Aligned spins: orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders

Tessmer, Manuel; Hartung, Johannes; Schäfer, Gerhard

doi:10.1088/0264-9381/30/1/015007

Cited by 25 publications

(35 citation statements)

References 56 publications

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“…In this section, using the results of Ref. [12] we explicitly write down the PN expression of the periastron advance for circular orbits, including all spin-independent, spin-orbit (SO), and spin-spin (SS) contributions up to 3.5PN order included. Higher-order interactions in the spins [47,48] will be neglected; hence we do not include the leadingorder 3.5PN terms cubic in the spins.…”

Section: Post-newtonian Approximationmentioning

confidence: 99%

“…Reference [12] provides an explicit, 3.5PN-accurate solution of the orbital equations of motion of a binary system of spinning point particles (at quadratic order in the spins S i ), for a generic bound orbit and aligned or antialigned spins, in the form of a quasi-Keplerian parametrization of the motion. 1 The orbital elements are expressed in terms of the two constants of the motion: the reduced binding energy " jEj=ðmÞ (recall that E < 0 for bound orbits) and the dimensionless angular momentum h L=ðm 2 Þ, where m ¼ m 1 þ m 2 is the total mass and ¼ m 1 m 2 =m 2 the symmetric mass ratio, such that ¼ 1=4 for equal masses and !…”

Section: Post-newtonian Approximationmentioning

confidence: 99%

“…The expressions (7) can also be recovered from the quasi-Keplerian parametrization of Ref. [12], by imposing the zero-eccentricity condition e t ¼ 0 (or equivalently e r ¼ 0 or e ' ¼ 0) appropriate for a circular orbit.…”

Section: Post-newtonian Approximationmentioning

confidence: 99%

“…[8][9][10]. Spin-orbit and spin-spin effects were computed up to 3.5PN order for aligned or antialigned spins [11,12], as well as for generic spin orientations in special binary configurations [13,14]; see Ref. [9] for earlier references.…”

Section: Introductionmentioning

confidence: 99%

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Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

et al. 2013

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We study the general relativistic periastron advance in spinning black hole binaries on quasicircular orbits, with spins aligned or antialigned with the orbital angular momentum, using numerical-relativity simulations, the post-Newtonian approximation, and black hole perturbation theory. By imposing a symmetry by exchange of the bodies' labels, we devise an improved version of the perturbative result and use it as the leading term of a new type of expansion in powers of the symmetric mass ratio. This allows us to measure, for the first time, the gravitational self-force effect on the periastron advance of a nonspinning particle orbiting a Kerr black hole of mass M and spin S ¼ À0:5M 2 , down to separations of order 9M. Comparing the predictions of our improved perturbative expansion with the exact results from numerical simulations of equal-mass and equal-spin binaries, we find a remarkable agreement over a wide range of spins and orbital separations.

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Section: Post-newtonian Approximationmentioning

confidence: 99%

Section: Post-newtonian Approximationmentioning

confidence: 99%

Section: Post-newtonian Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

et al. 2013

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“…Their derivation is given in, e. g., [44] and for the aligned-spin case in [31], including the energy and angular momentum decay due to radiation reaction. For the leading-order spin-orbit case with (i), single spin or (ii), equal masses, the above terms get spin-orientation corrections, see [29], and the following orientation equation…”

Section: Solution To the Eccentric Spin-orbit Problem At Leadingmentioning

confidence: 99%

Eccentric motion of spinning compact binaries

Tessmer¹,

Schäfer

2014

Phys. Rev. D

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The equations of motion for spinning compact binaries on eccentric orbits are treated perturbatively in powers of a fractional mass-difference ordering parameter. The solution is valid through first order in the mass-difference parameter. A canonical point transformation removes the leading order terms of the spin-orbit Hamiltonian which induce a wiggling precession of the orbital angular momentum around the conserved total angular momentum, a precession which disappears in the case of equal masses or one single spin. Action-angle variables are applied which make a canonical perturbation theory easily treatable.

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Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

2013

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The next-to-next-to-leading order post-Newtonian spin-orbit and spin(1)-spin(2) Hamiltonians for binary compact objects in general relativity are derived. The Arnowitt-Deser-Misner canonical formalism and its generalization to spinning compact objects in general relativity are presented and a fully reduced matter-only Hamiltonian is obtained. Several simplifications using integrations by parts are discussed. Approximate solutions to the constraints and evolution equations of motion are provided. Technical details of the integration procedures are given including an analysis of the short-range behavior of the integrands around the sources. The Hamiltonian of a test-spin moving in a stationary Kerr spacetime is obtained by rather simple approach and used to check parts of the mentioned results. Kinematical consistency checks by using the global (post-Newtonian approximate) Poincaré algebra are applied. Along the way a self-contained overview for the computation of the 3PN ADM point-mass Hamiltonian is provided, too. 3641 947 102 1 The following literature and in particular [88] gives a complete overview over the research area of parameterization. See e.g. [89] for a point-mass 1PN parameterization, [90] for a point-mass 2PN parameterization, [91] for a quasi-Keplerian 3PN point-mass parameterization, [92, 93] for point-mass parameterizations under leading order spin-orbit coupling, [94] for using a 3PN point-mass parameterization including radiative dynamics for the phasing of gravitational waves, [95] for a post-equal-mass parameterization of a binary at 3PN point-mass level under leading order spin-orbit coupling, and finally [96] for a parameterization up to 2.5PN with orbital angular momentum aligned spins. [97] incorporates the linear-in-spin Hamiltonians given in the present article into the orbital elements for orbital momentum aligned spins.3 series. Such a resummation was successfully implemented into the effective-one-body approach, which analytically provides complete gravitational waveforms for binary inspiral that are in good agreement with numerical relativity. This succeeded so far for point-masses [127,128] and for non-precessing spins [129] by calibrations to full numerical simulations, but more work is needed for precessing spins [130,131]. Here the Hamiltonians derived in the present paper should be very useful, and the spin-orbit one was indeed already incorporated into the effective-one-body approach [132,133]. See also [134] for a very complete overview of the literature on the effective-one-body approach. Alternative ways of resumming the post-Newtonian series by Padé approximants are possible, which is most interesting for certain gauge invariant quantities [135,136]. Within the overlap region of post-Newtonian approximation and numerical relativity in which the gravitational field is not too strong and the number of orbits can be handled by numerical simulations the results of both approaches can be compared. The mentioned resummation methods can make these approximate results competitive ...

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Aligned spins: orbital elements, decaying orbits, and last stable circular orbit to high post-Newtonian orders

Cited by 25 publications

References 56 publications

Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

Periastron advance in spinning black hole binaries: Gravitational self-force from numerical relativity

Eccentric motion of spinning compact binaries

Next‐to‐next‐to‐leading order post‐Newtonian linear‐in‐spin binary Hamiltonians

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