Quasi-Keplerian parametrization for eccentric compact binaries in scalar-tensor theories at second post-Newtonian order and applications

Abstract

The generalized post-Keplerian parametrization for compact binaries on eccentric bound orbits is established at second post-Newtonian (2PN) order in a class of massless scalar-tensor theories. This result is used to compute the orbit-averaged flux of energy and angular momentum at Newtonian order, which means relative 1PN order beyond the leading-order dipolar radiation of scalar-tensor theories. The secular evolution of the orbital elements is then computed at 1PN order. At leading order, the closed form "Peters and Mathews" relation between the semi-major axis $a$ and the eccentricity $e$ is found to be independent of any scalar-tensor parameter, and is given by $a\propto e^{4/3}/(1-e^2)$. Finally, the waveform is obtained at Newtonian order in the form of a spherical harmonic mode decomposition, extending to eccentric orbits the results obtained in arXiv:2201.10924.

22 pages, 1 table, 3 figures. v2: some references were added. v3: title changed, and other minor changes reflecting the referee report. v4: minor modifications, matches the version published in PRD. v5: minor typos corrected

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• Signatures of modified gravity from the gravitational Aharonov-Bohm effect
• Testing modified gravity with the eccentric neutron star--black hole merger GW200105
• Quasi-Keplerian parametrization for compact binaries on hyperbolic orbits in scalar-tensor theories at second post-Newtonian order
• Ten years of extreme gravity tests of general theory of relativity with gravitational-wave observations
• Post-Newtonian Dynamics of Radiating Charges: Canonical Formulation and Binary Inspiral Laws
• Constraining scalar-tensor theories from higher harmonics with GW230529
• Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders
• Generalized Perturbed Kepler Problem: Gravitational Wave Imprints from Eccentric Compact Binaries