaxies (DRGs) measured by Quadri et al 2008. We find that, with robust estimates of the measurement errors and realistic halo occupation distribution modeling, the measured clustering can be well fit within standard halo occupation models, in contrast to previous results. However, in order to fit the strong break in w(theta) at theta=10 arcsec, nearly all satellite galaxies in the DRG luminosity range are required to be DRGs. Within this luminosity-threshold sample, the fraction of galaxies that are DRGs is ~44%, implying that the formation of DRGs is more efficient for satellite galaxies than for central galaxies. Despite the evolved stellar populations contained within DRGs at z=2.3, 90% of satellite galaxies in the DRG luminosity range have been accreted within 500 Myr. Thus, satellite DRGs must have known they would become satellites well before the time of their accretion. This implies that the formation of DRGs correlates with large-scale environment at fixed halo mass, although the large-scale bias of DRGs can be well fit without such assumptions. Further data are required to resolve this issue. Using the observational estimate that ~30% of DRGs have no ongoing star formation, we infer a timescale for star formation quenching for satellite galaxies of 450 Myr, although the uncertainty on this number is large. However, unless all non-star forming satellite DRGs were quenched before accretion, the quenching timescale is significantly shorter than z~0 estimates. Down to the completeness limit of the Quadri et al sample, we find that the halo masses of central DRGs are ~50% higher than non-DRGs in the same luminosity range, but at the highest halo masses the central galaxies are DRGs only ~2/3 of the time.

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arXiv2008

Extending Recovery of the Primordial Matter Power Spectrum

The shape of the primordial matter power spectrum Plin(k) encodes critical information on cosmological parameters. At large scales, the observable galaxy power spectrum Pobs(k) is expected to follow the shape of Plin(k), but on smaller scales the effects of nonlinearity and galaxy bias make the ratio Pobs(k)/Plin(k) scale-dependent. We develop a method that can extend the dynamic range of the Plin(k) recovery by incorporating constraints on the galaxy halo occupation distribution (HOD) from the projected galaxy correlation function wp. We devise an analytic model to calculate Pobs(k) in real-space and redshift-space. Once HOD parameters are determined by matching wp for a given cosmological model, galaxy bias is completely specified, and our analytic model predicts both the shape and normalization of Pobs(k). Applying our method to SDSS main galaxy samples, we find that the real-space Pobs(k) follows the shape of the nonlinear matter power spectrum at the 1-2% level up to k=0.2 h/Mpc. When we apply our method to SDSS LRG samples, the linear bias approximation is accurate to 5% at k<0.08 h/Mpc, but the scale-dependence of LRG bias prevents the use of linear theory at k>0.08 h/Mpc. Our HOD model prediction is in good agreement with the recent SDSS LRG Pobs(k) measurements at all measured scales (k<0.2 h/Mpc), naturally explaining the shape of Pobs(k). The "Q-model" prescription is a poor description of galaxy bias for the LRG samples, and it can lead to biased cosmological parameter estimates when measurements at k>0.1 h/Mpc are included in the analysis. We quantify the potential bias and constraints on cosmological parameters that arise from applying linear theory and Q-model fitting, and we demonstrate the utility of HOD modeling of future high precision measurements of Pobs(k) on quasi-linear scales.

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arXiv2008

The Baryon Content of Dark Matter Halos: Empirical Constraints from MgII Absorbers

