Mergers of Irrotational Neutron Star Binaries in Conformally Flat Gravity

TL;DR

This paper introduces a new relativistic hydrodynamics code using conformally flat gravity to simulate neutron star mergers, confirming stability of quasi-equilibrium configurations and matching gravitational wave signals with theoretical estimates.

Contribution

The paper presents the first implementation of a conformally flat gravity code with SPH for neutron star mergers, demonstrating accurate simulation of merger dynamics and gravitational wave signals.

Findings

Quasi-equilibrium neutron star binaries can remain stable up to cusp formation.

Mass loss during merger is highly suppressed by relativistic effects.

Gravitational wave spectra match quasi-equilibrium estimates, deviating below 1 kHz.

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 methodsin spherical coordinates. The code was tested on models for which the CF limit is exact, finding good agreement with the classical Oppenheimer-Volkov solution for a relativistic static spherical star as well as the exact semi-analytic solution for a collapsing spherical dust cloud. By 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 all the way to the development of a cusp. With 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 and ringdown, finding good agreement withprevious 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, i.e., within the reach of advanced interferometric detectors.