Typical values of the surface magnetic fields of radio pulsars are . In Figure 41
we
compare plots of
and
for the pure iron envelope with
of a neutron star
with
and
km with and without a magnetic field. The
approximation for
the crust is used. Typical values of the surface magnetic field of radio pulsars are
. At such
magnetic fields, the effect of
is seen only in the outer envelope, which is
cm thick. We can see
there quantum oscillations of the density as a function of depth. They are associated with the filling of the
lowest Landau levels
by the electrons (Section 2.2). Increasing
to
G,
associated with the most magnetized radio pulsars, leads to much deeper magnetization of the
crust, down to the depth of 30 m, where the prevailing density reaches
. The effect
of the magnetic field in the outer 30 cm of the crust is dramatic; in spite of a gravitational
acceleration
, the density is only slowly decreasing, and is
still
at 10 cm depth, ten times higher than in a nonmagnetized envelope at
the same depth. So, magnetized iron plasma is “condensed”, and much less compressible than
nonmagnetized (Section 2.2). At 1013 G, the
Landau level begins to be populated only at
4
105 g cm–3 (depth 3 m), to be compared with 2
104 g cm–3 (depth 30 cm) at
1012 G. It should be stressed that, as the surface temperature at pulsar age 103 – 104 y is
, inclusion of
will weaken the magnetization effects on the structure of the
crust [184
].
Typical surface magnetic fields of magnetars are 1015 G. In Figure 42
we see that for
, the effect of such a huge
on the crust EoS is strong and becomes dramatic at lower
. For example, at 107 g cm–3, the matter pressure decreases by two orders of magnitude, compared to
the
case. The
Landau level begins to be populated only at 108.7 g cm–3, at a depth of
about 50 m.
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