The evolution of Kerr discs and late-time tidal disruption event light curves

An encounter between a passing star and a massive black hole at the centre of a galaxy, a so-called tidal disruption event or TDE, may leave a debris disc that subsequently accretes on to the hole. We solve for the time evolution of such a TDE disc, using an evolutionary equation valid for both the Newtonian and Kerr regimes. The late-time luminosity emergent from such a disc is of interest as a model diagnostic, as it tends to follow a power law decline. The original simple ballistic fallback model, with equal mass in equal energy intervals, produces a -5/3 power law, while standard viscous disc descriptions yield a somewhat more shallow decline, with an index closer to -1.2. Of four recent, well-observed TDE candidates however, all had fall-off power-law indices smaller than one in magnitude. In this work, we revisit the problem of thin disc evolution, solving this reduced problem in full general relativity. Our solutions produce power-law indices that are in much better accord with observations. The late-time observational data from many TDEs are generally supportive, not only of disc accretion models, but of finite stress persisting down to the innermost stable circular orbit.