Accretion within the innermost stable circular orbit: analytical thermodynamic solutions in the adiabatic limit

Abstract

We present analytical solutions for the thermodynamic (temperature, pressure, density, etc.) properties of thin accretion flows in the region within the innermost stable circular orbit (ISCO) of a Kerr black hole, the first analytical solutions of their kind. These solutions are constructed in the adiabatic limit and neglect radiative losses, an idealization valid for a restricted region of parameter space. We highlight a number of remarkable properties of these solutions, including that these solutions cool for radii rI/2 < r < rI, before increasing in temperature for 0 < r