Excitation of scalar quasi-normal modes from boson clouds
Massive scalar fields on black hole backgrounds generally admit two families of modes: quasi-bound states (QBS) and quasinormal modes (QNM). We demonstrate the orthogonality between the two mode families with respect to a relativistic product. We also find that, although the two families appear on different Riemann sheets of the Green's function of massive scalar perturbations, they can be brought to a single sheet with an appropriate redefinition of the frequency variable. In this variable, it is more natural to see how both mode families can be excited by initial data, and to approximate the Green's function with saddle points. Finally, we investigate the QNM emission from boson clouds - the latter effectively consisting of a single QBS - driven by the tidal perturbation of a second compact object. We show that while the resonant emission of QNMs is generally suppressed, QNM transitions may be more prominent when the interaction with the perturber is non-resonant, such as in the dynamical capture of unbound objects, and when the perturber transits close to the light ring.