Equilibria and oscillations of magnetised neutron stars

Abstract

We investigate equilibrium configurations and oscillation spectra of neutron stars,
modelled as rotating magnetised fluid bodies in Newtonian gravity. We also explore
the idea that these model neutron stars could have dynamics analogous to rigid-body
free precession.

In axisymmetry, the equations of magnetohydrodynamics reduce to a purely
toroidal-field case and a mixed-field case (with a purely poloidal-field limit). We
solve these equations using a nonlinear code which finds stationary rotating magnetised
stars by an iterative procedure. We find that despite the general nature of
our approach, the mixed-field configurations we produce are all dominated by their
poloidal component. We calculate distortions induced both by magnetic fields and
by rotation; our results suggest that the relationship between the magnetic energy
and the induced ellipticity should be close to linear for all known neutron stars.

We then investigate the oscillation spectra of neutron stars, using these stationary
configurations as a background on which to study perturbations. This is done
by evolving the perturbations numerically, making the Cowling approximation and
specialising to purely toroidal fields for simplicity. The results of the evolutions
show a number of magnetically-restored Alfv´en modes. We find that in a rotating
star pure inertial and pure Alfv´en modes are replaced by hybrid magneto-inertial
modes. We also show that magnetic fields appear to reduce the effect of the r-mode
instability.

Finally, we look at precession-like dynamics in magnetised fluid stars, using both
analytic and numerical methods. Whilst these studies are only preliminary, they
indicate deficiencies in previous research on this topic. We suggest ways in which
the problem of magnetised-fluid precession could be better understood.

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Identifiers

ORCID for D.I. Jones: orcid.org/0000-0002-0117-7567

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