Long-term stream evolution in tidal disruption events

A large number of tidal disruption event (TDE) candidates have been observed recently, often differing in their observational features. Two classes appear to stand out: X-ray and optical TDEs, the latter featuring lower effective temperatures and luminosities. These differences can be explained if the radiation detected from the two categories of events originates from different locations. In practice, this location is set by the evolution of the debris stream around the black hole and by the energy dissipation associated with it. In this paper, we build an analytical model for the stream evolution, whose dynamics is determined by both magnetic stresses and shocks. Without magnetic stresses, the stream always circularizes. The ratio of the circularization timescale to the initial stream period is $t_{\rm ev}/t_{\rm min} = 8.3 (M_{\rm h}/10^6 M_{\odot})^{-5/3} \beta^{-3}$, where $M_{\rm h}$ is the black hole mass and $\beta$ is the penetration factor. If magnetic stresses are strong, they can lead to the stream ballistic accretion. The boundary between circularization and ballistic accretion corresponds to a critical magnetic stresses efficiency $v_{\rm A}/v_{\rm c} \approx 10^{-1}$, largely independent of $M_{\rm h}$ and $\beta$. However, the main effect of magnetic stresses is to accelerate the stream evolution by strengthening self-crossing shocks. Ballistic accretion therefore necessarily occurs on the stream dynamical timescale. The shock luminosity associated to energy dissipation is sub-Eddington but decays as $t^{-5/3}$ only for a slow stream evolution. Finally, we find that the stream thickness rapidly increases if the stream is unable to cool completely efficiently. A likely outcome is its fast evolution into a thick torus, or even an envelope completely surrounding the black hole.