Tidal disruption radii of spherical mass distributions with central black holes
A star that ventures too close to a compact object, such as a black hole, is expected to be tidally disrupted within the tidal radius, rt. In this paper, we investigate the tidal disruption radius for spherically symmetric mass distributions with central black holes. The tidal radius is calculated by equating the tidal field of the SMBH to the surface stellar gravity. Our analysis reveals that for black hole systems with extended spherical mass distributions, the tidal radii exhibit dependencies on the characteristic size parameter. Specifically, in potentials characterized by the scale length, b, the tidal radii deviate from the canonical value at intermediate values of b, while approaching the Keplerian value in the small and large b-limits. Additionally, we explore the tidal radius of a homogeneous sphere with a central black hole, finding that it depends on the radius of the sphere, Rs, with the tidal radius vanishing in the small Rs-limit and converging to the Keplerian value in the large Rs-limit. This investigation extends our understanding of tidal disruption events beyond the Keplerian regime and offers valuable insights into the underlying physical processes governing gravitational interactions in galactic systems.