Matthias Hempel

A statistical model for a complete supernova equation of state

Abstract A statistical model for the equation of state and the composition of supernova matter is presented. It consists of an ensemble of nuclei and interacting nucleons in nuclear statistical equilibrium. A relativistic mean field model is applied for the nucleons. The masses of the nuclei are taken from experimental data and from nuclear structure calculations. Excluded volume effects are implemented in a thermodynamic consistent way so that the transition to uniform nuclear matter can be described. Thus the model can be applied at all densities relevant for supernova simulations, i.e. ρ = 10 5 – 10 15 g / cm 3 , and it is possible to calculate a complete supernova equation of state table. The importance of the nuclear distributions for the composition is shown and the role of shell effects is investigated. We find a significant contribution of light clusters which is only poorly represented by α-particles alone. The equation of state is systematically compared to two commonly used models for supernova matter which are based on the single nucleus approximation. In general only small differences are found. These are most pronounced around the (low-density) liquid–gas phase transition line where the distribution of light and intermediate clusters has an important effect.

Signals of the QCD phase transition in core-collapse supernovae

We explore the implications of the QCD phase transition during the postbounce evolution of core-collapse supernovae. Using the MIT bag model for the description of quark matter, we model phase transitions that occur during the early postbounce evolution. This stage of the evolution can be simulated with general relativistic three-flavor Boltzmann neutrino transport. The phase transition produces a second shock wave that triggers a delayed supernova explosion. If such a phase transition happens in a future galactic supernova, its existence and properties should become observable as a second peak in the neutrino signal that is accompanied by significant changes in the energy of the emitted neutrinos. This second neutrino burst is dominated by the emission of antineutrinos because the electron degeneracy is reduced when the second shock passes through the previously neutronized matter.

CORE-COLLAPSE SUPERNOVA EQUATIONS OF STATE BASED ON NEUTRON STAR OBSERVATIONS

Many of the currently available equations of state for core-collapse supernova simulations give large neutron star radii and do not provide large enough neutron star masses, both of which are inconsistent with some recent neutron star observations. In addition, one of the critical uncertainties in the nucleon-nucleon interaction, the nuclear symmetry energy, is not fully explored by the currently available equations of state. In this article, we construct two new equations of state which match recent neutron star observations and provide more flexibility in studying the dependence on nuclear matter properties. The equations of state are also provided in tabular form, covering a wide range in density, temperature, and asymmetry, suitable for astrophysical simulations. These new equations of state are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics with three-flavor Boltzmann neutrino transport. The results are compared with commonly used equations of state in supernova simulations of 11.2 and 40 M ☉ progenitors. We consider only equations of state which are fitted to nuclear binding energies and other experimental and observational constraints. We find that central densities at bounce are weakly correlated with L and that there is a moderate influence of the symmetry energy on the evolution of the electron fraction. The new models also obey the previously observed correlation between the time to black hole formation and the maximum mass of an s = 4 neutron star.

QUARK MATTER IN MASSIVE COMPACT STARS

The recent observation of the pulsar PSR J1614-2230 with a mass of 1.97 ± 0.04 M ☉ gives a strong constraint on the quark and nuclear matter equations of state (EoS). We explore the parameter ranges for a parameterized EoS for quark stars. We find that strange stars, made of absolutely stable strange quark matter, comply with the new constraint only if effects from the strong coupling constant and color-superconductivity are taken into account. Hybrid stars, compact stars with a quark matter core and a hadronic outer layer, can be as massive as 2 M ☉, but only for a significantly limited range of parameters. We demonstrate that the appearance of quark matter in massive stars crucially depends on the stiffness of the nuclear matter EoS. We show that the masses of hybrid stars stay below the ones of hadronic and pure quark stars, due to the softening of the EoS at the quark-hadron phase transition.

NEW EQUATIONS OF STATE IN SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE

We discuss three new equations of state (EOS) in core-collapse supernova simulations. The new EOS are based on the nuclear statistical equilibrium model of Hempel and Schaffner-Bielich (HS), which includes excluded volume effects and relativistic mean-field (RMF) interactions. We consider the RMF parameterizations TM1, TMA, and FSUgold. These EOS are implemented into our spherically symmetric core-collapse supernova model, which is based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport. The results obtained for the new EOS are compared with the widely used EOS of H. Shen et al. and Lattimer & Swesty. The systematic comparison shows that the model description of inhomogeneous nuclear matter is as important as the parameterization of the nuclear interactions for the supernova dynamics and the neutrino signal. Furthermore, several new aspects of nuclear physics are investigated: the HS EOS contains distributions of nuclei, including nuclear shell effects. The appearance of light nuclei, e.g., deuterium and tritium, is also explored, which can become as abundant as alphas and free protons. In addition, we investigate the black hole formation in failed core-collapse supernovae, which is mainly determined by the high-density EOS. We find that temperature effects lead to a systematically faster collapse for the non-relativistic LS EOS in comparison with the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows the determination of the maximum mass of proto-neutron stars, if the neutrino signal from such a failed supernova would be measured in the future. This would give a constraint for the nuclear EOS at finite entropy, complementary to observations of cold neutron stars.

Core-collapse supernova explosions triggered by a quark-hadron phase transition during the early post-bounce phase

We explore explosions of massive stars, which are triggered via the quark-hadron phase transition during the early post-bounce phase of core-collapse supernovae. We construct a quark equation of state, based on the bag model for strange quark matter. The transition between the hadronic and the quark phases is constructed applying Gibbs conditions. The resulting quark-hadron hybrid equations of state are used in core-collapse supernova simulations, based on general relativistic radiation hydrodynamics and three-flavor Boltzmann neutrino transport in spherical symmetry. The formation of a mixed phase reduces the adiabatic index, which induces the gravitational collapse of the central protoneutron star (PNS). The collapse halts in the pure quark phase, where the adiabatic index increases. A strong accretion shock forms, which propagates toward the PNS surface. Due to the density decrease of several orders of magnitude, the accretion shock turns into a dynamic shock with matter outflow. This moment defines the onset of the explosion in supernova models that allow for a quark-hadron phase transition, where otherwise no explosions could be obtained. The shock propagation across the neutrinospheres releases a burst of neutrinos. This serves as a strong observable identification for the structural reconfiguration of the stellar core. The ejected matter expands on a short timescale and remains neutron-rich. These conditions might be suitable for the production of heavy elements via the r-process. The neutron-rich material is followed by proton-rich neutrino-driven ejecta in the later cooling phase of the PNS where the νp-process might occur.

Equations of state for supernovae and compact stars

A review is given of 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 quarks. As the development of an EoS requires joint efforts from many directions, different theoretical approaches are considered and relevant experimental and observational constraints which provide insights for future research are discussed. Finally, results from applications of the discussed EoS models are summarized.

Neutrino spectra evolution during protoneutron star deleptonization

The neutrino-driven wind, which occurs after the onset of a core-collapse supernova explosion, has long been considered as the possible site for the synthesis of heavy

Symmetry energy impact in simulations of core-collapse supernovae

r

Outer crust of nonaccreting cold neutron stars

-process elements in the Universe. Only recently, it has been possible to simulate supernova explosions up to