Tidal Interaction between a Fluid Star and a Kerr Black Hole: Relativistic Roche-Riemann Model

We present a semi-analytic study of the equilibrium models of close binary systems containing a fluid star (mass m and radius R0) and a Kerr black hole (mass M) in 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 (1973). Tidal disruption occurs at orbital radius rtide ∼ R0(M/m), but the dimensionless ratio r̂tide = rtide/[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 r̂tide than the Newtonian tide; the difference is particularly prominent if the disruption occurs in the vicinity of the black hole’s horizon. In general, r̂tide 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 which may result from such disruption. Subject headings: stars: neutron – stars: black hole – stars: white dwarf – gravitation – hydrodynamics – gamma ray burst Also Department of Applied and Engineering Physics, Cornell University.