Orbital Deformation of Satellites by Dynamical Friction in Spherical Halos with Anisotropic Velocity Dispersion

Deformation of satellite orbits around a spherical galaxy is considered. In general, a satellite sinks into the center of its parent galaxy by dynamical friction. Unless the orbit is exactly circular, the orbital shape changes, owing to a difference in decaying rate between energy and angular momentum. This deformation depends on the density and velocity distributions of the surrounding galactic halo. We have made a perturbative analysis of the orbital deformation in a scale-free halo that has a density profile ρ ∝ rn(-3 ≤ n ≤ 0), with anisotropic velocity dispersion characterized by β = 1 - σ/σ(-1 ≤ β ≤ 1). We classify four major effects on the orbital deformation. The dominant effect originates from the density gradient for n -2. Both effects lead to more circular orbits. Larger β makes the rate of orbital circularization smaller. For positive β (radially dominated anisotropy), initially eccentric orbits conserve their shape during orbital decay when the velocity dispersion is radially dominated.