Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole: Effects of Black Hole Absorption

Tagoshi, Hideyuki; Mano, Shuhei; Takasugi, Eiichi

doi:10.1143/ptp.98.829

Cited by 82 publications

(106 citation statements)

References 6 publications

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“…They rapidly grow as ∆N Flux,5 ∼ ν −1 ln(ν) and ∆N Flux,7 ∼ ∆N SSS ∼ ν −5/4 as ν decreases, and their values become as large as O(10 3 ) ∼ O(10 4 ) when ν ∼ 10 −5 , depending on the values of χ 1,2 . While our results for high-mass-ratio inspirals (ν 10 −3 ) are only indicative because the PN approximation is not so accurate for these BBHs [89,90,91,92], these results are basically consistent with previous results made by many authors, which showed that for quasicircular, extreme mass-ratio BBH inspirals with ν ∼ 10 −6 and nearly extremal spins the horizon-flux effects significantly increases the duration of inspiral phase [65,68,69,70].…”

Section: Results 1: the Error In Gw Cyclessupporting

confidence: 85%

“…While their expressions at the relative 1.5PN order do not recover the expressions in the test-particle limit ν → 0 [65,68] † †, for the purpose of our analysis at the 3.5PN accuracy level, we only need them up to the relative 1PN order that do agree with the test-mass results. Importing the results in (42) and (43) of [62], the horizon energy and angular-momentum fluxes for the spinning, non-precessing, quasicircular BBH are defined by…”

Section: The Horizon Fluxesmentioning

confidence: 99%

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Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

Isoyama¹,

Nakano²

2017

Class. Quantum Grav.

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Abstract. Black holes (BHs) in an inspiraling compact binary system absorb the gravitational-wave (GW) energy and angular-momentum fluxes across their event horizons and this leads to the secular change in their masses and spins during the inspiral phase. The goal of this paper is to present ready-to-use, 3.5 postNewtonian (PN) template families for spinning, non-precessing, binary BH inspirals in quasicircular orbits, including the 2.5PN and 3.5PN horizon-flux contributions as well as the correction due to the secular change in the BH masses and spins through 3.5PN order, respectively, in phase. We show that, for binary BHs observable by Advanced LIGO with high mass ratios (larger than ∼ 10) and large aligned-spins (larger than ∼ 0.7), the mismatch between the frequency-domain template with and without the horizon-flux contribution is typically above the 3% mark. For (supermassive) binary BHs observed by LISA, even a moderate mass-ratios and spins can produce a similar level of the mismatch. Meanwhile, the mismatch due to the secular time variations of the BH masses and spins is well below the 1% mark in both cases, hence this is truly negligible. We also point out that neglecting the cubic-in-spin, point-particle phase term at 3.5PN order would deteriorate the effect of BH absorption in the template.

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Section: Results 1: the Error In Gw Cyclessupporting

confidence: 85%

Section: The Horizon Fluxesmentioning

confidence: 99%

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

Isoyama¹,

Nakano²

2017

Class. Quantum Grav.

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“…Similarly, it should likely be possible to develop a similar simplifying factorization for the horizon-absorbed flux (for Kerr or Schwarzschild) for circular, equatorial orbits. This flux has recently been calculated to 8PN by Fujita [31] completely analytically (again significantly improving upon the previous 4PN accurate calculation by Tagoshi, Mano, and Takasugi [34]), and has also been calculated numerically (again with analytic forms determined for some coefficients) to 20PN by Shah [33].…”

Section: Discussionmentioning

confidence: 81%

“…We thus are unable to determine q ℓm for ℓ ≥ 7 and s ℓ for ℓ ≥ 5 from the 22PN energy flux expressions: For q 77 , we would need to know the v 36 term inη 77 , but only know this through v 34 . Similarly, for s 5 , we would need to know, e.g., the v 39 term ofη 55 but only know this through v 38 .…”

