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Neal Katz

Publications and source records attributed to Neal Katz.

At least 91 records · Page 5Linked to original sources

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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Accretion, feedback and galaxy bimodality: a comparison of the GalICS semi-analytic model and cosmological SPH simulations

We compare the galaxy population of an SPH simulation to those predicted by the GalICS semi-analytic model and a stripped down version without supernova and AGN feedback. The SPH simulation and the no-feedback GalICS model make similar predictions for the baryonic mass functions of galaxies and for the dependence of these mass functions on environment and redshift. The two methods also make similar predictions for the galaxy content of dark matter haloes as a function of halo mass and for the gas accretion history of galaxies. Both the SPH and no-feedback GalICS models predict a bimodal galaxy population at z=0. The "red'' sequence of gas poor, old galaxies is populated mainly by satellite systems while, contrary to observations, the central galaxies of massive haloes lie on the "blue'' star-forming sequence as a result of continuing hot gas accretion at late times. Furthermore, both models overpredict the observed baryonic mass function, especially at the high mass end. In the full GalICS model, supernova-driven outflows reduce the masses of low and intermediate mass galaxies by about a factor of two. AGN feedback suppresses gas cooling in large haloes, producing a sharp cut-off in the baryonic mass function and moving the central galaxies of these massive haloes to the red sequence. Our results imply that the observational failings of the SPH simulation and the no-feedback GalICS model are a consequence of missing input physics rather than computational inaccuracies, that truncating gas accretion by satellite galaxies automatically produces a bimodal galaxy distribution with a red sequence, but that explaining the red colours of the most massive galaxies requires a mechanism like AGN feedback that suppresses the accretion onto central galaxies in large haloes.

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On the Evolutionary History of Stars and their Fossil Mass and Light

The total extragalactic background radiation can be an important test of the global star formation history (SFH). Using direct observational estimates of the SFH, along with standard assumptions about the initial mass function (IMF), we calculate the total extragalactic background radiation and the observed stellar density today. We show that plausible SFHs allow a significant range in each quantity, but that their ratio is very tightly constrained. Current estimates of the stellar mass and extragalactic background are difficult to reconcile, as long as the IMF is fixed to the Salpeter slope above 1 Msun. The joint confidence interval of these two quantities only agrees with that determined from the allowed range of SFH fits at the 3-sigma level, and for our best-fit values the discrepancy is about a factor of two. Alternative energy sources that contribute to the background, such as active galactic nuclei (AGN), Population III stars, or decaying particles, appear unlikely to resolve the discrepancy. However, changes to the IMF allow plausible solutions to the background problem. The simplest is an average IMF with an increased contribution from stars around 1.5--4 Msun. A ``paunchy'' IMF of this sort could emerge as a global average if low mass star formation is suppressed in galaxies experiencing rapid starbursts. Such an IMF is consistent with observations of star-forming regions, and would help to reconcile the fossil record of star formation with the directly observed SFH.

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Baryon Dynamics, Dark Matter Substructure, and Galaxies

By comparing a collisionless cosmological N-body simulation (DM) to an SPH simulation with the same initial conditions, we investigate the correspondence between the dark matter subhalos produced by collisionless dynamics and the galaxies produced by dissipative gas dynamics in a dark matter background. When galaxies in the SPH simulation become satellites in larger groups, they retain local dark matter concentrations (SPH subhalos) whose mass is typically five times their baryonic mass. The more massive subhalos of the SPH simulation have corresponding subhalos of similar mass and position in the DM simulation; at lower masses, there is fairly good correspondence, but some DM subhalos are in different spatial positions and some suffer tidal stripping or disruption. The halo occupation statistics of DM subhalos -- the mean number of subhalos, pairs, and triples as a function of host halo mass -- are very similar to those of SPH subhalos and SPH galaxies. Gravity of the dissipative baryon component amplifies the density contrast of subhalos in the SPH simulation, making them more resistant to tidal disruption. Relative to SPH galaxies and SPH subhalos, the DM subhalo population is depleted in the densest regions of the most massive halos. The good agreement of halo occupation statistics between the DM subhalo and SPH galaxy populations leads to good agreement of their two-point correlation functions and higher order moments on large scales. The depletion of DM subhalos in dense regions depresses their clustering at R<1 Mpc/h. In these simulations, the "conversation" between dark matter and baryons is mostly one-way, with dark matter dynamics telling galaxies where to form and how to cluster, but the "back talk" of the baryons influences small scale clustering by enhancing the survival of substructure in the densest environments.

