The origin of the elements is a fascinating question that scientists have been trying to answer for the last seven decades. The formation of light elements in the primordial universe and heavier elements in astrophysical sources occurs through nuclea
r reactions. We can say that nuclear processes are responsible for the production of energy and synthesis of elements in the various astrophysical sites. Thus, nuclear reactions have a determining role in the existence and evolution of several astrophysical environments, from the Sun to the spectacular explosions of supernovae. Nuclear astrophysics attempts to address the most basic and important questions of our existence and future. There are still many issues that are unresolved such as, how stars and our Galaxy have formed and how they evolve, how and where are the heaviest elements made, what is the abundance of nuclei in the universe and what is the nucleosynthesis output of the various production processes and why the amount of lithium-7 observed is less than predicted. In this paper, we review our current understanding of the different astrophysical nuclear processes leading to the formation of chemical elements and pay particular attention to the formation of heavy elements occurring during high-energy astrophysical events. Thanks to the recent multi-messenger observation of a binary neutron star merger, which also confirmed production of heavy elements, explosive scenarios such as short gamma-ray bursts and the following kilonovae are now strongly supported as nucleosynthesis sites.
In this work we investigate the structure of white dwarfs using the Tolman-Oppenheimer-Volkoff equations and compare our results with those obtained from Newtonian equations of gravitation in order to put in evidence the importance of General Relativ
ity (GR) for the structure of such stars. We consider in this work for the matter inside white dwarfs two equations of state, frequently found in the literature, namely, the Chandrasekhar and Salpeter equations of state. We find that using Newtonian equilibrium equations, the radii of massive white dwarfs ($M>1.3M_{odot}$) are overestimated in comparison with GR outcomes. For a mass of $1.415M_{odot}$ the white dwarf radius predicted by GR is about 33% smaller than the Newtonian one. Hence, in this case, for the surface gravity the difference between the general relativistic and Newtonian outcomes is about 65%. We depict the general relativistic mass-radius diagrams as $M/M_{odot}=R/(a+bR+cR^2+dR^3+kR^4)$, where $a$, $b$, $c$ and $d$ are parameters obtained from a fitting procedure of the numerical results and $k=(2.08times 10^{-6}R_{odot})^{-1}$, being $R_{odot}$ the radius of the Sun in km. Lastly, we point out that GR plays an important role to determine any physical quantity that depends, simultaneously, on the mass and radius of massive white dwarfs.
We propose a generalization of pseudospin and spin symmetries, the SU(2) symmetries of Dirac equation with scalar and vector mean-field potentials originally found independently in the 70s by Smith and Tassie, and Bell and Ruegg. As relativistic symm
etries, they have been extensively researched and applied to several physical systems for the last 18 years. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrodinger-like equations, i.e, without a matrix structure. In this paper we use the original formalism of Bell and Ruegg to derive general requirements for the Lorentz structures of potentials in order to have these SU(2) symmetries in the Dirac equation, again allowing for the suppression of the matrix structure of the second-order equation of either the upper or lower components of the Dirac spinor. Furthermore, we derive equivalent conditions for spin and pseudospin symmetries with 2- and 1-dimensional potentials and list some possible candidates for 3, 2, and 1 dimensions. We suggest applications for physical systems in three and two dimensions, namely electrons in graphene.
In the 70s Smith and Tassie, and Bell and Ruegg independently found SU(2) symmetries of the Dirac equation with scalar and vector potentials. These symmetries, known as pseudospin and spin symmetries, have been extensively researched and applied to s
everal physical systems. Twenty years after, in 1997, the pseudospin symmetry has been revealed by Ginocchio as a relativistic symmetry of the atomic nuclei when it is described by relativistic mean field hadronic models. The main feature of these symmetries is the suppression of the spin-orbit coupling either in the upper or lower components of the Dirac spinor, thereby turning the respective second-order equations into Schrodinger-like equations, i.e, without a matrix structure. In this paper we propose a generalization of these SU(2) symmetries for potentials in the Dirac equation with several Lorentz structures, which also allow for the suppression of the matrix structure of second-order equation equation of either the upper or lower components of the Dirac spinor. We derive the general properties of those potentials and list some possible candidates, which include the usual spin-pseudospin potentials, and also 2- and 1-dimensional potentials. An application for a particular physical system in two dimensions, electrons in graphene, is suggested.
Massive, highly magnetized white dwarfs with fields up to $10^9$ G have been observed and theoretically used for the description of a variety of astrophysical phenomena. Ultramagnetized white dwarfs with uniform interior fields up to $10^{18}$ G, hav
e been recently purported to obey a new maximum mass limit, $M_{rm max}approx 2.58~M_odot$, which largely overcomes the traditional Chandrasekhar value, $M_{rm Ch}approx 1.44~M_odot$. Such a much larger limit would make these astrophysical objects viable candidates for the explanation of the superluminous population of type Ia supernovae. We show that several macro and micro physical aspects such as gravitational, dynamical stability, breaking of spherical symmetry, general relativity, inverse $beta$-decay, and pycnonuclear fusion reactions are of most relevance for the self-consistent description of the structure and assessment of stability of these objects. It is shown in this work that the first family of magnetized white dwarfs indeed satisfy all the criteria of stability, while the ultramagnetized white dwarfs are very unlikely to exist in nature since they violate minimal requests of stability. Therefore, the canonical Chandrasekhar mass limit of white dwarfs has to be still applied.
We investigate the hadron-quark phase transition inside neutron stars and obtain mass-radius relations for hybrid stars. The equation of state for the quark phase using the standard NJL model is too soft leading to an unstable star and suggesting a m
odification of the NJL model by introducing a momentum cutoff dependent on the chemical potential. However, even in this approach, the instability remains. In order to remedy the instability we suggest the introduction of a vector coupling in the NJL model, which makes the EoS stiffer, reducing the instability. We conclude that the possible existence of quark matter inside the stars require high densities, leading to very compact stars.
In this work we study the Nambu-Jona-Lasinio model in the SU (2) version with repulsive vector coupling and apply it to quark stellar matter. We discuss the influence of the vector interaction on the equation of state (EoS) and study quark stars that
are composed of pure quark matter with two flavors. We show that, increasing the vector coupling, we obtain more massive stars with larger radii for the same central energy density.
The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. The most promising sources of gravitational waves are neutron stars and black holes. These objects emit waves in a very wide spe
ctrum of frequencies determined by their quasi-normal modes oscillations. In this work we are concerned with the information we can extract from f and p$_I$-modes when a candidate leaves its signature in the resonant mass detectors ALLEGRO, EXPLORER, NAUTILUS, MiniGrail and SCHENBERG. Using the empirical equations, that relate the gravitational wave frequency and damping time with the mass and radii of the source, we have calculated the radii of the stars for a given interval of masses $M$ in the range of frequencies that include the bandwidth of all resonant mass detectors. With these values we obtain diagrams of mass-radii for different frequencies that allowed to determine the better candidates to future detection taking in account the compactness of the source. Finally, to determine which are the models of compact stars that emit gravitational waves in the frequency band of the mass resonant detectors, we compare the mass-radii diagrams obtained by different neutron stars sequences from several relativistic hadronic equations of state (GM1, GM3, TM1, NL3) and quark matter equations of state (NJL, MTI bag model). We verify that quark stars obtained from MIT bag model with bag constant equal to 170 MeV and quark of matter in color-superconductivity phase are the best candidates for mass resonant detectors.
