FirstpostNewtonian quadrupole tidal interactions in binary systems
Abstract
We consider orbitaltidal coupling in a binary stellar system to firstpostNewtonian (1PN) 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. We note that spinorbit coupling must be included in a 1PN treatment of tidal interactions in order to maintain consistency (except in the special case of adiabatically induced quadrupoles): the inclusion of 1PN quadrupolar tidal effects while omitting spin effects would lead to a failure of momentum conservation for generic evolution of the quadrupoles. We use momentum conservation to specialize our analysis to the system’s centerofmassenergy 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 (in which case it is consistent to ignore spin effects). 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 gravitationalwave signal of inspiralling binary neutron stars.
 Publication:

Physical Review D
 Pub Date:
 July 2013
 DOI:
 10.1103/PhysRevD.88.024046
 arXiv:
 arXiv:1009.4919
 Bibcode:
 2013PhRvD..88b4046V
 Keywords:

 04.30.Db;
 Wave generation and sources;
 General Relativity and Quantum Cosmology
 EPrint:
 34 pages