Generalised Inverse-Cowling Approximation for Polar $w$-mode Oscillations of Neutron Stars

TL;DR

This paper introduces the generalized inverse-Cowling approximation (GICA) for neutron star $w$-mode oscillations, simplifying the analysis by neglecting pressure changes, and accurately predicts oscillation frequencies and damping rates.

Contribution

The paper develops GICA, a new approximation that simplifies the modeling of neutron star $w$-modes by assuming negligible pressure change, providing accurate mode predictions.

Findings

GICA accurately predicts $w$-mode frequencies.

GICA simplifies the oscillation equations.

Negligible pressure change in $w$-modes is confirmed.

Abstract

Adopting the Lindblom-Detweiler formalism for polar oscillations of neutron stars, we study the $w$-mode oscillation and find that the Lagrangian change in pressure, measured by the physical quantity $X$, is negligibly small. Based on this observation, we develop the generalised inverse-Cowling approximation (GICA) with the approximation $X=X'=0$, where $X'$ is the derivative of $X$ with respect to the circumferential radius, for $w$-mode oscillations of neutron stars. Under GICA, $w$-mode oscillations are described by a second-order differential system, which can yield accurate frequencies and damping rates of quasi-normal modes.