Neutron star deformation due to multipolar magnetic fields

TL;DR

This paper investigates how higher-order multipolar magnetic fields in neutron stars influence their shape (ellipticity) and observational signatures, with implications for gravitational wave detection and understanding neutron star magnetic structures.

Contribution

It provides a detailed calculation of neutron star ellipticity considering multipolar magnetic fields, extending previous models to include arbitrary multipoles and their observational consequences.

Findings

Higher multipoles can significantly affect neutron star ellipticity.

Strong quadrupole and octupole components still produce ellipticity within gravitational wave limits.

Mixed multipolar fields can cause observable mismatches in inertia axes and magnetic inclination.

Abstract

Certain multi-wavelength observations of neutron stars, such as intermittent radio emissions from rotation-powered pulsars beyond the pair-cascade death line, the pulse profile of the magnetar SGR 1900+14 after its 1998 August 27 giant flare, and X-ray spectral features of PSR J0821-4300 and SGR 0418+5729, suggest that the magnetic fields of non-accreting neutron stars are not purely dipolar and may contain higher-order multipoles. Here, we calculate the ellipticity of a non-barotropic neutron star with (i) a quadrupole poloidal-toroidal field, and (ii) a purely poloidal field containing arbitrary multipoles, deriving the relation between the ellipticity and the multipole amplitudes. We present, as a worked example, a purely poloidal field comprising dipole, quadrupole, and octupole components. We show the correlation between field energy and ellipticity for each multipole, that the l=4 multipole has the lowest energy, and that l=5 has the lowest ellipticity. We show how a mixed multipolar field creates an observationally testable mismatch between the principal axes of inertia (to be inferred from gravitational wave data) and the magnetic inclination angle. Strong quadrupole and octupole components (with amplitudes ~ 10^2 times higher than the dipole) in SGR 0418+5729 still yield ellipticity ~ 10^{-8}, consistent with current gravitational wave upper limits. The existence of higher multipoles in fast-rotating objects (e.g., newborn magnetars) has interesting implications for the braking law and hence phase tracking during coherent gravitational wave searches.