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We study turbulent convection during the core helium flash close to its peak by comparing the results of two and three-dimensional hydrodynamic simulations. We use a multidimensional Eulerian hydrodynamics code based on state-of-the-art numerical techniques to simulate the evolution of the helium core of a $1.25 M_{\odot}$ Pop I star. Our three-dimensional hydrodynamic simulations of the evolution of a star during the peak of the core helium flash do not show any explosive behavior. The convective flow patterns developing in the three-dimensional models are structurally different from those of the corresponding two-dimensional models, and the typical convective velocities are smaller than those found in their two-dimensional counterparts. Three-dimensional models also tend to agree better with the predictions of mixing length theory. Our hydrodynamic simulations show the presence of turbulent entrainment that results in a growth of the convection zone on a dynamic time scale. Contrary to mixing length theory, the outer part of the convection zone is characterized by a sub-adiabatic temperature gradient., Comment: 19 pages, 18 figures

We investigate the hydrodynamics of the core helium flash near its peak. Past research concerned with the dynamics of this event is inconclusive. However, the most recent multidimensional hydrodynamic studies suggest a quiescent behavior and seem to rule out an explosive scenario. Previous work indicated, that depending on initial conditions, employed turbulence models, grid resolution, and dimensionality of the simulation, the core helium flash leads either to the disruption of a low-mass star or to a quiescent quasi-hydrostatic evolution. We try to clarify this issue by simulating the evolution with advanced numerical methods and detailed microphysics. Assuming spherical or axial symmetry, we simulate the evolution of the helium core of a $1.25 M_{\odot}$ star with a metallicity Z=0.02 during the core helium flash at its peak with a grid-based hydrodynamics code. We find that the core helium flash neither rips the star apart, nor that it significantly alters its structure, as convection plays a crucial role in keeping the star in hydrostatic equilibrium. In addition, our simulations show the presence of overshooting, which implies new predictions concerning mixing of chemical species in red giants., Comment: 13 pages, 23 figures

By 2D hydrodynamic simulations including a detailed equation of state and neutrino transport, we investigate the interplay between different non-radial hydrodynamic instabilities that play a role during the postbounce accretion phase of collapsing stellar cores. The convective mode of instability, which is driven by negative entropy gradients caused by neutrino heating or by time variations of the shock strength, can be identified clearly by the development of typical Rayleigh-Taylor mushrooms. However, in 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 such a situation the shocked flow nevertheless can develop non-radial asymmetry with an oscillatory growth of the amplitude. This phenomenon has been termed ``standing 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 of the average shock radius and of the mass in the gain layer. Both hydrodynamic instabilities in combination stretch the advection time of matter 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 NS turns out to be favorable for explosions, because the accretion luminosity and neutrino heating are larger and the growth rate of the SASI is higher. Moreover, we show that the oscillation period of the SASI and a variety of other features in our simulations agree with estimates 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. (abridged), Comment: 23 pages, 20 figures; revised version with extended Sect.5, accepted by Astronomy & Astrophysics; high-resolution images can be obtained upon request

By means of two-dimensional (2D) simulations we study hydrodynamic instabilities during the first seconds of neutrino-driven supernova explosions, using a PPM hydrodynamics code, supplemented with a gray, non-equilibrium approximation of radial neutrino transport. We consider three 15 solar mass progenitors with different structures and one rotating model, in which we replace the dense core of the newly formed neutron star (NS) by a contracting inner grid boundary, and trigger neutrino-driven explosions by systematically varying the neutrino fluxes emitted at this boundary. Confirming more idealized studies as well as supernova simulations with spectral transport, we find that random seed perturbations can grow by hydrodynamic instabilities to a globally asymmetric mass distribution, leading to a dominance of dipole (l=1) and quadrupole (l=2) modes in the explosion ejecta. Anisotropic gravitational and hydrodynamic forces are found to accelerate the NS on a timescale of 2-3 seconds. Since the explosion anisotropies develop chaotically, the magnitude of the corresponding kick varies stochastically in response to small differences in the fluid flow. Our more than 70 models separate into two groups, one with high and the other with low NS velocities and accelerations after 1s of post-bounce evolution, depending on whether the l=1 mode is dominant in the ejecta or not. This leads to a bimodality of the distribution when the NS velocities are extrapolated to their terminal values. The fast group has an average velocity of about 500 km/s and peak values in excess of 1000 km/s. Establishing a link to the measured distribution of pulsar velocities, however, requires a much larger set of calculations and ultimately 3D modeling. (abridged), Comment: 40 pages, 28 figures; significantly shortened and revised version according to referee's comments; accepted by Astronomy & Astrophysics

