  We consider an inelastic dark matter model, where a fermion is charged under
a broken U(1) gauge symmetry, and introduce a tiny Majorana mass term to split
the fermion into two states with the light one being a dark matter candidate.
If the gauge boson is light, it can mediate both elastic and inelastic dark
matter self-interactions in dark halos, leading to observational consequences.
Using a numerical technique based on partial wave analysis, we accurately
calculate the elastic and inelastic self-scattering cross sections. We assume a
thermal freeze-out scenario and fix the gauge coupling constant using the relic
density constraint. Then, we focus on six benchmark masses of dark matter,
covering a wide range from $10~{\rm MeV}$ to $160~{\rm GeV}$ and map parameter
regions where the elastic scattering cross section per unit mass is within
$1~{\rm cm^2/g} - 5~{\rm cm^2/g}$, favored to solve small-scale issues of cold
dark matter. If the heavy state can decay to the light state and a massless
species, the inelastic up-scattering process can cool the halo and lead to core
collapse. Taking galaxies with evidence of dark matter density cores, we
further derive constraints on the parameter space. For dark matter masses below
$10~{\rm GeV}$, the mass splitting must be large enough to forbid up scattering
in the dwarf halo for evading the core-collapse constraint; while for higher
masses, the up-scattering process can still be allowed. Our results show
astrophysical observations can provide powerful tests for dark matter models
with large elastic and inelastic self-interactions.
