Stalling of Globular Cluster Orbits in Dwarf Galaxies

Abstract

We apply the Tremaine-Weinberg theory of dynamical friction to compute the orbital decay of a globular cluster (GC), on an initially circular orbit inside a cored spherical galaxy with isotropic stellar velocities. The retarding torque on the GC, T(rp) < 0 , is a function of its orbital radius rp . The torque is exerted by stars whose orbits are resonant with the GC's orbit, and given as a sum over the infinitely many possible resonances by the Lynden-Bell Kalnajs (LBK) formula. We calculate the LBK torque T(rp) and determine rp(t), for a GC of mass Mp = 2 x 10^5 M_sun and an Isochrone galaxy of core mass Mc = 4 x 10^8 M_sun and core radius b = 1000pc. (i) When rp > 300 pc many strong resonances are active and, as expected, T = T_C , the classical Chandrasekhar torque. (ii) For rp < 300 pc, T comes mostly from stars nearly co-rotating with the GC, trailing or leading it slightly; Trailing resonances exert stronger torques. (iii) As rp decreases the number and strength of resonances drop, so |T| also decreases, with |T| < 10^{-2} |T_C| at rp = r* = (Mp/Mc)^{1/5} b = 220 pc , a characteristic `filtering' radius. (iv) Many resonances cease to exist inside r* ; this includes all Leading and low-order Trailing ones. (v) The higher-order Trailing resonances inside r* are very weak, with |T| < 10^{-4} |T_C| at rp = 150 pc. (vi) Inspiral times for rp(t) to decay from 300 pc to r* far exceed 10 Gyr.