The orbital eccentricity distribution of solar-neighbourhood halo stars

We present theoretical calculations for the differential distribution of stellar orbital eccentricity for a sample of solar-neighbourhood 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-neighbourhood 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 centre, such that beta is below unity (near-isotropic velocity dispersion) in the central region and asymptotically approaches similar to 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 a profile in comparison with some observational properties of Delta N(obs+)(e) recently reported by Carollo et al. In particular, the linear e-distribution and the fraction of higher e stars for their sample of solar-neighbourhood inner-halo stars rule out a constant profile of beta, contrary to the opposite claim by Bond et al. Our constraint of beta greater than or similar to 0.5 at the galaxy centre indicates that the violent relaxation that has acted on the inner halo is effective within a scale radius of similar to 10 kpc from the galaxy centre. We argue that our result would help to understand the formation and evolution of the Milky Way halo.