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

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, ${\Omega }_W^{\mathrm{halo}}$, and the mean thermal energy density of baryons, ${\Omega }_{\mathrm{th}}$. These quantities can be obtained using two fundamentally different estimates: we compute ${\Omega }_W^{\mathrm{halo}}$ using the theoretical framework of the halo model which is driven by dark matter statistics, and measure ${\Omega }_{\mathrm{th}}$ 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 ${\Omega }_W^{\mathrm{halo}}$ originates from massive halos with $M>10^{13}{M}_{\odot }$. Then, using our measurements of the SZ background, we find that ${\Omega }_{\mathrm{th}}$ 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 ${\Omega }_{\mathrm{non}-\mathrm{th}}\simeq 0.4\times 10^{-8}$ at $z=0$.

11 pages + references, 4 figures, 2 tables. (v2) Expanded discussion on the modelling uncertainty. (v3) Fixed a minor typo in Eq.(22). Accepted for publication in the Astrophysical Journal. Julia codes to reproduce the figures and tables are available in https://github.com/komatsu5147/OmegaGrav.jl