Computing inspirals in Kerr in the adiabatic regime: I. The scalar case

The inspiral of a stellar mass (1 − 100 M⊙) compact body into a massive (10 5 − 10 7 M⊙) black hole has been a focus of much effort, both for the promise of such systems as astrophysical sources of gravitational waves, and because they are a clean limit of the general relativistic two-body problem. Our understanding of this problem has advanced significantly in recent years, with much progress in modeling the "self force" arising from the small body's interaction with its own spacetime deformation. Recent work has shown that this self interaction is especially interesting when the frequencies associated with the orbit's θ and r motions are in an integer ratio: Ω θ /Ωr = β θ /βr, with β θ and βr both integers. In this paper, we show that key aspects of the self interaction for such "resonant" orbits can be understood with a relatively simple Teukolsky-equation-based calculation of gravitational-wave fluxes. We show that fluxes from resonant orbits depend on the relative phase of radial and angular motions. The purpose of this paper is to illustrate in simple terms how this phase dependence arises using tools that are good for strong-field orbits, and to present a first study of how strongly the fluxes vary as a function of this phase and other orbital parameters. Future work will use the full dissipative self force to examine resonant and near resonant strong-field effects in greater depth, which will be needed to characterize how a binary evolves through orbital resonances.

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“…3 of Ref. [21]. Here the function ∆t r is periodic with period Λ r and ∆t θ is periodic with period Λ θ , etc.…”

Section: Setupmentioning

confidence: 99%

“…The parameter set (ψ 0 , χ 0 , φ 0 , t 0 ) is equivalent to the set (λ r 0 , λ θ 0 , φ 0 , t 0 ) used in Ref. [21]. Following this reference, χ 0 = 0 will label the "fiducial geodesic."…”

Section: Kerr Geodesics and Orbital Resonancesmentioning

confidence: 99%

Resonantly enhanced and diminished strong-field gravitational-wave fluxes

Flanagan

Hughes

Ruangsri³

2014

Phys. Rev. D

113

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“…The initial conditions of the geodesic can then be characterized by the values t 0 and 0 of the coordinates t and when 0, the value r0 of the Carter time nearest to 0 at which r r0 r p , and the value 0 of the Carter time nearest to 0 at which 0 min [42]. Let us first fix the geodesic under consideration by choosing the parameters p, e, and inc so as to obtain a bound and stable orbit (see Ref.…”

Section: B Adiabatic Approximationmentioning

confidence: 99%

Influence of the hydrodynamic drag from an accretion torus on extreme mass-ratio inspirals

Barausse

Rezzolla

2008

Phys. Rev. D

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We have studied extreme mass-ratio inspirals (EMRIs) in spacetimes containing a rotating black hole and a non-self-gravitating torus with a constant distribution of specific angular momentum. We have found that the dissipative effect of the hydrodynamic drag exerted by the torus on the satellite is much smaller than the corresponding one due to radiation reaction, for systems such as those generically expected in active galactic nuclei and at distances from the central supermassive black hole (SMBH) which can be probed with the Laser Interferometer Space Antenna (LISA). However, given the uncertainty on the parameters of these systems, namely, on the masses of the SMBH and of the torus, as well as on its size, there exist configurations in which the effect of the hydrodynamic drag on the orbital evolution can be comparable to the radiation reaction one in phases of the inspiral which are detectable by the Laser Interferometer Space Antenna. This is the case, for instance, for a 10 6 M SMBH surrounded by a corotating torus of comparable mass and with radius of 10 3 -10 4 gravitational radii, or for a 10 5 M SMBH surrounded by a corotating 10 4 M torus with radius of 10 5 gravitational radii. Should these conditions be met in astrophysical systems, EMRI-gravitational waves could provide a characteristic signature of the presence of the torus. In fact, while radiation reaction always increases the inclination of the orbit with respect to the equatorial plane (i.e., orbits evolve towards the equatorial retrograde configuration), the hydrodynamic drag from a torus corotating with the SMBH always decreases it (i.e., orbits evolve towards the equatorial prograde configuration). However, even when initially dominating over radiation reaction, the influence of the hydrodynamic drag decays very rapidly as the satellite moves into the very strong-field region of the SMBH (i.e., p & 5M), thus allowing one to use pure-Kerr templates for the last part of the inspiral. Although our results have been obtained for a specific class of tori, we argue that they will be qualitatively valid also for more generic distributions of the specific angular momentum.

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“…Because this Green's function is sourcefree, it is regular at the particle. Approximating the self-force by its dissipative part is an adiabatic approximation [3,4,5], and several computations of orbits and waveforms have recently been carried out [6,7,8,9].…”

Section: Introductionmentioning

confidence: 99%

Finding fields and self-force in a gauge appropriate to separable wave equations

2007

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Gravitational waves from the inspiral of a stellar-size black hole to a supermassive black hole can be accurately approximated by a point particle moving in a Kerr background. This paper presents progress on finding the electromagnetic and gravitational field of a point particle in a black-hole spacetime and on computing the self-force in a "radiation gauge." The gauge is chosen to allow one to compute the perturbed metric from a gauge-invariant component ψ 0 (or ψ 4 ) of the Weyl tensor and follows earlier work by Chrzanowski and Cohen and Kegeles (we correct a minor, but propagating, error in the Cohen-Kegeles formalism). The electromagnetic field tensor and vector potential of a static point charge and the perturbed gravitational field of a static point mass in a Schwarzschild geometry are found, surprisingly, to have closed-form expressions. The gravitational field of a static point charge in the Schwarzschild background must have a strut, but ψ 0 and ψ 4 are smooth except at the particle, and one can find local radiation gauges for which the corresponding spin ±2 parts of the perturbed metric are smooth. Finally a method for finding the renormalized self-force from the Teukolsky equation is presented. The method is related to the Mino, Sasaki, Tanaka and Quinn and Wald (MiSaTaQuWa) renormalization and to the DetweilerWhiting construction of the singular field. It relies on the fact that the renormalized ψ 0 (or ψ 4 ) is a sourcefree solution to the Teukolsky equation; and one can therefore reconstruct a nonsingular renormalized metric in a radiation gauge.

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Computing inspirals in Kerr in the adiabatic regime: I. The scalar case

Cited by 91 publications

References 58 publications

Resonantly enhanced and diminished strong-field gravitational-wave fluxes

Resonantly enhanced and diminished strong-field gravitational-wave fluxes

Influence of the hydrodynamic drag from an accretion torus on extreme mass-ratio inspirals

Finding fields and self-force in a gauge appropriate to separable wave equations

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