We study the nuclear isentropic equation of state for a stellar matter composed of nucleons, hyperons, and Δ-resonances. We investigate different snapshots of the evolution of a neutron star, from its birth as a lepton-rich proto-neutron star in the aftermath of a supernova explosion to a lepton-poor regime when the star starts cooling to a catalysed configuration. We use a relativistic model within the mean-field approximation to describe the hot stellar matter and adopt density-dependent couplings adjusted by the DDME2 parameterization. We use baryon–meson couplings for the spin-1/2 baryonic octet and spin-3/2 decuplet determined in a unified manner relying on SU(6) and SU(3) symmetry arguments. We observe that Λ is the dominant exotic particle in the star at different entropies for both neutrino-free and neutrino-trapped stellar matter. For a fixed entropy, the inclusion of new particles (hyperons and/or delta resonances) in the stellar matter decreases the temperature. Also, an increase in entropy per baryon (1–2) with decreasing lepton number density (0.4–0.2) leads to an increase in stellar radii and a decrease in its mass due to neutrino diffusion. In the neutrino transparent matter, the radii decrease from entropy per baryon 2 to $T\, =\, 0$ without a significant change in stellar mass.

Strong magnetic fields can modify the microscopic composition of matter with consequences on stellar macroscopic properties. Within this context, we study, for the first time, the possibility of the appearance of spin-3/2 $\mathrm{\Delta }$ baryons in magnetars. We make use of two different relativistic models for the equation of state of dense matter under the influence of strong magnetic fields considering the effects of Landau levels and the anomalous magnetic moment (AMM) proportional to the spin of all baryons and leptons. In particular, we analyze the effects of the AMM of $\mathrm{\Delta }$ baryons in dense matter for the first time. We also obtain global properties corresponding to the EoS models numerically and study the corresponding role of the $\mathrm{\Delta }$ baryons. We find that they are favored over hyperons, which causes an increase in isopin asymmetry and a decrease in spin polarization. We also find that, contrary to what generally occurs when new degrees of freedom are introduced, the $\mathrm{\Delta }$'s do not make the EoS significantly softer and magnetars less massive. Finally, the magnetic field distribution inside a given star is not affected by the presence of $\mathrm{\Delta }$'s.

Baryonic matter close to the saturation density is very likely to present complex inhomogeneous structures collectively known under the name of nuclear pasta phase. At finite temperature, the different geometric structures are expected to coexist with potential consequences on the neutron star crust conductivity and neutrino transport in supernova matter. In the framework of a statistical multicomponent approach, we calculate the composition of matter in the pasta phase considering density, proton fraction, and geometry fluctuations. Using a realistic energy functional from relativistic mean-field theory and a temperature- and isospin-dependent surface tension fitted from Thomas-Fermi calculations, we show that different geometries can coexist in a large fraction of the pasta phase, down to temperatures of the order of the crystallization temperature of the neutron star crust. Quantitative estimates of the charge fluctuations are given.

The presence of nuclear pasta is expected to modify the transport properties in the mantle of neutron stars. The non-spherical geometry of the pasta nuclear clusters leads to anisotropies in the collision frequencies, impacting the thermal and electrical conductivity. We derive analytical expressions for the anisotropic collision frequencies using the Boltzmann equation in the relaxation time approximation. The average parallel, perpendicular, and Hall electrical conductivities are computed in the high-temperature regime above crustal melting, considering incoherent elastic electron-pasta scattering and randomly oriented pasta structures. Numerical values are obtained at different densities and temperatures by using the Indiana University–Florida State University (IUFSU) parametrization of the non-linear Walecka model to determine the crustal structure. We find that the anisotropy of the collision frequencies grows with the length of the pasta structures and, independently of the magnetic field, the presence of rod and slab phases decreases the conductivity by more than one order of magnitude. Our numerical results indicate that, even if the pasta structures might survive above the crustal melting point, no strong anisotropies are to be expected in the conduction properties in this temperature regime, even in the presence of a very high magnetic field.