We propose a new explanation for the origin of angular momentum in galaxies and their dark halos,... more We propose a new explanation for the origin of angular momentum in galaxies and their dark halos, in which the halos obtain their spin through the cumulative acquisition of angular momentum from satellite accretion. In our model, the build-up of angular momentum is a random walk process associated with the mass assembly history of the halo's major progenitor. We assume no correlation between the angular momenta of accreted objects. Using the extended Press-Schechter approximation, we calculate the growth of mass, angular momentum, and spin parameter $\lambda$ for many halos. Our random walk model reproduces the key features of the angular momentum of halos found in N-body simulations: a lognormal distribution in $\lambda$ with an average of $<\lambda> \approx 0.04$, independent of mass and redshift. The evolution of the spin parameter in individual halos in this model is quite different from the steady increase with time of angular momentum in the tidal torque picture. We find both in N-body simulations and in our random walk model that the value of $\lambda$ changes significantly with time for a halo's major progenitor. It typically has a sharp increase due to major mergers, and a steady decline during periods of gradual accretion of small satellites. The model predicts that on average the $\lambda$ of halos which had major mergers after redshift $z=2$ should be substantially larger than the $\lambda$ of those which did not. Perhaps surprisingly, this suggests that halos that host late-forming elliptical galaxies should rotate faster than halos of spiral galaxies.
Astronomical observations strongly suggest that our universe is now accelerating and contains a s... more Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant density of dark energy), we show that astronomical structures freeze out in the near future and that the density profiles of dark matter halos approach the same general form. Every dark matter halo grows asymptotically isolated and thereby becomes the center of its own island universe. Each of these isolated regions of space-time approaches a universal geometry and we calculate the corresponding form of the space-time metric.
Standard LCDM predicts that the major merger rate of galaxy-size dark matter halos rises rapidly ... more Standard LCDM predicts that the major merger rate of galaxy-size dark matter halos rises rapidly with redshift. The average number of close companions per galaxy, Nc, is often used to infer the galaxy merger rate, however, recent observational studies suggest that Nc evolves very little with redshift. Here we use a "hybrid" N- body simulation plus analytic substructure model to predict Nc directly. We identify dark matter subhalos with galaxies and show that the observed lack of close pair count evolution arises because the high merger rate per halo at early times is counteracted by a decrease in the number of halos massive enough to host a galaxy pair. We compare our results to data compiled from the DEEP2, SSRS2, and the UZC redshift surveys. Observed pair counts match our predictions if we assume a monotonic mapping between galaxy luminosity and the maximum circular velocity that each subhalo had when it was first accreted onto its host halo. This suggests that satellite galaxies are significantly more resilient to destruction than are dissipationless dark matter subhalos. We argue that while Nc does not provide a direct measure of the halo merger rate, it offers a powerful means to constrain the Halo Occupation Distribution and the spatial distribution of galaxies within halos. Interpreted in this way, close pair counts provide a useful test of galaxy formation processes on < 100 kpc scales.
We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster c... more We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.
Monthly Notices of The Royal Astronomical Society, 2001
We discuss how current and future data on the clustering and number density of z~3 Lyman-break ga... more We discuss how current and future data on the clustering and number density of z~3 Lyman-break galaxies (LBGs) can be used to constrain their relationship to dark matter haloes. We explore a three-parameter model in which the number of LBGs per dark halo scales like a power-law in the halo mass: N(M) = (M/M_1)^S for M>M_m. Here, M_m is the minimum mass halo that can host an LBG, M_1 is a normalization parameter, associated with the mass above which haloes host more than one observed LBG, and S determines the strength of the mass dependence. We show how these three parameters are constrained by three observable properties of LBGs: the number density, the large-scale bias, and the fraction of objects in close pairs. Given these three quantities, the three unknown model parameters may be estimated analytically, allowing a full exploration of parameter space. As an example, we assume an LCDM cosmology and consider the observed properties of a recent sample of spectroscopically confirmed LBGs. We find that the favored range for our model parameters is M_m = (0.4-8)x10^10 Msun/h, M_1 = (6-10)x10^12 Msun/h, and 0.9 < S < 1.1. The preferred region in M_m expands by an order of magnitude and slightly shallower slopes are acceptable if the allowed range of bias is permitted to span all recent observational estimates. We also discuss how the observed clustering of LBGs as a function of luminosity can be used to constrain halo occupation, although due to current observational uncertainties we are unable to reach any strong conclusions. Our methods and results can be used to constrain more realistic models that aim to derive the occupation function N(M) from first principles, and offer insight into how basic physical properties affect the observed properties of LBGs.
