Resonances of compressible stars in precessing orbits around a spinning black hole

Abstract

In our previous paper, we reported the presence of a new resonance of an incompressible star orbiting a spinning black hole and showed that it can set in before the tidal disruption limit if the star has an inclined spherical orbit around the black hole. Using the affine model developed by Carter and Luminet, we extend our result to the stars with polytropic equations of state. We give further credence to the result previously given. We also derive the formula for the growth rate of the resonant motion, which is useful for checking the results of hydrodynamics simulations.