Following a simulation approach of recent publications we explore the viability of the neutrino-heating explosion mechanism in dependence on the spatial dimension. Our results disagree with previous findings. While we also observe that two-dimensional (2D) models explode for lower driving neutrino luminosity than spherically symmetric (1D) models, we do not find that explosions in 3D occur easier and earlier than in 2D. Moreover, we find that the average entropy of matter in the gain layer hardly depends on the dimension and thus is no good diagnostic quantity for the readiness to explode. Instead, mass, integrated entropy, total neutrino-heating rate, and nonradial kinetic energy in the gain layer are higher when models are closer to explosion. Coherent, largescale mass motions as typically associated with the standing accretion-shock instability (SASI) are observed to be supportive for explosions because they drive strong shock expansion and thus enlarge the gain layer. While 2D models with better angular resolution explode clearly more easily, the opposite trend is seen in 3D. We interpret this as a consequence of the turbulent energy cascade, which transports energy from small to large spatial scales in 2D, thus fostering SASI activity. In contrast, the energy flow in 3D is in the opposite direction, feeding fragmentation and vortex motions on smaller scales and thus making the 3D evolution with finer grid resolution more similar to 1D. More favorable conditions for explosions in 3D may therefore be tightly linked to efficient growth of low-order SASI modes including nonaxisymmetric ones.

The relevance of the standing accretion shock instability (SASI) compared to neutrino-driven convection in three-dimensional (3D) supernova-core environments is still highly controversial. Studying a 27 M ⊙ progenitor, we demonstrate, for the first time, that violent SASI activity can develop in 3D simulations with detailed neutrino transport despite the presence of convection. This result was obtained with the Prometheus-Vertex code with the same sophisticated neutrino treatment so far used only in 1D and 2D models. While buoyant plumes initially determine the nonradial mass motions in the postshock layer, bipolar shock sloshing with growing amplitude sets in during a phase of shock retraction and turns into a violent spiral mode whose growth is only quenched when the infall of the Si/SiO interface leads to strong shock expansion in response to a dramatic decrease of the mass accretion rate. In the phase of large-amplitude SASI sloshing and spiral motions, the postshock layer exhibits nonradial deformation dominated by the lowest-order spherical harmonics (ℓ = 1, m = 0, ±1) in distinct contrast to the higher multipole structures associated with neutrino-driven convection. We find that the SASI amplitudes, shock asymmetry, and nonradial kinetic energy in 3D can exceed those of the corresponding 2D case during extended periods of the evolution. We also perform parametrized 3D simulations of a 25 M ⊙ progenitor, using a simplified, gray neutrino transport scheme, an axis-free Yin-Yang grid, and different amplitudes of random seed perturbations. They confirm the importance of the SASI for another progenitor, its independence of the choice of spherical grid, and its preferred growth for fast accretion flows connected to small shock radii and compact proto-neutron stars as previously found in 2D setups.

During the stalled-shock phase of our three-dimensional, hydrodynamical core-collapse simulations with energy-dependent, three-flavor neutrino transport, the lepton-number flux (ν e minusν e ) emerges predominantly in one hemisphere. This novel, spherical-symmetry breaking neutrino-hydrodynamical instability is termed LESA for "Lepton-number Emission Self-sustained Asymmetry." While the individual ν e andν e fluxes show a pronounced dipole pattern, the heavy-flavor neutrino fluxes and the overall luminosity are almost spherically symmetric. Initially, LESA seems to develop stochastically from convective fluctuations. It exists for hundreds of milliseconds or more and persists during violent shock sloshing associated with the standing accretion shock instability. The ν e minusν e flux asymmetry originates predominantly below the neutrinosphere in a region of pronounced proto-neutron star (PNS) convection, which is stronger in the hemisphere of enhanced lepton-number flux. On this side of the PNS, the mass-accretion rate of lepton-rich matter is larger, amplifying the lepton-emission asymmetry, because the spherical stellar infall deflects on a dipolar deformation of the stalled shock. The increased shock radius in the hemisphere of less mass accretion and minimal lepton-number flux (ν e flux maximum) is sustained by stronger convection on this side, which is boosted by stronger neutrino heating due to ν e > ν e . Asymmetric heating thus supports the global deformation despite extremely nonstationary convective overturn behind the shock. While these different elements of the LESA phenomenon form a consistent picture, a full understanding remains elusive at present. There may be important implications for neutrino-flavor oscillations, the neutron-to-proton ratio in the neutrino-heated supernova ejecta, and neutron-star kicks, which remain to be explored.