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On the origin of cold dark matter halo density profiles

N-body simulations predict that CDM halo-assembly occurs in two phases: 1) a fast accretion phase with a rapidly deepening potential well; and 2) a slow accretion phase characterised by a gentle addition of mass to the outer halo with little change in the inner potential well. We demonstrate, using one-dimensional simulations, that this two-phase accretion leads to CDM halos of the NFW form and provides physical insight into the properties of the mass accretion history that influence the final profile. Assuming that the velocities of CDM particles are effectively isotropised by fluctuations in the gravitational potential during the fast accretion phase, we show that gravitational collapse in this phase leads to an inner profile rho(r) ~ r^{-1}. Slow accretion onto an established potential well leads to an outer profile with rho(r) ~ r^{-3}. The concentration of a halo is determined by the fraction of mass that is accreted during the fast accretion phase. Using an ensemble of realistic mass accretion histories, we show that the model predictions of the dependence of halo concentration on halo formation time, and hence the dependence of halo concentration on halo mass, and the distribution of halo concentrations all match those found in cosmological N-body simulations. Using a simple analytic model that captures much of the important physics we show that the inner r^{-1} profile of CDM halos is a natural result of hierarchical mass assembly with a initial phase of rapid accretion.

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The Bar-Halo Interaction - II. Secular evolution and the religion of N-body simulations

This paper explores resonance-driven secular evolution between a bar and dark-matter halo using N-body simulations. We make direct comparisons to our analytic theory (Weinberg & Katz 2005) to demonstrate the great difficulty that an N-body simulation has representing these dynamics for realistic astronomical interactions. In a dark-matter halo, the bar's angular momentum is coupled to the central density cusp (if present) by the Inner Lindblad Resonance. Owing to this angular momentum transfer and self-consistent re-equilibration, strong realistic bars WILL modify the cusp profile, lowering the central densities within about 30% of the bar radius in a few bar orbits. Past results to the contrary (Sellwood 2006, McMillan & Dehnen 2005) may be the result of weak bars or numerical artifacts. The magnitude depends on many factors and we illustrate the sensitivity of the response to the dark-matter profile, the bar shape and mass, and the galaxy's evolutionary history. For example, if the bar length is comparable to the size of a central dark-matter core, the bar may exchange angular momentum without changing its pattern speed significantly. We emphasise that this apparently simple example of secular evolution is remarkably subtle in detail and conclude that an N-body exploration of any astronomical scenario requires a deep investigation into the underlying dynamical mechanisms for that particular problem to set the necessary requirements for the simulation parameters and method (e.g. particle number and Poisson solver). Simply put, N-body simulations do not divinely reveal truth and hence their results are not infallible. They are unlikely to provide useful insight on their own, particularly for the study of even more complex secular processes such as the production of pseudo-bulges and disk heating.

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Nature and completeness of galaxies detected in the Two Micron All Sky Survey

