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Testing the multipole structure and conservative dynamics of compact binaries using gravitational wave observations: The spinning case
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Abstract
In an earlier work [S. Kastha et al., PRD {\bf 98}, 124033 (2018)], we developed the {\it parametrized multipolar gravitational wave phasing formula} to test general relativity, for the non-spinning compact binaries in quasi-circular orbit. In this paper, we extend the method and include the important effect of spins in the inspiral dynamics. Furthermore, we consider parametric scaling of PN coefficients of the conserved energy for the compact binary, resulting in the parametrized phasing formula for non-precessing spinning compact binaries in quasi-circular orbit. We also compute the projected accuracies with which the second and third generation ground-based gravitational wave detector networks as well as the planned space-based detector LISA will be able to measure the multipole deformation parameters and the binding energy parameters. Based on different source configurations, we find that a network of third-generation detectors would have comparable ability to that of LISA in constraining the conservative and dissipative dynamics of the compact binary systems. This parametrized multipolar waveform would be extremely useful not only in deriving the first upper limits on any deviations of the multipole and the binding energy coefficients from general relativity using the gravitational wave detections, but also for science case studies of next generation gravitational wave detectors.
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If gravitation is propagated by a massive field, then the velocity of
gravitational waves (gravitons) will depend upon their frequency and the
effective Newtonian potential will have a Yukawa form. In the case of
inspiralling compact binaries, gravitational waves emitted at low frequency
early in the inspiral will travel slightly slower than those emitted at high
frequency later, modifying the phase evolution of the observed inspiral
gravitational waveform, similar to that caused by post-Newtonian corrections to
quadrupole phasing. Matched filtering of the waveforms can bound such
frequency-dependent variations in propagation speed, and thereby bound the
graviton mass. The bound depends on the mass of the source and on noise
characteristics of the detector, but is independent of the distance to the
source, except for weak cosmological redshift effects. For observations of
stellar-mass compact inspiral using ground-based interferometers of the
LIGO/VIRGO type, the bound on the graviton Compton wavelength is of the order
of $6 \times 10^{12}$ km, about double that from solar-system tests of Yukawa
modifications of Newtonian gravity. For observations of super-massive black
hole binary inspiral at cosmological distances using the proposed laser
interferometer space antenna (LISA), the bound can be as large as $6 \times
10^{16}$ km. This is three orders of magnitude weaker than model-dependent
bounds from galactic cluster dynamics.
We show how to use dimensional regularization to determine, within the Arnowitt–Deser–Misner canonical formalism, the reduced Hamiltonian describing the dynamics of two gravitationally interacting point masses. Implementing, at the third post-Newtonian (3PN) accuracy, our procedure we find that dimensional continuation yields a finite, unambiguous (no pole part) 3PN Hamiltonian which uniquely determines the heretofore ambiguous “static” parameter: namely, ωs=0. Our work also provides a remarkable check of the perturbative consistency (compatibility with gauge symmetry) of dimensional continuation through a direct calculation of the “kinetic” parameter ωk, giving the unique answer compatible with global Poincaré invariance (ωk=41/24) by summing ∼50 different dimensionally continued contributions.
We present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center-of-mass vector uniquely determined by an ansatz. The authors present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincaré algebra with the center-of-mass vector uniquely determined by an ansatz.
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