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 Physics , 2013, DOI: 10.1093/mnras/stt1201 Abstract: We study the systematic bias introduced when selecting the spectroscopic redshifts of brighter cluster galaxies to estimate the velocity dispersion of galaxy clusters from both simulated and observational galaxy catalogues. We select clusters with Ngal > 50 at five low redshift snapshots from a semi-analytic model galaxy catalogue, and from a catalogue of SDSS DR8 groups and clusters across the redshift range 0.021
 Physics , 2015, DOI: 10.1093/mnras/stv1267 Abstract: It is often claimed that overdensities of (or even individual bright) submillimetre-selected galaxies (SMGs) trace the assembly of the most-massive dark matter structures in the Universe. We test this claim by performing a counts-in-cells analysis of mock SMG catalogues derived from the Bolshoi cosmological simulation to investigate how well SMG associations trace the underlying dark matter structure. We find that SMGs exhibit a relatively complex bias: some regions of high SMG overdensity are underdense in terms of dark matter mass, and some regions of high dark matter overdensity contain no SMGs. Because of their rarity, Poisson noise causes scatter in the SMG overdensity at fixed dark matter overdensity. Consequently, rich associations of less-luminous, more-abundant galaxies (i.e. Lyman-break galaxy analogues) trace the highest dark matter overdensities much better than SMGs. Even on average, SMG associations are relatively poor tracers of the most significant dark matter overdensities because of 'downsizing': at z < ~2.5, the most-massive galaxies that reside in the highest dark matter overdensities have already had their star formation quenched and are thus no longer SMGs. At a given redshift, of the 10 per cent most-massive overdensities, only ~25 per cent contain at least one SMG, and less than a few per cent contain more than one SMG.
 R. G. Carlberg Physics , 1994, DOI: 10.1086/174659 Abstract: Hierarchical gravitational clustering creates galaxies that usually do not fully share the dynamical history of an average particle in the mass field. In particular, galaxy tracers identified in numerical simulations can have individual velocity dispersions in virialized regions a factor \bvs\ lower than the dark matter. The field average of the pairwise velocity dispersion depends on the statistical weighting of collapsed regions, so that the tracer pairwise dispersion is a different factor, \bvp, times the density field value. A model of a cool equilibrium tracer population demonstrates that mass to light segregation is very sensitive to single particle velocity bias. For the $\phi=-GM/(r+a)$ potential a $\bvs=0.9$ tracer indicates a virial mass about a factor of 5 low. The likely value of \bvs\ is estimated and the simple equilibrium model is tested for applicability using a $10^6$ particle simulation of the formation of a single cluster from cosmological initial conditions. From this simulation, the value of \bvs\ is estimated as $0.8\pm0.1$. The pairwise velocity dispersion bias, \bvp, which is equal to \bvs\ augmented with any anti-bias of galaxies against high velocity dispersion clusters. The value of \bvp\ is estimated to be 15\% less than \bvs, consequently $\bvp=0.6^{+0.2}_{-0.1}$. Comparison of cluster mass and luminosity profiles at large radii is a test for the existence of single particle velocity bias. [compressed postscript file cluster.ps.Z via anonymous ftp from orca.astro.washington.edu in ~ftp/pub/hpcc, or carlberg@astro.washington.edu]
 Physics , 1999, DOI: 10.1086/309248 Abstract: We use N-body simulations to study the velocity bias of dark matter halos, the difference in the velocity fields of dark matter and halos, in a flat low- density LCDM model. The high force, 2kpc/h, and mass, 10^9Msun/h, resolution allows dark matter halos to survive in very dense environments of groups and clusters making it possible to use halos as galaxy tracers. We find that the velocity bias pvb measured as a ratio of pairwise velocities of the halos to that of the dark matter evolves with time and depends on scale. At high redshifts (z ~5) halos move generally faster than the dark matter almost on all scales: pvb(r)~1.2, r>0.5Mpc/h. At later moments the bias decreases and gets below unity on scales less than r=5Mpc/h: pvb(r)~(0.6-0.8) at z=0. We find that the evolution of the pairwise velocity bias follows and probably is defined by the spatial antibias of the dark matter halos at small scales. One-point velocity bias b_v, defined as the ratio of the rms velocities of halos and dark matter, provides a more direct measure of the difference in velocities because it is less sensitive to the spatial bias. We analyze b_v in clusters of galaxies and find that halos are hotter'' than the dark matter: b_v=(1.2-1.3) for r=(0.2-0.8)r_vir, where r_vir is the virial radius. At larger radii, b_v decreases and approaches unity at r=(1-2)r_vir. We argue that dynamical friction may be responsible for this small positive velocity bias b_v>1 found in the central parts of clusters. We do not find significant difference in the velocity anisotropy of halos and the dark matter. The dark matter the velocity anisotropy can be approximated as beta(x)=0.15 +2x/(x^2+4), where x is measured in units of the virial radius.
