Assessment of Cowling approximation in computing ellipticity of a magnetized non-barotropic star

TL;DR

This paper evaluates the accuracy of the Cowling approximation in calculating neutron star ellipticity caused by magnetic fields, finding it underestimates ellipticity by about half compared to full gravitational perturbation calculations.

Contribution

It assesses the impact of gravitational perturbation neglected in previous models, providing a correction factor for more accurate ellipticity estimates.

Findings

Ellipticity with gravitational perturbation is roughly twice that from Cowling approximation.

Cowling approximation introduces about 50% error in ellipticity calculations.

Results inform more precise gravitational wave emission predictions from magnetized neutron stars.

Abstract

A deformation of a neutron star due to its own magnetic field is an important issue in gravitational wave astronomy, since a misaligned rotator with small ellipticity may emit continuous gravitational wave that may be observed by ground-based detectors. Recently Mastrano et al. (2011,2013) evaluated deformations induced by both poloidal and toroidal magnetic field in non-barotropic model stars by neglecting the gravitational field perturbation (Cowling approximation). Following their treatment in non-barotropic fluid and magnetic configurations, we here assess the effect of gravitational perturbation that they neglected. We show that the ellipticity computed with gravitational perturbation is roughly twice as large as that obtained by Cowling approximation. We should allow this amount of error in using the neat analytic treatment proposed by them.