Matter In Core-collapse Supernovae Research Articles

Effects of nuclear matter and composition in core-collapse supernovae and long-term proto-neutron star cooling

Abstract We study the influence of hot and dense matter in core-collapse supernovae by adopting an up-to-date nuclear equation of state (EOS) based on the microscopic nuclear many-body frameworks. We explore effects of the EOS based on the Dirac–Brückner–Hartree–Fock theory through comparisons with those based on the variational method. We also examine effects of the differences in the composition of nuclei and nucleons by using the same EOS as the variational method but employing two different treatments in computations of nuclear abundances. We perform numerical simulations of core-collapse supernovae adopting the three EOSs. We also perform numerical simulations of the long-term evolution over 70 s of the proto-neutron star cooling. We show that the impacts of different modeling of the composition are remarkable as in those due to different treatments of uniform matter in the gravitational collapse, bounce and shock propagation. The cooling of a proto-neutron star and the resulting neutrino emission are also affected by the compositional difference even if the same treatment is used in computing uniform matter of the EOS.

Role of the conserved charges in the chiral symmetry restoration phase transition

The effect of conserved baryon, isospin and strangeness charges on the behavior of phase transitions in dense matter is studied. Baryonic matter is described within the three-flavor Polyakov$-$Nambu$-$Jona-Lasinio model and several charge fractions $Y_Q$ are considered. The role of the vector interaction, which can be important to describe dense systems, is discussed. Special attention is given to the case with charge fraction $Y_Q=0.4$, due to its importance in heavy-ion collisions and core-collapse supernova matter. It is shown that the possible formation of chiral-symmetric quark matter in the laboratory will be favored in asymmetric matter. Besides, the inclusion of the vector interaction reinforces the formation of quark matter at lower densities.

Short Gamma-Ray Bursts and the Decompression of Neutron Star Matter in Tidal Streams

Abstract Short gamma-ray bursts (sGRBs) are generally thought to result from the merger of two neutron stars or the merger of a neutron star with a black hole. It is becoming standard practice to model these mergers with hydrodynamical simulations that employ equations of state that are derived, for example, for determining the behavior of matter in core-collapse supernovae, and which therefore make use of the assumption that the matter is hot and in nuclear statistical equilibrium (NSE). In this Letter we draw attention to the fact that the hydrodynamical timescale (roughly the gravitational timescale of the neutron star) may be several orders of magnitude shorter than the timescale on which such equilibrium can be reestablished in the tidal debris ejected during an sGRB, and that on the initial decompression timescales the unshocked tidal ejecta may remain sufficiently cool that the employed equations of state are not appropriate for modeling the dynamics of this part of the flow. On timescales short compared with the timescale on which NSE can be (re)established, the equation of state can remain relatively stiff and thus the stream of tidal debris can remain narrow and vulnerable to gravitational instability, as has recently been suggested. These findings suggest that estimates of the type and abundances of heavy elements formed in short gamma-ray bursts need to be revisited. We suggest that the most direct method of testing the physical and dynamical properties of tidal ejecta in sGRBs will come from modeling of their lightcurves, which provides the cleanest source of information on the system dynamics.

Full distribution of clusters with universal couplings and in-medium effects

Light and heavy clusters are calculated for asymmetric warm nuclear matter in a relativistic mean-field approach. In-medium effects, introduced via a universal cluster-meson coupling, and a binding energy shift contribution, calculated in a Thomas-Fermi approximation, were taken into account. This work considers, besides the standard lightest bound clusters $^4$He, $^3$He, $^3$H, and $^2$H, also stable and unstable clusters with higher number of nucleons, in the range $5\leq A \leq 12$, as it is natural that heavier clusters also form in core-collapse supernova matter, before the pasta phases set in. We show that these extra degrees of freedom contribute with non-negligible mass fractions to the composition of nuclear matter, and may prevail over deuterons and $\alpha$ particles at high density in strongly asymmetric matter, and not too high temperatures. The presence of the light clusters reduces the contribution of heavy clusters to a much smaller density range, and to a smaller mass fraction.

