
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 Xray bursters, is considered to be weak. Typical pulsars are magnetized neutron stars, with the value of near the magnetic pole 10^{12} G. Much stronger magnetic fields are associated with magnetars, 10^{14} – 10^{15} G; such magnetic fields with are often called “superstrong”. 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 frequency^{14}
The magnetic field bends electron trajectories in the plane, and suppresses the electron transport across . Therefore, the transport properties become anisotropic, and we must consider tensors and , which can be written as In what follows we will consider three basic regimes of transport in magnetic fields.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 ,
where are the effective relaxation times at for the thermal and electric conductivities, respectively. The nonzero components of the tensors are As an example, consider strongly degenerate electrons and dominating scattering, . Then, Equation (196) yields .
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 [338], the formulae for the nonzero components of the tensors can be written in a form similar to Equation (218):
At a fixed temperature and in the presence of a weakly quantizing , the density dependence of the components of the and tensors exhibits characteristic oscillations around the nonquantized (classical) values. Each oscillation corresponds to the filling of a new Landau level. The amplitude of these oscillations decreases with decreasing density. An example of the density dependence of and , and of the same components of the tensor, is presented in Figure 59. As we see in Figure 59, the “density period”of oscillation decreases with increasing , and the oscillation amplitude decreases with increasing . At , a magnetic field of 10^{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 [338], the formulae for and are still given by Equations (219). Analytical fitting formulae for and are given in [338]. As seen in Figure 59, at a field of 10^{12} 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[100]. 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[100].
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