Secondary spins of extreme mass-ratio inspirals: A probe to the formation channels

Extreme mass-ratio inspirals (EMRIs), consisting of a secondary (stellar mass) black hole (BH) orbiting around a supermassive BH, are one of the primary targets for future spaceborne gravitational wave (GW) detectors. The spin of the secondary BH encodes the formation history of the stellar mass BH and the formation process of the EMRI. In this work, we construct a kludge EMRI waveform model taking the secondary spin into account and preliminarily forecast the measurement precision of the secondary spin by future spaceborne GW detectors with the Fisher information matrix. We find the secondary spin might be measured with reasonably good precision for generic eccentric and inclined EMRIs, with the caveat that the predictive precision may be constrained by the model's inherent simplifications. As an example of its astrophysical applications, we propose that the secondary spin can be used for distinguishing dry (loss cone) EMRIs (where the secondary BHs were born in the collapse of individual massive stars and are of low spin) and Hills EMRIs (where the secondary BHs are remnants of massive star binaries and the secondary spins follow a bimodal distribution).