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The baryonic-to-halo mass relation from mass and energy cascade in self-gravitating collisionless dark matter flow
Zhijie Xu
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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 εᵤ. 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 mₕ, halo virial size rₕ, and flat rotation speed v_f, BHMR can be analytically derived by combining the baryonic Tully-Fisher relation and constant εᵤ in small and large halos. A maximum BHMR ratio ~0.076 is found for halos with a critical mass m_(hc)∼10¹²M_⊙ 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 mₕ<m_(hc), we have εᵤ∝v_f/rₕ, v_f∝rₕ, and m_b∝mₕ^(4/3); ii) for large halos with mass mₕ>m_(hc), we have εᵤ∝v_f³/rₕ, v_f∝rₕ^(1/3), and m_b∝mₕ^(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 ∝t^(1/3). The SPARC (Spitzer Photometry & Accurate Rotation Curves) data with 175 late-type galaxies were used for derivation and comparison.
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