Prof Steven Balbus FRS, FInstP

Abstract:

We present exact solutions of test particle orbits spiraling inward from the innermost stable circular orbit (ISCO) of a Kerr black hole. Our results are valid for any allowed value of the angular momentum a parameter of the Kerr metric. These solutions are of considerable physical interest. In particular, the radial four-velocity of these orbits is both remarkably simple and, with the radial coordinate scaled by its ISCO value, universal in form, otherwise completely independent of the black hole spin.

Abstract:

The probability density function of accretion disc luminosity fluctuations at high observed energies (i.e. energies larger than the peak temperature scale of the disc) is derived, under the assumption that the temperature fluctuations are lognormally distributed. Thin disc theory is used throughout. While lognormal temperature fluctuations would imply that the disc’s bolometric luminosity is also lognormal, the observed Wien-like luminosity behaves very differently. For example, in contrast to a lognormal distribution, the standard deviation of the derived distribution is not linearly proportional to its mean. This means that these systems do not follow a linear rms-flux relationship. Instead they exhibit very high intrinsic variance, and undergo what amounts to a phase transition, in which the mode of the distribution (in the statistical sense) ceases to exist, even for physically reasonable values of the underlying temperature variance. The moments of this distribution are derived using asymptotic expansion techniques. A result that is important for interpreting observations is that the theory predicts that the fractional variability of these disc systems should increase as the observed frequency is increased. The derived distribution will be of practical utility in quantitatively understanding the variability of disc systems observed at energies above their peak temperature scale, including X-ray observations of tidal disruption events.