Streams collision as possible precursor of double tidal disruption events

The rate of tidal disruption events (TDEs) can vary by orders of magnitude depending on the environment and the mechanism that launches the stars towards the black hole's vicinity. For the largest rates, two disruptions can take place shortly one after the other in a double TDE. In this case, the two debris streams may collide with each other before falling back to the black hole resulting in an electromagnetic emission that is absent from single TDEs. We analytically evaluate the conditions for this streams collision to occur. It requires that the difference in pericenter location between the two disruptions makes up for the time delay between them. In addition, the width of the streams must compensate for the vertical offset induced by the inclination of their orbital planes. If the double TDE happens following the tidal separation of a binary, we find that the streams can collide with a probability as high as $44\%$. We validate our analytical conditions for streams collision through hydrodynamical simulations and find that the associated shocks heat the gas significantly. If photons are able to rapidly escape, a burst of radiation ensues lasting a few days with a luminosity $\sim 10^{43}\, \rm erg\, s^{-1}$, most likely in the optical band. This signal represents a precursor to the main flare of TDEs that could in particular be exploited to determine the efficiency of disc formation from the stellar debris.