Mass functions of dark matter halos from maximum entropy distributions for selfgravitating collisionless flow
Abstract
The halomediated inverse mass cascade is a key feature of the intermediate statistically steady state for selfgravitating collisionless flow (SGCFD). A broad spectrum of halos and halo groups are necessary to form from inverse mass cascade for longrange interaction system to maximize its entropy. The limiting velocity ($\textbf X$), speed ($\textbf Z$), and energy ($\textbf E$) distributions of collisionless particles can be obtained analytically from a maximum entropy principle. Halo mass function, i.e. the spectrum of halo mass, is a fundamental quantity for structure formation and evolution. Instead of basing mass functions on simplified spherical/elliptical collapse models, it is possible to reformulate mass function as an intrinsic distribution to maximize system entropy during the everlasting statistically steady state. Starting from halobased description of nonequilibrium collisionless flow, distributions of particle virial dispersion ($\textbf H$), square of particle velocity ($\textbf P$), and number of halos ($\textbf J$) are proposed. Their statistical properties and connections with the limiting velocity distribution ($\textbf X$) are well studied and established. With $\textbf H$ being essentially the halo mass function, two limiting cases of $\textbf H$ distribution are analyzed for large halos ($\textbf H_\infty$) and small halos ($\textbf H_s$), respectively. For large halos, $\textbf H_\infty$ is shown to also be a maximum entropy distribution. For small halos, $\textbf H_s$ approximates the $\textbf P$ distribution and recovers the PressSchechter mass function. The full solution of $\textbf H$ distribution depends on the limiting distribution ($\textbf X$) that maximizes system entropy and the exact models of halo velocity dispersions.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.09676
 Bibcode:
 2021arXiv211009676X
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics;
 Astrophysics  Astrophysics of Galaxies;
 Physics  Fluid Dynamics
 EPrint:
 3 Tables and 4 Figures