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, which 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 β, we find that the eccentricity distribution is a monotonically increasing function of e for the case of highly radially anisotropic velocity dispersions (β >~ 0.6), while showing a hump-like shape for the cases from radial through tangential velocity anisotropy (β <~ 0.6). We also find that when the velocity anisotropy agrees with that observed for the Milky Way halo stars (β ~= 0.5-0.7), a nearly linear eccentricity distribution of N(e) ~ 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.