Detecting secondary spin with extreme mass ratio inspirals in scalar-tensor theory*

In this study, we investigate the detectability of the secondary spin in an extreme mass ratio inspiral (EMRI) system within a modified gravity model coupled with a scalar field. The central black hole, which reduces to a Kerr one, is circularly spiralled by a scalar-charged spinning secondary body on the equatorial plane. The analysis reveals that the presence of the scalar field amplifies the secondary spin effect, allowing for a lower limit of the detectability and an improved resolution of the secondary spin when the scalar charge is sufficiently large. Our findings suggest that secondary spin detection is more feasible when the primary mass is not large, and TianQin is the optimal choice for detection.