Kinematics of Milky Way Satellites: Mass Estimates, Rotation Limits, and
  Proper Motions
  In the past several years high resolution kinematic data sets from Milky Way
satellite galaxies have confirmed earlier indications that these systems are
dark matter dominated objects. Further understanding of what these galaxies
reveal about cosmology and the small scale structure of dark matter relies in
large part on a more detailed interpretation of their internal kinematics. This
article discusses a likelihood formalism that extracts important quantities
from the kinematic data, including the amplitude of rotation, proper motion,
and the mass distribution. In the simplest model the projected error on the
rotational amplitude is shown to be $\sim 0.5 $ km s$^{-1}$ with $\sim 10^3$
stars from either classical or ultra-faint satellites. The galaxy Sculptor is
analyzed for the presence of a rotational signal; no significant detection of
rotation is found, and given this result limits are derived on the Sculptor
proper motion. A criteria for model selection is discussed that determines the
parameters required to describe the dark matter halo density profiles and the
stellar velocity anisotropy. Applied to four data sets with a wide range of
velocities, the likelihood is found to be more sensitive to variations in the
slope of the dark matter density profile than variations in the velocity
anisotropy. Models with variable radial velocity anisotropy are shown to be
preferred relative to those in which this quantity is constant at all radii in
the galaxy.
