  We examine the bounds on resonantly-produced sterile neutrino dark matter
from phase-space densities of Milky Way dwarf spheroidal galaxies (dSphs). The
bounds result from a derivation of the dark matter coarse-grained phase-space
density from the stellar kinematics, which allows us to explore bounds from
some of the most compact dSphs without suffering the resolution limitation from
N-body simulations that conventional methods have. We find that the strongest
constraints come from very compact dSphs, such as Draco II and Segue 1. We
additionally forecast the constraining power of a few dSph candidates that do
not yet have associated stellar kinematic data, and show that they can improve
the bounds if they are confirmed to be highly dark matter dominated systems.
Our results demonstrate that compact dSphs provide important constraints on
sterile neutrino dark matter that are comparable to other methods using as
Milky Way satellite counts. In particular, if more compact systems are
discovered from current or future surveys such as LSST or HSC, it should be
possible to test models that explain the 3.5 keV X-ray line signal with a 7.1
keV sterile neutrino particle decay.
