Mergers of Irrotational Neutron Star Binaries in Conformally Flat Gravity
Abstract
We present the first results from our new general relativistic, Lagrangian hydrodynamics code, which treats gravity in the conformally flat (CF) limit. The evolution of fluid configurations is described using smoothed particle hydrodynamics (SPH), and the elliptic field equations of the CF formalism are solved using spectral methods in spherical coordinates. The code was tested on models for which the CF approximation is exact, finding good agreement with the classical Oppenheimer-Volkov solution for a relativistic static spherical star as well as that for a collapsing spherical dust cloud. In computing the evolution of quasi-equilibrium neutron star binary configurations in the absence of gravitational radiation backreaction, we have confirmed that these configurations can remain dynamically stable up to the development of a cusp. By including an approximate treatment of radiation reaction, we have calculated the complete merger of an irrotational binary configuration from the innermost point on an equilibrium sequence through merger and remnant formation, finding good agreement with previous relativistic calculations. In particular, we find that mass loss is highly suppressed by relativistic effects, but that, for a reasonably stiff neutron star equation of state, the remnant is initially stable against gravitational collapse because of its strong differential rotation. The gravity wave signal derived from our numerical calculation has an energy spectrum which matches extremely well with estimates based solely on quasi-equilibrium results, deviating from the Newtonian power law form at frequencies below 1 kHz, within the reach of an advanced interferometer.Keywords
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