Orbital Decay in Aspherical Galaxies. I. Oblate Systems

The slow orbital decay of a satellite galaxy into a larger aspherical system is calculated semi-analytically. The main galaxy is modeled by an axisymmetric oblate Stackel potential, assumed fixed, and the satellite by a softened point mass. Dynamical friction is described by the local Chandrasehkar formula. Both rotation and velocity anisotropy of the main galaxy are neglected in the main part of the discussion; their effects are estimated and are found to be important in some cases, especially in disks. Analytic expressions for the rate of change of the instantaneous turning points of the orbit (ν_0_,λ_0_, λ_1_), are derived, supplemented by direct numerical orbit integrations. The evolution of the orbit is represented as a path in turning-point space. Decaying orbits tend toward inclined thin tubes, i.e., tube orbits with small radial and large vertical excursions. The "latitudinal turning point" ν_0_, which measures the angular excursion out of the equatorial plane, is nearly constant until the orbit has almost completely decayed. Hence the initial inclination of the satellite's orbit is remembered for long times. The rate at which the orbit becomes thin (the "circularization" rate) depends on the density profile of the main galaxy, being larger, compared to the radial decay rate, in systems with steeper profiles. Using a simple model for tidal stripping, it is shown that stars removed from the satellite form a subsystem that appears X-shaped in projection, making the final galaxy distinctly boxy even if the satellite has only 1% of the luminosity of the main galaxy. The model may therefore be applicable to the formation of boxy elliptical galaxies. Similar slow cannibalism may be able to place stars on inclined thin tube orbits in the Galactic halo, as suggested by velocity dispersion measurements of Population II stars at 2 <~ 25 kpc.