1D and 2D supernova simulations for stars between 11 and 25 solar masses are presented, making use of the Prometheus/Vertex neutrino-hydrodynamics code, which employs a full spectral treatment of the neutrino transport. Multi-dimensional transport aspects are treated by the ``ray-by-ray plus'' approximation described in Paper I. Our set of models includes a 2D calculation for a 15 solar mass star whose iron core is assumed to rotate rigidly with an angular frequency of 0.5 rad/s before collapse. No important differences were found depending on whether random seed perturbations for triggering convection are included already during core collapse, or whether they are imposed on a 1D collapse model shortly after bounce. Convection below the neutrinosphere sets in about 40 ms p.b. at a density above 10**12 g/cm^3 in all 2D models, and encompasses a layer of growing mass as time goes on. It leads to a more extended proto-neutron star structure with accelerated lepton number and energy loss and significantly higher muon and tau neutrino luminosities, but reduced mean energies of the radiated neutrinos, at times later than ~100 ms p.b. In case of an 11.2 solar mass star we find that low (l = 1,2) convective modes cause a probably rather weak explosion by the convectively supported neutrino-heating mechanism after ~150 ms p.b. when the 2D simulation is performed with a full 180 degree grid, whereas the same simulation with 90 degree wedge fails to explode like all other models. This sensitivity demonstrates the proximity of our 2D models to the borderline between success and failure, and stresses the need of simulations in 3D, ultimately without the axis singularity of a polar grid. (abridged), Comment: 42 pages, 44 figures; revised according to referee comments; accepted to Astronomy & Astrophysics

Two-dimensional simulations of strongly anisotropic supernova explosions of a nonrotating 15 solar mass blue supergiant progenitor are presented, which follow the hydrodynamic evolution from times shortly after shock formation until hours later. It is shown that explosions which around the time of shock revival are dominated by low-order unstable modes (i.e. by a superposition of the l=2 and l=1 modes, in which the former is strongest), are consistent with all major observational features of SN 1987A, in contrast to models which show high-order mode perturbations only and were published in earlier work. Among other items, the low-mode models exhibit final iron-group velocities of up to 3300 km/s, strong mixing at the He/H composition interface, with hydrogen being mixed downward in velocity space to only 500 km/s, and a final prolate anisotropy of the ejecta with a major to minor axis ratio of about 1.6. The success of low-mode explosions with an energy of about 2x10**51 erg to reproduce these observed features is based on two effects: the (by 40%) larger initial maximum velocities of metal-rich clumps compared to our high-mode models, and the initial global deformation of the shock. The latter triggers the growth of a strong Richtmyer-Meshkov instability at the He/H interface that results in a global anisotropy of the inner ejecta at late times (i.e. t > 10000 s), although the shock itself has long become spherical by then. The simulations suggest a coherent picture, which explains the observational data of SN 1987A within the framework of the neutrino-driven explosion mechanism using a minimal set of assumptions. It is therefore argued that other paradigms, which are based on (more) controversial physics, may not be required to explain this event. (abbreviated), Comment: 21 pages, 9 figures; revised version to include referee's comments; Astronomy & Astrophysics, in press; high resolution figures available upon request

Supernova models with a full spectral treatment of the neutrino transport are presented, employing the Prometheus/Vertex neutrino-hydrodynamics code with a ``ray-by-ray plus'' approximation for treating two- (or three-) dimensional problems. The method is described in detail and critically assessed with respect to its capabilities, limitations, and inaccuracies in the context of supernova simulations. In this first paper of a series, 1D and 2D core-collapse calculations for a (nonrotating) 15 M_sun star are discussed, uncertainties in the treatment of the equation of state -- numerical and physical -- are tested, Newtonian results are compared with simulations using a general relativistic potential, bremsstrahlung and interactions of neutrinos of different flavors are investigated, and the standard approximation in neutrino-nucleon interactions with zero energy transfer is replaced by rates that include corrections due to nucleon recoil, thermal motions, weak magnetism, and nucleon correlations. Models with the full implementation of the ``ray-by-ray plus'' spectral transport were found not to explode, neither in spherical symmetry nor in 2D with a 90 degree lateral wedge. The success of previous 2D simulations with grey, flux-limited neutrino diffusion can therefore not be confirmed. Omitting the radial velocity terms in the neutrino momentum equation leads to ``artificial'' explosions by increasing the neutrino energy density in the convective gain layer by about 20--30% and thus the integral neutrino energy deposition in this region by about a factor of two. (abbreviated), Comment: 46 pages plus 13 pages online material; 49 figures; referee's comments included, version accepted by Astronomy & Astrophysics