We cross correlate the well-defined and very complete spectroscopic Main Galaxy Sample (MGS) of 156,000 bright (r<17.5 mag) galaxies from the SDSS with 2MASS sources to explore the nature and completeness of the 2MASS K-band selection of nearby galaxies. 2MASS detects 90% of the MGS brighter than r=17 mag. For r<16, 93.1% of the MGS is found in the 2MASS Extended Source Catalog (XSC). These detections span the representative range of optical and near-IR galaxy properties, but with a surface brightness-dependent bias to preferentially miss the most blue and low-concentration sources, consistent with the most morphologically late-type galaxy population. An XSC completeness of 97.5% is achievable at bright magnitudes, with blue LSBs being the only major source of incompleteness, if one follows our careful matching criteria and weeds out spurious SDSS sources. We conclude that the rapid drop in XSC completeness at r>16 reflects the sharp surface-brightness limit of the extended source detection algorithm in 2MASS. As a result, the r>16 galaxies found in the XSC are over-representative in red early types and under-representative in blue latetypes. At r>16 the XSC suffers an additional selection effect from the 2-3" spatial resolution limit of 2MASS. Therefore, 2MASS continues to detect 90% of of the MGS at 16<r<17, but with a growing fraction found in the Point Source Catalog (PSC) only. Overall, one third of the MGS is detected in the 2MASS PSC but not the XSC. A combined K<13.57 and r<16 selection provides the most representative inventory of galaxies in the local cosmos with near-IR and optical measurements, and 90.8% completeness. Using data from SDSS-DR2, this sample contains 19,156 galaxies with a median redshift of 0.052. (abridged)

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Building Galaxies with Simulations

We present an overview of some of the issues surrounding current models of galaxy formation, highlighting recent insights obtained from cosmological hydrodynamic simulations. Detailed examination of gas accretion processes show a hot mode of gas cooling from near the halo's virial temperature, and a previously underappreciated cold mode where gas flows in along filaments on dynamical timescales, emitting its energy in line radiation. Cold mode dominates in systems with halo masses slightly smaller than the Milky Way and below, and hence dominates the global accretion during the heydey of galaxy formation. This rapid accretion path enables prompt assembly of massive galaxies in the early universe, and results in $z\sim 4$ galaxy properties in broad agreement with observations, with the most massive galaxies being the most rapid star formers. Massive galaxies today are forming stars at a much reduced rate, a trend called downsizing. The trend of downsizing is naturally reproduced in simulations, owing to a transition from cold mode accretion in the early growth phase to slower hot mode accretion once their halos grow large. However, massive galaxies at the present epoch are still observed to have considerably redder colors than simulations suggest, suggesting that star formation is not sufficiently truncated in models by the transition to hot mode, and that another process not included in current simulations is required to suppress star formation.

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Galaxy Merger Statistics and Inferred Bulge-to-Disk Ratios in Cosmological SPH Simulations

We construct merger trees for galaxies identified in a cosmological hydrodynamical simulation and use them to characterize predicted merger rates as a function of redshift, galaxy mass, and merger mass ratio. At z=0.3, we find a mean rate of 0.054 mergers per galaxy per Gyr above a 1:2 mass ratio threshold for massive galaxies (baryonic mass above 6.4E10 \Msun), but only 0.018 / Gyr for lower mass galaxies. The mass ratio distribution is proportional to R_merg^-1.2 for the massive galaxy sample, so high mass mergers dominate the total merger growth rate. The predicted rates increase rapidly with increasing redshift, and they agree reasonably well with observational estimates. A substantial fraction of galaxies do not experience any resolved mergers during the course of the simulation, and even for the high mass sample only 50% of galaxies experience a greater than 1:4 merger since z=1. Typical galaxies thus have fairly quiescent merger histories. We assign bulge-to-disk ratios to simulated galaxies by assuming that mergers above a mass ratio threshold R_major convert stellar disks into spheroids. With R_major of 1:4, we obtain a fairly good match to the observed dependence of early-type fraction on galaxy mass. However, the predicted fraction of truly bulge-dominated systems (f_bulge} > 0.8) is small, and producing a substantial population of bulge-dominated galaxies may require a mechanism that shuts off gas accretion at late times and/or additional processes (besides major mergers) for producing bulges.

