Stalling of Globular Cluster Orbits in Dwarf Galaxies

Abstract

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, , is a function of its orbital radius . 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 and determine for a GC of mass and an isochrone galaxy of core mass and core radius . (i) When , many strong resonances are active, and as expected, , the classical Chandrasekhar torque. (ii) For , comes mostly from stars nearly corotating with the GC, trailing or leading it slightly; trailing resonances exert stronger torques. (iii) As decreases, the number and strength of resonances drop, so also decreases, with at , a characteristic “filtering” radius. (iv) Many resonances cease to exist inside this includes all leading and low-order trailing ones. (v) The higher-order trailing resonances inside are very weak, with at . (vi) Inspiral times for to decay from to far exceed .