H.-Th. Janka

Theory of core-collapse supernovae

Advances in our understanding and the modeling of stellar core-collapse and supernova explosions over the past 15 years are reviewed, concentrating on the evolution of hydrodynamical simulations, the description of weak interactions and nuclear equation of state effects, and new insights into the nucleosynthesis occurring in the early phases of the explosion, in particular the neutrino-p process. The latter is enabled by the proton-richness of the early ejecta, which was discovered because of significant progress has been made in the treatment of neutrino transport and weak interactions. This progress has led to a new generation of sophisticated Newtonian and relativistic hydrodynamics simulations in spherical symmetry. Based on these, it is now clear that the prompt bounce-shock mechanism is not the driver of supernova explosions, and that the delayed neutrino-heating mechanism can produce explosions without the aid of multi-dimensional processes only if the progenitor star has an ONeMg core inside a very dilute He-core, i.e., has a mass in the 8–10 M⊙ range. Hydrodynamic instabilities of various kinds have indeed been recognized to occur in the supernova core and to be of potential importance for the explosion. Neutrino-driven explosions, however, have been seen in two-dimensional simulations with sophisticated neutrino transport so far only when the star has a small iron core and low density in the surrounding shells as being found in stars near 10–11 M⊙. The explosion mechanism of more massive progenitors is still a puzzle. It might involve effects of three-dimensional hydrodynamics or might point to the relevance of rapid rotation and magnetohydrodynamics, or to still incompletely explored properties of neutrinos and the high-density equation of state. Hardly any other astrophysical event is as complex and physically diverse as the death of massive stars in a gravitational collapse and subsequent supernova explosion. All four known forces of nature are involved and play an important role in extreme regimes of conditions. Relativistic plasma dynamics in a strong gravitational field sets the stage, weak interactions govern the energy and lepton number loss of the system via the transport of neutrinos from regions of very high opacities to the free-streaming regime, electromagnetic and strong interactions determine the thermodynamic properties, and nuclear and weak interactions change the composition of the stellar gas. Supernova explosions thus offer a fascinating playground of physics on most different scales of length and time and also provide a testbed for new or exotic phenomena. Naturally, these spectacular astrophysical events have attracted — and have deserved — the interest and attention of researchers with very different backgrounds. To the advantage of the field, also Hans Bethe has preserved for many years his interest in the large diversity of physics problems posed by supernovae.

Energy Input and Mass Redistribution by Supernovae in the Interstellar Medium

We present the results of numerical studies of supernova remnant evolution and its effects on galactic and globular cluster evolution. We show that parameters such as the density and the metallicity of the environment significantly influence the evolution of the remnant and thus change its effects on the global environment (e.g., globular clusters, galaxies) as a source of thermal and kinetic energy. We conducted our studies using a one-dimensional hydrodynamics code, in which we implemented a metallicity-dependent cooling function. Global time-dependent quantities such as the total kinetic and thermal energies and the radial extent are calculated for a grid of parameter sets. The quantities calculated are the total energy, the kinetic energy, the thermal energy, the radial extent, and the mass. We distinguished between the hot, rarefied bubble and the cold, dense shell, since these two phases are distinct in their roles in a gas-stellar system. We also present power-law fits to those quantities as a function of environmental parameters after the extensive cooling has ceased. The power-law fits enable simple incorporation of improved supernova energy input and matter redistribution (including the effect of the local conditions) in galactic/globular cluster models. Our results for the energetics of supernova remnants in the late stages of their expansion give total energies ranging from ≈ 9 × 1049 to ≈ 3 × 1050 ergs, with a typical case being ≈ 1050 ergs, depending on the surrounding environment. About 8.5 × 1049 ergs of this energy can be found in the form of kinetic energy. Supernovae play an important role in the evolution of the interstellar medium and galaxies as a whole, providing mechanisms for kinetic energy input and for phase transitions of the interstellar medium. However, we have found that the total energy input per supernova is about 1 order of magnitude smaller than the initial explosion energy.

Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods

Accurate neutrino transport has been built into spherically symmetric simulations of stellar core collapse and postbounce evolution. The results of such simulations agree that spherically symmetric models with standard microphysical input fail to explode by the delayed, neutrino-driven mechanism. Independent groups implemented fundamentally different numerical methods to tackle the Boltzmann neutrino transport equation. Here we present a direct and detailed comparison of such neutrino radiation-hydrodynamics simulations for two codes, AGILE-BOLTZTRAN of the Oak Ridge-Basel group and VERTEX of the Garching group. The former solves the Boltzmann equation directly by an implicit, general relativistic discrete-angle method on the adaptive grid of a conservative implicit hydrodynamics code with second-order TVD advection. In contrast, the latter couples a variable Eddington factor technique with an explicit, moving-grid, conservative high-order Riemann solver with important relativistic effects treated by an effective gravitational potential. The presented study is meant to test our neutrino radiation-hydrodynamics implementations and to provide a data basis for comparisons and verifications of supernova codes to be developed in the future. Results are discussed for simulations of the core collapse and postbounce evolution of a 13 M☉ star with Newtonian gravity and a 15 M☉ star with relativistic gravity.

