A new test for the Galactic formation and evolution -- prediction for
  the orbital eccentricity distribution of the halo stars
  We present theoretical calculations for the differential distribution of
stellar orbital eccentricity in a galaxy halo, assuming that the stars
constitute a spherical, collisionless system in dynamical equilibrium with a
dark matter halo. In order to define the eccentricity e of a halo star for
given energy E and angular momentum L, we adopt two types of gravitational
potential, such as an isochrone potential and a Navarro-Frenk-White potential,
that could form two ends covering in-between any realistic potential of dark
matter halo. Based on a distribution function of the form f(E,L) that allows
constant anisotropy in velocity dispersions characterized by a parameter \beta,
we find that the eccentricity distribution is a monotonically increasing
function of e for the case of highly radially anisotropic velocity dispersions
(\beta > 0.6), while showing a hump-like shape for the cases from radial
through tangential velocity anisotropy (\beta < 0.6). We also find that when
the velocity anisotropy agrees with that observed for the Milky Way halo stars
(\beta = 0.5-0.7), a nearly linear eccentricity distribution of N(e) \alpha e
results at e < 0.7, largely independent of the potential adopted. Our
theoretical eccentricity distribution would be a vital tool of examining how
far out in the halo the dynamical equilibrium has been achieved, through
comparison with kinematics of halo stars sampled at greater distances. Given
that large surveys of the SEGUE and Gaia projects would be in progress, we
discuss how our results would serve as a new guide in exploring the formation
and evolution of the Milky Way halo.
