Neutron star deformation due to poloidal–toroidal magnetic fields of arbitrary multipole order: a new analytic approach

Abstract

A recipe is presented to construct an analytic, self-consistent model of a non-barotropic neutron star with a poloidal-toroidal field of arbitrary multipole order, whose toroidal component is confined in a torus around the neutral curve inside the star, as in numerical simulations of twisted tori. The recipe takes advantage of magnetic-field-aligned coordinates to ensure continuity of the mass density at the surface of the torus. The density perturbation and ellipticity of such a star are calculated in general and for the special case of a mixed dipole-quadrupole field as a worked example. The calculation generalises previous work restricted to dipolar, poloidal-toroidal and multipolar, poloidal-only configurations. The results are applied, as an example, to magnetars whose observations (e.g., spectral features and pulse modulation) indicate that the internal magnetic fields may be at least one order of magnitude stronger than the external fields, as inferred from their spin downs, and are not purely dipolar.

General relativistic models for rotating magnetized neutron stars in conformally flat space–time

“…As a result even a weakly energetic toroidal field (with H tor 10%H tot ) is able to induce, at a given total energy H tot , a substantial reduction (of the order of 40% for our models) of the oblateness of the star. This is in agreement with Mastrano, Suvorov & Melatos (2015). Computing TT models for non-barotropic NSs, they showed how it is possible to reduce the effectiveness of the poloidal/toroidal component, augmenting the weight of the quadrupolar component of the poloidal mag-netic field or enlarging the volume occupied by the toroidal field.…”

Many-body Forces in Magnetic Neutron Stars

“…It is important to emphasize that, because of the choice of poloidal magnetic field distributions, oblate shapes are favored for highly magnetic stars. Note, however, that several studies suggest that toroidal contributions might play an important role in the stability of magnetic stars Braithwaite & Spruit (2004), Marchant et al (2011), Lasky et al (2011), Ciolfi & Rezzolla (2013, Akgun et al (2013), Mitchell et al (2015), Armaza et al (2015), Mastrano et al (2015). Still, even in this case, we expect our qualitative results to hold.…”

Gravitational radiation from neutron stars deformed by crustal Hall drift

“…The zeroth-order density profile ρ(r) is chosen to be that of an n = 1 polytropic star [unlike, e.g., Mastrano et al (2011) and Mastrano et al (2015)]…”

“…In this current paper, two representatives of these different initial field configurations (which return the same polar cap field structure conducive to radio pulsar emission) are taken as an input to explore their effect on the neutron star deformation. Mastrano et al (2015) recently presented a method to calculate the deformation of a neutron star caused by poloidal-toroidal magnetic fields consisting of arbitrary multipoles [see also Mastrano et al (2013)]. In order to explore whether the magnetic spots and strong toroidal fields in radio pulsars produce an ellipticity which is potentially detectable through gravitational wave (hereafter GW) emission, we do not present an exhaustive study of magnetic field structures and their resulting ellipticities; we simply aim to convince the reader that magnetic field structures arising from Hall drift in radio pulsars may induce stellar deformations, which make them potentially detectable as GW sources.…”