Can supernova kicks trigger EMRIs in the Galactic Centre?

One of the most promising gravitational wave (GW) sources detectable by the forthcoming LISA observatory are the so-called extreme-mass ratio inspirals (EMRIs), i.e. GW-driven inspirals of stellar-mass compact objects onto supermassive black holes (SMBHs). In this paper, we suggest that supernova (SN) kicks may trigger EMRIs in galactic nuclei by scattering newborn stellar black holes and neutron stars on extremely eccentric orbits; as a consequence, the time-scale over which these compact objects are expected to inspiral onto the central SMBH via GW emission may become shorter than the time-scale for other orbital perturbations to occur. By applying this argument to the Galactic Centre, we show that the S-cluster and the clockwise disc are optimal regions for the generation of such events: one SN out of about 10 000 (100 000) occurring in the S-cluster (clockwise disc) is expected to induce an EMRI. If we assume that the natal kicks affecting stellar black holes are significantly slower than those experienced by neutron stars, we find that most SN-driven EMRIs involve neutron stars. We further estimate the time spanning from the SN to the final plunge onto the SMBH to be of the order of few Myr. Finally, we extrapolate the rate of SN-driven EMRIs per Milky Way to be up to 10^-8/yr, thus we expect that LISA will detect up to a few tens of SN-driven EMRIs every year.