Interior magnetohydrodynamic structure of a rotating relativistic star

Abstract

We study the interior magnetohydrodynamic structure of a rotating stationary axisymmetric neutron star. We assume the fluid is ideal, infinitely conducting, and flows only azimuthaly. We justify this assumption by considering in detail the superfluid physics in the interior. We obtain some of our results by taking a certain limit of previously discovered magnetohydrodynamic conservation laws. We show that the angular velocity, electric and magnetic potentials, and the red-shifted chemical potential are constant on magnetic surfaces. We demonstrate that the absence of meridional circulation implies the vanishing of the toriodal magnetic field. This clashes with previous arguments from the probable evolution of the magnetic field during the collapse to the neutron star. We solve completely Maxwell's equations for the distribution of magnetic field strength, and we show that the magnetic surfaces are the equipotentials of a simple geometrical invariant. With neglect of gravitational effects the magnetic field must be uniform in the interior in accordance with the Deutsch model, but at variance with numerous other models which have been proposed for ordinary stars. Gravitation causes the magnetic surfaces to flare out toward the polar regions and enhances the central field as compared to the polar field. The star must be charged; the charge distribution depends on the magnetic field strength and on the angular velocity relative to the local inertial frames.

General relativistic simulations of passive-magneto-rotational core collapse with microphysics

“…A second consideration is whether or not the initial model should be an equilibrium model. In general, if one tries to construct a stationary model without meridional currents and assuming an isentropic flow, the only possible magnetic field configuration is poloidal (see Bekenstein & Oron 1979). Stationary models of magnetized stars have been computed under these assumptions by Bocquet et al (1995).…”

Grad-Shafranov equation in noncircular stationary axisymmetric spacetimes

“…Bekenstein and Oron [19,20] showed that a stationary axisymmetric system has several conserved quantities along each flow line. This is a general relativistic generalization of Ferraro's integrability condition [40,41,42].…”

“…General relativistic effects are sizable in the interior of a neutron star, so that any quantitative investigation of the magnetars has to be based on general relativistic magnetohydrodynamics (MHD) [17,18,19,20]. Therefore, we have to solve the matter and electromagnetic field configurations in a curved spacetime, and have to take account of the electromagnetic energy-momentum as a source of the gravitational field.…”

“…In Sec. II, we briefly review the conservation laws in stationary axisymmetric general relativistic ideal MHD systems [19,20] that are used to characterize the matter and electromagnetic field configurations. We neglect dissipative effects, which is a reasonable assumption because of the high conductivity and the low viscosity in neutron stars.…”

String behaviour of magnetic field lines and their rotation in neutron star’s interior

“…Thus a fully consistent relativistic magnetohydrodynamic model is required to learn the evolution of a rotating neutron star's interior. A significant step in this direction has been the work of Bekenstein and Oron [3] in which interior hydromagnetic structure of a rotating neutron star's interior is coupled to gravitational interaction. Invoking electrons theory of the conductivity of matter, it has been argued by Bekenstein and Oron [4] that the electric field vanishes in a frame comoving with the fluid if the electric current is to be maintained finite in the limit of infinite electrical conductivity.…”