Approaching the dynamics of hot nucleons in supernovae

All recent numerical simulations agree that stars in the main sequence mass range of 9-40 solar masses do not produce a prompt hydrodynamic ejection of the outer layers after core collapse and bounce. Rather they suggest that stellar core collapse and supernova explosion are dynamically distinct astrophysical events, separated by an unspectacular accretion phase of at least ~40 ms duration. As long as the neutrinospheres remain convectively stable, the explosion dynamics is determined by the neutrons, protons, electrons and neutrinos in the layer of impact-heated matter piling up on the protoneutron star. The crucial role of neutrino transport in this regime has been emphasized in many previous investigations. Here, we search for efficient means to address the role of magnetic fields and fluid instabilities in stellar core collapse and the postbounce phase.Comment: 4 pages, contribution to Nuclei in the Cosmos VIII, Jul. 19-23, submitted to Nucl. Phys.

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 to the RMF EOS. We deduce a new correlation for the time until black hole formation, which allows to determine 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.Comment: 26 pages, 17 figures. v3: replaced Fig. 1 with the published one, text unchange

The Innermost Ejecta of Core Collapse Supernovae

We ensure successful explosions (of otherwise non-explosive models) by enhancing the neutrino luminosity via reducing the neutrino scattering cross sections or by increasing the heating efficiency via enhancing the neutrino absorption cross sections in the heating region. Our investigations show that the resulting electron fraction Ye in the innermost ejecta is close to 0.5, in some areas even exceeding 0.5. We present the effects of the resulting values for Ye on the nucleosynthesis yields of the innermost zones of core collapse supernovae.Comment: 4pages, 2figures; contribution to Nuclei In The Cosmos VIII, to appear in Nucl. Phys.

Massive Stars and their Supernovae

Massive stars and their supernovae are prominent sources of radioactive isotopes, the observations of which thus can help to improve our astrophysical models of those. Our understanding of stellar evolution and the final explosive endpoints such as supernovae or hypernovae or gamma-ray bursts relies on the combination of magneto-hydrodynamics, energy generation due to nuclear reactions accompanying composition changes, radiation transport, and thermodynamic properties (such as the equation of state of stellar matter). Nuclear energy production includes all nuclear reactions triggered during stellar evolution and explosive end stages, also among unstable isotopes produced on the way. Radiation transport covers atomic physics (e.g. opacities) for photon transport, but also nuclear physics and neutrino nucleon/nucleus interactions in late phases and core collapse. Here we want to focus on the astrophysical aspects, i.e. a description of the evolution of massive stars and their endpoints, with a special emphasis on the composition of their ejecta (in form of stellar winds during the evolution or of explosive ejecta). Low and intermediate mass stars end their evolution as a white dwarf with an unburned C and O composition. Massive stars evolve beyond this point and experience all stellar burning stages from H over He, C, Ne, O and Si-burning up to core collapse and explosive endstages. In this chapter we discuss the nucleosynthesis processes involved and the production of radioactive nuclei in more detail.Comment: 79 pages; Chapter of "Astronomy with Radioactivities", a book in Springer's 'lecture notes in physics series, Vol. 812, Eds. Roland Diehl, Dieter H. Hartmann, and Nikos Prantzos, to appear in summer 201

A new multi-dimensional general relativistic neutrino hydrodynamics code for core-collapse supernovae. I. Method and code tests in spherical symmetry

We present a new general relativistic (GR) code for hydrodynamic supernova simulations with neutrino transport in spherical and azimuthal symmetry (1D/2D). The code is a combination of the CoCoNuT hydro module, which is a Riemann-solver based, high-resolution shock-capturing method, and the three-flavor, energy-dependent neutrino transport scheme VERTEX. VERTEX integrates the neutrino moment equations with a variable Eddington factor closure computed from a model Boltzmann equation and uses the ray-by-ray plus approximation in 2D, assuming the neutrino distribution to be axially symmetric around the radial direction, and thus the neutrino flux to be radial. Our spacetime treatment employs the ADM 3+1 formalism with the conformal flatness condition for the spatial three-metric. This approach is exact in 1D and has been shown to yield very accurate results also for rotational stellar collapse. We introduce new formulations of the energy equation to improve total energy conservation in relativistic and Newtonian hydro simulations with Eulerian finite-volume codes. Moreover, a modified version of the VERTEX scheme is developed that simultaneously conserves energy and lepton number with better accuracy and higher numerical stability. To verify our code, we conduct a series of tests, including a detailed comparison with published 1D results for stellar core collapse. Long-time simulations of proto-neutron star cooling over several seconds both demonstrate the robustness of the new CoCoNuT-VERTEX code and show the approximate treatment of GR effects by means of an effective gravitational potential as in PROMETHEUS-VERTEX to be remarkably accurate in 1D. (abridged)Comment: 36 pages, 19 eps figures; submitted to ApJS (minor revisions; some typos corrected

