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 case.
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.
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 investigate the thermal properties of the potential model equation of state of Akmal, Pandharipande and Ravenhall. This equation of state approximates the microscopic model calculations of Akmal and Pandharipande, which feature a neutral pion condensate. We treat the bulk homogeneous phase for isospin asymmetries ranging from symmetric nuclear matter to pure neutron matter and for temperatures and densities relevant for simulations of core-collapse supernovae, proto-neutron stars, and neutron star mergers. Numerical results of the state variables are compared with those of a typical Skyrme …
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 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.
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…
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 (…
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…
We present an equation of state and the composition of low-density supernova matter composed of light nuclei with mass number A \le 13. We work within the quasiparticle gas model, which accounts for bound states with decay time scales larger than the relevant time scale of supernova and protoneutron star evolution. The mean-field contribution is included in terms of Skyrme density functional. Deuterons, tritons, and 3H(e) nuclei appear in matter in concentrations that are substantially higher than those of heavier nuclei. We calculate the critical temperature of deuteron condensation in such m…
Herein, we review the nuclear equations of state (EOSs) %for core-collapse supernova simulations and the constituent nuclei of core-collapse supernovae (CCSNe) and their roles in CCSN simulations. Various nuclei such as deuterons, iron, and extremely neutron-rich nuclei compose in the central engines of CCSNe. The center of a collapsing core is dominated by neutron-rich heavy nuclei prior to the occurrence of core bounce. Their weak interactions significantly affect the neutrino emission and the size of the produced proto-neutron star. After a core bounce, heavy nuclei are dissolved to protons…
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 review various theoretical approaches for the equation of state (EoS) of dense matter, relevant for the description of core-collapse supernovae, compact stars and compact star mergers. The emphasis is put on models that are applicable to all of these scenarios. Such EoS models have to cover large ranges in baryon number density, temperature and isospin asymmetry. The characteristics of matter change dramatically within these ranges, from a mixture of nucleons, nuclei, and electrons to uniform, strongly interacting matter containing nucleons, and possibly other particles such as hyperons or …
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…
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 investigate the liquid-gas phase transition of hot protoneutron stars shortly after their birth following supernova explosion and the composition and structure of hyperon-rich (proto)neutron stars within a relativistic mean-field model where the nuclear symmetry energy has been constrained from the measured neutron skin thickness of finite nuclei. Light clusters are abundantly formed with increasing temperature well inside the neutrino-sphere for an uniform supernova matter. Liquid-gas phase transition is found to suppress the cluster yield within the coexistence phase as well as decrease c…
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…
We present a review of a broad selection of nuclear matter equations of state (EOSs) applicable in core-collapse supernova studies. The large variety of nuclear matter properties, such as the symmetry energy, which are covered by these EOSs leads to distinct outcomes in supernova simulations. Many of the currently used EOS models can be ruled out by nuclear experiments, nuclear many-body calculations, and observations of neutron stars. In particular the two classical supernova EOS describe neutron matter poorly. Nevertheless, we explore their impact in supernova simulations since they are comm…
Effects of Random Density Fluctuations on Matter-Enhanced Neutrino Flavor Transitions in Supernovae and Implications for Supernova Dynamics and Nucleosynthesis
We compute a new equation of state table including Bose-Einstein condensate of $K^{-}$ mesons for core collapse supernova and neutron star merger simulations. Nuclei and interacting nucleons in non-uniform matter is described in an extended version of the nuclear statistical equilibrium model including excluded volume effects whereas the uniform matter at higher densities is treated in the relativistic hadron field theory with density dependent couplings. The equation of state table is generated for a wide range of density ($10^{-12}$ to $\sim 1$ fm$^{-3}$), positive charge fraction (0.01 to 0…
Muons can be created in nascent neutron stars (NSs) due to the high electron chemical potentials and the high temperatures. Because of their relatively lower abundance compared to electrons, their role has so far been ignored in numerical simulations of stellar core collapse and NS formation. However, the appearance of muons softens the NS equation of state, triggers faster NS contraction and thus leads to higher luminosities and mean energies of the emitted neutrinos. This strengthens the postshock heating by neutrinos and can facilitate explosions by the neutrino-driven mechanism.
Role of Matter Inhomogeneity on Fast Flavor Conversion of Supernova Neutrinos
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及物理学研究所）；National Center for Theoretical Sciences（国家理论科学中心）；GSI Helmholtzzentrum für Schwerionenforschung（德国重离子研究中心）
We study the influence of density-dependent symmetry energy at high densities in simulations of core-collapse supernovae, black hole formation and proto-neutron star cooling by extending the relativistic mean field (RMF) theory used for the Shen EOS table. We adopt the extended RMF theory to examine the density dependence of the symmetry energy with a small value of the slope parameter $L$, while the original properties of the symmetric nuclear matter are unchanged. In order to assess matter effects at high densities, we perform numerical simulations of gravitational collapse of massive stars …
Strongly interacting matter with criticality induced by modified excluded volume in core-collapse supernova simulations
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）；University of Wroclaw（弗罗茨瓦夫大学）；Silesian University in Opava（奥帕瓦西里西亚大学）；Technische Universität Darmstadt（达姆施塔特工业大学）；GSI Helmholtzzentrum für Schwerionenforschung（德国重离子研究中心）；Helmholtz Forschungsakademie Hessen für FAIR (HFHF)（黑森亥姆霍兹FAIR研究学院）；Universitat de Valéncia（瓦伦西亚大学）；Observatori Astronòmic, Universitat de València（瓦伦西亚大学天文台）
