arXiv subjects

Ravi K. Sheth

Publications and source records attributed to Ravi K. Sheth.

176 records · Page 10Linked to original sources

arXiv2000

Peculiar velocities of galaxies and clusters

We present a simple model for the shape of the distribution function of galaxy peculiar velocities. We show how both nonlinear and linear theory terms combine to produce a distribution which has an approximately Gaussian core with exponential wings. The model is easily extended to study how the statistic depends on the type of particle used to trace the velocity field (dark matter particles, dark matter haloes, galaxies), and on the density of the environment in which the test particles are. Comparisons with simulations suggest that our model is accurate. We also show that the evolution of the peculiar velocities depends on the local, rather than the global density. Since clusters populate denser regions on average, using cluster velocities with the linear theory scaling may lead to an overestimate of the global value of Omega. Conversely, using linear theory with the global value of Omega to scale cluster velocities from the initial to the present time results in an underestimate of their true velocities. In general, however, the directions of motions of haloes are rather well described by linear theory. Our results help to simplify models of redshift-space distortions considerably.

astro-ph↗

arXiv2000

Linear and nonlinear contributions to pairwise peculiar velocities

We write the correlation function of dark matter particles, xi(r), as the sum of two terms - one which accounts for nonlinear evolution, and dominates on small scales, and another which is essentially the term from linear theory, and dominates on large scales. We use models of the number and spatial distribution of haloes and halo density profiles to describe the nonlinear term and its evolution. The result provides a good description of the evolution of xi(r) in simulations. We then use this decomposition to provide simple and accurate models of how the single particle velocity dispersion evolves with time, and how the first and second moments of the pairwise velocity distribution depend on scale. The key idea is to use the simple physics of linear theory on large scales, the simple physics of the virial theorem on small scales, and our model for the correlation function to tell us how to weight the two types of contributions (linear and nonlinear) to the pairwise velocity statistics. When incorporated into the streaming model, our results will allow a simple accurate description of redshift-space distortions over the entire range of linear to highly nonlinear regimes.

astro-ph↗

arXiv2000

How Many Galaxies Fit in a Halo? Constraints on Galaxy Formation Efficiency from Spatial Clustering

We study galaxy clustering using halo models, where gravitational clustering is described in terms of dark matter halos. At small scales, clustering statistics are dominated by halo density profiles, whereas at large scales, correlations are the result of combining non-linear perturbation theory with halo biasing. Galaxies are assumed to follow the dark matter profiles, and galaxy formation efficiency is given by the number of galaxies as a function of halo mass. This approach leads to generic predictions: the galaxy power spectrum shows a power-law behavior even though the dark matter does not, and the galaxy higher-order correlations show smaller amplitudes at small scales than their dark matter counterparts, as observed in galaxy catalogs. We find that requiring to fit both the second and third order moments of the APM galaxies provides a strong constraint on galaxy formation models. The data at large scales require that galaxy formation be relatively efficient at small masses, m =10^10 Msun/h, whereas data at smaller scales require that the number of galaxies in a halo scale as the mass to the 0.8th power in the high-mass limit. These constraints are independent of those derived from the luminosity function or Tully-Fisher relation. We also predict the power spectrum, bispectrum, and higher-order moments of the mass density field. Although halo models agree well with measurements of the mass power spectrum and the higher order Sp parameters in N-body simulations, the model assumption that halos are spherical leads to disagreement in the configuration dependence of the bispectrum at small scales. We stress the importance of finite volume effects in higher-order statistics and show how they can be estimated in this approach.

astro-ph↗

arXiv1999

Ellipsoidal collapse and an improved model for the number and spatial distribution of dark matter haloes

The Press--Schechter, excursion set approach allows one to make predictions about the shape and evolution of the mass function of bound objects. It combines the assumption that objects collapse spherically with the assumption that the initial density fluctuations were Gaussian and small. While the predicted mass function is reasonably accurate at the high mass end, it has more low mass objects than are seen in simulations of hierarchical clustering. This discrepancy can be reduced substantially if bound structures are assumed to form from an ellipsoidal, rather than a spherical collapse. In the spherical model, a region collapses if the initial density within it exceeds a threshold value, delta_sc. This value is independent of the initial size of the region, and since the mass of the collapsed object is related to its initial size, delta_sc is independent of final mass. In the ellipsoidal model, the collapse of a region depends on the surrounding shear field, as well as on its initial overdensity. Therefore, there is a relation between the density threshold value required for collapse, and the mass of the final object. We provide a fitting function to this delta_ec(m) relation for initially Gaussian fields which simplifies the inclusion of ellipsoidal dynamics in the excursion set approach. We discuss the relation between the excursion set predictions and the halo distribution in high resolution N-body simulations, and show that our simple parametrization of the ellipsoidal collapse model represents a significant improvement on the spherical model on an object-by-object basis. Finally, we show that the associated statistical predictions, the mass function and the large scale halo-to-mass bias relation, are also more accurate than the standard predictions.

