Post-1-Newtonian quadrupole tidal interactions in binary systems

Details Post-1-Newtonian quadrupole tidal interactions in binary systems Post-1-Newtonian quadrupole tidal interactions in binary systems

2010-09-24

arxiv.org/abs/1009.4919v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

32 pages; v2: modified presentation, corrected errors of omission in appendix B

Scientific paper

We consider orbital-tidal coupling in a binary stellar system to post-1-Newtonian order. We derive the orbital equations of motion for bodies with spins and mass quadrupole moments and show that they conserve the total linear momentum of the binary. Momentum conservation also allows us to specialize our analysis to the system's center-of-mass-energy frame; we find the binary's relative equation of motion in this frame and also present a generalized Lagrangian from which it can be derived. We then specialize to the case in which the quadrupole moment is adiabatically induced by the tidal field. We show how the adiabatic dynamics for the quadrupole can be incorporated into our action principle and present the simplified orbital equations of motion and conserved energy for the adiabatic case. These results are relevant to the gravitational wave signal of inspiralling binary neutron stars.

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