The work at my Master’s Degree Thesis consisted in studying how matter in the interior of a neutron star influences the deformability of the star itself. We considered a neutron star belonging to a binary system in the last stage of its life (i.e. shortly before the merging of the two objects), where the deformation of the star is due to the tidal interaction between the two objects. The matter that constitutes the star is described by an appropriate Equation of State (EOS) that, at present, is unknown in the most internal and most compact region of a neutron star, i.e. the core. For this reason, it is necessary to choose different appropriate EOS (obtained theoretically by nuclear physicists) in order to study neutron stars that we suppose to have different microscopic properties. In our work, we considered the softest and the stiffest EOS published in literature to describe matter in the interior of a neutron star. They describe, respectively, the most compressible (most compact) stars and the least compressible (least compact) stars or, equivalently, the least deformable stars and the most deformable stars. In addition, we considered other EOS in order to guarantee a wider variety of microscopic configurations too. In practice, we parametrized these EOS with the “piecewise polytropics” parametrization, which approximates each EOS via polytropic functions defined in adjacent mass density intervals.
Our study is based on the evaluation of the contributes of the internal regions of a neutron star (internal core, external core, internal crust, external crust) to the “tidal deformability” \Pi for different EOS. \Pi is a physical parameter that describes how much the star is deformed when there is an external tidal quadrupolar gravitational field (in our case, the source of such field is supposed to be the second object of the binary system, e.g. another neutron star or a black hole). We found that the complete core (internal plus external) gives the main contribution to \Pi for softer EOS, while the complete crust gives the main contribution to \Pi for stiffer EOS. Moreover,external core always determines the 40%-50% of \Pi independently of the EOS.
In the future, when the gravitational signal emitted by a binary system in the last stage of its life has been measured, it will be possible to estimate \Pi. Our analysis says that, if this estimate was near to the value obtained in our work for neutron stars described by stiffer EOS, we could not obtain information about the EOS in the most internal region of the star. In fact we discovered that, in this case, \Pi would be mainly determined by the crust and therefore it could provide information about the crust principally. Instead, if the estimate of \Pi was near to the value obtained in our work for neutron stars described by softer EOS, \Pi would be mainly determined by the core. Therefore, in this case we could obtain information about the EOS in the core: specifically, we could say that it is soft, i.e. the core matter is more compressible than it was in the case of stiffer EOS. This would make us able to reduce the set of EOS used to describe matter in a neutron star and so to reduce the uncertainty about the structure of matter in the core.