Section: Simplifying the Modes Of The Energy Fluxmentioning

confidence: 99%

Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole

Johnson-McDaniel

2014

Phys. Rev. D

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High-order terms in the post-Newtonian (PN) expansions of various quantities for compact binaries exhibit a combinatorial increase in complexity, with an ever-increasing number of terms, including more transcendentals and logarithms of the velocity, higher powers of these transcendentals and logarithms, and larger and larger rational numbers as coefficients. Here we consider the gravitational wave energy flux at infinity from a point particle in a circular orbit around a Schwarzschild black hole, which is known to 22PN [O(v 44 ), where v is the particle's orbital velocity] beyond the lowest-order Newtonian prediction, at which point each order has over 1000 terms. We introduce a factorization that considerably simplifies the spherical harmonic modes of the energy flux (and thus also the amplitudes of the spherical harmonic modes of the gravitational waves); it is likely that much of the complexity this factorization removes is due to wave propagation on the Schwarzschild spacetime (e.g., tail effects). For the modes with azimuthal number ℓ ≥ 7, this factorization reduces the expressions for the modes that enter the 22PN total energy flux to pure integer PN series with rational coefficients, which amounts to a reduction of up to a factor of ∼ 150 in the total number of terms in a given mode (and also in the size of the entire expression for the mode). The reduction in complexity becomes less dramatic for smaller ℓ, due to the structure of the expansion, and one only obtains purely rational coefficients up to some order, though the factorization is still able to remove all the half-integer PN terms. For the 22PN ℓ = 2 modes, this factorization still reduces the total number of terms (and size) by a factor of ∼ 10 and gives purely rational coefficients through 8PN. This factorization also improves the convergence of the series, though we find the exponential resummation introduced for the full energy flux in [Isoyama et al., Phys. Rev. D 87, 024010 (2013)] to be even more effective at improving the convergence of the individual modes, producing improvements of over four orders of magnitude over the original series for some modes. However, the exponential resummation is not as effective at simplifying the series, particularly for the higher-order modes.

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“…[66] included the spinning horizon flux in an EOB model, using the Taylor-expanded expressions of Refs. [67,68]; the inclusion of absorption turned out to be important to obtain good agreement with the full Teukolsky flux, at least up to the ISCO. When modeling spinning binaries, one should bear in mind that the spin changes the PN order (with respect to the leading order flux at infinity) at which absorption enters in the energy flux: while this effect enters at 4PN order for Schwarzschild BHs, it enters at 2.5PN order for nonzero spin.…”

Section: The Comparable-mass Effective-one-body Model In the Tesmentioning

confidence: 99%

Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms

et al. 2014

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We numerically solve the Teukolsky equation in the time domain to obtain the gravitational-wave emission of a small mass inspiraling and plunging into the equatorial plane of a Kerr black hole. We account for the dissipation of orbital energy using the Teukolsky frequency-domain gravitational-wave fluxes for circular, equatorial orbits, down to the light-ring. We consider Kerr spins −0.99 ≤ q ≤ 0.99, and compute the inspiral-merger-ringdown (2,2), (2,1), (3,3), (3,2), (4,4), and (5,5) modes. We study the largespin regime, and find a great simplicity in the merger waveforms, thanks to the extremely circular character of the plunging orbits. We also quantitatively examine the mixing of quasinormal modes during the ringdown, which induces complicated amplitude and frequency modulations in the waveforms. Finally, we explain how the study of small mass-ratio black-hole binaries helps extending effective-one-body models for comparable-mass, spinning black-hole binaries to any mass ratio and spin magnitude.

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Post-Newtonian Expansion of Gravitational Waves from a Particle in Circular Orbits around a Rotating Black Hole: Effects of Black Hole Absorption

Cited by 82 publications

References 6 publications

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

Post-Newtonian templates for binary black-hole inspirals: the effect of the horizon fluxes and the secular change in the black-hole masses and spins

Taming the post-Newtonian expansion: Simplifying the modes of the gravitational wave energy flux at infinity for a point particle in a circular orbit around a Schwarzschild black hole

Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms

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