Modelling the light-curves of objects tidally disrupted by a black hole

We consider an object as a sphere approaching a black hole. After Roche radius crossing pressure forces become negligible with respect to inertial forces and the particles that constitute the object start to fall freely in the gravitational field of the black hole. We use very efficient ray-tracing from points on the object’s surface to the distant observer to determine its appearance and light-curve. To determine geodesics which connect two points in space-time, we calculate the exact analytical solutions of relativistic orbit equations, including the calculation of the time of flight. Ray tracing procedures are described in details in Čadež & Kostić (2005) and are freely available upon request from authors. To calculate the lightcurves we take into account primary and secondary image only, since contribution of higher order images is negligible. We also take into account relativistic effects, such as gravitational redshift, Doppler blue/redshift and aberration of light. The images are calculated at equal observer’s times for primary and secondary photons.

Tidal disruption of a gaseous star has been studied by a number of authors (Carter & Luminet 1982, 1985;Laguna et al. 1993;Luminet & Marck 1985) with emphasis on stellar structure during the encounter. How such an event would be seen, i.e. luminosity variations occurring to the star in the vicinity of the black hole, is discussed in Gomboc & Čadež (2005).

We also study tidal effects of a black hole on small compact objects (e.g. asteroids). It has been shown ( Čadež et al. 2008) that solid objects can melt due to work done by tidal forces. Once melted, the object is prone to tidal deformations. Results show that relativistic tidal effects depend predominantly on the ratio ζ = (E/mc 2 -V min )/(V max -V min ). Here E is the energy of the object. V min and V max are the minimum and the maximum of the relativistic effective potential, respectively. Tidal deformations grow exponentially with time for infall of a deformable object on a critical orbit, i.e. orbit with ζ ∼ 1.

The light-curves show a slow component which is due to increasing tidal deformations, and a fast component which is represented by sharp peaks due to relativistic effects. Both components depend also on the orientation of the orbit with respect to the observer. More details in Kostić (2008).