Hunting intermediate-mass black holes with LISA binary radial velocity measurements

Abstract: Despite their potential role as massive seeds for quasars, in dwarf galaxy feedback, and in tidal disruption events, the observational evidence for intermediate-mass black holes (IMBHs) is scarce. LISA may observe stellar-mass black hole binaries orbiting Galactic IMBHs, and reveal the presence of the IMBH by measuring the Doppler shift in the gravitational waveform induced by the binary's radial velocity. We estimate the number of detectable Doppler shift events from the Milky Way globular clusters (assuming they host IMBHs) and we find that it decreases with the IMBH mass. A few Galactic globular clusters (including M22 and $\omega$ Centauri) may produce at least one event detectable by LISA. Even in more pessimistic scenarios, one could still expect $\sim$ 1 event overall in the Milky Way. We also estimate the number of Doppler shift events for IMBHs wandering in the Milky Way as a result of the disruption of their parent clusters. If there is at least one binary black hole orbiting around each wandering IMBH, LISA may detect up to a few tens of Doppler shift events from this elusive IMBH population. Under more pessimistic assumptions, LISA may still detect $\sim 1$ wandering IMBH that would hardly be observable otherwise.