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6.4 Effects of magnetic fields on the crust structure

The structure of the outer layers of the crust (neutron star “envelope”) can be affected by the presence of a magnetic field. Effects of magnetic fields on the EoS were briefly mentioned in Section 2.2. Here we consider examples showing effects of BBB on the crust structure.

Typical values of the surface magnetic fields of radio pulsars are 12 B ∼ 10 G. In Figure 41View Image we compare plots of ρ(z) and ΔM (z) for the pure iron envelope with 5 − 3 ρ ≲ 10 g cm of a neutron star with M = 1.4 M ⊙ and R = 10km with and without a magnetic field. The T = 0 approximation for the crust is used. Typical values of the surface magnetic field of radio pulsars are B ∼ 1012 G. At such magnetic fields, the effect of B is seen only in the outer envelope, which is ∼ 30cm 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 n = 0,1,... by the electrons (Section 2.2). Increasing B to 1013G, 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 106 g cm− 3. The effect of the magnetic field in the outer 30 cm of the crust is dramatic; in spite of a gravitational acceleration 2 14 −2 g = GM ∕R = 2.43 × 10 cm s, the density is only slowly decreasing, and is still ∼ 105 g cm −3 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 n = 1 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 Ts ∼ 106 K, inclusion of T will weaken the magnetization effects on the structure of the crust [184Jump To The Next Citation Point].

Typical surface magnetic fields of magnetars are ∼ 1015 G. In Figure 42View Image we see that for 9 −3 ρ < 10 g cm, the effect of such a huge BBB on the crust EoS is strong and becomes dramatic at lower ρ. For example, at 107 g cm–3, the matter pressure decreases by two orders of magnitude, compared to the BBB = 0 case. The n = 1 Landau level begins to be populated only at 108.7 g cm–3, at a depth of about 50 m.

View Image

Figure 42: Nonmagnetized (solid line), and magnetized crust (dash-dotted line) calculated with ground state composition calculated at BBB = 0. The dashed magenta line in the bottom-right panel corresponds to the BBB = 0 compressible liquid drop model of [125], and is smooth due to its quasiclassical nature, while the curve with discontinuous drops in pressure as obtained using the ground-state model of [183Jump To The Next Citation Point]. Figure made by A.Y. Potekhin.

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