The general relativistic thin disc evolution equation
Abstract
In the classical theory of thin disc accretion discs, the constraints of mass and angular momentum conservation lead to a diffusion-like equation for the turbulent evolution of the surface density. Here, we revisit this problem, extending the Newtonian analysis to the regime of Kerr geometry relevant to black holes. A diffusion-like equation once again emerges, but now with a singularity at the radius at which the effective angular momentum gradient passes through zero. The equation may be analysed using a combination of Wentzel-Kramers-Brillouin techniques, local techniques and matched asymptotic expansions. It is shown that imposing the boundary condition of a vanishing stress tensor (more precisely the radial-azimuthal component thereof) allows smooth stable modes to exist external to the angular momentum singularity, the innermost stable circular orbit, while smoothly vanishing inside this location. The extension of the disc diffusion equation to the domain of general relativity introduces a new tool for numerical and phenomenological studies of accretion discs, and may prove to be a useful technique for understanding black hole X-ray transients.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- November 2017
- DOI:
- 10.1093/mnras/stx1955
- arXiv:
- arXiv:1707.08884
- Bibcode:
- 2017MNRAS.471.4832B
- Keywords:
-
- accretion;
- accretion discs;
- black hole physics;
- turbulence;
- Astrophysics - High Energy Astrophysical Phenomena
- E-Print:
- 7 Pages, 1 figure. Accepted for publication in MNRAS. Revised version corrects minor typos in equations (64) and (66) of original, otherwise unaltered