Selecting Microscopic Equations of State of Nuclear Matter for the study of Neutron Stars

I developed my PhD thesis in the aerea of astronuclear theory, an inter- disciplinary field where many aspects of nuclear physics, particle physics and astrophysics converge. The research carried out is the study of the equation of state of nuclear matter and its implications for the structure of neutron stars. Neutron stars are compact objects produced in the gravitational collapse of very massive stars just after they explode as supernova, and are characterized by central density extremely high, up to one order of magnitude greater than the nuclear saturation density. Therefore the knowledge of the equation of state (EoS) of nuclear matter at high density is critical for the understanding of stellar structure. During these 3 years, I derived an equation of state for nuclear matter using the many-body microscopic theory by Brueckner-Bethe- Goldstone. The term microscopic comes from the fact that the only ingredient required as input is the nucleon-nucleon interaction, which in the case of nucleons is known from scattering experiments. The in- clusion of nucleonic three-body forces turns out crucial, so that the EoS not only gives the correct values of density and binding energies at the saturation point, but also the correct compressibility and symme- try energy, which all turn out to be compatible with values extracted from phenomenology. The theoretical approach is widely discussed in the Chapter 3. I have systematically explored the different nucleon-nucleon interactions and three body forces (both phenomenological and microscopic ones). With the EoS obtained, I solved the equations of hydrostatic equilibrium of the star, known as Tolman - Oppenheimer - Volkoff equations, and I calculated the stellar configurations for the equilibrium for several EoSs. The calculated maximum masses of neu- tron stars are equal approximately to 2 solar masses, and radii ranging from 12 to 14 km, according to the observational data recently obtained from satellites in X-ray and Gamma of new generation (Chandra, XMM Newton and Integral). The obtained results were published in a Phys- ical Review C [1] and in a proceeding [6]. The results are shown in Chapter 4. This work has been further extended to the calculation of the ef- fective masses of nucleons, always within the Brueckner theory. This calculation is crucial for the study of neutron star cooling, where one of the main ingredients is the neutrino emissivity, which depends largely on the effective masses of nucleons. I have systematically explored the effective masses with different two- and three-body interactions, and several values of matter asymmetry. This work was published in Phys. Rev, C [2]. Afterwards, the effective masses obtained from the calcu- lation were included in the cooling codes, which are publicly available, along with the stellar cooling gaps of superfluidity, calculated in the same theoretical approach. The results obtained have shown for the first time the important role of the Urca processes in stellar cooling, giving rise to a high flux of neutrinos, and superfluidity in channels 1S0 and 3PF2 of proton and neutron respectively. It is thus explained the cooling of Cassiopeia A, a supernova remnant whose thermal emis- sion has been monitored for many years, and the analysis of which is compatible with the idea that the stellar core is in a superfluid state. The work was published in Monthly Notices of the Royal Astronomical Society (MNRAS) [4] and is discussed in Chapter 5.