2018ApJ...868..134K

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 (r_p)< 0, is a function of its orbital radius r_p. 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 (r_p) and determine r_p(t) for a GC of mass M_p=2×10⁵M_☉ and an isochrone galaxy of core mass M_c=4×10⁸M_☉ and core radius b=1000pc. (i) When r_p≳300pc, many strong resonances are active, and as expected, T ~T_C, the classical Chandrasekhar torque. (ii) For r_p< 300pc, T comes mostly from stars nearly corotating with the GC, trailing or leading it slightly; trailing resonances exert stronger torques. (iii) As r_p decreases, the number and strength of resonances drop, so | T | also decreases, with | T | < 10^–2| T_C| at r_p=r_*≃(M_p/M_c)^1/5b≃220pc, 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 r_p=150pc. (vi) Inspiral times for r_p(t) to decay from 300pc to r_* far exceed 10Gyr.