Showing papers by "Ravi K. Sheth published in 2009"

A halo model of galaxy colours and clustering in the Sloan Digital Sky Survey

Abstract: Successful halo-model descriptions of the luminosity dependence of clustering distinguish between the central galaxy in a halo and all the others (satellites). To include colours, we provide a prescription for how the colour–magnitude relation of centrals and satellites depends on halo mass. This follows from two assumptions: (i) the bimodality of the colour distribution at a fixed luminosity is independent of halo mass and (ii) the fraction of satellite galaxies which populate the red sequence increases with luminosity. We show that these two assumptions allow one to build a model of how galaxy clustering depends on colour without any additional free parameters than those required to model the luminosity dependence of galaxy clustering. We then show that the resulting model is in good agreement with the distribution and clustering of colours in the Sloan Digital Sky Survey, both by comparing the predicted correlation functions of red and blue galaxies with measurements and by comparing the predicted colour–mark correlation function with the measured one. Mark correlation functions are powerful tools for identifying and quantifying correlations between galaxy properties and their environments: our results indicate that the correlation between halo mass and environment is the primary driver for correlations between galaxy colours and the environment; additional correlations associated with halo ‘assembly bias’ are relatively small. Our approach shows explicitly how to construct mock catalogues which include both luminosities and colours – thus providing realistic training sets for, e.g., galaxy cluster-finding algorithms. Our prescription is the first step towards incorporating the entire spectral energy distribution into the halo model approach.

Halo abundances in the fnl model

Abstract: We show how the excursion set moving barrier model for halo abundances may be generalized to the local non-Gaussian f n1 model. Our estimate assumes that the distribution of step sizes depends on f n1 , but that they are otherwise uncorrelated. Our analysis is consistent with previous results for the case of a constant barrier, and highlights some implicit assumptions. It also clarifies the basis of an approximate analytic solution to the moving barrier problem in the Gaussian case, and shows how it might be improved.

Halo abundances in the f_{nl} model

Abstract: We show how the excursion set moving barrier model for halo abundances may be generalized to the local non-Gaussian f_{nl} model. Our estimate assumes that the distribution of step sizes depends on f_{nl}, but that they are otherwise uncorrelated. Our analysis is consistent with previous results for the case of a constant barrier, and highlights some implicit assumptions. It also clarifies the basis of an approximate analytic solution to the moving barrier problem in the Gaussian case, and shows how it might be improved.

Spherical Collapse and Cluster Counts in Modified Gravity Models

Abstract: Modifications to the gravitational potential affect the nonlinear gravitational evolution of large scale structures in the Universe. To illustrate some generic features of such changes, we study the evolution of spherically symmetric perturbations when the modification is of Yukawa type; this is nontrivial, because we should not and do not assume that Birkhoff's theorem applies. We then show how to estimate the abundance of virialized objects in such models. Comparison with numerical simulations shows reasonable agreement: When normalized to have the same fluctuations at early times, weaker large scale gravity produces fewer massive halos. However, the opposite can be true for models that are normalized to have the same linear theory power spectrum today, so the abundance of rich clusters potentially places interesting constraints on such models. Our analysis also indicates that the formation histories and abundances of sufficiently low mass objects are unchanged from standard gravity. This explains why simulations have found that the nonlinear power spectrum at large k is unaffected by such modifications to the gravitational potential. In addition, the most massive objects in models with normalized cosmic microwave background and weaker gravity are expected to be similar to the high-redshift progenitors of the most massive objectsmore » in models with stronger gravity. Thus, the difference between the cluster and field galaxy populations is expected to be larger in models with stronger large scale gravity.« less

The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances

Abstract: We generalize the Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian f nl model. This is possible because, to at least second order in f nl , distributions at fixed overdensity are unchanged from the case f nl = 0. We use this generalization to estimate the effect of f nl ≠ 0 on the abundance of virialized haloes. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity) or its smallest eigenvalue. The approach based on a critical overdensity yields results which are in excellent agreement with numerical measurements. We then use these same methods to develop approximations describing the sensitivity of void abundances on f nl . While a positive f nl produces more extremely massive haloes, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalization of the density fluctuation field σ 8 . Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.