(Abridged) We present a semi-analytic model for Cold Dark Matter halo substructure that can be us... more (Abridged) We present a semi-analytic model for Cold Dark Matter halo substructure that can be used as a framework for studying galaxy formation and an ingredient in halo models of galaxy clustering. We perform a comprehensive comparison of the model to the results of a suite of high-resolution cosmological simulations. The comparisons reveal that subhalo statistics, such as velocity and mass functions, radial distributions, and the halo occupation distributions, agree well over three orders of magnitude in host halo mass at various redshifts. Both in the simulations and in our model, the radial distributions of subhalos are significantly shallower than that of the dark matter density. The abundance of subhalos in a host is set by competition between destruction and new accretion. High mass halos and halos at high redshift tend to host more subhalos because the subhalos have, on average, been accreted more recently. Similarly, at fixed mass, halos that formed more recently host more subhalos. Observed "fossil groups" may represent an extreme tail of this correlation. We find a related correlation between host halo concentration and subhalo abundance at fixed host mass, Nsat ~ c^-a, where a changes with redshift and host-to-subhalo mass ratio. Lastly, we use our model to populate host halos in one of our high-resolution cosmological simulations, replacing the subhalos resolved in the simulation with subhalos computed according to our model. We show that the resulting 2pt correlation function of such a "hybrid" halo ensemble is indistinguishable from that measured directly in the simulation. This supports one of the key tenets of the standard halo model -- the assumption that the halo occupation distribution is statistically independent of host halo environment.
We analyze the halo occupation distribution (HOD), the probability for a halo of mass M to host a... more We analyze the halo occupation distribution (HOD), the probability for a halo of mass M to host a number of subhalos N, and two-point correlation function of galaxy-size dark matter halos using high-resolution dissipationless simulations of the concordance flat LCDM model. The halo samples include both the host halos and the subhalos, distinct gravitationally-bound halos within the virialized regions of larger host systems. We find that the first moment of the HOD, <N>(M), has a complicated shape consisting of a step, a shoulder, and a power law high-mass tail. The HOD can be described by a Poisson statistics at high halo masses but becomes sub-Poisson for <N><4. We show that the HOD can be understood as a combination of the probability for a halo of mass M to host a central galaxy and the probability to host a given number Ns of satellite galaxies. The former can be approximated by a step-like function, while the latter can be well approximated by a Poisson distribution, fully specified by its first moment <Ns>(M). We find that <Ns>~M^b with b~1 for a wide range of number densities, redshifts, and different power spectrum normalizations. This formulation provides a simple but accurate model for the halo occupation distribution found in simulations. At z=0, the two-point correlation function (CF) of galactic halos can be well fit by a power law down to ~100/h kpc with an amplitude and slope similar to those of observed galaxies. At redshifts z>~1, we find significant departures from the power-law shape of the CF at small scales. If the deviations are as strong as indicated by our results, the assumption of the single power law often used in observational analyses of high-redshift clustering is likely to bias the estimates of the correlation length and slope of the correlation function.
We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model ... more We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model the observed luminosity dependence and evolution of galaxy clustering through most of the age of the universe, from z~5 to z~0. We use a simple, non-parametric model which monotonically relates galaxy luminosities to the maximum circular velocity of dark matter halos (V_max) by preserving the observed galaxy luminosity function in order to match the halos in simulations with observed galaxies. The novel feature of the model is the use of the maximum circular velocity at the time of accretion, V_max,acc, for subhalos, the halos located within virial regions of larger halos. We argue that for subhalos in dissipationless simulations, V_max,acc reflects the luminosity and stellar mass of the associated galaxies better than the circular velocity at the epoch of observation, V_max,now. The simulations and our model L-V_max relation predict the shape, amplitude, and luminosity dependence of the two-point correlation function in excellent agreement with the observed galaxy clustering in the SDSS data at z~0 and in the DEEP2 samples at z~1 over the entire probed range of projected separations, 0.1<r_p/(Mpc/h)<10.0. In particular, the small-scale upturn of the correlation function from the power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced very well. At z~3-5, our predictions also match the observed shape and amplitude of the angular two-point correlation function of Lyman-break galaxies (LBGs) on both large and small scales, including the small-scale upturn.
Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness rel... more Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness relation for a large sample of galaxy clusters. Using population subtraction methods, we determine the radius at which the cluster galaxy number density is 200/Omega_m times the mean galaxy density, without assuming a model for the radial distribution of galaxies in clusters. If these galaxies are unbiased on Mpc scales, this galaxy-density-based R_200 reflects the characteristic radii of clusters. We measure the scaling of this characteristic radius with richness over an order of magnitude in cluster richness, from rich clusters to poor groups. We use this information to examine the radial profiles of galaxies in clusters as a function of cluster richness, finding that the concentration of the galaxy distribution decreases with richness and is systematically lower than the concentrations measured for dark matter profiles in N-body simulations. Using these scaled radii, we investigate the behavior of the cluster luminosity function, and find that it is well matched by a Schechter function for galaxies brighter than M_r = -18 only after the central galaxy has been removed. We find that the luminosity function varies with richness and with distance from the cluster center, underscoring the importance of using an aperture that scales with cluster mass to compare physically equivalent regions of these different systems. We note that the lowest richness systems in our catalog have properties consistent with those expected of the earliest-forming halos; our cluster-finding algorithm, in addition to reliably finding clusters, may be efficient at finding fossil groups.
Monthly Notices of The Royal Astronomical Society, 2005
Using six high resolution dissipationless simulations with a varying box size in a flat LCDM univ... more Using six high resolution dissipationless simulations with a varying box size in a flat LCDM universe, we study the mass and redshift dependence of dark matter halo shapes for M_vir = 9.0e11 - 2.0e14, over the redshift range z=0-3, and for two values of sigma_8=0.75 and 0.9. Remarkably, we find that the redshift, mass, and sigma_8 dependence of the mean smallest-to-largest axis ratio of halos is well described by the simple power-law relation <s> = (0.54 +- 0.02)(M_vir/M_*)^(-0.050 +- 0.003), where s is measured at 0.3 R_vir and the z and sigma_8 dependences are governed by the characteristic nonlinear mass, M_*=M_*(z,sigma_8). We find that the scatter about the mean s is well described by a Gaussian with sigma ~ 0.1, for all masses and redshifts. We compare our results to a variety of previous works on halo shapes and find that reported differences between studies are primarily explained by differences in their methodologies. We address the evolutionary aspects of individual halo shapes by following the shapes of the halos through ~100 snapshots in time. We determine the formation scalefactor a_c as defined by Wechsler et al. (2002) and find that it can be related to the halo shape at z = 0 and its evolution over time.
We use a set of simulation-based models for the dissipationless evolution of galaxies since z=1 t... more We use a set of simulation-based models for the dissipationless evolution of galaxies since z=1 to constrain the fate of accreted satellites embedded in dark matter subhalos. These models assign stellar mass to dark matter halos at z=1 by relating the observed galaxy stellar mass function (GSMF) to the halo+subhalo mass function monotonically. The evolution of the stellar mass content is then followed using halo merger trees extracted from N-body simulations. Our models are differentiated only in the fate assigned to satellite galaxies once subhalos, within which satellites are embedded, disrupt. These models are confronted with the observed evolution in the massive end of the GSMF, the z~0 brightest cluster galaxy (BCG)-cluster mass relation, and the combined BCG and intracluster light (ICL) luminosity distribution -- all observables expected to evolve approximately dissipationlessly since z=1. The combined observational constraints favor a model in which the vast majority (>80%) of satellite stars from disrupted subhalos go into the ICL. Conversely, models that leave behind a significant population of satellite galaxies once the subhalo has disrupted are strongly disfavored, as are models that put a significant fraction of satellite stars into the BCG. Our results show that observations of the ICL provide useful and unique constraints on models of galaxy merging and the dissipationless evolution of galaxies in groups and clusters.
