Dissipation in extreme mass-ratio binaries with a spinning secondary

Abstract

We present the gravitational-wave flux balance law in an extreme mass-ratio binary with a spinning secondary. This law relates the flux of energy (angular momentum) radiated to null infinity and through the event horizon to the local change in the secondary's orbital energy (angular momentum) for generic (non-resonant) bound orbits in Kerr spacetime. As an explicit example we compute these quantities for a spin-aligned body moving on a circular orbit around a Schwarzschild black hole. We perform this calculation both analytically, via a high-order post-Newtonian expansion, and numerically in two different gauges. Using these results we demonstrate explicitly that our new balance law holds. I. INTRODUCTION Gravitational wave physics is now firmly established as an observational science. Ground-based detectors regularly observe the binary mergers of stellar-mass black holes and neutron stars [1]. Looking to the future, the construction of the space-based millihertz detector, LISA [2], will open a new window on binaries with a total mass in the range 10 4-10 7 M. One particularly interesting class of such systems are extreme mass-ratio inspirals (EMRIs) [3]. In these binaries, a compact object, such as a stellar mass black hole or neutron star, spirals into a massive black hole driven by the emission of gravitational waves. These systems have a (small) mass-ratio in the range of 10 −4 − 10 −7. In general EMRIs are not expected to completely circularize by the time of merger, resulting in a rich orbital and waveform structure that carries with it detailed information about the spacetime of the EMRI [4]. Additional complexity is added by the expectation that both the primary (larger) and secondary (smaller) compact object will be spinning, with no preferred alignment between the secondary's spin and the orbital angular momentum. Modelling the effects of the spin of the secondary is the focus of the present work. Extracting EMRI signals from the LISA data stream will require precise theoretical waveform models of these binaries. This is because the instantaneous signal-to-noise ratio of a typical EMRI will be very small, and so the waveforms can only be separated from the instrumental noise and the potentially many other competing sources by semi-coherent matched filtering techniques [3]. The small mass ratio in EMRIs naturally suggests black hole perturbation theory as a modelling approach. With this method, the spacetime of the binary is expanded around the analytically-known spacetime of the primary. The leading order contribution to the waveform phase comes from the orbit-averaged fluxes of gravitational radiation. These were calculated for a non-spinning secondary moving along a circular orbit about Kerr black hole in the 1970's [5]. These calculations were extended to eccentric [6] and fully generic (inclined) motion [7-9] in the 2000's. The waveforms that can be constructed from these results will likely be sufficient for detection of the very loudest EMRIs. In order to detect the many weaker signals, to perform...

Two-timescale evolution of extreme-mass-ratio inspirals: Waveform generation scheme for quasicircular orbits in Schwarzschild spacetime

“…[30]. We will not include this source in our two-timescale analysis, but doing so should be relatively straightforward [25].…”

“…For post-adiabatic modeling, the full first-order selfforce can now also be calculated along generic bound orbits in Kerr spacetime [22], and there is ongoing work to incorporate first-order effects of the small object's spin [23][24][25]. However, calculations of f α 2 are far less mature.…”

Adiabatic equatorial inspirals of a spinning body into a Kerr black hole

“…The error in the adiabatic term must be less than the mass ratio to obtain the sub-radian precision. It has been proven for a non-spinning secondary [16,17], but also for a spinning secondary [18] that the time-averaged dissipative part of the self-force can be reconstructed from the time-averaged energy and angular momentum fluxes calculated at infinity and at the horizon of the primary black hole. Therefore, for the calculations in the adiabatic order, we do not need to calculate the perturbation h…”

Gravitational-Wave Energy Flux for Compact Binaries through Second Order in the Mass Ratio

“…We first consider binaries with a spinning secondary and a nonspinning primary. In perturbation theory, many authors have computed F SF,spin,2 lm (x) for circular orbits [42][43][44]. Here we make use of the results of [43], where the linear-in-spin flux is computed as a function of the orbital frequency.…”

“…In perturbation theory, many authors have computed F SF,spin,2 lm (x) for circular orbits [42][43][44]. Here we make use of the results of [43], where the linear-in-spin flux is computed as a function of the orbital frequency. As before, even for a small-q binary and a rapidly rotating secondary, we find good agreement with NR simulations -see Fig.…”