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

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 strength of internal gravity in 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 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 corrections to the Newtonian tidal distortion of each star, both of which occur at third order in the tidal expansion parameter, and there are 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. There are additional interactions with no Newtonian analogs, but these do not change the central density of each star up to 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 general-relativistic crushing forces that could cause the stars to collapse to black holes prior to the dynamical orbital instability, and (ii) the conventional wisdom with respect to coalescing binary 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 purpose of detecting the coalescences.

22 pages, 2 figures. Replaced 13 July: proof corrected, result unchanged

References in corpus (16)

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• Gauge dependence in the theory of non-linear spacetime perturbations
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• The central density of neutron stars in close binaries
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• Location of the innermost stable circular orbit of binary neutron stars in the post Newtonian approximations of general relativity

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• Interpreting Binary Neutron Star Mergers: Describing the Binary Neutron Star Dynamics, Modelling Gravitational Waveforms, and Analyzing Detections
• Tidal Stabilization of Rigidly Rotating, Fully Relativistic Neutron Stars
• Post-Newtonian Gravitational and Scalar Waves in Scalar-Gauss-Bonnet Gravity
• An aligned-spin neutron-star--black-hole waveform model based on the effective-one-body approach and numerical-relativity simulations
• Properties of general relativistic, irrotational binary neutron stars in close quasiequilibrium orbits : Polytropic equations of state
• Irrotational binary neutron stars in quasiequilibrium
• Post-Newtonian spin-tidal couplings for compact binaries
• Towards a Realistic Neutron Star Binary Inspiral: Initial Data and Multiple Orbit Evolution in Full General Relativity
• Revised Relativistic Hydrodynamical Model for Neutron-Star Binaries
• Post-1-Newtonian equations of motion for systems of arbitrarily structured bodies
• Impact of Dynamical Tides on the Reconstruction of the Neutron Star Equation of State
• Probing the equation of state of neutron star matter with gravitational waves from binary inspirals in light of GW170817: a brief review
• Tidal response from scattering and the role of analytic continuation
• Effective action and linear response of compact objects in Newtonian gravity
• Possible explanation for star-crushing effect in binary neutron star simulations
• Are neutron stars crushed? Gravitomagnetic tidal fields as a mechanism for binary-induced collapse
• New perspectives on neutron star and black hole spectroscopy and dynamic tides
• The gauge invariance of general relativistic tidal heating
• Dipolar tidal effects in gravitational waves from scalarized black hole binary inspirals in quadratic gravity
• Binary-induced collapse of a compact, collisionless cluster
• General Relativistic Decompression of Binary Neutron Stars During Dynamic Inspiral
• Measuring Hubble Constant with Dark Neutron Star-Black Hole Mergers
• Quasilocal energy exchange and the null cone