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Probing Galaxy Formation with He II Cooling Lines

Using high resolution cosmological simulations, we study hydrogen and helium gravitational cooling radiation. We focus on the HeII cooling lines, which arise from gas with a different temperature history (T_max ~ 10^5K) than HI line emitting gas. We examine whether three major atomic cooling lines, HI 1216A, HeII 1640A and HeII 304A are observable, finding that HI 1216A and HeII 1640A cooling emission at z=2-3 are potentially detectable with deep narrow band (R>100) imaging and/or spectroscopy from the ground. While the expected strength of HI 1216A cooling emission depends strongly on the treatment of the self-shielded phase of the IGM in the simulations, our predictions for the HeII 1640A line are more robust because the HeII 1640A emissivity is negligible below T~10^4.5 K and less sensitive to the UV background. Although HeII 1640A cooling emission is fainter than HI 1216A by at least a factor of 10 and, unlike HI 1216A, might not be resolved spatially with current observational facilities, it is more suitable to study gas accretion in the galaxy formation process because it is optically thin and less contaminated by the recombination lines from star-forming galaxies. The HeII 1640A line can be used to distinguish among mechanisms for powering the so-called "Lyman alpha blobs" -- including gravitational cooling radiation, photoionization by stellar populations, and starburst-driven superwinds -- because (1) HeII 1640A emission is limited to very low metallicity (log(Z/Z_sun) < -5.3) and Population III stars, and (2) the blob's kinematics are probed unambiguously through the HeII 1640A line width, which, for cooling radiation, is narrower (sigma < 400 km/s) than typical wind speeds.

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Preheating by Previrialization and its Impact on Galaxy Formation

We use recent observations of the HI-mass function to constrain galaxy formation. The data conflicts with the standard model where most of the gas in a low-mass dark matter halo is assumed to settle into a disk of cold gas that is depleted by star formation and supernova-driven outflows until the disk becomes gravitationally stable. A consistent model can be found if low-mass haloes are embedded in a preheated medium, with a specific gas entropy ~ 10Kev cm^2. Such a model simultaneously matches the faint-end slope of the galaxy luminosity function. We propose a preheating model where the medium around low-mass haloes is preheated by gravitational pancaking. Since gravitational tidal fields suppress the formation of low-mass haloes while promoting that of pancakes, the formation of massive pancakes precedes that of the low-mass haloes within them. We demonstrate that the progenitors of present-day dark matter haloes with M<10^{12}h^{-1}\msun were embedded in pancakes of masses $~5x10^{12}h^{-1}\msun$ at z~2. The formation of such pancakes heats the gas to a temperature of 5x10^5K and compresses it to an overdensity of ~10. Such gas has a cooling time that exceeds the age of the Universe at z~2, and has a specific entropy of ~15Kev cm^2, almost exactly the amount required to explain the stellar and HI mass functions. (Abridged)

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Lyman Alpha Flux Power Spectrum and Its Covariance

We analyze the flux power spectrum and its covariance using simulated Lyman alpha forests. We find that pseudo-hydro techniques are good approximations of hydrodynamical simulations at high redshift. However, the pseudo-hydro techniques fail at low redshift because they are insufficient for characterizing some components of the low-redshift intergalactic medium, notably the warm-hot intergalactic medium. Hence, to use the low-redshift Lyman alpha flux power spectrum to constrain cosmology, one would need realistic hydrodynamical simulations. By comparing one-dimensional mass statistics with flux statistics, we show that the nonlinear transform between density and flux quenches the fluctuations so that the flux power spectrum is much less sensitive to cosmological parameters than the one-dimensional mass power spectrum. The covariance of the flux power spectrum is nearly Gaussian. As such, the uncertainties of the underlying mass power spectrum could still be large, even though the flux power spectrum can be precisely determined from a small number of lines of sight.

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The Bar--Halo Interaction--I. From Fundamental Dynamics to Revised N-body Requirements

Only through resonances can non-axisymmetric features such as spiral arms and bars exert torques over large scales and change the overall structure of a near-equilibrium galaxy. We describe the resonant interaction mechanism in detail and derive explicit criteria for the particle number required to simulate these dynamical processes accurately using N-body simulations and illustrate them with numerical experiments. To do this, we perform direct numerical solution of perturbation theory and make detailed comparisons with N-body simulations. The criteria include: sufficient particle coverage in phase space near the resonance and enough particles to minimize gravitational potential fluctuations that will change the dynamics of the resonant encounter. Some of our more surprising findings are as follows. First, the Inner-Lindblad-like resonance (ILR), responsible for coupling the bar to the central halo cusp, requires almost 10^9 equal mass particles within the virial radius for a Milky-Way-like bar in an NFW profile. Second, orbits that linger near the resonance receive more angular momentum than orbits that move through the resonance quickly. Small-scale fluctuations present in state-of-the-art particle-particle simulations can knock orbits out of resonance, preventing them from lingering and, thereby, decrease the torque. The required particle numbers are sufficiently high for scenarios of interest that apparent convergence in particle number is misleading: the convergence is in the noise-dominated regime. State-of-the-art simulations are not adequate to follow all aspects of secular evolution driven by the bar-halo interaction. We present a procedure to test the requirements for individual N-body codes for the actual problem of interest. [abridged]

