Thermal origin of neutron star magnetic fields

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Abstract
It is proposed that magnetic field arises naturally in neutron stars as a consequence of thermal effects occurring in their outer crusts. The heat flux through the crust, which is carried mainly by degenerate electrons, can give rise to a possible thermoelectric instability in the solid crust which causes horizontal magnetic field components to grow exponentially with time. However, in order for the thermally driven growth to exceed ohmic decay, either the electron collision time must exceed existing estimates by a factor ∼ 3 or the surface layers comprise helium. A second instability is possible if the liquid phase that lies above the solid crust also contains a horizontal magnetic field. The heat flux will drive circulation which should amplify the field strength provided that there is a seed field in excess of ∼ 108 G. If either of these two instabilities develops the field will quickly grow to a strength of ∼ 1012 G, where the instabilities become non-linear. Further growth will saturate when either the magnetic stress exceeds the lattice yield stress or the temperature perturbations become non-linear, both of which occur at a subsurface field strength of ∼ 1014 G; the corresponding surface field strength is ∼ 1012 G. Further evolution of the magnetic field should lead to long-range order and yield neutron star magnetic dipole moments ∼ 1030 G cm3, comparable with those observed. Newly-formed neutron stars should be able to develop their dipole moments in a hundred thousand years and maintain them for as long as heat flows through the crust. Thereafter, the dipole moment should decay in several million years, as observed in the case of most radio pulsars. Neutron stars that are formed spinning rapidly, like that in the Crab Nebula, should be able to grow magnetic fields far more rapidly since their rotational energy can also be tapped to drive thermoelectric currents. The interiors of neutron stars in binary systems may be heated by the energy released by accreting matter. The resulting heat flux may cause the production of magnetic fields in these objects. Binary pulsars, with their unusually low and persistent fields, have probably passed through this phase.

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