 Physics , 2009, DOI: 10.1088/1475-7516/2009/08/020 Abstract: On very large scales, density fluctuations in the Universe are small, suggesting a perturbative model for large-scale clustering of galaxies (or other dark matter tracers), in which the galaxy density is written as a Taylor series in the local mass density, delta, with the unknown coefficients in the series treated as free "bias" parameters. We extend this model to include dependence of the galaxy density on the local values of nabla_i nabla_j phi and nabla_i v_j, where phi is the potential and v is the peculiar velocity. We show that only two new free parameters are needed to model the power spectrum and bispectrum up to 4th order in the initial density perturbations, once symmetry considerations and equivalences between possible terms are accounted for. One of the new parameters is a bias multiplying s_ij s_ji, where s_ij=[nabla_i nabla_j \nabla^-2 - 1/3 delta^K_ij] delta. The other multiplies s_ij t_ji, where t_ij=[nabla_i nabla_j nabla^-2 - 1/3 delta^K_ij](theta-delta), with theta=-(a H dlnD/dlna)^-1 nabla_i v_i. (There are other, observationally equivalent, ways to write the two terms, e.g., using theta-delta instead of s_ij s_ji.) We show how short-range (non-gravitational) non-locality can be included through a controlled series of higher derivative terms, starting with R^2 nabla^2 delta, where R is the scale of non-locality (this term will be a small correction as long as k^2 R^2 is small, where k is the observed wavenumber). We suggest that there will be much more information in future huge redshift surveys in the range of scales where beyond-linear perturbation theory is both necessary and sufficient than in the fully linear regime.
 Physics , 2010, DOI: 10.1051/0004-6361/200913948 Abstract: When clusters of galaxies are viewed in projection, one cannot avoid picking up foreground/background interlopers (FBIs), that lie within the virial cone (VC), but outside the virial sphere. Structural & kinematic deprojection equations are not known for an expanding Universe, where the Hubble flow (HF) stretches the line-of-sight (LOS) distribution of velocities. We analyze 93 mock relaxed clusters, built from a cosmological simulation. The stacked mock cluster is well fit by an m=5 Einasto DM density profile (but only out to 1.5 virial radii [r_v]), with velocity anisotropy (VA) close to the Mamon-Lokas model with VA radius equal to that of density slope -2. The surface density of FBIs is nearly flat out to r_v, while their LOS velocity distribution shows a dominant gaussian cluster-outskirts component and a flat field component. This distribution of FBIs in projected phase space is nearly universal in mass. A local k=2.7 sigma velocity cut returns the LOS velocity dispersion profile (LOSVDP) expected from the NFW density and VA profiles measured in 3D. The HF causes a shallower outer LOSVDP that cannot be well matched by the Einasto model for any k. After this velocity cut, FBIs still account for 23% of DM particles within the VC (close to the observed fraction of cluster galaxies lying off the Red Sequence). The best-fit projected NFW/Einasto models underestimate the 3D concentration by 6+/-6% (16+/-7%) after (before) the velocity cut, unless a constant background is included in the fit. Assuming the correct mass profile, the VA profile is well recovered from the measured LOSVDP, with a slight bias towards more radial orbits in the outer regions. These small biases are overshadowed by large cluster-cluster variations caused by cosmic variance. An appendix provides an analytical approximation to the surface density, projected mass and tangential shear profiles of the Einasto model.
