Numerical study of the tidal disruption of neutron stars moving around a black hole - Compressible jeans and Roche problems

摘要

The tidal disruption limit of neutron stars moving around a black hole is numerically studied in the framework of Newtonian gravity. The black hole is described as a point particle, and the neutron stars are modeled using polytropic equations of state. In this paper, we focus both on the Jeans problem, in which the system is axisymmetric and the stars located along a symmetric axis are momentarily static, and on the Roche problem, in which stars are in a corotating circular orbit on the equatorial plane. We find that these two approaches provide qualitatively the same numerical results, which are the following. (i) For given values of the central density and radius, neutron stars with softer equations of state are more fragile with respect to tidal disruption. However, for given values of the mass and radius, the strength with respect to tidal disruption depends very weakly on the equations of state. (ii) The tidal disruption limit determined in the so-called tidal approximation for the black hole tidal field yields an error of magnitude of order R/L, where R and L are the neutron star radius and the separation of two stars. (iii) The third-order term of the tidal field plays an important role in accurately determining the tidal disruption limit for R/L similar to O(0.1). The dependence of the tidal disruption limit for black hole-neutron star binary systems on the equations of state and the mass ratio can be obtained from the study for the momentarily static case. This indicates that the momentarily static approaches should be helpful as a first step in obtaining a full understanding of the tidal disruption limit in general relativity.