We have initiated a survey of MgII 2796, 2803 absorbers near known galaxies at projected distances rho<~100 h^-1 kpc to a background QSO, in order to constrain the extent and covering fraction of Mg^+ ions around galaxies of different luminosity and mass. The current sample consists of 13 galaxy and absorber pairs and 10 galaxies that do not produce MgII absorption lines to within sensitive upper limits. The redshifts of the galaxy and absorber pairs range from z = 0.2067 to 0.892 with a median of z = 0.3818. We find that galaxies at larger impact parameters produce on average weaker MgII absorbers. This anti-correlation is substantially improved when accounting for the intrinsic luminosities of individual galaxies. In addition, there exists a distinct boundary at rho=R_gas, beyond which no MgII absorbers are found. A maximum likelihood analysis shows that the observations are best described by an isothermal density profile and a scaling relation R_gas = 91 x (L_B/L_{B_*})^(0.35 +/- 0.05) h^-1 kpc (or 69 h^-1 kpc at W(2796)=0.3 Ang) with a mean covering factor of =80-86%. Together with the scaling relation between halo mass and galaxy luminosity inferred from halo occupation studies, this scaling of R_gas indicates that gas radius is a fixed fraction of the dark matter halo radius. We compare our results with previous studies and discuss the implications of our analysis for constraining the baryon content of galactic halos and for discriminating between competing scenarios for understanding the nature of the extended gas.

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arXiv2008

The Void Phenomenon Explained

We use high-resolution N-body simulations, combined with a halo occupation model of galaxy bias, to investigate voids in the galaxy distribution. Our goal is to address the 'void phenomenon' of Peebles (2001), which presents the observed dearth of faint galaxies in voids as a challenge to the current cosmology. In our model, galaxy luminosity is determined only as a function of dark matter halo mass. With this simple assumption, we demonstrate that large, empty voids of ~15 Mpc/h in diameter are expected even for galaxies seven magnitudes fainter than L*. The predictions of our model are in excellent agreement with several statistical measures; (i) the luminosity function of galaxies in underdense regions, (ii) nearest neighbor statistics of dwarf galaxies, (iii) the void probability function of faint galaxies. In the transition between filaments and voids in the dark matter, the halo mass function changes abruptly, causing the maximum galaxy luminosity to decrease by ~5 magnitudes over a range of ~1 Mpc/h. Thus the boundary between filaments and voids in the galaxy distribution is nearly as sharp for dwarfs as for ~L* objects. These results support a picture in which galaxy formation is driven predominantly by the mass of the host dark matter halo, and is nearly independent of the larger-scale halo environment. Further, they demonstrate that LCDM, combined with a straightforward bias model, naturally explains the existence of the void phenomenon.

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arXiv2008

The Varied Fates of z~2 Star-forming Galaxies

Star-forming galaxies constitute the majority of galaxies with stellar masses >10^10 M_Sun/h^2 at z~2 and dominate the star-formation rate density of the Universe at this early epoch. It is thus critical to understand their origins, evolution, and connection to the underlying dark matter distribution. To this end, we identify the dark matter halos (including subhalos) that are likely to contain star-forming galaxies at z~2 (z2SFGs) within a large dissipationless cosmological simulation and then use halo merger histories to follow the evolution of z2SFG descendants to z~1 and z~0. The evolved halos at these epochs are then confronted with an array of observational data in order to uncover the likely descendants of z2SFGs. Though the evolved halos have clustering strengths comparable to red galaxies at z~1 and z~0, we find that the bulk of z2SFGs do not evolve into red galaxies, at either epoch. This conclusion is based primarily on the fact that the space density of z2SFGs is much higher than that of lower redshift red galaxies, even when accounting for the merging of z2SFG descendants, which decreases the number density of z2SFG descendants by at most a factor of two by z~0. Of the ~50% of z2SFGs that survive to z~0, ~70% reside at the center of z~0 dark matter halos with M>10^12 M_Sun/h. Halo occupation modeling of z~0 galaxies suggests that such halos are occupied by galaxies with M_r<-20.5, implying that these z2SFGs evolve into ``typical'' ~ L* galaxies today, including our own Galaxy. The remaining ~30% become satellite galaxies by z~0, and comparison to halo occupation modeling suggests that they are rather faint, with M_r<-19.5. (ABRIDGED)

