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Register a new userGeneral Relativistic Decompression of Binary Neutron Stars During Dynamic Inspiral
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Mark Miller
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We investigate the dynamic stability of inspiraling neutron stars by performing multiple-orbit numerical relativity simulations of the binary neutron star inspiral process. By introducing eccentricities in the orbits of the neutron stars, significant changes in orbital separation are obtained within orbital timescales. We find that as the binary system evolves from apastron to periastron (as the binary separation decreases), the central rest mass density of each star decreases, thus stabilizing the stars against individual prompt collapse. As the binary system evolves from periastron to apastron, the central rest mass density increases; the neutron stars re-compress as the binary separation increases.
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We have studied the dynamics of an equal-mass magnetized neutron-star binary within a resistive magnetohydrodynamic (RMHD) approach in which the highly conducting stellar interior is matched to an electrovacuum exterior. Because our analysis is aimed at assessing the modifications introduced by resistive effects on the dynamics of the binary after the merger and through to collapse, we have carried out a close comparison with an equivalent simulation performed within the traditional ideal magnetohydrodynamic approximation. We have found that there are many similarities between the two evolutions but also one important difference: the survival time of the hyper massive neutron star increases in a RMHD simulation. This difference is due to a less efficient magnetic-braking mechanism in the resistive regime, in which matter can move across magnetic-field lines, thus reducing the outward transport of angular momentum. Both the RMHD and the ideal magnetohydrodynamic simulations carried here have been performed at higher resolutions and with a different grid structure than those in previous work of ours [L. Rezzolla, B. Giacomazzo, L. Baiotti, J. Granot, C. Kouveliotou, and M. A. Aloy, Astrophys. J. Letters 732, L6 (2011)], but confirm the formation of a low-density funnel with an ordered magnetic field produced by the black hole--torus system. In both regimes the magnetic field is predominantly toroidal in the highly conducting torus and predominantly poloidal in the nearly evacuated funnel. Reconnection processes or neutrino annihilation occurring in the funnel, none of which we model, could potentially increase the internal energy in the funnel and launch a relativistic outflow, which, however, is not produced in these simulations.
An approach to general relativity based on conformal flatness and quasiequilibrium (CFQE) assumptions has played an important role in the study of the inspiral dynamics and in providing initial data for fully general relativistic numerical simulations of coalescing compact binaries. However, the regime of validity of the approach has never been established. To this end, we develop an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. With this analysis, we show that the CFQE assumption is significantly violated even at relatively large orbital separations in the case of corotational neutron star binaries. We also demonstrate that the innermost stable circular orbit (ISCO) determined in the CFQE approach for corotating neutron star binaries may have no astrophysical significance.
This paper reports on our effort in modeling realistic astrophysical neutron star binaries in general relativity. We analyze under what conditions the conformally flat quasiequilibrium (CFQE) approach can generate ``astrophysically relevant initial data, by developing an analysis that determines the violation of the CFQE approximation in the evolution of the binary described by the full Einstein theory. We show that the CFQE assumptions significantly violate the Einstein field equations for corotating neutron stars at orbital separations nearly double that of the innermost stable circular orbit (ISCO) separation, thus calling into question the astrophysical relevance of the ISCO determined in the CFQE approach. With the need to start numerical simulations at large orbital separation in mind, we push for stable and long term integrations of the full Einstein equations for the binary neutron star system. We demonstrate the stability of our numerical treatment and analyze the stringent requirements on resolution and size of the computational domain for an accurate simulation of the system.
Although general relativistic cosmological solutions, even in the presence of pressure, can be mimicked by using neo-Newtonian hydrodynamics, it is not clear whether there exists the same Newtonian correspondence for spherical static configurations. General relativity solutions for stars are known as the Tolman-Oppenheimer-Volkoff (TOV) equations. On the other hand, the Newtonian description does not take into account the total pressure effects and therefore can not be used in strong field regimes. We discuss how to incorporate pressure in the stellar equilibrium equations within the neo-Newtonian framework. We compare the Newtonian, neo-Newtonian and the full relativistic theory by solving the equilibrium equations for both three approaches and calculating the mass-radius diagrams for some simple neutron stars equation of state.
We compute the internal modes of a non-spinning neutron star and its tidal metric perturbation in general relativity, and determine the effect of relativistic corrections to the modes on mode coupling and the criterion for instability. Claims have been made that a new hydrodynamic instability can occur in a neutron star in a binary neutron star system triggered by the nonlinear coupling of the companions tidal field to pairs of p-modes and g-modes in it as the binary inspirals toward merger. This PG instability may be significant since it can influence the binarys inspiral phase by extracting orbital energy, thereby potentially causing large deviations in their gravitational waveforms from those predicted by theoretical models that do not account for it. This can result in incorrect parameter estimation, at best, or mergers going undetected, at worst, owing to the use of deficient waveform models. On the other hand, better modeling of this instability and its effect on binary orbits can unravel a new phenomenon and shed light on stellar instabilities, via gravitational wave observations. So far, all mode-tide coupling instability studies have been formulated in Newtonian perturbation theory. Neutron stars are compact objects, so relativistic corrections might be important. We present and test a new code to calculate the relativistic eigenmodes of nonrotating relativistic stars. We use these relativistic tide and neutron star eigenmodes to compute the mode-tide coupling strength (MTCS) for a few selected equations of state. The MTCS thus calculated can be at most tens of percent different from its purely Newtonian value, but we confirm the dependencies on orbital separation and equation of state found by Newtonian calculations. For some equations of state, the MTCS is very sensitive to the neutron star crust region, demonstrating the importance of treating this region accurately.
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