We study the formation of fifty-three galaxy cluster-size dark matter halos formed within a pair ... more We study the formation of fifty-three galaxy cluster-size dark matter halos formed within a pair of cosmological LCDM N-body simulations, and track the accretion histories of cluster subhalos with masses large enough to host 0.1L* galaxies. By associating subhalos with cluster galaxies, we find the majority of galaxies in clusters experience no pre-processing in the group environment prior to their accretion into the cluster. On average, ~70% of cluster galaxies fall into the cluster potential directly from the field, with no luminous companions in their host halos at the time of accretion; and less than ~12% are accreted as members of groups with five or more galaxies. Moreover, we find that cluster galaxies are significantly less likely to have experienced a merger in the recent past (~6 Gyr) than a field halo of the same mass. These results suggest that local, cluster processes like ram-pressure stripping, galaxy harassment, or strangulation play the dominant role in explaining the difference between cluster and field populations at a fixed stellar mass; and that pre-evolution or past merging in the group environment is of secondary importance for setting cluster galaxy properties for most clusters. The accretion times for z = 0 cluster members are quite extended, with ~20% incorporated into the cluster halo more than 7 Gyr ago and ~20% within the last 2 Gyr. By comparing the observed morphological fractions in cluster and field populations, we estimate an approximate timescale for late-type to early-type transformation within the cluster environment to be ~6 Gyr.
We address the high peaks found by Steidel et al (1997) in the redshift distribution of ``Lyman-b... more We address the high peaks found by Steidel et al (1997) in the redshift distribution of ``Lyman-break'' objects (LBOs) at redshift z~3. The highest spike represents a relative overdensity of 2.6 in the distribution of LBOs in pixels of comoving size ~10Mpc/h. We examine the likelihood of such a spike in the redshift distribution within a suite of models for the evolution of structure in the Universe, including models with Omega=1 (SCDM and CHDM) and with Omega=0.4-0.5 (LCDM and OCDM). Using high-resolution dissipationless N-body simulations, we analyze deep pencil-beam surveys from these models in the same way that they are actually observed, identifying LBOs with the most massive dark matter halos. We find that all the models (with SCDM as a marginal exception) have a substantial probability of producing spikes similar to those observed, because the massive halos are much more clumped than the underlying matter -- i.e., they are biased. Therefore, the likelihood of such a spike is not a good discriminator among these models. We find in these models that the mean biasing parameter b of LBOs with respect to dark matter varies within a range b ~2-5 on a scale of ~10Mpc/h. We also compute the two-body correlation functions of LBOs predicted in these models. The LBO correlation functions are less steep than galaxies today (gamma ~1.4), but show similar or slightly longer correlation lengths.
We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters o... more We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with masses ranging from ~5x10^{12} to ~10^{15} M_{sun}/h. Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean \Delta \rho(r) = \rho(r) - \bar{\rho} for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density \Delta l(r) = l(r) - \bar{l} measured in the z=0.25 i-band. For both mass and light, we de-project the profiles to produce 3D mass and light profiles over scales from 25 kpc/ to 22 Mpc/h. From these profiles we calculate the cumulative excess mass M(r) and excess light L(r) as a function of separation from the BCG. On small scales, where \rho(r) >> \bar{\rho}, the integrated mass-to-light profile may be interpreted as the cluster mass-to-light ratio. We find the M/L_{200}, the mass-to-light ratio within r_{200}, scales with cluster mass as a power law with index 0.33+/-0.02. On large scales, where \rho(r) ~ \bar{\rho}, the M/L approaches an asymptotic value independent of cluster richness. For small groups, the mean M/L_{200} is much smaller than the asymptotic value, while for large clusters it is consistent with the asymptotic value. This asymptotic value should be proportional to the mean mass-to-light ratio of the universe <M/L>. We find <M/L>/b^2_{ml} = 362+/-54 h (statistical). There is additional uncertainty in the overall calibration at the ~10% level. The parameter b_{ml} is primarily a function of the bias of the L <~ L_* galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find \Omega_m/b^2_{ml} = 0.02+/-0.03, independent of the Hubble parameter.
We propose a new explanation for the origin of angular momentum in galaxies and their dark halos,... more We propose a new explanation for the origin of angular momentum in galaxies and their dark halos, in which the halos obtain their spin through the cumulative acquisition of angular momentum from satellite accretion. In our model, the build-up of angular momentum is a random walk process associated with the mass assembly history of the halo's major progenitor. We assume no correlation between the angular momenta of accreted objects. Using the extended Press-Schechter approximation, we calculate the growth of mass, angular momentum, and spin parameter $\lambda$ for many halos. Our random walk model reproduces the key features of the angular momentum of halos found in N-body simulations: a lognormal distribution in $\lambda$ with an average of $<\lambda> \approx 0.04$, independent of mass and redshift. The evolution of the spin parameter in individual halos in this model is quite different from the steady increase with time of angular momentum in the tidal torque picture. We find both in N-body simulations and in our random walk model that the value of $\lambda$ changes significantly with time for a halo's major progenitor. It typically has a sharp increase due to major mergers, and a steady decline during periods of gradual accretion of small satellites. The model predicts that on average the $\lambda$ of halos which had major mergers after redshift $z=2$ should be substantially larger than the $\lambda$ of those which did not. Perhaps surprisingly, this suggests that halos that host late-forming elliptical galaxies should rotate faster than halos of spiral galaxies.
