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By compressing matter to densities up to several times the density of atomic nuclei, the catastrophic gravitational collapse of the core of stars with a mass M≳8M⊙ during supernova explosions and the neutron star left behind (see, e [...]

The physics of neutron star crusts is vast, involving many different research fields, from nuclear and condensed matter physics to general relativity. This review summarizes the progress, which has been achieved over the last few years, in modeling neutron star crusts, both at the microscopic and macroscopic levels. The confrontation of these theoretical models with observations is also briefly discussed.

The interpretation of the thermal relaxation of some transiently accreting neutron stars in quasipersistent soft X-ray transients, especially MXB 1659-29, has been found to be challenging within the traditional deep crustal heating paradigm. Due to the pinning of quantized vortices, the neutron superfluid is not expected to remain at rest in the crust, as was generally assumed. We have recently shown that for sufficiently large relative superflows, the neutron superfluid could become gapless. This dynamical phase could naturally explain the late-time cooling of MXB 1659-29. However, the interpretation of the last observation of MXB 1659-29 in 2013 before its second accretion phase in 2015 remains debated, with some spectral fits being consistent with no further temperature decline. Here, we revisit the cooling of this neutron star considering the different fits. New simulations of the crust cooling are performed, accounting for neutron diffusion and allowing for gapless superfluidity. In all cases, gapless superfluidity is found to provide the best fit to observations.

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

In 1995, Glendenning, Kettner and Weber postulated the existence of a new class of compact stars resembling white dwarfs but containing a small strange quark-matter core surrounded by hadronic layers attaining much higher densities than those found in white dwarfs. In our previous study, we have shown that it could be possible to unmask these so-called strange dwarfs through gravitational-wave observations with future space-based detectors such as the Laser Interferometer Space Antenna. We calculated more realistic equations of state for the hadronic envelope, but the quark core was treated using the simplest MIT bag model. In this paper, we investigate more closely the role of the possibly solid core in the structure and the tidal deformability of strange dwarfs in the full general relativistic framework by considering different models of strange quark matter in the crystalline color -superconducting phase. We find that the effect of the extreme rigidity of the elastic core on the tidal deformability is almost completely canceled by the surrounding hadronic layers. However, in all cases, the tidal deformability of strange dwarfs remains sufficiently lower than that of white dwarfs, to be potentially observable with gravitational waves despite the uncertainties in the strange quark-matter equation of state.

We present a new numerical tool designed to probe the dense layers of neutron star crusts. It is based on the time-dependent Hartree-Fock-Bogoliubov theory with generalized Skyrme nuclear energy-density functionals of the Brussels-Montreal family. We use it to study the time evolution of a nucleus accelerating through superfluid neutron medium in the inner crust of a neutron star. We extract an effective mass in the low velocity limit. We observe a threshold velocity and specify mechanisms of dissipation: phonon emission, Cooper pairs breaking, and vortex rings creation. These microscopic effects are of key importance for understanding various neutron star phenomena. Moreover, the mechanisms we describe are general and apply also to other fermionic superfluids interacting with obstacles like liquid helium or ultracold gases.

The loss of magnetic pressure accompanying the decay of the magnetic field in a magnetar may trigger exothermic electron captures by nuclei in the shallow layers of the stellar crust. Very accurate analytical formulas are obtained for the threshold density and pressure, as well as for the maximum amount of heat that can be possibly released, taking into account the Landau–Rabi quantization of electron motion. These formulas are valid for arbitrary magnetic field strengths, from the weakly quantizing regime to the most extreme situation in which electrons are all confined to the lowest level. Numerical results are also presented based on experimental nuclear data supplemented with predictions from the Brussels-Montreal model HFB-24. This same nuclear model has been already employed to calculate the equation of state in all regions of magnetars.

We investigate the effects of temperature on the properties of the inner crust of a non-accreting neutron star. To this aim, we employ two different treatments: the compressible liquid drop model (CLDM) and the temperature-dependent extended Thomas–Fermi (TETF) method. Our systematic comparison shows an agreement between the two methods on their predictions for the crust thermodynamic properties. We find that the CLDM description can also reproduce reasonably well the TETF composition especially if the surface energy is optimized on the ETF calculation. However, the neglect of neutron skin in CLDM leads to an overestimation of the proton radii.

The interior of neutron stars may contain a mantle made of very exotic neutron-proton clusters with unusual shapes such as rods or slabs collectively referred to as “nuclear pastas” coexisting with free nucleons and a charge neutralizing gas of electrons. Adding shell and pairing effects perturbatively and consistently to the fourth-order extended Thomas-Fermi method using the Brussels-Montreal functional BSk24, we find that nuclear pastas are much less abundant than previously thought from liquid-drop models, thus questioning their very existence in neutron stars.

The interpretation of the thermal evolution of the transiently accreting neutron stars MXB 1659−29 and KS 1731−260 after an outburst is challenging, both within the traditional deep-crustal heating paradigm and the thermodynamically consistent approach of Gusakov and Chugunov that accounts for neutron diffusion throughout the crust. All these studies assume that the neutron superfluid in the crust is at rest. However, we have recently shown that a finite superflow could exist and could lead to a new gapless superfluid phase if quantized vortices are pinned. We have revisited the cooling of MXB 1659−29 and KS 1731−260 and we have found that gapless superfluidity could naturally explain their late time cooling. We pursue here our investigation by performing new simulations of the thermal relaxation of the crust of MXB 1659−29 and KS 1731−260 within a Markov Chain Monte Carlo method accounting for neutron diffusion and allowing for gapless superfluidity. We have varied the global structure of the neutron star, the composition of the heat-blanketing envelope, and the mass accretion rate. In all cases, observations are best fitted by models with gapless superfluidity. Finally, we make predictions that could be tested by future observations.