The stream-stream collision after the tidal disruption of a star around a massive black hole

A star can be tidally disrupted around a massive black hole. It is known that the debris forms a precessing stream, which may collide with itself. The stream collision is a key process in determining the subsequent evolution of the stellar debris: if the orbital energy is efficiently dissipated, the debris will eventually form a circular disk (or torus). In this paper, we have numerically studied such a stream collision resulting from the encounter between a 10⁶ M⊙ black hole and a 1 M⊙ normal star with a pericenter radius of 100 R⊙. A simple treatment for radiative cooling has been adopted for both optically thick and optically thin regions. We have found that approximately 10% to 15% of the initial kinetic energy of the streams is converted into thermal energy during the collision. The spread in angular momentum of the incoming stream is increased by a factor of 2 to 3, and such an increase, together with the decrease in kinetic energy, significantly helps the circularization process. The initial luminosity burst produced by the collision may reach as high as 10⁴¹ ergs s^-1 in 10⁴ s, after which the luminosity increases again (but slowly this time) to a steady value of a few 10⁴⁰ ergs s^-1 in a few times 10₅ s. The radiation from the system is expected to be close to Planckian, with an effective temperature of ∼ 10⁵ K.