Quasi-equilibrium models for triaxially deformed rotating compact stars

TL;DR

This paper models rapidly rotating, triaxially deformed neutron stars in general relativity, exploring their existence, properties, and potential gravitational wave signals to probe nuclear matter equations of state.

Contribution

It introduces quasi-equilibrium models of triaxially deformed stars using conformally flat gravity and polytropic equations, extending understanding of their stability and gravitational wave emission.

Findings

Triaxial solutions exist for various compactness and polytropic indices.

Sequences shorten and may vanish at high compactness for certain parameters.

Maximally deformed triaxial configurations are plausible during proto-neutron star contraction.

Abstract

Quasi-equilibrium models of rapidly rotating triaxially deformed stars are computed in general relativistic gravity, assuming a conformally flat spatial geometry (Isenberg-Wilson-Mathews formulation) and a polytropic equation of state. Highly deformed solutions are calculated on the initial slice covered by spherical coordinate grids, centered at the source, in all angular directions up to a large truncation radius. Constant rest mass sequences are calculated from nearly axisymmetric to maximally deformed triaxial configurations. Selected parameters are to model (proto-) neutron stars; the compactness is M/R = 0.001, 0.1, 0.14, 0.2 for polytropic index n = 0.3 and M/R = 0.001, 0.1, 0.12, 0.14 for n = 0.5. We confirmed that the triaxial solutions exist for these parameters as in the case of Newtonian polytropes. However, it is also found that the triaxial sequences become shorter for higher compactness, and those may disappear at a certain large compactness for the n = 0.5 case. In the scenario of the contraction of proto-neutron stars being subject to strong viscosity and rapid cooling, it is plausible that, once the viscosity driven secular instability sets in during the contraction, the proto-neutron stars are always maximally deformed triaxial configurations, as long as the compactness and the equation of state parameters allow such triaxial sequences. Detection of gravitational waves from such sources may be used as another probe for the nuclear equation of state.