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

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 $X=X^{\prime }=0$, where $X^{\prime }$ 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.

11 pages, 4 figures, accepted for publication in MNRAS

References in corpus (2)

• Upper limits on gravitational wave emission from 78 radio pulsars
• Determination of the internal structure of neutron stars from gravitational wave spectra