Effective contact pairing forces from realistic calculations in infinite homogeneous nuclear matter

Non-empirical effective contact pairing forces to be used in self-consistent mean-field calculations are presented. These pairing forces, constructed so as to reproduce exactly any given microscopic pairing gaps in infinite homogeneous nuclear matter for any isospin asymmetry, are given in analytical form. As a by-product, this work provides an analytical solution of the BCS gap equations which could be applied to describe various many-body systems.Comment: 6 pages, 5 figures ; accepted for publication in Physical Review

Entrainment effects in neutron-proton mixtures within the nuclear-energy density functional theory. II. Finite temperatures and arbitrary currents

Mutual entrainment effects in hot neutron-proton superfluid mixtures are studied in the framework of the self-consistent nuclear energy-density functional theory. The local mass currents in homogeneous or inhomogeneous nuclear systems, which we derive from the time-dependent Hartree-Fock-Bogoliubov equations at finite temperatures, are shown to have the same formal expression as the ones we found earlier in the absence of pairing at zero temperature. Analytical expressions for the entrainment matrix are obtained for application to superfluid neutron-star cores. Results are compared to those obtained earlier using Landau's theory. Our formulas, valid for arbitrary temperatures and currents, are applicable to various types of functionals including the Brussels-Montreal series for which unified equations of state have been already calculated, thus laying the ground for a fully consistent microscopic description of superfluid neutron stars.Comment: 23 pages, expanded version including the exact solution of TDHFB. Accepted for publication in Physical Review

Role of dense matter in tidal deformations of inspiralling neutron stars and in gravitational waveform with unified equations of state

The role of dense-matter properties in the tidal deformability of a cold nonaccreted neutron star is further investigated. Using the set of Brussels-Montreal unified equations of state, we have computed the gravitoelectric Love numbers $k_\ell$ and the gravitomagnetic Love numbers $j_\ell$ up to $\ell=5$. Their relative importance and their sensitivity to the symmetry energy and the neutron-matter stiffness are numerically assessed. Their impact on the phase of the gravitational-wave signal emitted by binary neutron star inspirals is also discussed.Comment: 35 pages, 25 figures, accepted for publication in Physical Review

Covariant analysis of Newtonian multi-fluid models for neutron stars: III Transvective, viscous, and superfluid drag dissipation

As a follow up to articles dealing firstly with a convective variational formulation in a Milne-Cartan framework for non-dissipative multi fluid models, and secondly with various ensuing stress energy conservation laws and generalised virial theorems, this work continues a series showing how analytical procedures developed in the context of General Relativity can be usefully adapted for implementation in a purely Newtonian framework where they provide physical insights that are not so easy to obtain by the traditional approach based on a 3+1 space time decomposition. The present article describes the 4-dimensionally covariant treatment of various dissipative mechanisms, including viscosity in non-superfluid constituents, superfluid vortex drag, ordinary resistivity (mutual friction) between relatively moving non-superfluid constituents, and the transvective dissipation that occurs when matter is transformed from one constituent to another due to chemical disequilibrium such as may be produced by meridional circulation in neutron stars. The corresponding non dissipative limit cases of vortex pinning, convection, and chemical equilibrium are also considered.Comment: 27 pages late

Global numerical simulations of the rise of vortex-mediated pulsar glitches in full general relativity

In this paper, we study in detail the role of general relativity on the global dynamics of giant pulsar glitches as exemplified by Vela. For this purpose, we carry out numerical simulations of the spin up triggered by the sudden unpinning of superfluid vortices. In particular, we compute the exchange of angular momentum between the core neutron superfluid and the rest of the star within a two-fluid model including both (non-dissipative) entrainment effects and (dissipative) mutual friction forces. Our simulations are based on a quasi-stationary approach using realistic equations of state (EoSs). We show that the evolution of the angular velocities of both fluids can be accurately described by an exponential law. The associated characteristic rise time $\tau_{\text{r}}$, which can be precisely computed from stationary configurations only, has a form similar to that obtained in the Newtonian limit. However, general relativity changes the structure of the star and leads to additional couplings between the fluids due to frame-dragging effects. As a consequence, general relativity can have a large impact on the actual value of $\tau_{\text{r}}$: the errors incurred by using Newtonian gravity are thus found to be as large as $\sim 40 \%$ for the models considered. Values of the rise time are calculated for Vela and compared with current observational limits. Finally, we study the amount of gravitational waves emitted during a glitch. Simple expressions are obtained for the corresponding characteristic amplitudes and frequencies. The detectability of glitches through gravitational wave observatories is briefly discussed.Comment: 19 pages, 12 figures, minor changes to match version to be published in MNRA

