The interaction of the magnetic field with the heat flux in neutron stars is investigated.
It is proposed that the magnetic field develops as a result of thermal processes in the liquid and solid phases of neutron star envelopes. Necessary conditions for the growth to occur are derived and it is shown that surface fields comparable to those observed would result. The magnetization of neutron stars in binary systems (which have magnetic properties differing substantially from those of isolated pulsars) can be explained by thermal processes associated with accretion flows.
In order to study magnetic effects on neutron star cooling a number of subsidiary issues are considered.
The thermal structure of unmagnetized neutron star envelopes is examined using approximate analytical models. From the results it is possible to justify a number of simplifying assumptions and extend them to the magnetized case. For example, it is shown that an accurate treatment of photon transport is not required in order to determine the relation between the heat flux and the core temperature of neutron stars.
The effect of the field on the magnetic properties of the electron gas in neutron star crusts is considered. It is shown that the gas is unstable to the formation of domains of alternating magnetization. It is further argued that the domain structure will have a negligible influence on the heat flux because of the small free energy associated with the domains.
The influence of the field on the electron transport properties of neutron star envelopes is examined in detail. Accurate expressions are derived for all components of the relevant transport tensors, taking into account quantum mechanical and relativistic effects. In addition, allowance is made for arbitrary degree of degeneracy and scattering mechanism.
Finally, these results are used to study the thermal structure of magnetized neutron star envelopes. It is shown that the enhancement in the heat flux due to quantum effects is almost completely canceled by the suppression of the heat flux due to geometrical effects. Thus the magnetic field is expected to play only a minor role in neutron star cooling, contrary to earlier claims.
