Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity

Angelica Albertini, Rossella Gamba, Alessandro Nagar, and Sebastiano Bernuzzi

Phys. Rev. D 109, 044022 – Published 9 February 2024

Abstract

We present a first complete implementation of an effective-one-body (EOB) model for extreme-mass-ratio inspirals (EMRIs) that incorporates aligned spins (on both the primary and the secondary) as well as orbital eccentricity. The model extends TEOBResumS-Dalí for these binaries by (i) recasting conservative first-order gravitational self-force (1GSF) information in the resummed EOB potentials, (ii) employing a post-Newtonian (PN) $3^{+ 19} PN$ -accurate (3PN comparable-mass terms hybridized with test-particle terms up to 22PN relative order) expression for the gravitational-wave flux at infinity, and (iii) using an improved implementation of the horizon flux that better approximates its test-mass representation. With respect to our previous work [A. Albertini et al., Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large-mass-ratio case, Phys. Rev. D 106, 084062 (2022).], we demonstrate that the inclusion of the $3^{+ 19} PN$ -accurate $ℓ = 9$ and $ℓ = 10$ modes in the flux at infinity significantly improves the model’s agreement with second-order accurate GSF (2GSF) circular waveforms. For a standard EMRI with mass ratio $q \equiv m_{1} / m_{2} = 5 \times 10^{4}$ and $m_{2} = 10 M_{⊙}$ , the accumulated EOB/2GSF dephasing is $≲ rad$ for $\sim 1 yr$ of evolution, which is consistent with the standard accuracy requirements for EMRIs. We also showcase the generation of eccentric and spinning waveforms and discuss future extensions of our EOB towards a physically complete model for EMRIs.

Received 20 October 2023
Accepted 11 January 2024

DOI:https://doi.org/10.1103/PhysRevD.109.044022

Physics Subject Headings (PhySH)

General relativity Gravitational waves

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Angelica Albertini ^1,2, Rossella Gamba³, Alessandro Nagar^4,5, and Sebastiano Bernuzzi ³

¹Astronomical Institute of the Czech Academy of Sciences, Boční II 1401/1a, CZ-141 00 Prague, Czech Republic
²Faculty of Mathematics and Physics, Charles University in Prague, 18000 Prague, Czech Republic
³Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universität Jena, 07743 Jena, Germany
⁴INFN Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁵Institut des Hautes Etudes Scientifiques, 91440 Bures-sur-Yvette, France

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Issue

Vol. 109, Iss. 4 — 15 February 2024

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Images

Figure 1
Probing how the EOB/GSF difference in $Q_{ω}$ for $q = 50 000$ changes when adding more multipoles to the EOB flux. The red line is related to the same model used in Ref. [20] (see the lower panel in Fig. 7 therein), where the EOB infinity flux includes modes up to $ℓ = 8$ and corresponds to an integrated phase difference $Δ ϕ_{ℓ_{\max} = 8}^{EOBGSF} = 3.1 rad$ . The yellow line corresponds to the addition of the $ℓ = 9$ , 10 modes to the infinity flux, and lowers the integrated phase difference to $Δ ϕ_{ℓ_{\max} = 10}^{EOBGSF} = - 1.1 rad$ . When considering the frequency interval $ω = [0.045, 0.12]$ , i.e., from the dashed grey line until the end, the integrated phase differences are, respectively, $Δ ϕ_{ℓ_{\max} = 8}^{EOBGSF} = 3.0$ and $Δ ϕ_{ℓ_{\max} = 10}^{EOBGSF} = - 0.7$ . This second interval corresponds to more physically meaningful EMRI parameters (see the text).
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Figure 2
EOB/GSF difference in $Q_{ω}^{(0)}, Q_{ω}^{(1)}, Q_{ω}^{(2)}$ both with the EOB flux using up to $ℓ = 8$ and up to $ℓ = 10$ . The lowered difference in $Q_{ω}^{(0)}$ further explains why the $ℓ_{\max} = 10$ model better agrees with GSF results.
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Figure 3
Benchmark of the quasicircular model for systems with total mass $M = 10^{7} M_{⊙}$ from an initial frequency of $10^{- 4} Hz$ . We display the time necessary to generate a waveform up to $r / M = 5$ for $\sim 700$ binary configurations with varying mass ratios $q$ and effective spin $χ_{eff} = χ_{1} m_{1} / M + χ_{2} m_{2} / M$ , with or without the iterated postadiabatic approximation [30] (top and bottom panels, respectively).
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Figure 4
Illustrative depiction of the boundaries we impose to determine the value of $r_{PA}$ at which we terminate the iterative postadiabatic evolution. Drawing inspiration from the dynamics of a test particle on a Kerr black hole, we evolve the system iteratively until either we reach the ISCO $r = r_{ISCO}^{Kerr}$ or we hit the fixed threshold $r = 5.5$ (red line in the plot). At that point, the evolution is continued numerically up to $r = r_{final} = 5$ .
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Figure 5
Multipoles generated by a binary with $q = 10^{3}$ , $e_{0} = 0.5$ , $χ_{1} = 0.3$ , and $χ_{2} = 0.1$ . The labels of the $y$ axes indicate the values ( $ℓ m$ ).
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Figure 6
Strain and trajectory generated by a binary with $q = 10^{3}$ , $e_{0} = 0.5$ , $χ_{1} = 0.3$ , and $χ_{2} = 0.1$ . As for the strain, we sum up to $ℓ = 8$ and do not include $m = 0$ modes, and we consider it as seen by an observer whose line of sight is inclined by 45° with the orbital plane. The lower left panels show a zoom-in on a radial period, and the portion of the strain shown in the upper panel corresponds to the trajectory highlighted in blue in the bottom right panel.
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