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Abstract

If a small compact object orbits a black hole, it is known that it can excite
the black hole's quasinormal modes (QNMs), leading to high-frequency
oscillations (``wiggles'') in the radiated field at $\mathcal{J}^+$, and in the
radiation-reaction self-force acting on the object after its orbit passes
through periapsis. Here we survey the phenomenology of these wiggles across a
range of black hole spins and equatorial orbits. In both the scalar-field and
gravitational cases we find that wiggles are a generic feature across a wide
range of parameter space, and that they are observable in field perturbations
at fixed spatial positions, in the self-force, and in radiated fields at
$\mathcal{J}^+$. For a given charge or mass of the small body, the QNM
excitations have the highest amplitudes for systems with a highly spinning
central black hole, a prograde orbit with high eccentricity, and an orbital
periapsis close to the light ring. The QNM amplitudes depend smoothly on the
orbital parameters, with only very small amplitude changes when the orbit's
(discrete) frequency spectrum is tuned to match QNM frequencies. The
association of wiggles with QNM excitations suggest that they represent a
situation where the \emph{nonlocal} nature of the self-force is particularly
apparent, with the wiggles arising as result of QNM excitation by the compact
object near periapsis, and then encountered later in the orbit.
Astrophysically, the effects of wiggles at $\mathcal{J}^+$ might allow direct
observation of Kerr QNMs in extreme-mass-ratio inspiral (EMRI) binary black
hole systems, potentially enabling new tests of general relativity.