COALESCING BINARY NEUTRON-STARS

The best models for the internal structure of a coalescing binary neutron star are the irrotational Roche-Riemann ellipsoids (IRREs). The IRREs have tidally locked figures but zero circulation in an inertial frame, and are the result of binary evolution in the absence of viscosity. The IRREs differ markedly from the more familiar Roche ellipsoids: where the fluid is static in the corotating frame for the Roche solution, the fluid counterrotates at the orbital frequency for the IRRE solutions, and where the Roche ellipsoids expand along both principal axes in the orbital plane, the IRREs expand along the separation vector and contract in the orthogonal direction. The structure of the stars begins to deviate from the IRRE structure if the average dynamical shear viscosity is larger than eta greater than or similar to 10(29) g cm-1 s-1, and will begin to approach the Roche solution just before coalescence if eta greater than or similar to 10(31) g cm-1 s-1. Viscosity grows in importance as the orbit shrinks because the strength of the viscous damping grows much more rapidly than gravitational radiation. Plastic or inelastic flow in the sold crust of the star can produce a maximum effective viscosity of eta(crust) approximately 10(28)(10(3)M(c)/M*) (R*/R)3/2 g cm-1 s-1, where M(c) is the mass of the solid crust. While this is still smaller than the estimated critical viscosity for significant deviations from the IRRE structure, it is many orders of magnitude larger than the microscopic viscosity (eta(micro) approximately 10(22) g cm-1 s-1). This suggests that in neutron star binaries, as in normal binaries and accretion disks, anomalous viscosities caused by dynamical processes are much more important than microscopic viscosities. Even so, the viscosity is insufficient to cause significant deviations from the IRRE structure. The structure of the stars has a negligible effect on the instantaneous amplitude of the gravitational waves emitted by the binary, but emission from the quadrupole moments of the stars and orbital precession slightly accelerate the coalescence and cause a monotonically growing phase difference between the true signal and a point mass binary model for the signal. For a coalescencing system like PSR 1913 + 16, the phase difference as a function of orbital radius R is DELTAphi congruent-to 13R(R*/R)5/2 (R*/10 km)5/2, where R* is the neutron star radius. While this is not large enough to interfere with detecting the gravitational waves, it is a measurable effect, and it may allow us to determine the size and approximate structure of the neutron star prior to coalescence. The magnitude of the phase shift grows rapidly if the neutron stars are much larger than R* = 10 km or the viscosity is larger than eta greater than or similar to 10(29) g cm-1 s-1.