Analytical determination of the structure of the outer crust of a cold nonaccreted neutron star: extension to strongly quantizing magnetic fields

The iterative method recently proposed for determining the internal constitution of the outer crust of a nonaccreted neutron star is extended to magnetars by taking into account the Landau-Rabi quantization of electron motion induced by the presence of a very high magnetic field. It is shown that in the strongly quantizing regime, the method can be efficiently implemented using new analytical solutions for the transitions between adjacent crustal layers. Detailed numerical computations are performed to assess the performance and precision of the method.Comment: 13 pages. Typos corrected. Accepted for publication in Physical Review C. A computer code is available on Zenodo at http://doi.org/10.5281/zenodo.3839787 arXiv admin note: text overlap with arXiv:2003.0098

Properties of a quantum vortex in neutron matter

We have studied systematically microscopic properties of a quantum vortex in neutron matter at finite temperatures and densities corresponding to different layers of the inner crust of a neutron star. To this end and in preparation of future simulations of the vortex dynamics, we have carried out fully self-consistent 3D Hartree-Fock-Bogoliubov calculations, using one of the latest nuclear energy-density functionals from the Brussels-Montreal family, which has been developed specifically for applications to neutron superfluidity in neutron-star crusts. By analyzing the flow around the vortex, we have determined the effective radius relevant for the vortex filament model. We have also calculated the specific heat in the presence of the quantum vortex and have shown that it is substantially larger than for a uniform system at low temperatures. The low temperature limit of the specific heat has been identified as being determined by Andreev states inside the vortex core. We have shown that the specific heat in this limit does not scale linearly with temperature. The typical energy scale associated with Andreev states is defined by the minigap, which we have extracted for various neutron-matter densities. Our results suggest that vortices may be spin-polarized in the crust of magnetars. Finally, we have obtained a lower bound for the specific heat of a collection of vortices with given surface density, taking into account both the contributions from the vortex core states and from the hydrodynamic flow

Skyrme-Hartree-Fock-Bogoliubov mass models on a 3D mesh: III. From atomic nuclei to neutron stars

We present BSkG3, the latest entry in the Brussels-Skyrme-on-a-grid series of large-scale models of nuclear structure based on an energy density functional. Compared to its predecessors, the new model offers a more realistic description of nucleonic matter at the extreme densities relevant to neutron stars. We achieve the former by incorporating a constraint on the infinite nuclear matter properties at high densities in the parameter adjustment, ensuring in this way that the predictions of BSkG3 for the nuclear Equation of State are compatible with the observational evidence for heavy pulsars with $M > 2 M_{\odot}$. Instead of the usual phenomenological pairing terms, we also employ a more microscopically founded treatment of nucleon pairing, resulting in extrapolations to high densities that are in line with the predictions of advanced many-body methods and are hence more suited to the study of superfluidity in neutron stars. By adopting an extended form of the Skyrme functional, we are able to reconcile the description of matter at high densities and at saturation density: the new model further refines the description of atomic nuclei offered by its predecessors. A qualitative improvement is our inclusion of ground state reflection asymmetry, in addition to the spontaneous breaking of rotational, axial, and time-reversal symmetry. Quantitatively, the model offers lowered root-mean-square deviations on 2457 masses (0.631 MeV), 810 charge radii (0.0237 fm) and an unmatched accuracy with respect to 45 primary fission barriers of actinide nuclei (0.33 MeV). Reconciling the complexity of neutron stars with those of atomic nuclei establishes BSkG3 as a tool of choice for applications to nuclear structure, the nuclear equation of state and nuclear astrophysics in general

Progress on Brussels-Skyrme atomic mass models on a grid: stiff neutron matter equation of state

We report here the current developments on the Brussels-Skyrme-on-a-Grid (BSkG) atomic mass models. In comparison with our previous models, BSkG3 improves the infinite nuclear matter (INM) properties which opens its applications to neutron stars. The results presented here show that BSkG3 preserve the excellent agreement with experimental nuclear masses and radii, together with fission barriers of actinides obtained by BSkG1 and BSkG2, while the nuclear matter properties are considerably improved.Comment: 3 pages, 2 figure