Semirelativistic approximation to gravitational radiation from encounters with nonspinning black holes

Abstract

The capture of compact bodies by black holes in galactic nuclei is an important prospective source for low frequency gravitational wave detectors, such as the planned Laser Interferometer Space Antenna. This paper calculates, using a semirelativistic approximation, the total energy and angular momentum lost to gravitational radiation by compact bodies on very high eccentricity orbits passing close to a supermassive, nonspinning black hole; these quantities determine the characteristics of the orbital evolution necessary to estimate the capture rate. The semirelativistic approximation improves upon treatments which use orbits at Newtonian order and quadrupolar radiation emission, and matches well onto accurate Teukolsky simulations for low eccentricity orbits. Formulas are presented for the semirelativistic energy and angular momentum fluxes as a function of general orbital parameters.

Production of EMRIs in supermassive black hole binaries

“…where X is either the specific energy E/c 2 or the (scaled) specific angular momentumL = L/(GM/c),rp is the periapsis distance in geometrized units, NE = 7, NL = 4, and the A X n , B X n , and C X n are coefficients given in Table 2. In Gair, Kennefick & Larson (2006) they note that N = 2 is sufficient for better than 0.2% accuracy everywhere. This is the order used in our code.…”

“…We deal with both by assuming the stars are on parabolic orbits. These losses are documented and fitting functions for the energy and angular momentum provided by Gair, Kennefick & Larson (2005). We use these fitting functions to determine the change in angular momentum and orbital energy during a complete periapsis passage, and apply these losses discretely at periapsis.…”

“…To compute the energy and angular momentum lost during a periapsis passage we assume the orbits are parabolic. We then relate the angular momentum in the orbit to the energy and angular momentum lost during each periapsis passage using the fitting functions for parabolic orbits from Gair, Kennefick & Larson (2006). In that paper they compute fitting functions to the energy and angular momentum loss using the Teukolsky equation.…”

Binary Black Hole Coalescence

“…For initially non-spinning, zero eccentricity binaries the higher order PN approximations and effective one body (EOB) resummations [54] give waveforms that are surprisingly close to full numerical results even until very close to merger, well beyond when naive arguments suggest they should fail [55,56,57,58,59]; comparisons for more generic scenarios have yet to be made. Extreme mass ratio inspirals (EMRIs) can also be well described by geodesic motion in a black hole background together with prescriptions for computing the gravitational wave emission and effects of radiation reaction [64,65,66,67,68,69,70,71]. Generic (non-equatorial) orbits about a Kerr black hole will not lie in a plane due to precession and frame-dragging effects, and thus during the lengthy course of an EMRI, which could be in LISA-band for thousands of cycles, the small black hole will "sample" much of the geometry of the background spacetime.…”

Gyroscope precession along unbound equatorial plane orbits around a Kerr black hole

“…context of recent progress being made in gravitational self-force /gravitational self-torque computations for a particle/gyroscope moving in a perturbed Kerr spacetime [27][28][29]. Indeed, in the near future may be possible to "analytically" compute the full gravitational wave rate of emission by a particle being scattered by the hole, the main difficulty being the existence of a continuous spectrum of frequencies instead of a single frequency as in the simpler case of circular motion.…”