Pulsar Recoil by Large-Scale Anisotropies in Supernova Explosions

Assuming that the neutrino luminosity from the neutron star core is sufficiently high to drive supernova explosions by the neutrino-heating mechanism, we show that low-mode (l=1,2) convection can develop from random seed perturbations behind the shock. A slow onset of the explosion is crucial, requiring the core luminosity to vary slowly with time, in contrast to the burstlike exponential decay assumed in previous work. Gravitational and hydrodynamic forces by the globally asymmetric supernova ejecta were found to accelerate the remnant neutron star on a time scale of more than a second to velocities above 500 km s(-1), in agreement with observed pulsar proper motions.

Three-dimensional Simulations of Mixing Instabilities in Supernova Explosions

We present the first three-dimensional (3D) simulations of the large-scale mixing that takes place in the shock-heated stellar layers ejected in the explosion of a 15.5 M ? blue supergiant star. The blast is initiated and powered by neutrino-energy deposition behind the stalled shock by means of choosing sufficiently high neutrino luminosities from the contracting, nascent neutron star, whose high-density core is excised and replaced by a retreating inner grid boundary. The outgoing supernova shock is followed beyond its breakout from the stellar surface more than 2 hr after the core collapse. Violent convective overturn in the post-shock layer causes the explosion to start with significant large-scale asphericity, which acts as a trigger of the growth of Rayleigh-Taylor instabilities at the composition interfaces of the exploding star. Despite the absence of a strong Richtmyer-Meshkov instability at the H/He interface, which only a largely deformed shock could instigate, deep inward mixing of hydrogen is found as well as fast-moving, metal-rich clumps penetrating with high velocities far into the hydrogen envelope of the star as observed, for example, in the case of Supernova 1987A. Also individual clumps containing a sizeable fraction of the ejected iron-group elements (up to several 10?3 M ?) are obtained in some models. The metal core of the progenitor is partially turned over with nickel-dominated fingers overtaking oxygen-rich bullets and both nickel and oxygen moving well ahead of the material from the carbon layer. Comparing with corresponding two-dimensional (axially symmetric; 2D) calculations, we determine the growth of the Rayleigh-Taylor fingers to be faster, the deceleration of the dense metal-carrying clumps in the helium and hydrogen layers to be reduced, the asymptotic clump velocities in the hydrogen shell to be higher (up to ~4500 km s?1 for the considered progenitor and an explosion energy of 1051 erg, instead of 2000 km s?1 in 2D), and the outward radial mixing of heavy elements and inward mixing of hydrogen to be more efficient in 3D than in 2D. We present a simple argument that explains these results as a consequence of the different action of drag forces on moving objects in the two geometries.

Instability of a stalled accretion shock: evidence for the advective-acoustic cycle

We analyze the linear stability of a stalled accretion shock in a perfect gas with a parametrized cooling function L ∝ ρ �−� P � . The instability is dominated by the l = 1 mode if the shock radius exceeds 2 −3 times the accretor radius, depending on the parameters of the cooling function. The growth rate and oscillation period are comparable to those observed in the numerical simulations of Blondin & Mezzacappa (2006). The instability mechanism is analyzed by separately measuring the efficiencies of the purely acoustic cycle and the advective-acoustic cycle. These efficiencies are estimated directly from the eigenspectrum, and also through a WKB analysis in the high frequency limit. Both methods prove that the advective-acoustic cycle is unstable, and that the purely acoustic cycle is stable. Extrapolating these results to low frequency leads us to interpret the dominant mode as an advective-acoustic instability, different from the purely acoustic interpretation of Blondin & Mezzacappa (2006). A simplified characterization of the instability is proposed, based on an advectiveacoustic cycle between the shock and the radius r∇ where the velocity gradients of the stationary flow are strongest. The importance of the coupling region in this mechanism calls for a better understanding of the conditions for an efficient advective-acoustic coupling in a decelerated, nonadiabatic flow, in order to extend these results to core-collapse supernovae. Subject headings: accretion – hydrodynamics – instabilities – shock waves – supernovae

Multidimensional supernova simulations with approximative neutrino transport II. Convection and the advective-acoustic cycle in the supernova core

