Dynamical friction and the escape of a compact supermassive object shot from the center of a galaxy (Q1068668)

A numerical study has been made of the motion of a compact object consisting of a supermassive black hole with a dense cluster of stars around through a galaxy which has recoiled from the center of the latter as a result of anisotropic emission of gravitational radiation or asymmetrical plasma emission. We find that the effect of dynamical friction on its motion through the galaxy \((mass\simeq 10^{11}M_{\odot})\) estimated using the impulsive approximation techniques, is minimal for an object \(mass\simeq 10^ 9M_{\odot}\) and for recoil taking place at a velocity larger than that of escape. A velocity \(\simeq 1.1\) times the escape velocity is needed for the object to escape from the galaxy, whereas for velocities of recoil less than this critical velocity, damped oscillatory motion ensures. The energy exchange of the object with the galaxy is not large enough to cause appreciable change in the internal energy of the latter.