Neutron star deformation due to multipolar magnetic fields

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 higherorder 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.

General solution for the vacuum electromagnetic field in the surroundings of a rotating star

“…Multi-wavelength observations of intermittent radio emissions from rotation-powered pulsars beyond the pair-cascade death line, of the pulse profile of the magnetar SGR 1900+14 after its 1998 August 27 giant flare and of the 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 (Mastrano et al 2013). Güver et al (2011) analysed upper bound on the spin-down rate and the high signal-to-noise ratio XMM-Newton spectra of the soft gamma-ray repeater SGR 0418+5729.…”

Parameter choices and ranges for continuous gravitational wave searches for steadily spinning neutron stars

“…Firstly, models where magnetic strains are responsible for deforming the star and generating the non-zero time varying mass quadrupole (see e.g. Mastrano et al (2013)) might lead to a prediction for the relative phasing of the gravitational wave and pulsar signals, giving a prediction of the value of φgw,0. Secondly, Bildsten (1998) proposed that temperature asymmetries in the star's crust could generate a non-zero mass quadrupole (see also Ushomirsky et al (2000)).…”

Gravitational waves from surface inhomogeneities of neutron stars

“…And if the higher multipole components are much stronger than the dipole then the mass content of the accretion column could be much larger. Recent investigations have shown that higher multipoles can generate large ellipticity and be good candidates for gravitational waves [26].…”

“…Strong magnetic fields can also distort the star if the magnetic axis is not aligned with the axis of rotation. Indeed the effects of strong higher multi-poles and toroidal components of the magnetic field in generating such non-axisymmetries have recently been investigated [25][26][27]. Other mechanisms for generating asymmetries could be the development of dynamic instabilities in rapidly rotating neutron stars driven by nuclear matter viscosity [28] or through r-mode oscillations (see [23] and references therein).…”