Tidal Interaction between a Fluid Star and a Kerr Black Hole in Circular Orbit

We present a semianalytic study of the equilibrium models of close binary systems containing a Newtonian fluid star (mass m and radius R₀) and a Kerr black hole (mass M) in a circular orbit. We consider the limit M ≫ m where spacetime is described by the Kerr metric. The tidally deformed star is approximated by an ellipsoid and satisfies the polytropic equation of state. The models also include fluid motion in the stellar interior, allowing binary models with nonsynchronized stellar spin (as expected for coalescing neutron star-black hole binaries) to be constructed. Our relativistic, compressible Roche-Riemann model is a generalization of the incompressible, corotating Roche model studied earlier by Fishbone. Tidal disruption occurs at orbital radius r_tide ~ R₀(M/m)^1/3, but the dimensionless ratio _tide = r_tide/[R₀(M/m)^1/3] depends on the spin parameter of the black hole as well as on the equation of state and the internal rotation of the star. We find that the general relativistic tidal field disrupts the star at a larger _tide than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole's horizon. In general, _tide is smaller for a (prograde rotating) Kerr black hole than for a Schwarzschild black hole. We apply our results to coalescing black hole-neutron star and black hole-white dwarf binaries. The tidal disruption limit is important for characterizing the expected gravitational wave signals and is relevant for determining the energetics of gamma-ray bursts that may result from such disruptions.