Interactions with neutrons and protons play a crucial role for the neutrino opacity of matter in the supernova core. Their current implementation in many simulation codes, however, is rather schematic and ignores not only modifications for the correlated nuclear medium of the nascent neutron star, but also free-space corrections from nucleon recoil, weak magnetism, or strange quarks, which can easily add up to changes of several 10% for neutrino energies in the spectral peak. In the Garching supernova simulations with the PROMETHEUS-VERTEX code, such sophistications have been included for a long time except for the strange-quark contributions to the nucleon spin, which affect neutral-current neutrino scattering. We demonstrate on the basis of a 20 M  progenitor star that a moderate strangeness-dependent contribution of g 0.2 a s = -to the axial-vector coupling constant g 1.26 a » can turn an unsuccessful three-dimensional (3D) model into a successful explosion. Such a modification is in the direction of current experimental results and reduces the neutral-current scattering opacity of neutrons, which dominate in the medium around and above the neutrinosphere. This leads to increased luminosities and mean energies of all neutrino species and strengthens the neutrino-energy deposition in the heating layer. Higher nonradial kinetic energy in the gain layer signals enhanced buoyancy activity that enables the onset of the explosion at ∼300 ms after bounce, in contrast to the model with vanishing strangeness contributions to neutrinonucleon scattering. Our results demonstrate the close proximity to explosion of the previously published, unsuccessful 3D models of the Garching group.

We present self-consistent, axisymmetric core-collapse supernova simulations performed with the PROMETHEUS-VERTEX code for 18 pre-supernova models in the range of 11-28 M e , including progenitors recently investigated by other groups. All models develop explosions, but depending on the progenitor structure, they can be divided into two classes. With a steep density decline at the Si/Si-O interface, the arrival of this interface at the shock front leads to a sudden drop of the mass-accretion rate, triggering a rapid approach to explosion. With a more gradually decreasing accretion rate, it takes longer for the neutrino heating to overcome the accretion ram pressure and explosions set in later. Early explosions are facilitated by high mass-accretion rates after bounce and correspondingly high neutrino luminosities combined with a pronounced drop of the accretion rate and ram pressure at the Si/Si-O interface. Because of rapidly shrinking neutron star radii and receding shock fronts after the passage through their maxima, our models exhibit short advection timescales, which favor the efficient growth of the standing accretion-shock instability. The latter plays a supportive role at least for the initiation of the reexpansion of the stalled shock before runaway. Taking into account the effects of turbulent pressure in the gain layer, we derive a generalized condition for the critical neutrino luminosity that captures the explosion behavior of all models very well. We validate the robustness of our findings by testing the influence of stochasticity, numerical resolution, and approximations in some aspects of the microphysics.

The neutrino emission characteristics of the first full-scale three-dimensional supernova simulations with sophisticated three-flavor neutrino transport for three models with masses 11.2, 20 and 27 M are evaluated in detail. All the studied progenitors show the expected hydrodynamical instabilities in the form of large-scale convective overturn. In addition, the recently identified LESA phenomenon (lepton-number emission self-sustained asymmetry) is generic for all our cases. Pronounced SASI (standing accretion-shock instability) activity appears in the 20 and 27 M cases, partly in the form of a spiral mode, inducing large but direction and flavor-dependent modulations of neutrino emission. These modulations can be clearly identified in the existing IceCube and future Hyper-Kamiokande detectors, depending on distance and detector location relative to the main SASI sloshing direction.

