Abstract
In a compact binary coalescence, the spins of the compact objects can have a significant effect on the orbital motion and gravitational-wave (GW) emission. For generic spin orientations, the orbital plane precesses, leading to characteristic modulations of the GW signal. The observation of precession effects is crucial to discriminate among different binary formation scenarios, and to carry out precise tests of General Relativity. Here, we work toward an improved description of spin effects in binary inspirals, within the effective-one-body (EOB) formalism, which is commonly used to build waveform models for LIGO and Virgo data analysis. We derive EOB Hamiltonians including the complete fourth post-Newtonian (4PN) conservative dynamics, which is the current state of the art. We place no restrictions on the spin orientations or magnitudes, or on the type of compact object (e.g., black hole or neutron star), and we produce the first generic-spin EOB Hamiltonians complete at 4PN order. We consider multiple spinning EOB Hamiltonians, which are more or less direct extensions of the varieties found in previous literature, and we suggest another simplified variant. Finally, we compare the circular-orbit, aligned-spin binding-energy functions derived from the EOB Hamiltonians to numerical-relativity simulations of the late inspiral. While finding that all proposed Hamiltonians perform reasonably well, we point out some interesting differences, which could guide the selection of a simpler, and thus faster-to-evolve EOB Hamiltonian to be used in future LIGO and Virgo inference studies.
Highlights
The observation of gravitational waves (GWs) from coalescing binaries [1,2,3,4] using a continually improving network of GW detectors [5,6,7,8] is a milestone in fundamental physics and astrophysics
We built spinning EOB Hamiltonians that include the complete fourth post-Newtonian conservative dynamics for generic spins. These Hamiltonians are valid for generic compact objects since we included multipole constants that parametrize the deformation of the compact object due to its rotation
We considered and extended four spinning EOB (SEOB) Hamiltonians: (i) an extension of the SEOB Hamiltonian from Ref. [17] by adding NNLO S2 and LO S3 contributions, in addition to adding the multipole constants; (ii) a simplified version of that Hamiltonian that differs in how the spin corrections are added to the Kerr metric, and that does not use the concept of centrifugal radius; (iii) the aligned-spin Hamiltonian from Refs. [19,23,47], which already includes complete 4PN information for generic compact objects, but considered here for comparison with the other Hamiltonians; (iv) an extension of the SEOB Hamiltonian from Refs. [27,28], which uses a test spin, by adding NLO S2, NNLO S2, LO S3, and LO S4 contributions, in addition to adding the multipole constants
Summary
The observation of gravitational waves (GWs) from coalescing binaries [1,2,3,4] using a continually improving network of GW detectors [5,6,7,8] is a milestone in fundamental physics and astrophysics. A second category of SEOB Hamiltonians is based on the Hamiltonian for a spinning test body (test spin) in a Kerr background [25,26], first developed with NLO [27] and NNLO [28] spin-orbit terms and with LO spin-squared terms Such Hamiltonians have always been applicable for generic (precessing) spins. The goal of the present paper is to construct SEOB Hamiltonians for compact binaries (black holes or neutron stars) that include all known PN results to 4PN order for generic orbits and spin orientations. [25,27,28] which recovers the dynamics of a spinning test body in the Kerr spacetime in the small-mass-ratio limit (see Table I for a summary of the differences between these Hamiltonians).
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