Neutron-rich matter in atomic nuclei and neutron stars

Abstract

The proper understanding of the equation of state (EoS) of highly asymmetric nuclear matter is essential when studying systems such as neutron stars (NSs). Using zero-range Skyrme interactions and finite-range interactions such as Gogny forces, momentum-dependent interactions (MDI) and simple effective interactions (SEI), we analyze the properties of the EoS and the influence they may have on the calculations for NSs. We start by studying the convergence properties of the Taylor series expansion of EoS in powers of the isospin asymmetry. Next, we analyze the accuracy of the results for β-stable nuclear matter, which is found in the interior of NSs, when it is computed using the Taylor expansion of the EoS. The agreement with the results obtained using the full expression of the EoS is better for interactions with small-to-moderate values of the slope of the symmetry energy L. The mass and radius relation for a NS is obtained by integrating the so-called Tolman-Oppenheimer-Volkoff (TOV) equations, where the input is the EoS of the system. We have studied the mass-radius relation for Skyrme and Gogny interactions, and we see that that very soft forces are not able to give stable solutions of the TOV equations and only the stiff enough parametrizations can provide 2M0 NSs. We also notice that none of the existing parametrizations of the standard Gogny D1 interaction is able to provide a NS inside the observational constraints. Because of that, we propose a new parametrization, which we name D1M∗, that is able to provide NSs of 2M0 while still providing the same good description of finite nuclei as D1M. A parametrization D1M∗∗ is also presented, which is fitted in the same way as D1M∗ and provides NSs up to 1.91M0. Moreover, we estimate the core-crust transition in NSs by finding where the nuclear matter in the core is unstable against fluctuations of the density. To do that, we employ two methods, the thermodynamical method and the dynamical method. In the case of finite-range interactions, such as the Gogny ones, to use the dynamical method we have had to derive the explicit expression of the energy curvature matrix in momentum space for this type of interactions. We observe a decreasing trend of the transition density with the slope L of the symmetry energy, while the correlation between the transition pressure and L is much lower. Finally different NS properties are studied. The crustal properties, such as the crustal mass, crustal thickness and crustal fraction of the moment of inertial have lower values if one computes them using the core-crust transition density obtained with the dynamical method instead of the one obtained with the thermodynamical method, pointing out the importance of the accurate evaluation of the transition density when studying observational phenomena. We have also studied the moment of inertia of NSs, which is compared to constraints proposed in the literature. Finally, the tidal deformability for NSs is also calculated and compared with the constraints coming from the GW170817 event detected by the LIGO and Virgo observatories and which accounts for the merger of two NSs in a binary system.

El coneixement de l’equació d’estat (EoS) de matèria altament densa i assimètrica és essencial per tal d’estudiar les estrelles de neutrons (NSs). En aquesta tesi s’analitzen, utilitzant interaccions de camp mig no relativistes, les propietats de l’EoS i la seva influència en càlculs de NSs. Primerament, s’estudia la convergència del desenvolupament en sèrie de Taylor de l’EoS en potències de l'assimetria d’isospí. Seguidament, s’analitza l’exactitud dels resultats per matèria β-estable, la qual es troba a l’interior de les NSs, quan es calcula utilitzant el desenvolupament de Taylor de l’EoS. La relació entre la massa i el radi obtinguda integrant les equacions Tolman-Oppenheimer-Volkoff (TOV) també és estudiada. A causa de que les interaccions de Gogny de la família D1 no aconsegueixen donar NSs compatibles amb observacions astrofísiques, en aquesta tesi proposem dues noves forces de Gogny, anomenades D1M∗ i D1M∗∗, les quals poden donar, respectivament, NSs de 2 i 1.91 masses solars. Una altra part de la tesi es dedica a l’estudi de la transició entre l’escorça i el nucli, buscant la densitat a la qual la matèria uniforme al nucli és inestable contra fluctuacions de densitat. Ho estudiem amb dos mètodes, el mètode termodinàmic i el mètode dinàmic. Finalment, s’analitzen diverses propietats de les NSs, com són la relació entre la massa i el radi de l’estrella, les propietats de l’escorça, el moment d’inèrcia, així com la deformació deguda als corrents de marea (tidal deformability) que està relacionada amb l’emissió d’ones gravitacionals en sistemes binaris d’estrelles de neutrons.