Modeling the Phase-Space Distribution around Massive Halos

TL;DR

This paper develops a semi-analytical halo model to describe phase-space distributions around massive halos, enabling tests of modified gravity theories through velocity dispersion measurements.

Contribution

It introduces a new semi-analytical approach based on the halo model to accurately predict phase-space distributions, including effects of modified gravity.

Findings

Model agrees well with modified gravity simulations.

Incorporates observational effects like Hubble flow.

Provides a sensitive test for hierarchical structure formation.

Abstract

The comparison between dynamical mass and lensing mass provides a targeted test for a wide range of modified gravity models. In our previous paper we showed, through numerical simulations, that the measurement of the line-of-sight velocity dispersion around stacked massive clusters whose lensing masses are known allows for stringent constraints on modified gravity on scales of 2 - 15 Mpc/h. In this work we develop a semi-analytical approach based on the halo model to describe the phase-space distribution and the line-of-sight velocity dispersion for different tracers. The model distinguishes contributions from the halo pairwise velocity and the virial velocity within halos. We also discuss observational complications, in particular the contribution from Hubble flow, and show how our model can incorporate these complications. We then incorporate the effects of modified gravity (specifically, f(R) and braneworld models), and show that the model predictions are in excellent agreement with modified gravity simulations. More broadly, the phase-space distribution provides a sensitive test of our understanding of hierarchical structure formation when confronted with observations via this model.