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arXiv2008

On the Halo Occupation of Dark Baryons

We introduce a new technique that adopts the halo occupation framework for understanding the origin of QSO absorption-line systems. Our initial study focuses specifically on MgII absorbers. We construct a model of the gaseous content in which the absorption equivalent width W_r is determined by the the amount of cold gas, in the form of discrete clouds, along a sightline through a halo. The two quantities that we specify per halo in the model are (1) the mean absorption strength per unit surface mass density A_W(M), and (2) the mean covering factor kappa_g(M) of the gaseous clouds. These parameters determine the conditional probability distribution of W_r as a function of halo mass, P(W_r|M). Two empirical measurements are applied to constrain the model: (i) the absorber frequency distribution function and (ii) the W_r-dependent clustering amplitude. We find that the data demand a rapid transition in the gas content of halos at ~10^11.5 Msol/h, below which halos contain predominantly cold gas and beyond which gas becomes predominantly hot. In order to reproduce the observed overall strong clustering of the absorbers and the anti-correlation between W_r and halo mass M, roughly 5% of gas in halos up to 10^14 Msol/h is required to be cold. The gas covering factor is near unity over a wide range of halo mass, supporting that Mg II systems probe an unbiased sample of typical galaxies. We discuss the implications of our study in the contexts of mass assembly of distant galaxies and the origin of QSO absorption line systems.

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arXiv2007

Void Statistics in Large Galaxy Redshift Surveys: Does Halo Occupation of Field Galaxies Depend on Environment?

We use measurements of the projected galaxy correlation function w_p and galaxy void statistics to test whether the galaxy content of halos of fixed mass is systematically different in low density environments. We present new measurements of the void probability function (VPF) and underdensity probability function (UPF) from Data Release Four of the Sloan Digital Sky Survey, as well as new measurements of the VPF from the full data release of the Two-Degree Field Galaxy Redshift Survey. We compare these measurements to predictions calculated from models of the Halo Occupation Distribution (HOD) that are constrained to match both w_p and the space density of galaxies. The standard implementation of the HOD assumes that galaxy occupation depends on halo mass only, and is independent of local environment. For luminosity-defined samples, we find that the standard HOD prediction is a good match to the observations, and the data exclude models in which galaxy formation efficiency is reduced in low-density environments. More remarkably, we find that the void statistics of red and blue galaxies (at L ~ 0.4L_*) are perfectly predicted by standard HOD models matched to the correlation function of these samples, ruling out "assembly bias" models in which galaxy color is correlated with large-scale environment at fixed halo mass. We conclude that the luminosity and color of field galaxies are determined predominantly by the mass of the halo in which they reside and have little direct dependence on the environment in which the host halo formed. In broader terms, our results show that the sizes and emptiness of voids found in the distribution of L > 0.2L_* galaxies are in excellent agreement with the predictions of a standard cosmological model with a simple connection between galaxies and dark matter halos. (abridged)

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arXiv2006

From Galaxy-Galaxy Lensing to Cosmological Parameters

Galaxy-galaxy lensing measures the mean excess surface density DS(r) around a sample of lensing galaxies. We develop a method for combining DS(r) with the galaxy correlation function xi_gg(r) to constrain Omega_m and sigma_8, going beyond the linear bias model to reach the level of accuracy demanded by current and future measurements. We adopt the halo occupation distribution (HOD) framework, and we test its applicability to this problem by examining the effects of replacing satellite galaxies in the halos of an SPH simulation with randomly selected dark matter particles from the same halos. The difference between dark matter and satellite galaxy radial profiles has a ~10% effect on DS(r) at r<1 Mpc/h. However, if radial profiles are matched, the remaining impact of individual subhalos around satellite galaxies and environmental dependence of the HOD at fixed halo mass is <5% in DS(r) for 0.1 2 Mpc/h, but it fails at the 30-50% level on smaller scales. The scaling of DS(r) ~ Omega_m^a(r) sigma_8^b(r) approaches the linear bias expectation a=b=1 at r>10 Mpc/h, but a(r) and b(r) vary from 0.8 to 1.6 at smaller r. We calculate a fiducial DS(r) and scaling indices a(r) and b(r) for two SDSS galaxy samples; galaxy-galaxy lensing measurements for these samples can be combined with our predictions to constrain Omega_m and sigma_8.