Astronomical observations strongly suggest that our universe is now accelerating and contains a s... more Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant density of dark energy), we show that astronomical structures freeze out in the near future and that the density profiles of dark matter halos approach the same general form. Every dark matter halo grows asymptotically isolated and thereby becomes the center of its own island universe. Each of these isolated regions of space-time approaches a universal geometry and we calculate the corresponding form of the space-time metric.
Standard LCDM predicts that the major merger rate of galaxy-size dark matter halos rises rapidly ... more Standard LCDM predicts that the major merger rate of galaxy-size dark matter halos rises rapidly with redshift. The average number of close companions per galaxy, Nc, is often used to infer the galaxy merger rate, however, recent observational studies suggest that Nc evolves very little with redshift. Here we use a "hybrid" N- body simulation plus analytic substructure model to predict Nc directly. We identify dark matter subhalos with galaxies and show that the observed lack of close pair count evolution arises because the high merger rate per halo at early times is counteracted by a decrease in the number of halos massive enough to host a galaxy pair. We compare our results to data compiled from the DEEP2, SSRS2, and the UZC redshift surveys. Observed pair counts match our predictions if we assume a monotonic mapping between galaxy luminosity and the maximum circular velocity that each subhalo had when it was first accreted onto its host halo. This suggests that satellite galaxies are significantly more resilient to destruction than are dissipationless dark matter subhalos. We argue that while Nc does not provide a direct measure of the halo merger rate, it offers a powerful means to constrain the Halo Occupation Distribution and the spatial distribution of galaxies within halos. Interpreted in this way, close pair counts provide a useful test of galaxy formation processes on < 100 kpc scales.
We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster c... more We measure the logarithmic scatter in mass at fixed richness for clusters in the maxBCG cluster catalog, an optically selected cluster sample drawn from SDSS imaging data. Our measurement is achieved by demanding consistency between available weak lensing and X-ray measurements of the maxBCG clusters, and the X-ray luminosity--mass relation inferred from the 400d X-ray cluster survey, a flux limited X-ray cluster survey. We find \sigma_{\ln M|N_{200}}=0.45^{+0.20}_{-0.18} (95% CL) at N_{200} ~ 40, where N_{200} is the number of red sequence galaxies in a cluster. As a byproduct of our analysis, we also obtain a constraint on the correlation coefficient between \ln Lx and \ln M at fixed richness, which is best expressed as a lower limit, r_{L,M|N} >= 0.85 (95% CL). This is the first observational constraint placed on a correlation coefficient involving two different cluster mass tracers. We use our results to produce a state of the art estimate of the halo mass function at z=0.23 -- the median redshift of the maxBCG cluster sample -- and find that it is consistent with the WMAP5 cosmology. Both the mass function data and its covariance matrix are presented.
Monthly Notices of The Royal Astronomical Society, 2001
We discuss how current and future data on the clustering and number density of z~3 Lyman-break ga... more We discuss how current and future data on the clustering and number density of z~3 Lyman-break galaxies (LBGs) can be used to constrain their relationship to dark matter haloes. We explore a three-parameter model in which the number of LBGs per dark halo scales like a power-law in the halo mass: N(M) = (M/M_1)^S for M>M_m. Here, M_m is the minimum mass halo that can host an LBG, M_1 is a normalization parameter, associated with the mass above which haloes host more than one observed LBG, and S determines the strength of the mass dependence. We show how these three parameters are constrained by three observable properties of LBGs: the number density, the large-scale bias, and the fraction of objects in close pairs. Given these three quantities, the three unknown model parameters may be estimated analytically, allowing a full exploration of parameter space. As an example, we assume an LCDM cosmology and consider the observed properties of a recent sample of spectroscopically confirmed LBGs. We find that the favored range for our model parameters is M_m = (0.4-8)x10^10 Msun/h, M_1 = (6-10)x10^12 Msun/h, and 0.9 < S < 1.1. The preferred region in M_m expands by an order of magnitude and slightly shallower slopes are acceptable if the allowed range of bias is permitted to span all recent observational estimates. We also discuss how the observed clustering of LBGs as a function of luminosity can be used to constrain halo occupation, although due to current observational uncertainties we are unable to reach any strong conclusions. Our methods and results can be used to constrain more realistic models that aim to derive the occupation function N(M) from first principles, and offer insight into how basic physical properties affect the observed properties of LBGs.