Performing two-dimensional hydrodynamic simulations including a detailed treatment of the equation of state of the stellar plasma and for the neutrino transport and interactions, we investigate here the interplay between different kinds of non-radial hydrodynamic instabilities that can play a role during the postbounce accretion phase of collapsing stellar cores. The convective mode of instability, which is driven by the negative entropy gradients caused by neutrino heating or by variations in the shock strength in transient phases of shock expansion and contraction, can be identified clearly by the development of typical Rayleigh-Taylor mushrooms. However, in those cases where the gas in the postshock region is rapidly advected towards the gain radius, the growth of such a buoyancy instability can be suppressed. In this situation the shock and postshock flow can nevertheless develop non-radial asymmetry with an oscillatory growth in the amplitude. This phenomenon has been termed “standing (or spherical) accretion shock instability” (SASI). It is shown here that the SASI oscillations can trigger convective instability, and like the latter, they lead to an increase in the average shock radius and in the mass of the gain layer. Both hydrodynamic instabilities in combination stretch the advection time of matter accreted through the neutrino-heating layer and thus enhance the neutrino energy deposition in support of the neutrino-driven explosion mechanism. A rapidly contracting and more compact nascent neutron star turns out to be favorable for explosions, because the accretion luminosity and neutrino heating are greater and the growth rate of the SASI is higher. Moreover, we show that the oscillation period of the SASI observed in our simulations agrees with the one estimated for the advective-acoustic cycle (AAC), in which perturbations are carried by the accretion flow from the shock to the neutron star and pressure waves close an amplifying global feedback loop. A variety of other features in our models, as well as differences in their behavior, can also be understood on the basis of the AAC hypothesis. The interpretation of the SASI in our simulations as a purely acoustic phenomenon, however, appears difficult.

Neutrino-driven convection versus advection in core collapse supernovae

A toy model is analyzed in order to evaluate the linear stability of the gain region immediately behind a stalled accretion shock, after core bounce. This model demonstrates that a negative entropy gradient is not sufficient to warrant linear instability. The stability criterion is governed by the ratio χ of the advection time through the gain region divided by the local timescale of buoyancy. The gain region is linearly stable if χ 3, perturbations are unstable in a limited range of horizontal wavelengths centered around twice the vertical size H of the gain region. The threshold horizontal wavenumbers kmin and kmax follow simple scaling laws such that Hkmin ∝ 1/χ and Hkmax ∝ χ. The convective stability of the l = 1 mode in spherical accretion is discussed, in relation with the asymmetric explosion of core-collapse supernovae. The advective stabilization of long-wavelength perturbations weakens the possible influence of convection alone on a global l = 1 mode.

Nucleosynthesis and Clump Formation in a Core-Collapse Supernova

High-resolution two-dimensional simulations were performed for the first 5 minutes of the evolution of a core-collapse supernova explosion in a 15 M middle dot in circle blue supergiant progenitor. The computations start shortly after bounce and include neutrino-matter interactions by using a lightbulb approximation for the neutrinos and a treatment of the nucleosynthesis due to explosive silicon and oxygen burning. We find that newly formed iron-group elements are distributed throughout the inner half of the helium core by Rayleigh-Taylor instabilities at the (Ni + Si)/O and (C + O)/He interfaces, seeded by convective overturn during the early stages of the explosion. Fast-moving nickel mushrooms with velocities up to approximately 4000 km s-1 are observed. This offers a natural explanation for the mixing required in light-curve and spectral synthesis studies of Type Ib explosions. A continuation of the calculations to later times, however, indicates that the iron velocities observed in SN 1987A cannot be reproduced because of a strong deceleration of the clumps in the dense shell left behind by the shock at the He/H interface.

Exploring the relativistic regime with Newtonian hydrodynamics: an improved effective gravitational potential for supernova simulations

We investigate the possibility approximating relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic code. Different modifications of a previously introduced effective relativistic potential are discussed. Corresponding hydrostatic solutions are compared with solutions of the TOV equations, and hydrodynamic simulations with two different codes are compared with fully relativistic results. One code is applied for one- and two-dimensional calculations with a simple equation of state and employs either the modified effective relativistic potential in a Newtonian framework or solves the general relativistic field equations under the assumption of the conformal flatness condition (CFC) for the three-metric. The second code allows for full-scale supernova runs including a microphysical equation of state and neutrino transport based on the solution of the Boltzmann equation and its moments equations. We present prescriptions for the effective relativistic potential for self-gravitating fluids to he used in Newtonian codes, which produce excellent agreement with fully relativistic solutions in spherical symmetry, leading to significant improvements compared to previously published approximations. Moreover, they also approximate qualitatively well relativistic solutions for models with rotation.