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How Do Galaxies Get Their Gas?

We examine the temperature history of gas accreted by forming galaxies in SPH simulations. About half the gas shock heats to roughly the virial temperature of the galaxy potential well before cooling, condensing, and forming stars, but the other half radiates its acquired gravitational energy at much lower temperatures, typically T<10^5 K, and the histogram of maximum gas temperatures is clearly bimodal. The "cold mode" of gas accretion dominates for low mass galaxies (M_baryon < 10^{10.3}Msun or M_halo < 10^{11.4}Msun), while the conventional "hot mode" dominates the growth of high mass systems. Cold accretion is often directed along filaments, allowing galaxies to efficiently draw gas from large distances, while hot accretion is quasi-spherical. The galaxy and halo mass dependence leads to redshift and environment dependence of cold and hot accretion rates, with cold mode dominating at high redshift and in low density regions today, and hot mode dominating in group and cluster environments at low redshift. Star formation rates closely track accretion rates, and we discuss the physics behind the observed environment and redshift dependence of galactic scale star formation. If we allowed hot accretion to be suppressed by conduction or AGN feedback, then the simulation predictions would change in interesting ways, perhaps resolving conflicts with the colors of ellipticals and the cutoff of the galaxy luminosity function. The transition between cold and hot accretion at M_h ~ 10^{11.4}Msun is similar to that found by Birnboim & Dekel (2003) using 1-d simulations and analytic arguments. The corresponding baryonic mass is tantalizingly close to the scale at which Kauffmann et al. (2003) find a marked shift in galaxy properties. We speculate on connections between these theoretical and observational transitions.

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Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies

The halo occupation distribution (HOD) describes the relation between galaxies and dark matter at the level of individual dark matter halos. The properties of galaxies residing at the centers of halos differ from those of satellite galaxies because of differences in their formation histories. Using a smoothed particle hydrodynamics (SPH) simulation and a semi-analytic (SA) galaxy formation model, we examine the separate contributions of central and satellite galaxies to the HOD, more specifically to the probability P(N|M) that a halo of virial mass M contains N galaxies of a particular class. In agreement with earlier results for dark matter subhalos, we find that the mean occupation function for galaxies above a baryonic mass threshold can be approximated by a step function for central galaxies plus a power law for satellites, and that the distribution of satellite numbers is close to Poisson at fixed halo mass. For galaxy samples defined by different baryonic mass thresholds, there is a nearly linear relation between the minimum halo mass Mmin required to host a central galaxy and the mass M1 at which an average halo hosts one satellite, with M1 ~ 14 Mmin (SPH) or M1 ~ 18 Mmin (SA). The mean occupation number of young galaxies exhibits a local minimum at M ~ 10 Mmin where halos are too massive to host a young central galaxy but not massive enough to host satellites. We show that the conditional galaxy mass function at fixed halo mass cannot be described by a Schechter function because central galaxies produce a "bump" at high masses. We suggest parameterizations for the HOD and the conditional luminosity function that can be used to model observed galaxy clustering. Many of our predictions are in good agreement with recent results inferred from clustering in the Sloan Digital Sky Survey.