The first full-scale three-dimensional (3D) core-collapse supernova (SN) simulations with sophisticated neutrino transport show pronounced effects of the standing accretion shock instability (SASI) for two high-mass progenitors (20 and 27 M⊙). In a low-mass progenitor (11.2 M⊙), large-scale convection is the dominant nonradial hydrodynamic instability in the postshock accretion layer. The SASI-associated modulation of the neutrino signal (80 Hz in our two examples) will be clearly detectable in IceCube or the future Hyper-Kamiokande detector, depending on progenitor properties, distance, and observer location relative to the main SASI sloshing direction. The neutrino signal from the next galactic SN can, therefore, diagnose the nature of the hydrodynamic instability.PACS numbers: 97.60. Bw, 14.60.Lm Introduction.-Bethe and Wilson's delayed neutrinodriven explosion mechanism [1] remains the standard core-collapse SN paradigm [2]. At core bounce a shock wave forms, stalls after reaching 100-200 km, and is revived by neutrino heating after tens to hundreds of ms, depending on progenitor properties and accretion rate of stellar matter that continues to collapse. One modern key ingredient to this scenario is its inherent multidimensional nature inferred from observed SN asymmetries [3] and from parametric and self-consistent 2D and 3D hydrodynamical simulations [4][5][6][7]. During the accretion phase, large-scale convective overturn develops in the neutrino-heated postshock layer [8] and the standing accretion shock instability (SASI) can arise, involving global dipolar and quadrupolar deformation and sloshing motions of the shock front [9,10] as well as spiral modes [11][12][13][14][15]. The next galactic SN may reveal these effects in gravitational waves [16][17][18][19] and in neutrino flux variations [20,21].Most SN investigations of convection and SASI have relied on axisymmetric simulations where sloshing motions are constrained to the symmetry axis [16,[22][23][24][25][26][27]. Several recent 3D models have treated neutrino heating and cooling in the SN core in various approximations [28][29][30][31][32][33][34]. They found SASI sloshing motions with considerably reduced amplitudes and stochastically changing direction or no clear SASI signature at all. Buoyancydriven convection was concluded to dominate post-shock turbulence and SASI to be a minor feature of SN dynamics at best [34][35][36]. However, self-consistent, 2D, general relativistic simulations with sophisticated neutrino transport suggest that a genuine SASI remains possible if the shock stagnation radius is sufficiently small [25]. SASI development may depend on both, progenitor properties and the exact behavior of the stalled shock, which requires reliable neutrino transport. So the importance of the SASI relative to neutrino-driven convection remains controversial. Therefore it is remarkable that the first 3D simulation with detailed neutrino transport (a 27 M ⊙ model) shows violent SASI activity [15].SASI activity strongly modulates the accr...

Core-collapse supernovae are among the most fascinating phenomena in astrophysics and provide a formidable challenge for theoretical investigation. They mark the spectacular end of the lives of massive stars and, in an explosive eruption, release as much energy as the sun produces during its whole life. A better understanding of the astrophysical role of supernovae as birth sites of neutron stars, black holes, and heavy chemical elements, and more reliable predictions of the observable signals from stellar death events are tightly linked to the solution of the long-standing puzzle how collapsing stars achieve to explode. In this article our current knowledge of the processes that contribute to the success of the explosion mechanism are concisely reviewed. After a short overview of the sequence of stages of stellar core-collapse events, the general properties of the progenitor-dependent neutrino emission will be briefly described. Applying sophisticated neutrino transport in axisymmetric (2D) simulations with general relativity as well as in simulations with an approximate treatment of relativistic effects, we could find successful neutrino-driven explosions for a growing set of progenitor stars. First results of three-dimensional (3D) models have been obtained, and magnetohydrodynamic simulations demonstrate that strong initial magnetic fields in the pre-collapse core can foster the onset of neutrino-powered supernova explosions even in nonrotating stars. These results are discussed in the context of the present controversy about the value of 2D simulations for exploring the supernova mechanism in realistic 3D environments, and they are interpreted against the background of the current disagreement on the question whether the standing accretion shock instability (SASI) or neutrino-driven convection is the crucial agency that supports the onset of the explosion.Subject Index: 483, 421, 423, 415, 451, 452, 242 §1. Supernova theory in a nutshell Massive stars in the range between ∼8 M ⊙ and several 10 M ⊙ develop lowentropy cores, in which relativistic electrons dominate the pressure. Heavy nuclei yield only a small, though important, contribution to providing stabilization against the inward pull of gravity. The core consists of the final products of the star's nuclear burning history. It is surrounded by concentric shells that, from outside inward, contain the successively heavier ashes of all previous burning stages (Fig. 1).Shell burning leads to a continuous growth of the mass of the central core until gravitational instability finally sets in. At this time the core resembles a hot white dwarf close to its maximum mass of the order of the Chandrasekhar mass. It has typeset using PTPT E X.cls Ver.0.9 * ) The effective (dynamically relevant) adiabatic index is defined as the logarithmic density derivative of the pressure, (∂ ln P/∂ ln ρ) m , along a fluid element's trajectory, averaged over the volume of the collapsing core. It governs the transition to gravitational instability and the collapse dynamics. 1) ...