We consider constraints on a phenomenological dark-matter model consisting of
two nearly degenerate particle species using observed properties of the Milky
Way satellite galaxy population. The two parameters of this model, assuming the
particle masses are >~ GeV, are v_k, the recoil speed of the daughter particle,
and tau, the lifetime of the parent particle. The satellite constraint that
spans the widest range of v_k is the number of satellites that have a mass
within 300 pc M300 > 5 x 10^6 solar masses, although constraints based on M300
in the classical dwarfs and the overall velocity function are competitive for
v_k >~ 50 km/s. In general, we find that tau <~ 30 Gyr is ruled out for 20 km/s
<~ v_k <~ 200 km/s, although we find that the limits on tau for fixed v_k can
change constraints by a factor of ~3 depending on the star-formation histories
of the satellites. We advocate using the distribution of M300 in Milky Way
satellites determined by next-generation all-sky surveys and follow-up
spectroscopy as a probe of dark-matter properties.Comment: 17 pages, 9 figures, submitted to Phys. Rev.