We provide an equation of state for high density supernova matter by applying a momentum-dependent effective interaction. We focus on the study of the equation of state of high-density and high-temperature nuclear matter containing leptons (electrons and neutrinos) under the chemical equilibrium condition. The conditions of charge neutrality and equilibrium under $β$-decay process lead first to the evaluation of the lepton fractions and afterwards the evaluation of internal energy, pressure, entropy and in total to the equation of state of hot nuclear matter for various isothermal cases. Thermal effects on the properties and equation of state of nuclear matter are evaluated and analyzed in the framework of the proposed effective interaction model. Since supernova matter is characterized by a constant entropy we also present the thermodynamic properties for isentropic case. Special attention is dedicated to the study of the contribution of the components of $β$-stable nuclear matter to the entropy per particle, a quantity of great interest for the study of structure and collapse of supernova.
Neutrino emission and their transport of energy to the supernova shock region are sensitive to the physics of hot and dense nuclear matter, which is a complex problem due to the strong correlations induced by nuclear forces. We derive charged-current opacities for electron neutrinos and antineutrinos in supernova matter using a self-consistent approach based on the Skyrme effective interaction. We include a mean field energy shift due to nuclear interaction and corrections due to RPA correlations. A complete treatment of the full Skyrme interaction, including a spin-orbit term, is given. To te…
We examine the model dependence of the phase diagram of inhomogeneous nulcear matter in supernova cores using the quantum molecular dynamics (QMD). Inhomogeneous matter includes crystallized matter with nonspherical nuclei - "pasta" phases - and the liquid-gas phase separating nuclear matter. Major differences between the phase diagrams of the QMD models can be explained by the energy of pure neutron matter at low densities and the saturation density of asymmetric nuclear matter. We show the density dependence of the symmetry energy is also useful to understand uncertainties of the phase diagr…
The pasta phase in core-collapse supernova matter (finite temperatures and fixed proton fractions) is studied within relativistic mean field models. Two different calculations are used for comparison, the Thomas-Fermi (TF) and the Coexisting Phases (CP) 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. Finally, a comparison with a finite temperature Skyrme-Hartree-Fock calculation is drawn.
We provide an equation of state for high density supernova matter by applying a momentum-dependent effective interaction. We focus on the study of the equation of state of high-density and high-temperature nuclear matter containing leptons (electrons and neutrinos) under the chemical equilibrium condition. Thermal effects on the properties and equation of state of nuclear matter are evaluated and analyzed in the framework of the proposed effective interaction model. Since supernova matter is characterized by a constant entropy we also present the thermodynamic properties for the isentropic cas…
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, pressure, entropy and chemical potentials in the range of particle number densities and temper…
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 (…
The symmetry energy coefficients, incompressibility, and single-particle and isovector potentials of clusterized dilute nuclear matter are calculated at different temperatures employing the $S$-matrix approach to the evaluation of the equation of state. Calculations have been extended to understand the aforesaid properties of homogeneous and clusterized supernova matter in the subnuclear density region. Comparison of the results in the $S$-matrix and mean-field approach reveals some subtle differences in the density and temperature region we explore.
In this review article we discuss selected developments regarding the role of the equation of state (EOS) in simulations of core-collapse supernovae. There are no first-principle calculations of the state of matter under supernova conditions since a wide range of conditions is covered, in terms of density, temperature and isospin asymmetry. Instead, model EOS are commonly employed in supernova studies. These can be divided into regimes with intrinsically different degrees of freedom: heavy nuclei at low temperatures, inhomogeneous nuclear matter where light and heavy nuclei coexist together wi…
In dense environments, standard and non-standard neutrino interactions with the background particles trigger a variety of flavor mechanisms, which can impact r-process nucleosynthetic abundances. Future observations of a(n) (extra)galactic supernova will tell us about properties of neutrinos and of the astrophysical source that produce them. The upcoming measurement of the diffuse supernova neutrino background constitute a unique source of information. We highlight some recent developments.
A simple, exactly solvable statistical model is presented for the description of baryonic matter in the thermodynamic conditions associated to the evolution of core-collapsing supernova. It is shown that the model presents a first order phase transition in the grandcanonical ensemble which is not observed in the canonical ensemble. Similar to other model systems studied in condensed matter physics, this ensemble in-equivalence is accompanied by negative susceptibility and discontinuities in the intensive observables conjugated to the order parameter. This peculiar behavior originates from the …
The role of weakly bound neutral clusters, such as dineutrons and tetraneutrons, in matter of high density and high temperature is discussed. Under such conditions, which are characteristic of core-collapse supernovae, the lifetime of multineutrons may prove to be sufficiently long for them to have a pronounced effect on the formation of the chemical composition. The influence of the multineutron binding energy and other nuclear properties on the magnitude of the effect being considered is examined.
