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 Ξ΅uβ. 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 mbβ, halo mass mhβ, halo virial size rhβ,
and flat rotation speed vfβ, BHMR can be analytically derived by combining
the baryonic Tully-Fisher relation and constant Ξ΅uβ in small and
large halos. A maximum BHMR ratio ~0.076 is found for halos with a critical
mass mhcββΌ1012Mββ 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 mhβ<mhcβ, we have
Ξ΅uββvfβ/rhβ, vfββrhβ, and mbββmh4/3β;
ii) for large halos with mass mhβ>mhcβ, we have Ξ΅uββvf3β/rhβ, vfββrh1/3β, and mbββmh4/9β. Combined with
double-Ξ» 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 βt1/3. The SPARC (Spitzer Photometry \& Accurate Rotation
Curves) data with 175 late-type galaxies were used for derivation and
comparison.Comment: Reformatted with data source provided, 10 pages, 12 figure