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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 [338
], the formulae for the nonzero components of the
tensors can be written
in a form similar to Equation (218
):
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 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[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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