The thermal and gravitational energy densities in the large-scale structure of the Universe

TL;DR

This paper investigates the relationship between gravitational potential energy and thermal energy in cosmic structures, using theoretical models and SZ measurements to quantify energy densities and non-thermal contributions in the Universe.

Contribution

It provides a novel comparison of theoretical halo model estimates with SZ observations to quantify thermal and gravitational energy densities in large-scale structures.

Findings

90% of gravitational potential energy density from halos with M>10^{13} M_sun

80% of baryonic thermal energy density at z<0.5 from SZ measurements

Non-thermal pressure contributes about 40% of the total pressure at z=0

Abstract

As cosmic structures form, matter density fluctuations collapse gravitationally and baryonic matter is shock-heated and thermalized. We therefore expect a connection between the mean gravitational potential energy density of collapsed halos, $\Omega_{W}^{\rm halo}$, and the mean thermal energy density of baryons, $\Omega_{\rm th}$. These quantities can be obtained using two fundamentally different estimates: we compute $\Omega_{W}^{\rm halo}$ using the theoretical framework of the halo model which is driven by dark matter statistics, and measure $\Omega_{\rm th}$ using the Sunyaev-Zeldovich (SZ) effect which probes the mean thermal pressure of baryons. First, we derive that, at the present time, about 90% of $\Omega_{W}^{\rm halo}$ originates from massive halos with $M>10^{13}\,M_\odot$. Then, using our measurements of the SZ background, we find that $\Omega_{\rm th}$ accounts for about 80% of the kinetic energy of the baryons available for pressure in halos at $z\lesssim 0.5$. This constrains the amount of non-thermal pressure, e.g., due to bulk and turbulent gas motion sourced by mass accretion, to be about $\Omega_{\rm non-th}\simeq 0.4\times 10^{-8}$ at $z=0$.