Stellar evolution of massive stars at very low metallicities

Recently, measurements of abundances in extremely metal poor (EMP) stars have brought new constraints on stellar evolution models. In an attempt to explain the origin of the abundances observed, we computed pre--supernova evolution models, explosion models and the related nucleosynthesis. In this paper, we start by presenting the pre-SN models of rotating single stars with metallicities ranging from solar metallicity down to almost metal free. We then review key processes in core-collapse and bounce, before we integrate them in a simplistic parameterization for 3D MHD models, which are well underway and allow one to follow the evolution of the magnetic fields during collapse and bounce. Finally, we present explosive nucleosynthesis results including neutrino interactions with matter, which are calculated using the outputs of the explosion models. The main results of the pre-SN models are the following. First, primary nitrogen is produced in large amount in models with an initial metallicity $Z=10^{-8}$. Second, at the same metallicity of $Z=10^{-8}$ and for models with an initial mass larger than about 60 Mo, rotating models may experience heavy mass loss (up to more than half of the initial mass of the star). The chemical composition of these winds can qualitatively reproduce the abundance patterns observed at the surface of carbon-rich EMP stars. Explosive nucleosynthesis including neutrino-matter interactions produce improved abundances for iron group elements, in particular for scandium and zinc. It also opens the way to a new neutrino and proton rich process ($\nu$p-process) able to contribute to the nucleosynthesis of elements with A > 64. (Abridged)Comment: 29 pages, 10 figures, Reviews of Modern Astronomy 19, proceedings for 79th Annual Scientific Meeting of the Deutsche Astronomische Gesellschaft 200

Multi-dimensional Core-Collapse Supernova Simulations with Neutrino Transport

We present multi-dimensional core-collapse supernova simulations using the Isotropic Diffusion Source Approximation (IDSA) for the neutrino transport and a modified potential for general relativity in two different supernova codes: FLASH and ELEPHANT. Due to the complexity of the core-collapse supernova explosion mechanism, simulations require not only high-performance computers and the exploitation of GPUs, but also sophisticated approximations to capture the essential microphysics. We demonstrate that the IDSA is an elegant and efficient neutrino radiation transfer scheme, which is portable to multiple hydrodynamics codes and fast enough to investigate long-term evolutions in two and three dimensions. Simulations with a 40 solar mass progenitor are presented in both FLASH (1D and 2D) and ELEPHANT (3D) as an extreme test condition. It is found that the black hole formation time is delayed in multiple dimensions and we argue that the strong standing accretion shock instability before black hole formation will lead to strong gravitational waves.Comment: 3 pages, proceedings for Nuclei in the Cosmos XIV, Niigata, Japan (2016

Two-Dimensional Core-Collapse Supernova Simulations with the Isotropic Diffusion Source Approximation for Neutrino Transport

The neutrino mechanism of core-collapse supernova is investigated via non-relativistic, two-dimensional (2D), neutrino radiation-hydrodynamic simulations. For the transport of electron flavor neutrinos, we use the interaction rates defined by Bruenn (1985) and the isotropic diffusion source approximation (IDSA) scheme, which decomposes the transported particles into trapped particle and streaming particle components. Heavy neutrinos are described by a leakage scheme. Unlike the "ray-by-ray" approach in some other multi-dimensional supernova models, we use cylindrical coordinates and solve the trapped particle component in multiple dimensions, improving the proto-neutron star resolution and the neutrino transport in angular and temporal directions. We provide an IDSA verification by performing 1D and 2D simulations with 15 and 20 $M_\odot$ progenitors from Woosley et al.~(2007) and discuss the difference of our IDSA results with those existing in the literature. Additionally, we perform Newtonian 1D and 2D simulations from prebounce core collapse to several hundred milliseconds postbounce with 11, 15, 21, and 27 $M_\odot$ progenitors from Woosley et al.~(2002) with the HS(DD2) equation of state. General relativistic effects are neglected. We obtain robust explosions with diagnostic energies $E_{\rm dig} \gtrsim 0.1- 0.5$~B for all considered 2D models within approximately $100-300$ milliseconds after bounce and find that explosions are mostly dominated by the neutrino-driven convection, although standing accretion shock instabilities are observed as well. We also find that the level of electron deleptonization during collapse dramatically affect the postbounce evolution, e.g.~the ignorance of neutrino-electron scattering during collapse will lead to a stronger explosion.Comment: 23 pages. Accepted for publication in Ap

The isotropic diffusion source approximation for supernova neutrino transport

Astrophysical observations originate from matter that interacts with radiation or transported particles. We develop a pragmatic approximation in order to enable multi-dimensional simulations with basic spectral radiative transfer when the computational resources are not sufficient to solve the complete Boltzmann transport equation. The distribution function of the transported particles is decomposed into trapped and streaming particle components. Their separate evolution equations are coupled by a source term that converts trapped particles into streaming particles. We determine this source term by requiring the correct diffusion limit. For a smooth transition to the free streaming regime, this 'diffusion source' is limited by the matter emissivity. The resulting streaming particle emission rates are integrated over space to obtain the streaming particle flux. A geometric estimate of the flux factor is used to convert the particle flux to the streaming particle density. The efficiency of the scheme results from the freedom to use different approximations for each particle component. In supernovae, reactions with trapped particles on fast time scales establish equilibria that reduce the number of primitive variables required to evolve the trapped particle component. On the other hand, a stationary-state approximation facilitates the treatment of the streaming particle component. Different approximations may apply in applications to stellar atmospheres, star formation, or cosmological radiative transfer. We compare the isotropic diffusion source approximation with Boltzmann neutrino transport of electron flavour neutrinos in spherically symmetric supernova models and find good agreement. An extension of the scheme to the multi-dimensional case is also discussed.Comment: revised version, 19 pages, 10 figures, submitted to Ap

Hauteurs de sous-espaces sur les corps non commutatifs

We study heights of subspaces of D N where D is a finite-dimensional rational division algebra and N a positive integer. We define them in terms of volumes of Euclidean lattices by extending a formula of W. Schmidt so that we recover the classical height if D is commutative. We review basic properties, prove a Siegel Lemma over D, a duality theorem and a new formula for the degree of certain abelian varieties. We further give matrix versions and compare our notion with the height defined through algebraic groups by J. Franke, Y. Manin and Y. Tschinke