Orbital Eccentricity Distribution of Solar-Neighbour Halo Stars
  We present theoretical calculations for the differential distribution of
stellar orbital eccentricity for a sample of solar-neighbour halo stars. Two
types of static, spherical gravitational potentials are adopted to define the
eccentricity e for given energy E and angular momentum L, such as an isochrone
potential and a Navarro-Frenk-White potential that can serve as two extreme
ends covering in-between any realistic potential of the Milky Way halo. The
solar-neighbour eccentricity distribution \Delta N(e) is then formulated, based
on a static distribution function of the form f(E,L) in which the velocity
anisotropy parameter \beta monotonically increases in the radial direction away
from the galaxy center, such that beta is below unity (near isotropic velocity
dispersion) in the central region and asymptotically approaches \sim 1
(radially anisotropic velocity dispersion) in the far distant region of the
halo. We find that \Delta N(e) sensitively depends upon the radial profile of
\beta, and this sensitivity is used to constrain such profile in comparison
with some observational properties of \Delta N_{obs}(e) recently reported by
Carollo et al. (2010). Especially, the linear e-distribution and the fraction
of higher-e stars for their sample of solar-neighbour inner-halo stars rule out
a constant profile of \beta, contrary to the opposite claim by Bond et al.
(2010). Our constraint of \beta \lesssim 0.5 at the galaxy center indicates
that the violent relaxation that has acted on the inner halo is effective
within a scale radius of \sim 10 kpc from the galaxy center. We discuss that
our result would help understand the formation and evolution of the Milky Way
halo.