Two- and three-dimensional simulations demonstrate that hydrodynamic instabilities can lead to low-mode (l=1,2) asymmetries of the fluid flow in the neutrino-heated layer behind the supernova shock. This provides a natural explanation for aspherical mass ejection and for pulsar recoil velocities even in excess of 1000 km/s. We propose that the bimodality of the pulsar velocity distribution might be a consequence of a dominant l=1 mode in case of the fast component, while higher-mode anisotropy characterizes the postshock flow and SN ejecta during the birth of the slow neutron stars. We argue that the observed large asymmetries of supernovae and the measured high velocities of young pulsars therefore do not imply rapid rotation of the iron core of the progenitor star, nor do they require strong magnetic fields to play a crucial role in the explosion. Anisotropic neutrino emission from accretion contributes to the neutron star acceleration on a minor level, and pulsar kicks do not make a good case for non-standard neutrino physics in the nascent neutron star., Comment: 10 pages, 5 figures, full resolution figures available on request or from Preprint P-MPA1651e on MPA web page. In: The Fate of the Most Massive Stars, Proc. Eta Carinae Science Symposium (Jackson Hole, May 2004); revision discusses new Cas A observations

We show by two-dimensional and first three-dimensional simulations of neutrino-driven supernova explosions that low (l=1,2) modes can dominate the flow pattern in the convective postshock region on timescales of hundreds of milliseconds after core bounce. This can lead to large global anisotropy of the supernova explosion and pulsar kicks in excess of 500 km/s., Comment: 3 pages, 2 figures, contribution to Procs. 12th Workshop on Nuclear Astrophysics, Ringberg Castle, March 22-27, 2004

Recent progress in modeling core-collapse supernovae is summarized and set in perspective. Two-dimensional simulations with state-of-the-art treatment of neutrino transport still fail to produce powerful explosions, but evidence is presented that they are very close to success., Comment: 8 pages, 3 figures, high-quality available upon request; contribution to Procs. IAU Coll. 192, "Supernovae", Eds. J.M. Marcaide ad K.W. Weiler, Springer

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 burst-like 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 timescale of more than a second to velocities above 500 km/s, in agreement with observed pulsar proper motions., Comment: 4 ps figures, 2 colored, high-quality available upon request; revised version, accepted by PRL

We investigate explosive nuclear burning in core collapse supernovae by coupling a tracer particle method to one and two-dimensional Eulerian hydrodynamic calculations. Adopting the most recent experimental and theoretical nuclear data, we compute the nucleosynthetic yields for 15 Msun stars with solar metallicity, by post-processing the temperature and density history of advected tracer particles. We compare our results to 1D calculations published in the literature., Comment: 10 pages, to appear in Carnegie Observatories Astrophysics Series, Vol. 4: Origin and Evolution of the Elements, ed. A. McWilliam and M. Rauch (Pasadena: Carnegie Observatories)

Two-dimensional hydrodynamic simulations of stellar core-collapse with and without rotation are presented which for the first time were performed by solving the Boltzmann equation for the neutrino transport including a state-of-the-art description of neutrino interactions. Although convection develops below the neutrinosphere and in the neutrino-heated region behind the supernova shock, the models do not explode. This suggests missing physics, possibly with respect to the nuclear equation of state and weak interactions in the subnuclear regime. However, it might also indicate a fundamental problem of the neutrino-driven explosion mechanism., Comment: PRL submitted; 3 eps figures, 1 colored, high-quality available upon request

Two-dimensional simulations of a Type II and a Type Ib-like supernova explosion are presented that encompass shock revival by neutrino heating, neutrino-driven convection, explosive nucleosynthesis, the growth of Rayleigh-Taylor instabilities, and the propagation of newly formed metal clumps through the exploding star. In both cases we find very high Ni56 velocities of 17000 km/s shortly after shock-revival, and a complete fragmentation of the progenitor's metal core within the first few minutes after core bounce, due to the growth of Rayleigh-Taylor instabilities at the Si/O and (C+O)/He composition interfaces. This leads to the formation of high-velocity, metal-rich clumps which eventually decouple from the flow and move ballistically through the ejecta. Maximum final metal velocities of 3500-5500 km/s and 1200 km/s are obtained for the Type Ib model and the Type II model, respectively. The low maximum metal velocities in the Type II model, which are significantly smaller than those observed in SN 1987A, are due to the massive hydrogen envelope of the progenitor. The envelope forces the supernova shock to decelerate strongly, leaving behind a reverse shock below the He/H interface, which interacts with the clumps and slows them down significantly. This reverse shock is absent in the Type Ib-like model. The latter is in fairly good agreement with observations of Type Ib supernovae. In addition, in this case the pattern of clump formation in the ejecta is correlated with the convective pattern prevailing during the shock-revival phase. This might be used to deduce observational constraints for the dynamics during this early phase of the evolution, and the role of neutrino heating in initiating the explosion., Comment: LaTeX, 30 pages, 19 figures, minor changes to text and figures to account for referees' comments, accepted by Astronomy & Astrophysics, abstract abridged, version with high-resolution color figures available from http://www.mpa-garching.mpg.de/PUBLICATIONS/REPORTS/mpa03/MPA1517.ps.gz, for associated mpeg file, see http://www.MPA-Garching.MPG.DE/~kok/MPG/MIXING

