$g$-mode of neutron stars in pseudo-Newtonian gravity

TL;DR

This paper investigates neutron star gravity g-modes using pseudo-Newtonian gravity, demonstrating it can accurately approximate general relativity results with less computational effort, especially for complex equations of state.

Contribution

The study shows pseudo-Newtonian gravity effectively models neutron star g-modes, closely matching GR solutions and enabling efficient analysis of oscillations with complex EOS.

Findings

Pseudo-Newtonian g-mode frequencies differ from GR by about 1%.

Pseudo-Newtonian approach reduces computational cost significantly.

Applicable to EOS with phase transitions and supernova simulations.

Abstract

The equation of state (EOS) of nuclear dense matter plays a crucial role in many astrophysical phenomena associated with neutron stars (NSs). Fluid oscillations are one of the most fundamental properties therein. NSs support a family of gravity $g$-modes, which are related to buoyancy. We study the gravity $g$-modes caused by composition gradient and density discontinuity in the framework of pseudo-Newtonian gravity. The mode frequencies are calculated in detail and compared with Newtonian and general-relativistic (GR) solutions. We find that the $g$-mode frequencies in one of the pseudo-Newtonian treatments can approximate remarkably well the GR solutions, with relative errors in the order of $1\%$. Our findings suggest that, with much less computational cost, pseudo-Newtonian gravity can be utilized to accurately analyze oscillation of NSs constructed from an EOS with a first-order phase transition between nuclear and quark matter, as well as to provide an excellent approximation of GR effects in core-collapse supernova (CCSN) simulations.