  Recent analysis on the stellar kinematics of ultra-faint dwarf (UFD) galaxies
has put a stringent upper limit on the self-scattering cross section of dark
matter, i.e., $\sigma/m<{\cal O}(0.1)\,{\rm cm^2/g}$ at the scattering velocity
of ${\cal O}(10)\,{\rm km/s}$. Resonant self-interacting dark matter (rSIDM) is
one possibility that can be consistent with the UFDs and explain the low
central densities of rotation-supported galaxies; the cross section is
resonantly enhanced to be $\sigma/m = {\cal O}(1)\,{\rm cm^2/g}$ around the
scattering velocity of ${\cal O}(100)\,{\rm km/s}$ while being suppressed at
lower velocities. To further assess this possibility, since the inferred dark
matter distribution of halos from astrophysical observations is usually
compared to that in constant-cross section SIDM (cSIDM), whether the structures
of rSIDM halos can be approximated by the cSIDM halo profiles needs to be
clarified. In this work, we employ the grovothermal fluid method to investigate
the structural evolution of rSIDM halos in a wide mass range. We find that
except for halos in a specific mass range, the present structures of rSIDM
halos are virtually indistinguishable from those of the cSIDM halos. For halos
in the specific mass range, the resonant self-scattering renders a break in
their density profile. We demonstrate how such a density-profile break appears
in astrophysical observations, e.g., rotation curves and line-of-sight velocity
dispersion profiles. We show that for halos above the specific mass range, the
density-profile break thermalizes to disappear before the present. We
demonstrate that such distinctive thermalization dynamics can leave imprints on
the orbital classes of stars with similar ages and metallicities.