Sizes and ages of SDSS ellipticals: Comparison with hierarchical galaxy formation models

Abstract: In a sample of about 45,700 early-type galaxies extracted from SDSS, we find that the shape, normalization, and dispersion around the mean size-stellar mass relation is the same for young and old systems, provided the stellar mass is greater than 3*10^10 Msun. This is difficult to reproduce in pure passive evolution models, which generically predict older galaxies to be much more compact than younger ones of the same stellar mass. However, this aspect of our measurements is well reproduced by hierarchical models of galaxy formation. Whereas the models predict more compact galaxies at high redshifts, subsequent minor, dry mergers increase the sizes of the more massive objects, resulting in a flat size-age relation at the present time. At lower masses, the models predict that mergers are less frequent, so that the expected anti-correlation between age and size is not completely erased. This is in good agreement with our data: below 3*10^10 Msun, the effective radius R_e is a factor of ~2 lower for older galaxies. These successes of the models are offset by the fact that the predicted sizes have other serious problems, which we discuss.

Dark matter halo creation in moving barrier models

Abstract: In hierarchical models of structure formation, the time derivative of the halo mass function may be thought of as the difference of two terms - a creation term, which describes the increase in the number of haloes of mass m from mergers of less massive objects, and a destruction term, which describes the decrease in the number of m-haloes as these merge with other haloes, creating more massive haloes as a result. The first part of this paper focuses on estimating the distribution of times when these creation events take place. In models where haloes form from a spherical collapse, this distribution can be estimated from the same formalism which is used to estimate halo abundances: the constant-barrier excursion-set approach. In the excursion-set approach, moving rather than constant barriers are necessary for estimating halo abundances when the collapse is triaxial. First, we generalize the excursion-set estimate of the creation time distribution by incorporating ellipsoidal collapse. Then, we show that these moving barrier based predictions are in better agreement with measurements in numerical simulations than are the corresponding predictions of the spherical collapse model. In the second part of the paper, we link the creation time distribution to the creation term mentioned above. For this quantity, the improvement provided by the ellipsoidal collapse model is more evident. These results should be useful for studies of merger-driven star formation rates and active galactic nucleus activity. We also present a similar study of the creation of haloes conditioned on belonging to an object of a certain mass today, and reach similar conclusions - the moving barrier based estimates are in substantially better agreement with the simulations. This part of the study may be useful for understanding the tendency for the oldest stars to exist in the most massive objects, and for star formation to only occur in lower mass objects at late times.

The non-linear probability distribution function in models with local primordial non-Gaussianity

Abstract: We use the spherical evolution approximation to investigate non-linear evolution from the non-Gaussian initial conditions characteristic of the local f nl model. We provide an analytic formula for the non-linearly evolved probability distribution function (PDF) of the dark matter which shows that the underdense tail of the non-linear PDF in the f nl model should differ significantly from that for Gaussian initial conditions. Measurements of the underdense tail in numerical simulations may be affected by discreteness effects, and we use a Poisson counting model to describe this effect. Once this has been accounted, our model is in good quantitative agreement with the simulations. In principle, our calculation is an important first step in programs which seek to reconstruct the shape of the initial PDF from observations of large-scale structures in the Lyα forest and the galaxy distribution at later times.

Galaxy luminosities, stellar masses, sizes, velocity dispersions as a function of morphological type

