Thin accretion disks around black holes modeling the secondary outburst

Accretion disks are efficient engines which convert gravitational energy into heat and radiation. Since it is not possible to observe a black hole directly, it is difficult to understand and probe the physics of such environments. Accretion disks may provide essential clues about the physics near such dense objects. If the secondary star in a low–mass black hole binary fills its Roche–lobe, matter will enter the gravitational influence of the black hole. Since the transfered matter will possess some initial angular momentum, it will start to orbit the black hole instead of directly fall onto it, hence, forming an accretion disk. Due to magnetorotational instabilities, eddies will form hence leading to enhanced viscosity. Due to the viscous torques, angular momentum will be transfered outwards, allowing matter transfer towards the black hole. The viscous dissipation in the disk will produce heat and also black body radiation in soft X–rays. Such a disk can be modeled as a viscous flow towards the black hole. It is possible to make relatively accurate models using the famous a–prescription for the viscosity. By taking advantage of the conservation of mass and angular momentum, a non–linear diffusion equation is obtained which describes the temporal evolution of accretion disks. In this work, this diffusion equation is solved numerically by implementing a finite differences scheme with Crank–Nicholson discretization. The disk instability model, which determines the stability regimes of various regions of the disk, is also implemented. Also, irradiation of the disk from a central source and irradiation by a lamppost–like source is included to the numerical model. The values of the opacities in the disk is determined by realistic opacity tables. In many observations of low–mass soft X–ray transients, it is seen that a secondary maximum occurs in the light curve during the decay phase. It is argued that the reason behind such a secondary outburst may be the formation of a radiating corona. It is proposed that the geometry of the corona, allows the previously shadowed parts of the disk to be irradiated, hence leading to an increase in mass flow towards the black hole. This, in turn, leads to a secondary outburst. The preliminary numerical results have been compared to Pringle's approximate analytical solutions to the disk equation. The results with different corona sizes, corona luminosities, and corona formation times have been obtained by using the HPC at Sabancı University. It may be possible to obtain clues about the geometry of the corona, which is still an unknown, by relating it with the observed secondary outbursts.