“Flux-balance formulae” for extreme mass-ratio inspirals

Isoyama, Soichiro; Fujita, Ryuichi; Nakano, Hiroyuki; Sago, Norichika; Tanaka, Takahiro

doi:10.1093/ptep/pty136

Cited by 31 publications

(32 citation statements)

References 157 publications

(385 reference statements)

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“…(ii) Our expressions are not valid for cases of orbital resonance. A recent work by Isoyama et al [36] successfully derived flux balance expressions for the non-spinning case which are valid during orbital resonance. While the calculations are more involved for the spinning particle case, the extension should be feasible.…”

Section: Discussionmentioning

confidence: 99%

“…Due to the similarity of the methods for the monopole and dipole computations, we anticipate that the flux-balance law for a small companion with spin could also be extended to the Carter constant. A more recent investigation [36] has applied a Hamiltonian method to extend flux-balance relations to resonant orbits.…”

Section: Flux-balance Law To Linear Order In Spinmentioning

confidence: 99%

“…The above discussion is given to emphasize the generic requirements of the mode decomposition such that the fluxbalance law may be given in terms of a sum over mode amplitudes. We now specialize the discussion to the radiation gauge, for which the separability of the radiative two-point function is well-documented by prior investigations [33,36,53]. The radiation gauge mode decompositions are defined in terms of the formalism of metric reconstruction from Teukolsky modes discussed in detail in Sec.…”

Section: Asymptotic Fluxesmentioning

confidence: 99%

“…The mode normalization coefficients s A out mω and s A down mω are explicitly derived in Refs. [33,36], and the corresponding mode normalization coefficients for in and up modes can be derived by similar methods to those described in the appendix of Ref. [33].…”

Section: Asymptotic Fluxesmentioning

confidence: 99%

“…Our goal here is to understand how the inspiral (and by extension the waveform from the EMRI) is influenced by the spin of the secondary. For a non-spinning secondary, well-known balance laws [7,[31][32][33][34][35][36] can be used to relate the leading-order fluxes to the first-order self-force contribution to the evolution of the inspiral. In this work we derive, for the first time, the appropriate balance law including the contribution from the spin of the secondary in the extreme mass-ratio inspiral context.…”

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confidence: 99%

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Dissipation in extreme mass-ratio binaries with a spinning secondary

et al. 2020

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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...

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Section: Discussionmentioning

confidence: 99%

Section: Flux-balance Law To Linear Order In Spinmentioning

confidence: 99%