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Measuring the Halo Mass of z=3 Damped Ly-alpha Absorbers from the Absorber-Galaxy Cross-correlation

[Abridged] We test the reliability of a method to measure the mean halo mass of Damped Ly-alpha absorbers (DLAs). The method is based on measuring the ratio of the cross-correlation between DLAs and galaxies to the auto-correlation of the galaxies themselves ($w_{\rm dg}/w_{\rm gg}$), which is (in linear theory) the ratio of their bias factor. This is shown to be true irrespective of the galaxy redshift distribution, provided that one uses the same galaxies for the two correlation functions. The method is applicable to all redshifts. Here, we focus on z=3 DLAs and we demonstrate that the method robustly constrains the mean DLA halo mass using smoothed particle hydrodynamics (SPH) cosmological simulations. If we use the bias formalism of Mo & White with the DLA and galaxy mass distributions of these simulations, we predict a bias ratio of 0.771. Direct measurement from the simulations of $w_{\rm dg}/w_{\rm gg}$ st yields a ratio of 0.73+/-0.08, in excellent agreement with that prediction. Equivalently, inverting the measured correlation ratio to infer a mean DLA halo mass yields (log. averaging, in solar units) =11.13+/-013, in excellent agreement with the true value in the simulations: 11.16. The cross- correlation method thus appears to yield a robust estimate of the average host halo mass even though the DLAs and the galaxies occupy a broad mass spectrum of halos, and massive halos contain multiple galaxies with DLAs. We show that the inferred mean DLA halo mass is independent of the galaxy sub-sample used, i.e. the cross-correlation technique is also reliable. Our results imply that the cross-correlation length between DLAs and LBGs is predicted to be, at most, 2.85 Mpc. Future observations will soon distinguish models in which DLAs are in low mass halos from those in which DLAs are in massive halos.

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The Galaxy Angular Correlation Functions and Power Spectrum from the Two Micron All Sky Survey

We calculate the angular correlation function of galaxies in the Two Micron All Sky Survey. We minimize the possible contamination by stars, dust, seeing and sky brightness by studying their cross correlation with galaxy density, and limiting the galaxy sample accordingly. We measure the correlation function at scales between 1-18 arcdegs using a half million galaxies. We find a best fit power law to the correlation function has a slope of 0.76 and an amplitude of 0.11. However, there are statistically significant oscillations around this power law. The largest oscillation occurs at about 0.8 degrees, corresponding to 2.8 h^{-1} Mpc at the median redshift of our survey, as expected in halo occupation distribution descriptions of galaxy clustering. We invert the angular correlation function using Singular Value Decomposition to measure the three-dimensional power spectrum and find that it too is in good agreement with previous measurements. A dip seen in the power spectrum at small wavenumber k is statistically consistent with CDM-type power spectra. A fit of CDM-type power spectra to k < 0.2 h Mpc^{-1} give constraints of Γ_{eff}=0.116 and σ_8=0.96. This suggest a K_s-band linear bias of 1.1+/-0.2. This Γ_{eff} is different from the WMAP CMB derived value. On small scales the power-law shape of our power spectrum is shallower than that derived for the SDSS. These facts together imply a biasing of these different galaxies that might be nonlinear, that might be either waveband or luminosity dependent, and that might have a nonlocal origin.

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Interpreting the Relationship Between Galaxy Luminosity, Color and Environment

We study the relationship between galaxy luminosity, color, and environment in a cosmological simulation of galaxy formation. We compare the predicted relationship with that found for SDSS galaxies and find that the model successfully predicts most of the qualitative features seen in the data, but also shows some interesting differences. Specifically, the simulation predicts that the local density around bright red galaxies is a strong increasing function of luminosity, but does not depend much on color at fixed luminosity. Moreover, we show that this is due to central galaxies in dark matter halos whose baryonic masses correlate strongly with halo mass. The simulation also predicts that the local density around blue galaxies is a strong increasing function of color, but does not depend much on luminosity at fixed color. We show that this is due to satellite galaxies in halos whose stellar ages correlate with halo mass. Finally, the simulation fails to predict the luminosity dependence of environment observed around low luminosity red galaxies. However, we show that this is most likely due to the simulation's limited resolution. A study of a higher resolution, smaller volume simulation suggests that this dependence is caused by the fact that all low luminosity red galaxies are satellites in massive halos, whereas intermediate luminosity red galaxies are a mixture of satellites in massive halos and central galaxies in less massive halos.

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