General-relativistic coupling between orbital motion and internal degrees of freedom for inspiraling binary neutron stars

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  • 16 June 1997
Abstract
We analyze the coupling between the internal degrees of freedom of neutron stars in a close binary, and the stars' orbital motion. Our analysis is based on the method of matched asymptotic expansions and is valid to all orders in the internal gravity of each star, but is perturbative in the ``tidal expansion parameter'' (stellar radius)/(orbital separation). At first order in the tidal expansion parameter, we show that the internal structure of each star is unaffected by its companion, in agreement with recent post-1-Newtonian results of Wiseman [gr-qc/9704018]. We also show that relativistic interactions that scale as higher powers of the tidal expansion parameter produce qualitatively similar effects to their Newtonian counterparts: there are post-Newtonian corrections to the Newtonian tidal distortion of each star, both of which occur at third order in the tidal expansion parameter; and there are post-Newtonian corrections to the Newtonian decrease in central density of each star (Newtonian ``tidal stabilization''), both of which are sixth order in the tidal expansion parameter. These results, in combination with previous analyses of Newtonian tidal interactions, indicate that (i) there are no large tidally-mediated crushing forces that could cause the stars to collapse to black holes before the dynamical orbital instability, and (ii) the conventional wisdom with respect to coalescing neutron stars as sources of gravitational-wave bursts is correct: namely, the finite-stellar-size corrections to the gravitational waveform will be unimportant for the purposes of detecting the coalescences.

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