Thermal structure of magnetized neutron-star envelopes

The influence of a strong magnetic field (B ∼ 10¹⁰–10¹⁴ G) on the thermal structure of neutron-star envelopes is investigated using the most recent calculations of radiative and electronic thermal conductivities. In particular, the relation between the core temperature, T_c and the heat flux, F, is considered for effective surface temperatures in the range $$T_\text s= 10^{5.5}-10^{6.5}\enspace \text K$$. For a purely vertical magnetic field it is found that quantum effects will enhance (relative to the zero-field case) the heat flux, for a fixed core temperature, by a factor ≲3. It is further argued that the anisotropic nature of electron transport in a magnetic field will suppress the heat flux for a more realistic field geometry by a factor ≲3. Thus the magnetic field is expected to have only a minor effect on neutron-star cooling. This conclusion differs substantially from those of earlier magnetized cooling calculations and a comparison is performed to isolate sources of discrepancy. (It is argued that the disagreement results primarily from inaccurate approximations to the electronic thermal conductivity used in past calculations.) The sensitivity of the flux–core temperature relation to variations in the input physics is studied in a manner analogous to Gudmundsson et al. The results of the sensitivity analysis are used to argue that disagreements among the existing calculations of the conductivity will not alter the basic conclusion that magnetic effects on the flux–core temperature relation are relatively unimportant.