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

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 $\varepsilon_u$. 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 $\varepsilon_u$ in small and large halos. A maximum BHMR ratio ~0.076 is found for halos with a critical mass $m_{hc}\sim 10^{12}M_{\odot}$ 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 $m_h<m_{hc}$, we have $\varepsilon_u\propto v_f/r_h$, $v_f\propto r_h$, and $m_b\propto m_h^{4/3}$; ii) for large halos with mass $m_h>m_{hc}$, we have $\varepsilon_u\propto v_f^3/r_h$, $v_f\propto r_h^{1/3}$, and $m_b\propto m_h^{4/9}$. Combined with double-$\lambda$ 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.