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13 Conclusion

The conditions prevailing inside the crusts of neutron stars are not so extreme as those encountered in the dense core. Nonetheless, they are still far beyond those accessible in terrestrial laboratories. The matter in neutron star crust is subject to very high pressures, as well as huge magnetic fields, which can attain up to 1014 – 1015 G in magnetars. For comparison, it is worth reminding ourselves that the strongest (explosive) magnetic fields ever produced on the Earth reach “only” 3 × 107 G [298]. The description of such environments requires the interplay of many different branches of physics, from nuclear physics to condensed matter and plasma physics.

Considerable progress in the microscopic modeling of neutron star crusts has been achieved during the last few years. Yet the structure and properties of the crust remain difficult to predict, depending on the formation and subsequent cooling of the star. Even in the ground state approximation, the structure of the neutron star crust is only well determined at ρ ≲ 1011 g cm–3, for which experimental data are available. Although all theoretical calculations predict the same large-scale picture of the denser layers of the crust, they do not quantitatively agree, reflecting the uncertainties in the properties of very exotic nuclei and uniform highly-asymmetric nuclear matter. The inner crust is expected to be formed of a lattice of neutron-rich nuclear clusters coexisting with a degenerate relativistic electron gas and a neutron liquid. The structure of the inner crust, its composition and the shape of the clusters are model dependent, especially in the bottom layers at densities ∼ 1014 g cm–3. However, the structure of the inner crust is crucial for calculating many properties, such as neutrino emissivities, as well as transport properties like electric and thermal conductivities. Superfluidity of unbound neutrons in the crust seems to be well established, both observationally and theoretically. However, much remains to be done to understand its properties in detail and, in particular, the effects of the nuclear lattice.

The interpretation of many observed neutron star phenomena, like pulsar glitches, X-ray bursts in low-mass X-ray binaries, initial cooling in soft X-ray transients, or quasi-periodic oscillations in soft gamma repeaters, can potentially shed light on the microscopic properties of the crust. However, their description requires consistent models of the crust from the nuclear scale up to the macroscopic scale. In particular, understanding the evolution of the magnetic field, the thermal relaxation of the star, the formation of mountains, the occurrence of starquakes and the propagation of seismic waves, requires the development of global models combining general relativity, elasticity, magnetohydrodynamics and superfluid hydrodynamics. Theoretical modeling of neutron star crusts is very challenging, but not out of reach. A confrontation of these models with observations could hopefully help us to unveil the intimate nature of dense matter at subnuclear densities. The improvement of observational techniques, as well as the development of gravitational wave astronomy in the near future, open very exciting perspectives.

We are aware that some aspects of the physics of neutron star crusts have not been dealt with in this review. Our intention was not to write an exhaustive monograph, but to give a glimpse of the great variety of topics that are necessarily addressed by different communities of scientists. We hope that this review will be useful to the reader for his/her own research.

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