astro-ph↗

arXiv1999

The correlation of peaks in the microwave background

We present accurate predictions of the correlation function of hotspots in the microwave background radiation for gaussian theories such as those predicted in most inflation models. The correlation function of peaks above a certain threshold depends only on the threshold and the power spectrum of temperature fluctuations. Since there are both potentially observable quantities in a microwave background map, there are no adjustable parameters in the predictions. These correlations should therefore provide a powerful test of the gaussian hypothesis, and provide a useful discriminant between inflation and topological defect models such as the cosmic string model. The correlations have a number of oscillatory features, which should be detectable at high signal-to-noise with future satellite experiments such as MAP and Planck.

astro-ph↗

arXiv1999

Large scale bias and the peak background split

Dark matter haloes are biased tracers of the underlying dark matter distribution. We use a simple model to provide a relation between the abundance of dark matter haloes and their spatial distribution on large scales. Our model shows that knowledge of the unconditional mass function alone is sufficient to provide an accurate estimate of the large scale bias factor. Then we use the mass function measured in numerical simulations of SCDM, OCDM and LCDM to compute this bias. Comparison with these simulations shows that this simple way of estimating the bias relation and its evolution is accurate for less massive haloes as well as massive ones. In particular, we show that haloes which are less/more massive than typical M* haloes at the time they form are more/less strongly clustered than formulae based on the standard Press-Schechter mass function predict.

astro-ph↗

arXiv1999

Biasing and the distribution of dark matter haloes

In hierarchical models of gravitational clustering, virialized haloes are biased tracers of the matter distribution. As discussed by Mo & White (1996), this bias is nonlinear and stochastic. They developed a model which allows one to write down analytic expressions for the mean of the bias relation, in the initial Lagrangian, and the evolved, Eulerian spaces. We provide analytic expressions for the higher order moments as well. We also show how the Mo-White approach can be extended to compute the evolution, not just of the haloes, but of the dark matter distribution itself. The model predictions for the mean and scatter in the Eulerian bias relation, as well as for the Eulerian halo-mass and halo-halo correlation functions, are in reasonable agreement with numerical simulations of hierarchical gravitational clustering for haloes of a wide range of masses, whereas the predictions for the corresponding Lagrangian quantities are accurate only for massive haloes.

astro-ph↗

arXiv1998

An excursion set model for the distribution of dark matter and dark matter haloes

A model of the gravitationally evolved dark matter distribution, in the Eulerian space, is developed. It is a simple extension of the excursion set model that is commonly used to estimate the mass function of collapsed dark matter haloes. In addition to describing the evolution of the dark matter itself, the model allows one to describe the evolution of the Eulerian space distribution of the haloes. It can also be used to describe density profiles, on scales larger than the virial radius, of these haloes, and to quantify the way in which matter flows in and out of Eulerian cells. When the initial Lagrangian space distribution is white noise Gaussian, the model suggests that the Inverse Gaussian distribution should provide a reasonably good approximation to the evolved Eulerian density field, in agreement with numerical simulations. Application of this model to clustering from more general Gaussian initial conditions is discussed at the end.

astro-ph↗

arXiv1998

The forest of merger history trees associated with the formation of dark matter halos

We describe a simple efficient algorithm that allows one to construct Monte-Carlo realizations of merger histories of dark matter halos. The algorithm is motivated by the excursion set model (Bond et al. 1991) for the conditional and unconditional halo mass functions. The forest of trees constructed using this algorithm depends on the underlying power spectrum. For Poisson or white-noise initial power-spectra, the forest has exactly the same properties as the ensemble of trees described by Sheth (1996) and Sheth & Pitman (1997). In this case, many ensemble averaged higher order statistics of the tree distribution can be computed analytically. For Gaussian initial conditions with more general power-spectra, mean properties of the ensemble closely resemble the mean properties expected from the excursion set approach. Various statistical quantities associated with the trees constructed using our algorithm are in good agreement with what is measured in numerical simulations of hierarchical gravitational clustering.

astro-ph↗

arXiv1998

The Generalized Poisson distribution and a model of clustering from Poisson initial conditions

This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson initial conditions. This new derivation can be used to construct a useful analytic model of the evolution of clustering measured in these simulations. The model is consistent with the assumption that, as the universe expands and the comoving sizes of regions change as a result of gravitational instability, the number of such expanding and contracting regions is conserved. The model neglects the influence of external tides on the evolution of such regions. Indeed, in the context of this model, the GPD can be thought of as arising from a simple variant of the well-studied spherical collapse model, in which tidal effects are also neglected. The model can be understood as a simple generalization of the excursion set model which is used to estimate the number density of collapsed, virialized halos. The generalization allows one to describe the spatial distribution of the halos and the mass simultaneously, so the extent to which these halos are biased tracers of the underlying matter distribution is easy to estimate.

