We consider a surface magnetic field to be strong if . Such magnetic fields affect the accretion of plasma onto the neutron star and modify the properties of atoms in the atmosphere. On the contrary, a magnetic field , such as associated with millisecond pulsars or with most of the X-ray bursters, is considered to be weak. Typical pulsars are magnetized neutron stars, with the value of near the magnetic pole 1012 G. Much stronger magnetic fields are associated with magnetars, 1014 – 1015 G; such magnetic fields with are often called “super-strong”. These magnetic fields can strongly affect transport processes within neutron star envelopes. Electron transport processes in magnetized neutron star envelopes and crusts are reviewed in [338, 412]. In the present section we limit ourselves to a very brief overview.
Locally, a magnetic field can be considered uniform. We will choose the axis of a coordinate system along , so that . We will limit ourselves to the case of strongly degenerate electrons and we will assume the validity of the relaxation time approximation. Let relaxation time for be . An important timescale associated with magnetic fields is the electron gyromagnetic frequency14
Many Landau orbitals are populated and quantum effects are smeared by thermal effects because . Transport along the magnetic field is not affected by , while transport across is fully described by the Hall magnetization parameters ,
Many Landau levels are populated by electrons, but quantization effects are well pronounced because . There are two relaxation times, and , which oscillate with density (see below). As shown by Potekhin , the formulae for the nonzero components of the tensors can be written in a form similar to Equation (218):12 G is weakly quantizing at .
Not only is , but also most of the electrons are populating the ground Landau level. Both the values of and and their density dependence are dramatically different from those of the nonquantizing (classical) case. As shown by Potekhin , the formulae for and are still given by Equations (219). Analytical fitting formulae for and are given in . As seen in Figure 59, at a field of 1012 G is strongly quantizing for
Thermal conduction by ions is much smaller than that by electrons along . However, the electron conduction across is strongly suppressed. In outer neutron star crust, heat flow across can be dominated by ion/phonon conduction. This is important for the heat conduction across in cooling magnetized neutron stars. Correct inclusion of the ion heat conductivity then leads to a significant reduction of the thermal anisotropy in the envelopes of magnetized neutron stars.
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