Abstract: We provide fits to the distribution of galaxy luminosity, size, velocity dispersion and stellar mass as a function of concentration index C_r and morphological type in the SDSS. We also quantify how estimates of the fraction of `early' or `late' type galaxies depend on whether the samples were cut in color, concentration or light profile shape, and compare with similar estimates based on morphology. Our fits show that Es account for about 20% of the r-band luminosity density, rho_Lr, and 25% of the stellar mass density, rho_*; including S0s and Sas increases these numbers to 33% and 40%, and 50% and 60%, respectively. Summed over all galaxy types, we find rho_* ~ 3 * 10^8 M_Sun Mpc^{-3} at z ~ 0. This is in good agreement with expectations based on integrating the star formation history. However, compared to most previous work, we find an excess of objects at large masses, up to a factor of ~ 10 at M_* ~ 5*10^{11} M_Sun. The stellar mass density further increases at large masses if we assume different IMFs for Es and spiral galaxies, as suggested by some recent chemical evolution models, and results in a better agreement with the dynamical mass function. We also show that the trend for ellipticity to decrease with luminosity is primarily because the E/S0 ratio increases at large L. However, the most massive galaxies, M_* > 5 * 10^{11} M_Sun, are less concentrated and not as round as expected if one extrapolates from lower L, and they are not well-fit by pure deVaucouleur laws. This suggests formation histories with recent radial mergers. Finally, we show that the age-size relation is flat for Es of fixed dynamical mass, but, at fixed M_dyn, S0s and Sas with large sizes tend to be younger. Explaining this difference between E and S0 formation is a new challenge for models of early-type galaxy formation.

On the equivalence between the effective cosmology and excursion set treatments of environment

Abstract: In studies of the environmental dependence of structure formation, the large-scale environment is often thought of as providing an effective background cosmology: for example the formation of structure in voids is expected to be just like that in a less dense universe with appropriately modified Hubble and cosmological constants However, in the excursion set description of structure formation which is commonly used to model this effect, no explicit mention is made of the effective cosmology Rather, this approach uses the spherical evolution model to compute an effective linear theory growth factor, which is then used to predict the growth and evolution of non-linear structures We show that these approaches are, in fact, equivalent: a consequence of Birkhoff's theorem We speculate that this equivalence will not survive in models where the gravitational force law is modified from an inverse square, potentially making the environmental dependence of clustering a good test of such models

Non-Gaussian distribution and clustering of hot and cold pixels in the five-year WMAP sky

Abstract: We present measurements of the clustering of hot and cold patches in the microwave background sky as measured from the Wilkinson Microwave Anisotropy Probe 5-year data. These measurements are compared with theoretical predictions which assume that the cosmological signal obeys Gaussian statistics. We find significant differences from the simplest Gaussian-based prediction. However, the measurements are sensitive to the fact that the noise is spatially inhomogeneous (e.g. because different parts of the sky were observed for different lengths of time). We show how to account for this spatial inhomogeneity when making predictions. Differences from the Gaussian-based expectation remain even after this more careful accounting of the noise. In particular, we note that hot and cold pixels cluster differently within the same temperature thresholds at few-degree scales. While these findings may indicate primordial non-Gaussianity, we discuss other plausible explanations for these discrepancies. In addition, we find some deviations from Gaussianity at sub-degree scales, especially in the W band, whose origin may be associated with extragalactic dust emission.

Density profiles and voids in modified gravity models

Abstract: We study the formation of voids in a modified gravity model in which gravity is generically stronger or weaker on large scales. We show that void abundances provide complementary information to halo abundances: if normalized to the CMB, models with weaker large-scale gravity have smaller large scale power, fewer massive halos and fewer large voids, although the scalings are not completely degenerate with $\sigma_8$. Our results suggest that, in addition to their abundances, halo and void density profiles may also provide interesting constraints on such models: stronger large scale gravity produces more concentrated halos, and thinner void walls. This potentially affects the scaling relations commonly assumed to translate cluster observables to halo masses, potentially making these too, useful probes of gravity.

Convolution and deconvolution based estimates of galaxy scaling relations from photometric redshift surveys

Abstract: In addition to the maximum likelihood approach, there are two other methods which are commonly used to reconstruct the true redshift distribution from photometric redshift datasets: one uses a deconvolution method, and the other a convolution. We show how these two techniques are related, and how this relationship can be extended to include the study of galaxy scaling relations in photometric datasets. We then show what additional information photometric redshift algorithms must output so that they too can be used to study galaxy scaling relations, rather than just redshift distributions. We also argue that the convolution based approach may permit a more efficient selection of the objects for which calibration spectra are required.