 Physics , 2014, DOI: 10.1103/PhysRevD.90.103529 Abstract: It has been recently shown that any halo velocity bias present in the initial conditions does not decay to unity, in agreement with predictions from peak theory. However, this is at odds with the standard formalism based on the coupled fluids approximation for the coevolution of dark matter and halos. Starting from conservation laws in phase space, we discuss why the fluid momentum conservation equation for the biased tracers needs to be modified in accordance with the change advocated in Baldauf, Desjacques & Seljak (2014). Our findings indicate that a correct description of the halo properties should properly take into account peak constraints when starting from the Vlasov-Boltzmann equation.
 Ray Carlberg Physics , 1993, Abstract: Velocity bias is a reduction of the velocity dispersion of tracer galaxies in comparison to the velocity dispersion of the underlying mass field. There are two distinct forms of velocity bias. The single particle velocity reduction, $b_v(1)$, is the result of energy loss of a tracer population, and in virialized regions, such as galaxy clusters, is intimately associated with mass segregation which together lead to cluster mass underestimates. The pairwise velocity bias, $b_v(2)$, has an additional statistical reduction if the total mass per galaxy rises with velocity dispersion of the virialized cluster. Values of the velocity bias are estimated from n-body simulations, finding $b_v(1)\simeq 0.85\pm0.1$ and $b_v(2)\simeq 0.6\pm0.2$. The value of $b_v(1)$ is relatively secure and predicts that the virial radius of the cluster light is about 20\% of the cluster mass, which can be tested with observations of cluster mass profiles beyond the apparent virial radius. The value of $b_v(2)$ is sensitive to the formation efficiency of galaxies over environments ranging from voids to rich clusters, the latter of which are not yet well resolved in simulations. An $n=1$, $\Omega=1$, COBE normalized CDM spectrum requires $b_v(2)\simeq0.20(15\mu K/Q)(\sigma_{12}/317 \kms)$ which is well below the measured range of $b_v(2)$. The pairwise velocities at 1 \hmpc\ allow $\Omega=1$ for a galaxy clustering bias near unity if $b_v(2)\simeq0.6$.
 Physics , 1996, DOI: 10.1093/mnras/290.3.566 Abstract: Analytical studies based on perturbative theory have shown that the moments of the Probability Distribution Function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter Omega in the quasi-linear regime. This dependence is particularly interesting as it does not involve the possible bias between the galaxy spatial distribution and the underlying mass distribution. This implies a new and promising method for determining a bias-independent value of Omega based on a reliable determination of the velocity divergence PDF. In this paper we study the Omega dependence of the velocity divergence PDF and its first moments in a set of N-body simulations, using the so-called Voronoi and Delaunay methods. We show that this dependence is in agreement with the theoretical prediction, even while the number density of velocity field tracers has been diluted to a value comparable to that available in current galaxy catalogues. In addition, we demonstrate that a sufficiently reliable determination of these statistical quantities is also possible when the measurement of the galaxy peculiar velocities is restricted to the one component along the line-of-sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Omega.
 Physics , 1999, DOI: 10.1086/308436 Abstract: The clustering of galaxies relative to the mass distribution declines with time because: first, nonlinear peaks become less rare events; second, the densest regions stop forming new galaxies because gas there becomes too hot to cool and collapse; third, after galaxies form, they are gravitationally debiased'' because their velocity field is the same as the dark matter. To show these effects, we perform a hydrodynamic cosmological simulation and examine the density field of recently formed galaxies as a function of redshift. We find the bias b_* of recently formed galaxies (the ratio of the rms fluctuations of these galaxies and mass), evolves from 4.5 at z=3 to around 1 at z=0, on 8 h^{-1} Mpc comoving scales. The correlation coefficient r_* between recently formed galaxies and mass evolves from 0.9 at z=3 to 0.25 at z=0. As gas in the universe heats up and prevents star formation, star-forming galaxies become poorer tracers of the mass density field. After galaxies form, the linear continuity equation is a good approximation to the gravitational debiasing, even on nonlinear scales. The most interesting observational consequence of the simulations is that the linear regression of the star-formation density field on the galaxy density field evolves from about 0.9 at z=1 to 0.35 at z=0. These effects also provide a possible explanation for the Butcher-Oemler effect, the excess of blue galaxies in clusters at redshift z ~ 0.5. Finally, we examine cluster mass-to-light ratio estimates of Omega, finding that while Omega(z) increases with z, one's estimate Omega_est(z) decreases. (Abridged)
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