Comparing the Dark Matter Halos of Spiral, Low Surface Brightness and
  Dwarf Spheroidal Galaxies
  We consider dark masses measured from kinematic tracers at discrete radii in
galaxies for which baryonic contributions to overall potentials are either
subtracted or negligible. Recent work indicates that rotation curves due to
dark matter (DM) halos at intermediate radii in spiral galaxies are remarkably
similar, with a mean rotation curve given by
$\log_{10}[V_{c,\mathrm{DM}}/(\mathrm{km
s^{-1}})]=1.47_{-0.19}^{+0.15}+0.5\log_{10}[r/\mathrm{kpc}]$. Independent
studies show that while estimates of the dark mass of a given dwarf spheroidal
(dSph) galaxy are robust only near the half-light radius, data from the Milky
Way's (MW's) dSph satellites are consistent with a narrow range of mass
profiles. Here we combine published constraints on the dark halo masses of
spirals and dSphs and include available measurements of low surface brightness
galaxies for additional comparison. We find that most measured MW dSphs lie on
the extrapolation of the mean rotation curve due to DM in spirals. The union of
MW-dSph and spiral data appears to follow a mass-radius relation of the form
$M_{\mathrm{DM}}(r)/M_{\odot}=200_{-120}^{+200}(r/\mathrm{pc})^2$, or
equivalently a constant acceleration $g_{\mathrm{DM}}=3_{-2}^{+3}\times
10^{-9}\mathrm{cm s^{-2}}$, spanning $0.02\la r \la 75$ kpc. Evaluation at
specific radii immediately generates two results from the recent literature: a
common mass for MW dSphs at fixed radius and a constant DM central surface
density for galaxies ranging from MW dSphs to spirals. However, recent
kinematic measurements indicate that M31's dSph satellites are systematically
less massive than MW dSphs of similar size. Such deviations from what is
otherwise a surprisingly uniform halo relation presumably hold clues to
individual formation and evolutionary histories.