(Abridged) We present a semi-analytic model for Cold Dark Matter halo substructure that can be us... more (Abridged) We present a semi-analytic model for Cold Dark Matter halo substructure that can be used as a framework for studying galaxy formation and an ingredient in halo models of galaxy clustering. We perform a comprehensive comparison of the model to the results of a suite of high-resolution cosmological simulations. The comparisons reveal that subhalo statistics, such as velocity and mass functions, radial distributions, and the halo occupation distributions, agree well over three orders of magnitude in host halo mass at various redshifts. Both in the simulations and in our model, the radial distributions of subhalos are significantly shallower than that of the dark matter density. The abundance of subhalos in a host is set by competition between destruction and new accretion. High mass halos and halos at high redshift tend to host more subhalos because the subhalos have, on average, been accreted more recently. Similarly, at fixed mass, halos that formed more recently host more subhalos. Observed "fossil groups" may represent an extreme tail of this correlation. We find a related correlation between host halo concentration and subhalo abundance at fixed host mass, Nsat ~ c^-a, where a changes with redshift and host-to-subhalo mass ratio. Lastly, we use our model to populate host halos in one of our high-resolution cosmological simulations, replacing the subhalos resolved in the simulation with subhalos computed according to our model. We show that the resulting 2pt correlation function of such a "hybrid" halo ensemble is indistinguishable from that measured directly in the simulation. This supports one of the key tenets of the standard halo model -- the assumption that the halo occupation distribution is statistically independent of host halo environment.
We analyze the halo occupation distribution (HOD), the probability for a halo of mass M to host a... more We analyze the halo occupation distribution (HOD), the probability for a halo of mass M to host a number of subhalos N, and two-point correlation function of galaxy-size dark matter halos using high-resolution dissipationless simulations of the concordance flat LCDM model. The halo samples include both the host halos and the subhalos, distinct gravitationally-bound halos within the virialized regions of larger host systems. We find that the first moment of the HOD, <N>(M), has a complicated shape consisting of a step, a shoulder, and a power law high-mass tail. The HOD can be described by a Poisson statistics at high halo masses but becomes sub-Poisson for <N><4. We show that the HOD can be understood as a combination of the probability for a halo of mass M to host a central galaxy and the probability to host a given number Ns of satellite galaxies. The former can be approximated by a step-like function, while the latter can be well approximated by a Poisson distribution, fully specified by its first moment <Ns>(M). We find that <Ns>~M^b with b~1 for a wide range of number densities, redshifts, and different power spectrum normalizations. This formulation provides a simple but accurate model for the halo occupation distribution found in simulations. At z=0, the two-point correlation function (CF) of galactic halos can be well fit by a power law down to ~100/h kpc with an amplitude and slope similar to those of observed galaxies. At redshifts z>~1, we find significant departures from the power-law shape of the CF at small scales. If the deviations are as strong as indicated by our results, the assumption of the single power law often used in observational analyses of high-redshift clustering is likely to bias the estimates of the correlation length and slope of the correlation function.
We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model ... more We employ high-resolution dissipationless simulations of the concordance LCDM cosmology to model the observed luminosity dependence and evolution of galaxy clustering through most of the age of the universe, from z~5 to z~0. We use a simple, non-parametric model which monotonically relates galaxy luminosities to the maximum circular velocity of dark matter halos (V_max) by preserving the observed galaxy luminosity function in order to match the halos in simulations with observed galaxies. The novel feature of the model is the use of the maximum circular velocity at the time of accretion, V_max,acc, for subhalos, the halos located within virial regions of larger halos. We argue that for subhalos in dissipationless simulations, V_max,acc reflects the luminosity and stellar mass of the associated galaxies better than the circular velocity at the epoch of observation, V_max,now. The simulations and our model L-V_max relation predict the shape, amplitude, and luminosity dependence of the two-point correlation function in excellent agreement with the observed galaxy clustering in the SDSS data at z~0 and in the DEEP2 samples at z~1 over the entire probed range of projected separations, 0.1<r_p/(Mpc/h)<10.0. In particular, the small-scale upturn of the correlation function from the power-law form in the SDSS and DEEP2 luminosity-selected samples is reproduced very well. At z~3-5, our predictions also match the observed shape and amplitude of the angular two-point correlation function of Lyman-break galaxies (LBGs) on both large and small scales, including the small-scale upturn.
Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness rel... more Imaging data from the Sloan Digital Sky Survey is used to measure the empirical size-richness relation for a large sample of galaxy clusters. Using population subtraction methods, we determine the radius at which the cluster galaxy number density is 200/Omega_m times the mean galaxy density, without assuming a model for the radial distribution of galaxies in clusters. If these galaxies are unbiased on Mpc scales, this galaxy-density-based R_200 reflects the characteristic radii of clusters. We measure the scaling of this characteristic radius with richness over an order of magnitude in cluster richness, from rich clusters to poor groups. We use this information to examine the radial profiles of galaxies in clusters as a function of cluster richness, finding that the concentration of the galaxy distribution decreases with richness and is systematically lower than the concentrations measured for dark matter profiles in N-body simulations. Using these scaled radii, we investigate the behavior of the cluster luminosity function, and find that it is well matched by a Schechter function for galaxies brighter than M_r = -18 only after the central galaxy has been removed. We find that the luminosity function varies with richness and with distance from the cluster center, underscoring the importance of using an aperture that scales with cluster mass to compare physically equivalent regions of these different systems. We note that the lowest richness systems in our catalog have properties consistent with those expected of the earliest-forming halos; our cluster-finding algorithm, in addition to reliably finding clusters, may be efficient at finding fossil groups.
Monthly Notices of The Royal Astronomical Society, 2005
Using six high resolution dissipationless simulations with a varying box size in a flat LCDM univ... more Using six high resolution dissipationless simulations with a varying box size in a flat LCDM universe, we study the mass and redshift dependence of dark matter halo shapes for M_vir = 9.0e11 - 2.0e14, over the redshift range z=0-3, and for two values of sigma_8=0.75 and 0.9. Remarkably, we find that the redshift, mass, and sigma_8 dependence of the mean smallest-to-largest axis ratio of halos is well described by the simple power-law relation <s> = (0.54 +- 0.02)(M_vir/M_*)^(-0.050 +- 0.003), where s is measured at 0.3 R_vir and the z and sigma_8 dependences are governed by the characteristic nonlinear mass, M_*=M_*(z,sigma_8). We find that the scatter about the mean s is well described by a Gaussian with sigma ~ 0.1, for all masses and redshifts. We compare our results to a variety of previous works on halo shapes and find that reported differences between studies are primarily explained by differences in their methodologies. We address the evolutionary aspects of individual halo shapes by following the shapes of the halos through ~100 snapshots in time. We determine the formation scalefactor a_c as defined by Wechsler et al. (2002) and find that it can be related to the halo shape at z = 0 and its evolution over time.
We use a set of simulation-based models for the dissipationless evolution of galaxies since z=1 t... more We use a set of simulation-based models for the dissipationless evolution of galaxies since z=1 to constrain the fate of accreted satellites embedded in dark matter subhalos. These models assign stellar mass to dark matter halos at z=1 by relating the observed galaxy stellar mass function (GSMF) to the halo+subhalo mass function monotonically. The evolution of the stellar mass content is then followed using halo merger trees extracted from N-body simulations. Our models are differentiated only in the fate assigned to satellite galaxies once subhalos, within which satellites are embedded, disrupt. These models are confronted with the observed evolution in the massive end of the GSMF, the z~0 brightest cluster galaxy (BCG)-cluster mass relation, and the combined BCG and intracluster light (ICL) luminosity distribution -- all observables expected to evolve approximately dissipationlessly since z=1. The combined observational constraints favor a model in which the vast majority (>80%) of satellite stars from disrupted subhalos go into the ICL. Conversely, models that leave behind a significant population of satellite galaxies once the subhalo has disrupted are strongly disfavored, as are models that put a significant fraction of satellite stars into the BCG. Our results show that observations of the ICL provide useful and unique constraints on models of galaxy merging and the dissipationless evolution of galaxies in groups and clusters.
