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

TL;DR

This paper investigates resonances of compressible stars in precessing orbits around spinning black holes, extending previous work on incompressible stars and providing formulas for resonance growth rates to aid hydrodynamics simulations.

Contribution

It extends earlier findings on star-black hole resonances to stars with polytropic equations of state using the affine model.

Findings

Resonance can occur before tidal disruption for inclined orbits.

Derived formula for the growth rate of resonant motion.

Confirmed previous results with extended models.

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.