The n-point streaming model: how velocities shape correlation functions in redshift space

Abstract

Starting from first principles, we derive the fundamental equations that relate the n-point correlation functions in real and redshift space. Our result generalises the so-called 'streaming model' to higher-order statistics: the full n-point correlation in redshift-space is obtained as an integral of its real-space counterpart times the joint probability density of n−1 relative line-of-sight peculiar velocities. Equations for the connected n-point correlation functions are obtained by recursively applying the generalised streaming model for decreasing n. Our results are exact within the distant-observer approximation and completely independent of the nature of the tracers for which the correlations are evaluated. Focusing on 3-point statistics, we use an N -body simulation to study the joint probability density function of the relative line-of-sight velocities of pairs of particles in a triplet. On large scales, we find that this distribution is approximately Gaussian and that its moments can be accurately computed with standard perturbation theory. We use this information to formulate a phenomenological 3-point Gaussian streaming model. A practical implementation is obtained by using perturbation theory at leading order to approximate several statistics in real space. In spite of this simplification, the resulting predictions for the matter 3-point correlation function in redshift space are in rather good agreement with measurements performed in the simulation. We discuss the limitations of the simplified model and suggest a number of possible improvements. Our results find direct applications in the analysis of galaxy clustering but also set the basis for studying 3-point statistics with future peculiar-velocity surveys and experiments based on the kinetic Sunyaev-Zel'dovich effect.

Information content in mean pairwise velocity and mean relative velocity between pairs in a triplet

“…dark matter particles, halos, and galaxies). This was first done for dark matter in Kuruvilla & Porciani (2020). In such a case, we consider two mean relative velocities: w 12 | 123 t and w 23 | 123 t (where the subscript t implies that the averages are computed over all particle triplets with separations 123 ).…”

“…For detailed derivations of these mean relative velocities between pairs in a triplet, we refer the reader to Kuruvilla & Porciani (2020), in which we also showcase how well the standard perturbation theory prescription at leading order works for an unbiased tracer (i.e. for dark matter species).…”

“…This shows the potential of three-point mean relative velocity statistics to be competitive with respect to clustering information in the future. Kuruvilla & Porciani (2020) introduced the mean relative velocity between pairs in a triplet, and derived the analytical prediction for it at leading order using standard perturbation theory. In this work, we quantified the information content in this three-point relative velocity statistics.…”

“…The three-point generalisation of the pairwise velocity, i.e. the relative velocities between pairs in a triplet, was recently introduced in Kuruvilla & Porciani (2020). However, the impact of cosmological parameters (especially massive neutrinos) on it remains unexplored.…”

Imprint of baryons and massive neutrinos on velocity statistics

“…These distortions can be leveraged to accurately constrain the growth rate of structure, and hence cosmological parameters, by measuring correlation functions in redshift space (Percival & White 2009). In configuration space clustering, the state-of-the-art modelling is based on the 'streaming model' (Peebles 1980;Fisher 1995;Scoccimarro 2004;Kuruvilla & Porciani 2018;Vlah & White 2019), recently generalised to npoint correlation function in redshift space (Kuruvilla & Porciani 2020). In two-point clustering, it provides a framework to map the two-point correlation function in redshift space, which is obtained as the integral of the real-space isotropic correlation function with the line-of-sight (los) pairwise velocity distribution.…”