Chiral magnetohydrodynamic turbulence in core-collapse supernovae

Macroscopic evolution of relativistic charged matter with chirality imbalance is described by the chiral magnetohydrodynamics (chiral MHD). One such astrophysical system is high-density lepton matter in core-collapse supernovae where the chirality imbalance of leptons is generated by the parity-violating weak processes. After developing the chiral MHD equations for this system, we perform numerical simulations for the real-time evolutions of magnetic and flow fields, and study the properties of the chiral MHD turbulence. In particular, we observe the inverse cascade of the magnetic energy and the fluid kinetic energy. Our results suggest that the chiral effects that have been neglected so far can reverse the turbulent cascade direction from direct to inverse cascade, which would impact the magnetohydrodynamics evolution in the supernova core toward explosion.

Pasta phases in core-collapse supernova matter

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean field models. Three different calculations are used for comparison, the Thomas-Fermi (TF), the Coexisting Phases (CP) and the Compressible Liquid Drop (CLD) approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy and pressure, in the space of particle number densities and temperatures expected to cover the pasta region, are calculated. Finally, a comparison with a finite temperature Skyrme-Hartree-Fock calculation is drawn.

Light clusters, pasta phases, and phase transitions in core-collapse supernova matter

The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean-field models. Three different calculations are used for comparison: the Thomas--Fermi, the coexisting phases, and the compressible liquid drop approximations. The effects of including light clusters in nuclear matter and the densities at which the transitions between pasta configurations and to uniform matter occur are also investigated. The free energy, pressure, entropy, and chemical potentials in the range of particle number densities and temperatures expected to cover the pasta region are calculated. Finally, a comparison with a finite-temperature Skyrme--Hartree--Fock calculation is drawn.

Equation of state for nuclear matter in core-collapse supernovae by the variational method

We construct a new nuclear equation of state (EOS) for core-collapse supernova (SN) simulations using the variational many-body theory. For uniform nuclear matter, the EOS is constructed with the cluster variational method starting from the realistic nuclear Hamiltonian composed of the Argonne v18 two-body potential and the Urbana IX three-body potential. The masses and radii of neutron stars calculated with the obtained EOS at zero temperature are consistent with recent observational data. For non-uniform nuclear matter, we construct the EOS in the Thomas-Fermi approximation. In this approximation, we assume a functional form of the density distributions of protons, neutrons, and alpha-particles, and minimize the free energy density in a Wigner-Seitz cell with respect to the parameters included in the assumed density distribution functions. The phase diagram of hot nuclear matter at a typical temperature is reasonable as compared with that of the Shen EOS.

Phase transitions in core-collapse supernova matter at sub-saturation densities

We perform a three-dimensional, finite temperature Skyrme-Hartree-Fock study of inhomogeneous nuclear matter to determine the critical density and temperature for the phase transition between the pasta phase and homogeneous matter and its properties. We employ four different parametrizations of the Skyrme nuclear energy-density functional, SkM$^*$, SLy4, NRAPR and SQMC700, which span a range of saturation-density symmetry energy behaviours constrained by a variety of nuclear experimental probes. For each of these interactions we calculate free energy, pressure, entropy and chemical potentials in the range of particle number densities where the nuclear pasta phases are expected to exist, 0.02 - 0.12 fm$^{-3}$, temperatures 2 - 8 MeV and a proton fraction of 0.3. We find unambiguous evidence for a first-order phase transition to uniform matter, unsoftened by the presence of the pasta phases. No conclusive signs of first-order phase transition between the pasta phases is observed, and it is argued that the thermodynamic quantities vary continuously right up to the first-order phase transition to uniform matter. We compare our results with thermodynamic spinodals calculated using the same Skyrme parameterizations, finding that the effect of short-range Coulomb correlations and quantum shell effects included in our model leads to the pasta phases existing at densities up to 0.1 fm$^{-3}$ above the spinodal boundaries, thus increasing the transition density to uniform matter by the same amount. The transition density is otherwise shown to be insensitive to the symmetry energy at saturation density within the range constrained by the concordance of a variety of experimental constraints, and can be taken to be a well-determined quantity.

