Observable gravitational waves from tidal disruption events and their electromagnetic counterpart

We estimate the rate of tidal disruption events (TDEs) that will be detectable with future gravitational wave detectors as well as the most probable properties of these events and their possible electromagnetic counterpart. To this purpose we combine standard gravitational waves and electromagnetic results with detailed rates estimates. We find that the \emph{Laser Interferometer Space Antenna} (LISA) should not detect any TDEs, unless black holes (BHs) are typically embedded by a young stellar population which, in this situation, could lead up to few 10 events during the duration of the mission. If there are gravitational wave observations, these events should also be observable in the X-ray or the optical/UV part of the electromagnetic spectrum, which may open up the multi-messenger era for TDEs. The generation of detectors following LISA will at least yearly observe $10^4$ TDEs at cosmological distances, allowing to do population studies and constrain the black hole mass function. In all cases, most probable events should be around black holes with a mass such that the Keplerian frequency at the Schwarzschild radius is similar to the optimal frequency of the detector and with a large penetration factor.