Detecting intermediate-mass ratio inspirals from the ground and space

The detection of the gravitational capture of a stellar-mass compact object by a massive black hole (MBH) will allow us to test gravity in the strong regime. The repeated, accumulated bursts of gravitational radiation from these sources can be envisaged as a geodesic mapping of space-time around the MBH. These sources form via two-body relaxation, by exchanging energy and angular momentum, and inspiral in a slow, progressive way down to the final merger. The frequencies fall in the millihertz range for MBHs with masses $\ensuremath{\sim}{10}^{6}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, i.e., that of space-borne gravitational-wave observatories such as LISA. In this article we show that, depending on their orbital parameters, intermediate-mass ratio inspirals (IMRIs) of MBHs with masses between a hundred and a few thousand ${M}_{\ensuremath{\bigodot}}$ have frequencies that make them detectable (i) with ground-based observatories, or (ii) with both LISA and ground-based observatories (such as advanced LIGO/Virgo) and third-generation observatories [such as the Einstein Telescope (ET)]. The binaries have a signal-to-noise ratio large enough to ensure detection. More extreme values of the orbital parameters correspond to systems that are only detectable with ground-based detectors and in particular enter the LIGO/Virgo band in many different harmonics for masses up to $2000\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. We show that environmental effects are negligible, so the source should not have this kind of complication. The accumulated phase shift is measurable with LISA and ET, and for some cases also with LIGO, so that it is possible to recover information about the eccentricity and formation scenario. For IMRIs with a total mass $⪅2000\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ and initial eccentricities up to 0.999, LISA can give a advanced warning to ground-based detectors with seconds of precision. The possibility of detecting IMRIs from the ground alone or combined with space-borne observatories opens new possibilities for gravitational-wave astronomy.

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