The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow

Zhijie Xu

paper

The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow

arXiv:2203.06899

Abstract

The relation between properties of galaxies and dark matter halos they reside in can be valuable for structure formation and evolution. This paper focus on the baryonic-to-halo mass ratio (BHMR) and its evolution. We first review unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their application to derive BHMR. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate inverse mass and energy cascade from small to large scales with a constant rate of energy cascade $ε_{u}$ . In addition, dark matter flow exhibits scale-dependent flow behaviors that is incompressible on small scale and irrotational on large scale. With these properties and considering a given halo with a total baryonic mass $m_{b}$ , halo mass $m_{h}$ , halo virial size $r_{h}$ , and flat rotation speed $v_{f}$ , BHMR can be analytically derived by combining the baryonic Tully-Fisher relation and constant $ε_{u}$ in small and large halos. A maximum BHMR ratio ~0.076 is found for halos with a critical mass $m_{h c} \sim 1 0^{12} M_{⊙}$ at z=0. That ratio is much lower for both smaller and larger halos such that two regimes can be identified: i) for incompressible small halos with mass $m_{h} < m_{h c}$ , we have $ε_{u} \propto v_{f} / r_{h}$ , $v_{f} \propto r_{h}$ , and $m_{b} \propto m_{h}^{4/3}$ ; ii) for large halos with mass $m_{h} > m_{h c}$ , we have $ε_{u} \propto v_{f}^{3} / r_{h}$ , $v_{f} \propto r_{h}^{1/3}$ , and $m_{b} \propto m_{h}^{4/9}$ . Combined with double- $λ$ halo mass function, the average BHMR ratio in all halos (~0.024 at z=0) can be analytically derived, along with its redshift evolution. The fraction of total baryons in all galaxies is ~7.6% at z=0 and increases with time $\propto t^{1/3}$ . The SPARC (Spitzer Photometry \& Accurate Rotation Curves) data with 175 late-type galaxies were used for derivation and comparison.

Reformatted with data source provided, 10 pages, 12 figures