Loïc Perot

Formed in gravitational core-collapse supernovae explosions, neutron stars are the most compact stars known in the Universe: their average density exceeds than that found in atomic nuclei. They have a mass typically between 1 and 2 solar masses for a radius of only 10 to 13 kilometers.
Their interior, constituted of a core and a crust, exhibits very different phases of matter, whose description requires theoretical nuclear models, here based on the nuclear energy-density functional theory. In this theory, nucleons are treated as independent quasiparticles in self-consistent potentials via the Hartree-Fock-Bogolyubov method. The family of energy-density functionals developed by the Brussels-Montreal group, named BSk, is based on effective nucleon-nucleon interactions and were precision-fitted to experimental atomic mass. To assess the role of nuclear uncertainties, the series BSk19-BSk26-BSk24 were simultaneously fitted to different neutron-matter equations of state with increasing degrees of stiffness, while the series BSk22-BSk24-BSk25 mainly differ in their predictions for the symmetry energy, which is defined as the difference between the energy per nucleon in neutron matter and that in symmetric nuclear matter (with equal number of neutrons and protons). All the energy-density functionals are consistent with current data at densities below 0.2 nucleons/fm³ and are well-suited for a unified description of all the regions in neutron stars.
In a binary neutron stars system, each star is deformed due to the tidal interactions. To first-order, the quadrupole mass moment of the star is related to the quadrupolar tidal field by a proportionality coefficient called the tidal deformability, depending on the dense-matter equation of state. Another quantity of interest is the Love number, which is equal to the tidal deformability coefficient multiplied by a constant and divided by the fifth power of the star radius. Comparing the results for the BSk22, BSk24, and BSk25 models shows that the Love number is essentially independent of the symmetry energy. On the other hand, comparing BSk19, BSk24, and BSk26 shows that uncertainties on the neutron-matter equation of state at high densities have a strong impact on it. The role of the crust was also studied: we compared the results obtained with the original model BSk24 to those calculated for a putative neutron star made entirely of homogeneous matter. The Love number is found to be very sensitive to the equation of state of the crust, but mainly through the stellar radius. On the other hand, the crust has a negligible impact on the measurable dimensionless tidal deformability parameter, which amounts to the Love number divided by the fifth power of the compactness.
The detection of the gravitational-wave signal GW170817 from the merger of two neutron stars offers new opportunities to probe the properties of dense matter. Apart from estimates of the masses of the two inspiralling stars, the analysis of this signal has also provided information on their tidal deformations during the last orbits. When comparing with the constraints inferred by the LIGO-Virgo collaboration, all the equations of state are consistent with the inferred tidal deformabilities of the two stars. Interestingly, BSk19 is here favored, thus confirming that the gravitational-wave data alone tend to favor a rather soft equation of state at densities relevant for medium-mass neutron stars. Observations of the electromagnetic counterparts, as well as the existence of massive neutron stars, provide additional constraints on the structure of neutron stars, ruling out our softest equation of state BSk19.