astro-ph↗

arXiv1996

Galton--Watson branching processes and the growth of gravitational clustering

The Press--Schechter description of gravitational clustering from an initially Poisson distribution is shown to be equivalent to the well studied Galton--Watson branching process. This correspondence is used to provide a detailed description of the evolution of hierarchical clustering, including a complete description of the merger history tree. The relation to branching process epidemic models means that the Press--Schechter description can also be understood using the formalism developed in the study of queues. The queueing theory formalism, also, is used to provide a complete description of the merger history of any given Press--Schechter clump. In particular, an analytic expression for the merger history of any given Poisson Press--Schechter clump is obtained. This expression allows one to calculate the partition function of merger history trees. It obeys an interesting scaling relation; the partition function for a given pair of initial and final epochs is the same as that for certain other pairs of initial and final epochs. The distribution function of counts in randomly placed cells, as a function of time, is also obtained using the branching process and queueing theory descriptions. Thus, the Press--Schechter description of the gravitational evolution of clustering from an initially Poisson distribution is now complete. All these interrelations show why the Press--Schechter approach works well in a statistical sense, but cannot provide a detailed description of the dynamics of the clustering particles themselves. One way to extend these results to more general Gaussian initial conditions is discussed.

astro-ph↗

arXiv1996

The non-linear correlation function and the shapes of virialized halos

The correlation function xi(r) of matter in the non-linear regime is assumed to be determined by the density profiles rho(r) and the mass distribution n(M) of virialized halos. The Press--Schechter approach is used to compute n(M), and the stable clustering hypothesis is used to determine the density profiles of these Press--Schechter halos. Thus, the shape and amplitude of xi(r) on small scales is related to the initial power spectrum of density fluctuations. The case of clustering from scale-free initial conditions is treated in detail. If n is the slope of the initial power spectrum of density fluctuations, then stable clustering requires that xi(r)\propto r^{-gamma}, where gamma is a known function of n. If halo--halo correlations can be neglected, then rho(r)\propto r^{-epsilon}, where epsilon = (gamma+3)/2 = 3(4+n)/(5+n). For all values of n of current interest, this slope is steeper than the value 3(3+n)/(4+n) that was obtained by Hoffman & Shaham in their treatment of the shapes of the outer regions of collapsed halos. Our main result is a prediction for the amplitude of the non-linear correlation function. The predicted amplitude and its dependence on n are in good quantitative agreement with N-body simulations of self-similar clustering. If stable clustering is a good approximation only inside the half-mass radii of Press--Schechter halos, then the density contrast required for the onset of stable clustering can be estimated. This density contrast is in the range ~300-600 and increases with the initial slope n, in agreement with estimates from N-body simulations.

astro-ph↗

arXiv1995

Constrained realizations and minimum variance reconstruction of non-Gaussian random fields

With appropriate modifications, the Hoffman--Ribak algorithm that constructs constrained realizations of Gaussian random fields having the correct ensemble properties can also be used to construct constrained realizations of those non-Gaussian random fields that are obtained by transformations of an underlying Gaussian field. For example, constrained realizations of lognormal, generalized Rayleigh, and chi-squared fields having $n$ degrees of freedom constructed this way will have the correct ensemble properties. The lognormal field is considered in detail. For reconstructing Gaussian random fields, constrained realization techniques are similar to reconstructions obtained using minimum variance techniques. A comparison of this constrained realization approach with minimum variance, Wiener filter reconstruction techniques, in the context of lognormal random fields, is also included. The resulting prescriptions for constructing constrained realizations as well as minimum variance reconstructions of lognormal random fields are useful for reconstructing masked regions in galaxy catalogues on smaller scales than previously possible, for assessing the statistical significance of small-scale features in the microwave background radiation, and for generating certain non-Gaussian initial conditions for $N$-body simulations.

astro-ph↗

arXiv1995

The distribution of pairwise peculiar velocities in the nonlinear regime

The distribution of pairwise, relative peculiar velocities, $f(u;r)$, on small nonlinear scales, $r$, is derived from the Press--Schechter approach. This derivation assumes that Press--Schechter clumps are virialized and isothermal. The virialized assumption requires that the circular velocity, $V_c \propto M^{1/3}$, where $M$ denotes the mass of the clump. The isothermal assumption means that the circular velocity is independent of radius. Further, it is assumed that the velocity distribution within a clump is Maxwellian, that the pairwise relative velocity distribution is isotropic, and that on nonlinear scales clump-clump motions are unimportant when calculating the distribution of velocity differences. Comparison with $N$-body simulations shows that, on small nonlinear scales, all these assumptions are accurate. For most power spectra of interest, the resulting line of sight, pairwise, relative velocity distribution, $f(u_{\rm r})$, is well approximated by an exponential, rather than a Gaussian distribution. This simple Press--Schechter model is also able to provide a natural explanation for the observed, non-Maxwellian shape of $f(v)$, the distribution of peculiar velocities.

astro-ph↗