Toward a unified equation of state for multi-messenger astronomy

Aims. We aim to present a first step in developing a benchmark equation-of-state (EoS) model for multi-messenger astronomy that unifies the thermodynamics of quark and hadronic degrees of freedom. Methods. A Lagrangian approach to the thermodynamic potential of quark-meson-nucleon matter was used. In this approach, dynamical chiral-symmetry breaking is described by the scalar mean-field dynamics coupled to quarks and nucleons and their chiral partners, whereby its restoration occurs in the hadronic phase by parity doubling, as well as in the quark phase. Quark confinement was achieved by an auxiliary scalar field that parametrizes a dynamical infrared cut-off in the quark sector, serving as an ultraviolet cut-off for the nucleonic phase space. The gap equations were solved for the isospin-symmetric case, as well as for neutron star (NS) conditions. We also calculated the mass-radius (MR) relation of NSs and their tidal deformability (TD) parameter. Results. The obtained EoS is in accordance with nuclear matter properties at saturation density and with the flow constraint from heavy ion collision experiments. For isospin-asymmetric matter, a sequential occurrence of light quark flavors is obtained, allowing for a mixed phase of chirally-symmetric nucleonic matter with deconfined down quarks. The MR relations and TDs for compact stars fulfill the constraints from the latest astrophysical observations for PSR J0740+6620, PSR J0030+0451, and the NS merger GW170817, whereby the tension between the maximum mass and compactness constraints rather uniquely fixes the model parameters. The model predicts the existence of stars with a core of chirally restored but purely hadronic (confined) matter for masses beyond 1.8 M⊙. Stars with pure-quark matter cores are found to be unstable against the gravitational collapse. This instability is shifted to even higher densities if repulsive interactions between quarks are included.

Microscopìc Study of the Response of Nuclear Matter

The correlated random-phase approximation (CRPAj), which provides a description of the linear response and elementary excitations of nuclear matter, is summarized. The density-density response functions of symmetrical nuclear matter and pure neutron matter are calculated using a local version of CRPA1 (LCRPA) based on the v2 model nucleon-nucleon interaction. Although simple, the calculation establishes some significant qualitative trends. It constitutes a prelude to calculations of response functions of realistic nucleon matter both with CRPA1 and with theories that go beyond it.

Phase Transitions and Bose–Einstein Condensation in Alpha-Nucleon Matter

The equation of state and the phase diagram of an isospin-symmetric chemically equilibrated mixture of a particles and nucleons (N) are studied in the mean-field approximation. We use a Skyrme-like parametrization of mean-field potentials as functions of the partial densities of particles. The parameters of these potentials are chosen by fitting the known properties of pure N- and pure a-matters at zero temperature. The sensitivity of results to the choice of the aN attraction strength is investigated. The phase diagram of the a − N mixture is studied with a special attention paid to the liquid-gas phase transitions and the Bose–Einstein condensation of a particles. We have found two first-order phase transitions, stable and metastable, which differ significantly by the fractions of a’s. It is shown that the states with a condensate are metastable.

THE ROLE OF ANTIKAON CONDENSATES IN THE EQUATION OF STATE OF NEUTRON STARS

We study the consequences of the presence of a negative electric charge condensate of antikaons in neutron stars using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω and ϱ mesons, in the presence of electrons and muons, to accomplish electric charge neutrality and beta equilibrium. The phase transition to the antikaon condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between nucleon matter and the antikaon condensate. Assuming neutrino-free matter, we observe a rapid decrease of the electron chemical potential produced by the gradual substitution of electrons by kaons to accomplish electric charge neutrality. The exotic composition of matter in neutron star including antikaon condensation and nucleons can yield a maximum mass of about M ns ~ 1.76 M ⊙.

THE ROLE OF ANTIKAON CONDENSATES IN THE ISOSPIN ASYMMETRY OF NEUTRON STARS

We study the effects of the scalar-isovector light mesons on the isospin asymmetry and phase transition of hadronic matter to hadronic matter with a condensate of antikaons, using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω, ϱ, δ, and ς mesons in the presence of electrons and muons to accomplish electric charge neutrality and beta equilibrium. The phase transition to the antikaons condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between nucleon matter and the condensed antikaons. As expected, our results indicate that the scalar-isovector mesons increase the range of the mixed phase–space, they operate for restoring isospin symmetry and they reduce the value of the effective nucleon mass, independently of the depth of the optical potential for antikaons. Also as expected the increase of the depth of optical potential favors the population of antikaons. Our results predict the density threshold of birth of the K-antikaons. The most expressive result of our calculation is the abrupt change in the isospin asymmetry due to the presence of the condensate. Moreover, we have found that scalar-isovector mesons increase the fraction of protons and reduced the fraction of neutrons in the system, since these mesons couple with the conserved isovector current of baryons and thus the minimum in the energy of the system corresponds to saturated isospin states (symmetric in isospin). Finally, we have found as expected that these mesons produce the stiffness of the EoS.

THE ROLE OF SCALAR-ISOVECTOR MESONS AND ANTIKAONS IN NEUTRON STARS

We study the effects of the scalar-isovector meson δ and those of a new light scalar-isovector resonance ς on the phase transition of hadronic matter to hadronic matter with a condensate of antikaons, using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω, ϱ, δ, and ς mesons in the presence of electrons and muons to accomplish electric charge neutrality and beta equilibrium. The phase-transition to the antikaon condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between nucleon matter and the condensed antikaons. Scalar-isovector mesons operate for restoring isospin symmetry and reduce this way the value of the effective nucleon mass, independent of the depth of the optical potential for antikaons. Moreover, as expected we found that an increase of the depth of optical potential favors the population of antikaons. Finally, assuming neutrino-free matter, we observe a rapid decrease of the electron chemical potential produced by the gradual substitution of electrons by kaons to accomplish electric charge neutrality.