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5.2 Accreted crust

A model of the EoS of accreted crusts was calculated by Haensel & Zdunik [185Jump To The Next Citation Point]. They used the compressible liquid drop model (see Section 3.2.1) with a “single nucleus” scenario.

In Figure 34View Image this EoS is compared with the SLy model of cold catalyzed matter described in Section 5.1. At ρ < ρ ND both EoSs are very similar. The reason is that for ρ < ρ ND, as discussed in Section 3.1, we have P ≃ Pe(ne) with ne = (Z ∕A )nb and the ratio Z ∕A is quite similar for both accreted and ground state crusts. Large differences appear for ρND ≲ ρ ≲ 10 ρND, where the EoS of accreted matter is stiffer than that of cold catalyzed matter. One also notices well-pronounced density jumps at constant pressure in the EoS of accreted matter. They are associated with discontinuous changes in nuclear composition, an artifact of the one-component plasma approximation. The jumps are particularly large for ρND ≲ ρ ≲ 10ρND.

View Image

Figure 34: Comparison of the SLy EoS for cold catalyzed matter (dotted line) and the EoS of accreted crust (solid line). Figure by A.Y. Potekhin.

The difference between the cold catalyzed and accreted matter EoSs decreases for large density. Both curves are very close to each other for ρ > 1013 g cm −3. This is because for such a high density the pressure is mainly produced by the neutron gas and is not sensitive to the detailed composition of the nuclear clusters. In view of this, one can use the EoS of the catalyzed matter for calculating the hydrostatic equilibrium of the high-density (13 −3 ρ > 10 g cm) internal layer of the accreted crust.

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