Post-Newtonian Models of Binary Neutron Stars

Abstract

Using an energy variational method, we calculate quasi-equilibrium configurations of binary neutron stars modeled as compressible triaxial ellipsoids obeying a polytropic equation of state. Our energy functional includes terms both for the internal hydrodynamics of the stars and for the external orbital motion. We add the leading post-Newtonian (PN) corrections to the internal and gravitational energies of the stars, and adopt hybrid orbital terms which are fully relativistic in the test-mass limit and always accurate to PN order. The total energy functional is varied to find quasi-equilibrium sequences for both corotating and irrotational binaries in circular orbits. We examine how the orbital frequency at the innermost stable circular orbit depends on the polytropic index n and the compactness parameter GM/Rc^2. We find that, for a given GM/Rc^2, the innermost stable circular orbit along an irrotational sequence is about 17% larger than the innermost secularly stable circular orbit along the corotating sequence when n=0.5, and 20% larger when n=1. We also examine the dependence of the maximum neutron star mass on the orbital frequency and find that, if PN tidal effects can be neglected, the maximum equilibrium mass increases as the orbital separation decreases.

53 pages, LaTex, 9 figures as 10 postscript files, accepted by Phys. Rev. D, replaced version contains updated references

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• Binary Neutron Stars in General Relativity: Quasi-Equilibrium Models
• Binary Induced Neutron-Star Compression, Heating, and Collapse
• The central density of neutron stars in close binaries
• The central density of a neutron star is unaffected by a binary companion at linear order in $\mu /R$
• Solving the Darwin problem in the first post-Newtonian approximation of general relativity

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