On the high frequency spectrum of a classical accretion disc

TL;DR

This paper derives explicit formulas for the high frequency spectrum of classical accretion discs, considering different boundary conditions and stress scenarios, which can help interpret observational data of black hole systems.

Contribution

It provides new analytical expressions for the high frequency spectral behavior of accretion discs under various boundary stress conditions, extending classical theory.

Findings

High frequency spectrum scales as ν^{2.5} with stress-free boundary.

Finite stress at the inner boundary leads to a ν^2 scaling.

Spectral asymptotics are robust and independent of detailed temperature profiles.

Abstract

We derive simple and explicit expressions for the high frequency spectrum of a classical accretion disc. Both stress-free and finite stress inner boundaries are considered. A classical accretion disc spectrum with a stress-free inner boundary departs from a Wien spectrum at large $\nu$, scaling as $\nu^{2.5}$ (as opposed to $\nu^3$) times the usual exponential cut-off. If there is finite stress at the inner disc boundary, the maximum disc temperature generally occurs at this edge, even at relatively modest values of the stress. In this case, the high frequency spectrum is proportional to $\nu^2$ times the exponential cut-off. If the temperature maximum is a local hot spot, instead of an axisymmetric ring, then an interior maximum produces a $\nu^2$ prefactor while an edge maximum yields $\nu^{1.5}$. Because of beaming effects, these latter findings should pertain to a classical relativistic disc. The asymptotics are in general robust and independent of the detailed temperature profile, provided only that the liberated free energy of differential rotation is dissipated locally, and may prove useful beyond the strict domain of classical disc theory. As observations continue to improve with time, our findings suggest the possibility of using the high energy spectral component of black hole candidates as a signature prediction of classical theory, as well as an diagnostic of the stress at the inner regions of an accretion disc.