Zoom & Whirl: Eccentric equatorial orbits around spinning black holes and their evolution under gravitational radiation reaction

Abstract

We study eccentric equatorial orbits of a test-body around a Kerr black hole under the influence of gravitational radiation reaction. We have adopted a well established two-step approach: assuming that the particle is moving along a geodesic (justifiable as long as the orbital evolution is adiabatic) we calculate numerically the fluxes of energy and angular momentum radiated to infinity and to the black hole horizon, via the Teukolsky-Sasaki-Nakamura formalism. We can then infer the rate of change of orbital energy and angular momentum and thus the evolution of the orbit. The orbits are fully described by a semi-latus rectum $p$ and an eccentricity $e$. We find that while, during the inspiral, $e$ decreases until shortly before the orbit reaches the separatrix of stable bound orbits (which is defined by $p_{s}(e)$), in many astrophysically relevant cases the eccentricity will still be significant in the last stages of the inspiral. In addition, when a critical value $p_{crit}(e)$ is reached, the eccentricity begins to increase as a result of continued radiation induced inspiral. The two values $p_{s}$, $p_{crit}$ (for given $e$) move closer to each other, in coordinate terms, as the black hole spin is increased, as they do also for fixed spin and increasing eccentricity. Of particular interest are moderate and high eccentricity orbits around rapidly spinning black holes, with $p(e) \approx p_{s}(e)$. We call these ``zoom-whirl'' orbits, because of their characteristic behaviour involving several revolutions around the central body near periastron. Gravitational waveforms produced by such orbits are calculated and shown to have a very particular signature. Such signals may well prove of considerable astrophysical importance for the future LISA detector.