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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.