Equation of state with an extended SU(3) quark-meson model under conditions prevailing in core collapse supernovae

The quark-meson model is investigated for the two- and three-flavor case extended by contributions of vector mesons under conditions encountered in core-collapse supernova matter. Typical temperature ranges, densities and electron fractions, as found in core-collapse supernova simulations, are studied by implementing charge neutrality and local beta-equilibrium with respect to weak interactions. Within this framework, we analyze the resulting phase diagram and equation of state (EoS) and investigate the impact of undetermined parameters of the model. The EoS turns out to be relatively independent on the entropy per baryon but there are significant changes when going from the two-flavor to the three-flavor case due to the nontrivial contribution from the strange quarks which stay massive even at high densities. While an increasing vector meson coupling constant leads to a substantial stiffening of the EoS, we find that the impact of changing the scalar meson mass is equally strong and results in a softening of the EoS for increasing values.

CONSTRAINING THE SYMMETRY PARAMETERS OF THE NUCLEAR INTERACTION

One of the major uncertainties in the dense matter equation of state has been the nuclear symmetry energy. The density dependence of the symmetry energy is important in nuclear astrophysics, as it controls the neutronization of matter in core-collapse supernovae, the radii of neutron stars and the thicknesses of their crusts, the rate of cooling of neutron stars, and the properties of nuclei involved in r-process nucleosynthesis. We show that fits of nuclear masses to experimental masses, combined with other experimental information from neutron skins, heavy ion collisions, giant dipole resonances and dipole polarizabilities, lead to stringent constraints on parameters that describe the symmetry energy near the nuclear saturation density. These constraints are remarkably consistent with inferences from theoretical calculations of pure neutron matter, and, furthermore, with astrophysical observations of neutron stars. The concordance of experimental, theoretical and observational analyses suggests that the symmetry parameters S_v and L are in the range 29.0 - 32.7 MeV and 40.5 - 61.9 MeV, respectively, and that the neutron star radius, for a 1.4 M_sun star, is in the narrow window 10.7 km < R < 13.1 km (90% confidence). We can also set tight limits to the size of neutron star crusts and the fractional moment of inertia they contain, as well as the overall moment of inertia and quadrupole polarizability of 1.4 M_sun stars. Our results also have implications for the disk mass and ejected mass of compact mergers involving neutron stars.

The equation of state and composition of hot, dense matter in core-collapse supernovae

The equation of state and composition of matter are calculated for conditions typical for pre-collapse and early collapse stages in core collapse supernovae. The composition is evaluated under the assumption of nuclear statistical equilibrium, when the matter is considered as an `almost' ideal gas with corrections due to thermal excitations of nuclei, to free nucleon degeneracy, and to Coulomb and surface energy corrections. The account of these corrections allows us to obtain the composition for densities a bit below the nuclear matter density. Through comparisons with the equation of state (EOS) developed by Shen et al. we examine the approximation of one representative nucleus used in most of recent supernova EOS's. We find that widely distributed compositions in the nuclear chart are different, depending on the mass formula, while the thermodynamical quantities are quite close to those in the Shen's EOS.

Signals of the QCD phase transition in core collapse supernovae—microphysical input and implications on the supernova dynamics

In contrast to heavy ion collisions, matter in astrophysical systems such as neutron stars, compact star mergers and supernova environments can be highly isospin asymmetric. We focus on core collapse supernova matter where temperatures reach tens of MeV. Both conditions, the high temperatures and isospin asymmetry, can favour an early phase transition to quark matter already close to nuclear saturation density. We examine the QCD phase transition during the early postbounce phase of core collapse supernovae. We discuss the microphysical input, i.e. the modelling of the phase transition to strange quark matter, and the consequences on the dynamical evolution as well as the observable neutrino signal from the phase transition. The equation of state for strange quark matter is based on the MIT bag model. The phase transition is constructed applying the Gibbs criterion which results in an extended coexistence region in the phase diagram between the hadronic and the quark phases, i.e. the mixed phase. The supernovae are simulated via general relativistic radiation hydrodynamics based on three-flavour Boltzmann neutrino transport in spherical symmetry. The dynamical evolution of the phase transition to quark matter is determined by an adiabatic collapse due to the softening of the equation of state in the mixed phase. The equation of state for the pure quark phase stiffens again which causes the collapse to halt and a shock wave forms at the boundary between the mixed and the pure hadronic phases. This shock accelerates and launches an explosion, which releases a burst of neutrinos dominated by electron anti-neutrinos due to the lifted degeneracy of the shock-heated hadronic material.