Large scale bias and the inaccuracy of the peak-background split

Abstract: The peak-background split argument is commonly used to relate the abundance of dark matter halos to their spatial clustering. Testing this argument requires an accurate determination of the halo mass function. We present a Maximum Likelihood method for fitting parametric functional forms to halo abundances which differs from previous work because it does not require binned counts. Our conclusions do not depend on whether we use our method or more conventional ones. In addition, halo abundances depend on how halos are defined. Our conclusions do not depend on the choice of link length associated with the friends-of-friends halo-finder, nor do they change if we identify halos using a spherical overdensity algorithm instead. The large scale halo bias measured from the matter-halo cross spectrum b_x and the halo autocorrelation function b_xi (on scales k~0.03h/Mpc and r ~50 Mpc/h) can differ by as much as 5% for halos that are significantly more massive than the characteristic mass M*. At these large masses, the peak background split estimate of the linear bias factor b1 is 3-5% smaller than b_xi, which is 5% smaller than b_x. We discuss the origin of these discrepancies: deterministic nonlinear local bias, with parameters determined by the peak-background split argument, is unable to account for the discrepancies we see. A simple linear but nonlocal bias model, motivated by peaks theory, may also be difficult to reconcile with our measurements. More work on such nonlocal bias models may be needed to understand the nature of halo bias at this level of precision.

The nonlinear redshift space probability distribution function in models with local primordial non-Gaussianity

Abstract: We use the ellipsoidal collapse approximation to investigate the nonlinear redshift space evolution of the density field with primordial non-Gaussianity of the local f_{nl}-type. We utilize the joint distribution of eigenvalues of the initial non-Gaussian shear field and evaluate the evolved redshift space probability distribution function (PDF). It is shown that, similar to the real space analysis, the underdense tail of the nonlinear redshift space PDF differs significantly from that for Gaussian initial conditions. We also derive the lowest order correction of the Kaiser's formulain the presence of a non-zero f_{nl}.

Reconstructing galaxy fundamental distributions and scaling relations from photometric redshift surveys. Applications to the SDSS early-type sample

Abstract: Noisy distance estimates associated with photometric rather than spectroscopic redshifts lead to a mis-estimate of the luminosities, and produce a correlated mis-estimate of the sizes. We consider a sample of early-type galaxies from the SDSS DR6 for which both spectroscopic and photometric information is available, and apply the generalization of the V_max method to correct for these biases. We show that our technique recovers the true redshift, magnitude and size distributions, as well as the true size-luminosity relation. We find that using only 10% of the spectroscopic information randomly spaced in our catalog is sufficient for the reconstructions to be accurate within about 3%, when the photometric redshift error is dz = 0.038. We then address the problem of extending our method to deep redshift catalogs, where only photometric information is available. In addition to the specific applications outlined here, our technique impacts a broader range of studies, when at least one distance-dependent quantity is involved. It is particularly relevant for the next generation of surveys, some of which will only have photometric information.

Linear theory and velocity correlations of clusters

Abstract: Linear theory provides a reasonable description of the velocity correlations of biased tracers both perpendicular and parallel to the line of separation, provided one accounts for the fact that the measurement is almost always made using pair-weighted statistics. This introduces an additional term which, for sufficiently biased tracers, may be large. Previous work suggesting that linear theory was grossly in error for the components parallel to the line of separation ignored this term.

Non-Gaussian Distribution and Clustering of Hot and Cold Pixels in the WMAP Five-Year Sky

Abstract: We present measurements of the clustering of hot and cold patches in the microwave background sky as measured from the Wilkinson Microwave Anisotropy Probe (WMAP) five-year data. These measurements are compared with theoretical predictions which assume that the cosmological signal obeys Gaussian statistics. We find significant differences from the simplest Gaussian-based prediction. However, the measurements are sensitive to the fact that the noise is spatially inhomogeneous (e.g., because different parts of the sky were observed for different lengths of time). We show how to account for this spatial inhomogeneity when making predictions. Differences from the Gaussian-based expectation remain even after this more careful accounting of the noise. In particular, we note that hot and cold pixels cluster differently within the same temperature thresholds at few-degree scales. While these findings may indicate primordial non-Gaussianity, we discuss other plausible explanations for these discrepancies. In addition, we find some deviations from Gaussianity at sub-degree scales, especially in the W band, whose origin may be associated with extragalactic dust emission.