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arXiv2006

Redshift-Space Distortions with the Halo Occupation Distribution II: Analytic Model

We present an analytic model for the galaxy two-point correlation function in redshift space. The model is constructed within the framework of the Halo Occupation Distribution (HOD), which quantifies galaxy bias on linear and non- linear scales. We model one-halo pairwise velocities by assuming that satellite galaxy velocities follow a Gaussian distribution with dispersion proportional to the virial dispersion of the host halo. Two-halo velocity statistics are a combination of virial motions and host halo motions. The velocity distribution function (DF) of halo pairs is a complex function with skewness and kurtosis that vary substantially with scale. Using a series of collisionless N-body simulations, we demonstrate that the shape of this DF is determined primarily by the distribution of local densities around a halo pair, and at fixed density the velocity DF is close to Gaussian and nearly independent of halo mass. We calibrate a model for the conditional probability function of densities around halo pairs on these simulations. With this model, the full shape of the halo velocity DF can be accurately calculated as a function of halo mass, radial separation, angle, and cosmology. The HOD approach to redshift-space distortions utilizes clustering data from linear to non-linear scales to break the standard degeneracies inherent in previous models of redshift-space clustering. The parameters of the occupation function are well constrained by real-space clustering alone, separating constraints on bias and cosmology. We demonstrate the ability of the model to separately constrain Omega_m, sigma_8, and galaxy velocity bias in models that are constructed to have the same value of beta at large scales as well as the same finger-of-god distortions at small scales. [Abridged]

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arXiv2006

On the Luminosity Dependence of the Galaxy Pairwise Velocity Dispersion

(Abridged) We make predictions for the pairwise velocity dispersion (PVD) of galaxies with models that are constrained to match the projected correlation function and luminosity function of galaxies in the Two-Degree Field Galaxy Redshift Survey (2dFGRS). We use these data to constrain the halo occupation distribution (HOD), then calculate the PVD by populating the halos of a high resolution N-body simulation. We examine the luminosity and scale dependence of the predicted PVD. At r<1 Mpc/h and r>3 Mpc/h, we find that the PVD decreases with increasing galaxy luminosity. This result is mostly driven by the fraction of satellite galaxies f_sat, which is well-constrained by the correlation function. We find f_sat~25% for galaxies fainter than L_star, while for brighter galaxies the satellite fraction rapidly declines, creating the decrease in the PVD with luminosity. At r=1 Mpc/h, the PVD has no dependence on luminosity because satellite galaxies dominate the statistics for all objects. Recent measurements of the PVD in Fourier space using the "dispersion model" have reported a strong decline in PVD with increasing luminosity at k=1 h/Mpc. We test this method with our HOD models, finding that there is no consistent comparison between the PVD at a given k and the true dispersion at a given value of r. This results in a luminosity dependence in k-space that is stronger than in configuration space. The luminosity dependence of the HOD results in Fourier space are consistent with those measured at k=1 h/Mpc; thus the recent measurements of the PVD are fully explainable in the context of halo occupation models. The normalization of the PVD is lower than predicted by our fiducial model, and reproducing it requires a lower value of Omega_m (~0.2 instead of 0.3), a lower value of sigma_8 (~0.7 instead of 0.9), or strong velocity bias.

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arXiv2006

Cosmic Voids and Galaxy Bias in the Halo Occupation Framework

(Abridged) We investigate the power of void statistics to constrain galaxy bias and the amplitude of dark matter fluctuations. We use the halo occupation distribution (HOD) framework to describe the relation between galaxies and dark matter. After choosing HOD parameters that reproduce the mean space density n_gal and projected correlation function w_p measured for galaxy samples with M_r<-19 and M_r<-21 from the Sloan Digital Sky Survey (SDSS), we predict the void probability function (VPF) and underdensity probability function (UPF) of these samples by populating the halos of a large, high-resolution N-body simulation. If we make the conventional assumption that the HOD is independent of large scale environment at fixed halo mass, then models constrained to match n_gal and w_p predict nearly identical void statistics, independent of the scatter between halo mass and central galaxy luminosity or uncertainties in HOD parameters. Models with sigma_8=0.7 and sigma_8=0.9 also predict very similar void statistics. However, the VPF and UPF are sensitive to environmental variations of the HOD in a regime where these variations have little impact on w_p. For example, doubling the minimum host halo mass in regions with large scale (5 Mpc/h) density contrast delta<-0.65 has a readily detectable impact on void probabilities of M_r<-19 galaxies, and a similar change for delta<-0.2 alters the void probabilities of M_r<-21 galaxies at a detectable level. The VPF and UPF provide complementary information about the onset and magnitude of density- dependence in the HOD. By detecting or ruling out HOD changes in low density regions, void statistics can reduce systematic uncertainties in the cosmological constraints derived from HOD modeling, and, more importantly, reveal connections between halo formation history and galaxy properties.