One of the central problems in supernova theory is the question how massive stars explode. Understanding the physical processes that drive the explosion is crucial for linking the stellar progenitors to the final remnants and for predicting observable properties like explosion energies, neutron star and black hole masses, nucleosynthetic yields, explosion anisotropies, and pulsar kicks. Here we review different suggestions for the explosion mechanism and discuss the constraints that can or cannot be deduced from observations. The most refined and detailed hydrodynamical models are available for neutrino-driven supernova explosions, although the viability of this mechanism has yet to be demonstrated convincingly. Since spherical models do not explode, the hope rests on the helpful effects of convection inside the nascent neutron star and in the neutrino-heated region behind the stalled shock. We present the first two-dimensional simulations of these processes which have been performed with a Boltzmann solver for the neutrino transport and a state-of-the-art description of neutrino-matter interactions. Our most complete models fail, but convection brings them encouragingly close to a success. An explosion could be obtained by just a minor modification of the neutrino transport, in which case the exploding model fulfills important requirements from observations (abridged)., Comment: 34 pages; 11 figures. Review for ``Core Collapse of Massive Stars'', Ed. C.L. Fryer, Kluwer, Dordrecht; minor revisions, typos removed

The rapidly growing base of observational data for supernova explosions of massive stars demands theoretical explanations. Central of these is a self-consistent model for the physical mechanism that provides the energy to start and drive the disruption of the star. We give arguments why the delayed neutrino-heating mechanism should still be regarded as the standard paradigm to explain most explosions of massive stars and show how large-scale and even global asymmetries can result as a natural consequence of convective overturn in the neutrino-heating region behind the supernova shock. Since the explosion is a threshold phenomenon and depends sensitively on the efficiency of the energy transfer by neutrinos, even relatively minor differences in numerical simulations can matter on the secular timescale of the delayed mechanism. To enhance this point, we present some results of recent one- and two-dimensional computations, which we have performed with a Boltzmann solver for the neutrino transport and a state-of-the-art description of neutrino-matter interactions. Although our most complete models fail to explode, the simulations demonstrate that one is encouragingly close to the critical threshold because a modest variation of the neutrino transport in combination with postshock convection leads to a weak neutrino-driven explosion with properties that fulfill important requirements from observations., Comment: 14 pages; 3 figures. Invited Review, in: ``From Twilight to Highlight: The Physics of Supernovae'', Eds. W. Hillebrandt and B. Leibundgut, Springer Series ``ESO Astrophysics Symposia'', Berlin

The current picture of the collapse and explosion of massive stars and the formation of neutron stars is reviewed. According to the favored scenario, however by no means proven and undisputed, neutrinos deposit the energy of the explosion in the stellar medium which surrounds the nascent neutron star. Observations, in particular of Supernova~1987A, suggest that mixing processes play an important role in the expanding star, and multi-dimensional simulations show that these are linked to convective instabilities in the immediate vicinity of the neutron star. Convectively enhanced energy transport inside the neutron star can have important consequences for the neutrino emission and thus the neutrino-heating mechanism. This also holds for a suppression of the neutrino interactions at nuclear densities. Multi-dimensional hydrodynamics, general relativity, and a better understanding of the neutrino interactions in neutron star matter may be crucial to resolve the problem that state-of-the-art spherical models do not yield explosions even with a very accurate treatment of neutrino transport by solving the Boltzmann equation., Comment: 29 pages; Proc. Workshop on Physics of Neutron Star Interiors (ECT*, Trento, June 19-July 7, 2000), ed. D. Blaschke, N.K. Glendenning, A.D. Sedrakian, Springer, in press; a postscript version with figures in full resolution is available at http://www.mpa-garching.mpg.de/~maria/greenreports/mpa01/reports_01.html