At low energies nucleon-nucleon interactions are resonant and therefore supernova matter at subnuclear densities has many similarities to atomic gases with interactions dominated by a Feshbach resonance. We calculate the rates of neutrino processes involving nucleon-nucleon collisions and show that these are enhanced in mixtures of neutrons and protons at subnuclear densities due to the large scattering lengths. As a result, the rate for neutrino pair bremsstrahlung and absorption is significantly larger below 10^{13} g cm^{-3} compared to rates used in supernova simulations.
This is an introduction to the tabulated data base of stellar matter properties calculated within the framework of the Statistical Model for Supernova Matter (SMSM). The tables present thermodynamical characteristics and nuclear abundances for 31 values of baryon density (10$^{-8}<ρ/ρ_0<$0.32, $ρ_0$=0.15 fm$^{-3}$ is the normal nuclear matter density), 35 values of temperature ($0.2<T<25$ MeV) and 28 values of electron-to-baryon ratio ($0.02<Y_e<0.56$). The properties of stellar matter in $β$-equilibrium are also considered. The main ingredients of the SMSM are briefly outlined, and the data s…
We revisit the rates of neutrino pair emission and absorption from nucleon-nucleon bremsstrahlung in supernova matter using the $T$-matrix formalism in the long-wavelength limit. Based on two-body potentials of chiral effective field theory ($χ$EFT), we solve the Lippmann-Schwinger equation for the $T$-matrix including non-diagonal contributions. We consider final-state Pauli blocking and hence our calculations are valid for nucleons with an arbitrary degree of degeneracy. We also explore the in-medium effects on the $T$-matrix and find that they are relatively small for supernova matter. We c…
We calculate the scattering rate of low energy neutrinos in hot and dense neutron matter encountered in neutrons stars and supernova in the hydrodynamic regime. We find that the Brillouin peak, associated with the sound mode, and the Rayleigh peak, associated with the thermal diffusion mode, dominate the dynamic structure factor. Although the total scattering cross section is constrained by the compressibility sum rule, the differential cross-section calculated using the hydrodynamic response function differs from results obtained in approximate treatments often used in astrophysics such as ra…
Recent developments in the theory of pure neutron matter and experiments concerning the symmetry energy of nuclear matter, coupled with recent measurements of high-mass neutron stars, now allow for relatively tight constraints on the equation of state of dense matter. We review how these constraints are formulated and describe the implications they have for neutron stars and core-collapse supernovae. We also examine thermal properties of dense matter, which are important for supernovae and neutron star mergers, but which cannot be nearly as well constrained at this time by experiment. In addit…
We generalize our virial approach to study the neutral current neutrino response of nuclear matter at low densities. In the long-wavelength limit, the virial expansion makes model-independent predictions for neutrino-nucleon scattering rates and the density S_V and spin S_A responses. We find S_A is significantly reduced from one even at low densities. We provide a simple fit S_A^f(n,T,Y_p) of the axial response as a function of density n, temperature T and proton fraction Y_p. This fit reproduces our model independent virial results at low densities and reproduces the Burrows and Sawyer rando…
We explore the appearance of light clusters at high densities of collapsing stellar cores. Special attention is paid to the unstable isotope H4, which was not included in previous studies. The importance of light clusters in the calculation of rates for neutrino matter interaction is discussed. The main conclusion is that thermodynamic quantities are only weakly sensitive to the chemical composition. The change in pressure and hence the direct change in collapse dynamics will be minor. But the change in neutrino heating and neutronization processes can be significant.
We study the influence of hot and dense matter in core-collapse supernovae by adopting up-to-date nuclear equation of state (EOS) based on the microscopic nuclear many-body frameworks. We explore effects of EOS based on the Dirac Brueckner 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 by the variational method but employing two different treatments in computations of nuclear abundances. We perform numerical simulations of core-collapse supernovae adop…
Phase transition from hadronic matter to quark-gluon matter is discussed for various regimes of temperature and baryon number density. For small and medium densities, the phase transition is accurately described in the framework of the Field Correlation Method, whereas at high density predictions are less certain and leave room for the phenomenological models. We study formation of multiquark states (MQS) at zero temperature and high density. Relevant MQS components of the nuclear matter can be described using a previously developed formalism of the quark compound bags (QCB). Partial-wave anal…