We study the formation of fifty-three galaxy cluster-size dark matter halos formed within a pair ... more We study the formation of fifty-three galaxy cluster-size dark matter halos formed within a pair of cosmological LCDM N-body simulations, and track the accretion histories of cluster subhalos with masses large enough to host 0.1L* galaxies. By associating subhalos with cluster galaxies, we find the majority of galaxies in clusters experience no pre-processing in the group environment prior to their accretion into the cluster. On average, ~70% of cluster galaxies fall into the cluster potential directly from the field, with no luminous companions in their host halos at the time of accretion; and less than ~12% are accreted as members of groups with five or more galaxies. Moreover, we find that cluster galaxies are significantly less likely to have experienced a merger in the recent past (~6 Gyr) than a field halo of the same mass. These results suggest that local, cluster processes like ram-pressure stripping, galaxy harassment, or strangulation play the dominant role in explaining the difference between cluster and field populations at a fixed stellar mass; and that pre-evolution or past merging in the group environment is of secondary importance for setting cluster galaxy properties for most clusters. The accretion times for z = 0 cluster members are quite extended, with ~20% incorporated into the cluster halo more than 7 Gyr ago and ~20% within the last 2 Gyr. By comparing the observed morphological fractions in cluster and field populations, we estimate an approximate timescale for late-type to early-type transformation within the cluster environment to be ~6 Gyr.
We address the high peaks found by Steidel et al (1997) in the redshift distribution of ``Lyman-b... more We address the high peaks found by Steidel et al (1997) in the redshift distribution of ``Lyman-break'' objects (LBOs) at redshift z~3. The highest spike represents a relative overdensity of 2.6 in the distribution of LBOs in pixels of comoving size ~10Mpc/h. We examine the likelihood of such a spike in the redshift distribution within a suite of models for the evolution of structure in the Universe, including models with Omega=1 (SCDM and CHDM) and with Omega=0.4-0.5 (LCDM and OCDM). Using high-resolution dissipationless N-body simulations, we analyze deep pencil-beam surveys from these models in the same way that they are actually observed, identifying LBOs with the most massive dark matter halos. We find that all the models (with SCDM as a marginal exception) have a substantial probability of producing spikes similar to those observed, because the massive halos are much more clumped than the underlying matter -- i.e., they are biased. Therefore, the likelihood of such a spike is not a good discriminator among these models. We find in these models that the mean biasing parameter b of LBOs with respect to dark matter varies within a range b ~2-5 on a scale of ~10Mpc/h. We also compute the two-body correlation functions of LBOs predicted in these models. The LBO correlation functions are less steep than galaxies today (gamma ~1.4), but show similar or slightly longer correlation lengths.
We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters o... more We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with masses ranging from ~5x10^{12} to ~10^{15} M_{sun}/h. Using cross-correlation weak lensing, we measure the excess mass density profile above the universal mean \Delta \rho(r) = \rho(r) - \bar{\rho} for clusters in bins of richness and optical luminosity. We also measure the excess luminosity density \Delta l(r) = l(r) - \bar{l} measured in the z=0.25 i-band. For both mass and light, we de-project the profiles to produce 3D mass and light profiles over scales from 25 kpc/ to 22 Mpc/h. From these profiles we calculate the cumulative excess mass M(r) and excess light L(r) as a function of separation from the BCG. On small scales, where \rho(r) >> \bar{\rho}, the integrated mass-to-light profile may be interpreted as the cluster mass-to-light ratio. We find the M/L_{200}, the mass-to-light ratio within r_{200}, scales with cluster mass as a power law with index 0.33+/-0.02. On large scales, where \rho(r) ~ \bar{\rho}, the M/L approaches an asymptotic value independent of cluster richness. For small groups, the mean M/L_{200} is much smaller than the asymptotic value, while for large clusters it is consistent with the asymptotic value. This asymptotic value should be proportional to the mean mass-to-light ratio of the universe <M/L>. We find <M/L>/b^2_{ml} = 362+/-54 h (statistical). There is additional uncertainty in the overall calibration at the ~10% level. The parameter b_{ml} is primarily a function of the bias of the L <~ L_* galaxies used as light tracers, and should be of order unity. Multiplying by the luminosity density in the same bandpass we find \Omega_m/b^2_{ml} = 0.02+/-0.03, independent of the Hubble parameter.
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Papers by Risa Wechsler