Roman Scoccimarro

We compute the bispectrum for the galaxy distribution in the IRAS QDOT, 2Jy, and 1.2Jy redshift catalogs for wavenumbers 0.05 1 at large scales, \chi^2 non-Gaussian initial conditions are ruled out at the 95% confidence level. The IRAS data do not distinguish between Lagrangian or Eulerian local bias.Comment: 30 pages, 11 figure

The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the bispectrum is well understood theoretically from non-linear perturbation theory and numerical simulations, applications to galaxy surveys require a number of issues to be addressed. In this paper we consider the effect on the bispectrum of stochastic non-linear biasing, radial redshift distortions, non-Gaussian initial conditions, survey geometry and sampling. We find that: 1) bias stochasticity does not affect the use of the bispectrum to recover the mean biasing relation between galaxies and mass, at least for models in which the scatter is uncorrelated at large scales. 2) radial redshift distortions do not change significantly the monopole power spectrum and bispectrum compared to their plane-parallel values. 3) survey geometry leads to finite volume effects which must be taken into account in current surveys before comparison with theoretical predictions can be made. 4) sparse sampling and survey geometry correlate different triangles leading to a breakdown of the Gaussian likelihood approximation. We develop a likelihood analysis using bispectrum eigenmodes, calculated by Monte Carlo realizations of mock surveys generated with second-order Lagrangian perturbation theory and checked against N-body simulations. In a companion paper we apply these results to the analysis of the bispectrum of IRAS galaxies.Comment: 46 pages, 18 figures. Accepted for publication in ApJ. Typos fixed and improved comparison with previous wor

A simple model of how objects of different masses stream towards each other as they cluster gravitationally is described. The model shows how the mean streaming velocity of dark matter particles is related to the motions of the parent dark matter haloes. It also provides a reasonably accurate description of how the pairwise velocity dispersion of dark matter particles differs from that of the parent haloes. The analysis is then extended to describe the streaming motions of galaxies. This shows explicitly that the streaming motions measured in a given galaxy sample depend on how the sample was selected, and shows how to account for this dependence on sample selection. In addition,we show that the pairwise dispersion should also depend on sample type. Our model predicts that, on small scales, redshift space distortions should affect red galaxies more strongly than blue.

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.

The bispectrum is the lowest-order statistic sensitive to the shape of structures generated by gravitational instability and is a potentially powerful probe of galaxy biasing and the Gaussianity of primordial fluctuations. Although the evolution of the bispectrum is well understood theoretically from non-linear perturbation theory and numerical simulations, applications to galaxy surveys require a number of issues to be addressed. In this paper we consider the effect on the bispectrum of stochastic non-linear biasing, radial redshift distortions, non-Gaussian initial conditions, survey geometry and sampling. We find that: 1) bias stochasticity does not affect the use of the bispectrum to recover the mean biasing relation between galaxies and mass, at least for models in which the scatter is uncorrelated at large scales. 2) radial redshift distortions do not change significantly the monopole power spectrum and bispectrum compared to their plane-parallel values. 3) survey geometry leads to finite volume effects which must be taken into account in current surveys before comparison with theoretical predictions can be made. 4) sparse sampling and survey geometry correlate different triangles leading to a breakdown of the Gaussian likelihood approximation. We develop a likelihood analysis using bispectrum eigenmodes, calculated by Monte Carlo realizations of mock surveys generated with second-order Lagrangian perturbation theory and checked against N-body simulations. In a companion paper we apply these results to the analysis of the bispectrum of IRAS galaxies.