The initial shear field in models with primordial local non-Gaussianity and implications for halo and void abundances

Abstract: We generalize Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian f_{nl} model. This is possible because, to at least second order in f_{nl}, distributions at fixed overdensity are unchanged from the case f_{nl}=0. We use this generalization to estimate the effect of f_{nl} e 0 on the abundance of virialized halos. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity), or its smallest eigenvalue. The approach based on a critical overdensity yields results which are in excellent agreement with numerical measurements. We then use these same methods to develop approximations describing the sensitivity of void abundances on f_{nl}. While a positive f_{nl} produces more extremely massive halos, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalisation of the density fluctuation field \sigma_8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.

The Substructure Hierarchy in Dark Matter Haloes

Abstract: We present a new algorithm for identifying the substructure within simulated dark matter haloes. The method is an extension of that proposed by Tormen et al. (2004) and Giocoli et al. (2008a), which identifies a subhalo as a group of self-bound particles that prior to being accreted by the main progenitor of the host halo belonged to one and the same progenitor halo (hereafter satellite). However, this definition does not account for the fact that these satellite haloes themselves may also have substructure, which thus gives rise to sub-subhaloes, etc. Our new algorithm identifies substructures at all levels of this hierarchy, and we use it to determine the mass function of all substructure (counting sub-haloes, sub-subhaloes, etc.). On average, haloes which formed more recently tend to have a larger mass fraction in substructure and to be less concentrated than average haloes of the same mass. We provide quantitative fits to these correlations. Even though our algorithm is very different from that of Gao et al. (2004), we too find that the subhalo mass function per unit mass at redshift z = 0 is universal. This universality extends to any redshift only if one accounts for the fact that host haloes of a given mass are less concentrated at higher redshifts, and concentration and substructure abundance are anti-correlated. This universality allows a simple parametrization of the subhalo mass function integrated over all host halo masses, at any given time. We provide analytic fits to this function which should be useful in halo model analyses which equate galaxies with halo substructure when interpreting clustering in large sky surveys. Finally, we discuss systematic differences in the subhalo mass function that arise from different definitions of (host) halo mass.

On the equivalence between the effective cosmology and excursion set treatments of environment

Abstract: In studies of the environmental dependence of structure formation, the large scale environment is often thought of as providing an effective background cosmology: e.g. the formation of structure in voids is expected to be just like that in a less dense universe with appropriately modified Hubble and cosmological constants. However, in the excursion set description of structure formation which is commonly used to model this effect, no explicit mention is made of the effective cosmology. Rather, this approach uses the spherical evolution model to compute an effective linear theory growth factor, which is then used to predict the growth and evolution of nonlinear structures. We show that these approaches are, in fact, equivalent: a consequence of Birkhoff's theorem. We speculate that this equivalence will not survive in models where the gravitational force law is modified from an inverse square, potentially making the environmental dependence of clustering a good test of such models.

Large Scale Structure and Galaxies

Abstract: These notes sketch the motivation for and ingredients of the Halo Model of nonlinear and biased structures in the Universe. A key part of this approach is the relation between halo abundances and their large scale clustering. These come from the excursion set approach, so I have taken the opportunity to collect together all the formulae associated with this approach into one place. These include expressions for: the unconditional mass function, the conditional mass function, the environmental dependence of the mass function, halo bias, merger rates, creation and destruction rates, the distribution of half‐mass assembly times, masses and mass at fixed assembly time. In addition, I discuss how the approach can be used to describe voids, filaments and sheets, as well as the nonlinear counts in cells distribution, and provide analytic formulae for a number of these statistics.Together these formulae show that, in hierarchical models: massive halos assemble their mass later than low mass halos; halos which ass...