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arXiv2005

On the Mass-to-Light Ratio of Large Scale Structure

We examine the dependence of the mass-to-light (M/L) ratio of large-scale structure on cosmological parameters, in models that are constrained to match observations of the projected galaxy correlation function w(rp). For a sequence of cosmological models with a fixed P(k) shape and increasing normalization \sig8, we find parameters of the galaxy halo occupation distribution (HOD) that reproduce SDSS measurements of w(rp) as a function of luminosity. Using these HOD models we calculate mean M/L ratios as a function of halo mass and populate halos of N-body simulations to compute M/L in larger scale environments, including cluster infall regions. For all cosmological models, the M/L ratio in high mass halos or high density regions is approximately independent of halo mass or smoothing scale. However, the "plateau" value of M/L depends on \sig8 as well as Ω_m, and it represents the universal mass-to-light ratio only for models in which the galaxy correlation function is approximately unbiased, i.e., with \sig8 ~ \sig8_gal. Our results for cluster mass halos follow the trend M/L = 577(Ω_m/0.3)(\sig8/0.9)^{1.7} h Msun/Lsun. Combined with Carlberg et al.'s (1996) mean M/L ratio of CNOC galaxy clusters, this relation implies (\sig8/0.9)(Ω_m/0.3)^{0.6} = 0.75 +/- 0.06. M/L ratios of clusters from the SDSS and CAIRNS surveys yield similar results. This constraint is inconsistent with parameter values Ω_m ~ 0.3, \sig8 ~ 0.9 favored by recent joint analyses of CMB measurements and other large-scale structure data. We discuss possible resolutions, none of which seems entirely satisfactory. Appendices present an improved formula for halo bias factors and an improved analytic technique for calculating the galaxy correlation function from a given cosmological model and HOD. (Abridged)

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arXiv2005

Redshift-Space Distortions with the Halo Occupation Distribution I: Numerical Simulations

We show how redshift-space distortions of the galaxy correlation function or power spectrum can constrain the matter density parameter Omega_m and the linear matter fluctuation amplitude sigma_8. We improve on previous treatments by adopting a fully non-linear description of galaxy clustering and bias, which allows us to break parameter degeneracies by combining large-scale and small- scale distortions. We consider different combinations of Omega_m and sigma_8 and find parameters of the galaxy halo occupation distribution (HOD) that yield nearly identical galaxy correlation functions in real space. We use these HOD parameters to populate the dark matter halos of large N-body simulations, from which we measure redshift-space distortions on small and large scales. We include a velocity bias parameter alpha_v that allows the velocity dispersions of satellite galaxies in halos to be systematically higher or lower than those of dark matter. Large-scale distortions are determined by the parameter combination beta = Omega_m^{0.6}/b_g, where b_g is the galaxy bias, in agreement with linear theory. However, linear theory does not accurately describe the distortions themselves on scales accessible to our simulations. We provide fitting formulas to estimate beta from the redshift-space correlation function or power spectrum, and we show that these formulas are significantly more accurate than those in the existing literature. On small scales, the ``finger-of-god'' distortions at projected separations ~0.1 Mpc/h depend on Omega_m*alpha_v^2 but are independent of sigma_8, while at intermediate separations they depend on sigma_8 as well. One can thus use redshift-space distortions over a wide range of scales to separately determine Omega_m, sigma_8, and alpha_v. (Abridged)

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