After decades of one-dimensional nucleosynthesis calculations, the growth of computational resources has meanwhile reached a level, which for the first time allows astrophysicists to consider performing routinely realistic multidimensional nucleosynthesis calculations in explosive and, to some extent, also in non-explosive environments. In the present contribution we attempt to give a short overview of the physical and numerical problems which are encountered in these simulations. In addition, we assess the accuracy that can be currently achieved in the computation of nucleosynthetic yields, using multidimensional simulations of core collapse supernovae as an example., Comment: 12 pages, LaTeX, 6 postscript figures, uses aipproc.sty, to appear in H. Utsunomiya, ed., Proceedings of the Tours Symposium on Nuclear Physics IV, held at Tours, France, Sept. 4th - 7th, 2000

Motivated by observations of supernova SN 1987A, various authors have simulated Rayleigh-Taylor (RT) instabilities in the envelopes of core collapse supernovae (for a review, see Mueller 1998). The non-radial motion found in these simulations qualitatively agreed with observations in SN 1987A, but failed to explain the extent of mixing of newly synthesized 56Ni quantitatively. Here we present results of a 2D hydrodynamic simulation which re-addresses this failure and covers the entire evolution of the first 5 hours after core bounce., Comment: 4 pages, 1 figure, LaTeX, requires espcrc1.sty. To appear in Nucl. Phys. A., the proceedings of the conference "Nuclei in the Cosmos 2000", held in Aarhus, Denmark, June 27-July 1, 2000

New two-dimensional, high-resolution calculations of a core collapse supernova in a 15 Msol blue supergiant are presented, which cover the entire evolution from shock revival until the first few hours of the explosion. Explosive nucleosynthesis, its dependence upon convective mixing during the first second of the evolution and the growth of Rayleigh-Taylor instabilities at the composition interfaces of the progenitor star are all modeled consistently and allow for a comparison with observational data. We confirm our earlier findings, that the perturbations induced by neutrino driven convection are sufficiently strong to seed large-scale Rayleigh-Taylor mixing and to destroy the onion-shell structure of the stellar He-core. As in our earlier calculations, the strong deceleration of the nickel clumps in the layers adjacent to the He/H interface suggests that the high velocities of iron-group elements observed in SN 1987A cannot be explained on the basis of currently favored progenitor models. Possible solutions to this dilemma and the implications of the mixing for type Ib explosions are briefly discussed., Comment: 4 pages, LaTeX, 1 postscript figure, in W. Hillebrandt and E. Mueller, eds., Proceedings of the 10th Workshop on "Nuclear Astrophysics" held at Ringberg Castle, Tegernsee, Germany, March 20-25, 2000; additional material and higher quality figures available from http://www.mpa-garching.mpg.de/~kok/

We present results of high-resolution two-dimensional simulations which follow the first five minutes of a core collapse supernova explosion in a 15 solar mass blue supergiant progenitor. The computations start shortly after core bounce and include neutrino-matter interactions by using a light-bulb 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 a significant fraction of the stellar helium core by the concerted action of convective and Rayleigh-Taylor instabilities. Fast moving nickel mushrooms with velocities up to 4000 km/s are observed. A continuation of the calculations to later times, however, indicates, that the iron velocities observed in SN 1987 A cannot be reproduced due to a strong deceleration of the clumps during their interaction with the dense shell left behind by the shock at the He/H interface. Therefore, we cannot confirm the claim that convective "premixing" of the nickel in the early phases of the explosion solves the problem of the high iron velocities., Comment: 8 pages, LaTeX, 4 postscript figures, to appear in R. Diehl, ed., Proceedings of the Workshop on "Astronomy with Radioactivities" held at Ringberg Castle, Tegernsee, Germany, Sep. 29th - Oct. 2nd, 1999

High-resolution two-dimensional simulations were performed for the first five minutes of the evolution of a core collapse supernova explosion in a 15 solar mass blue supergiant progenitor. The computations start shortly after bounce and include neutrino-matter interactions by using a light-bulb 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 about 4000 km/s 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 1987 A 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., Comment: 8 pages, LaTeX, 2 postscript figures, 2 gif figures, shortened and slightly revised text and references, accepted by ApJ Letters

In recent years the technique of Adaptive Mesh Refinement (AMR) has been successfully applied to several astrophysical problems. This method should also allow a consistent multi-dimensional modelling of supernova explosions. In this contribution we address some of the computational difficulties encountered when trying to apply the AMR method to explosive nucleosynthesis and supernova envelope ejection., Comment: 7 pages, latex, uses a4wide.sty, 4 figures (included); also available at http://www.camk.edu.pl/~tomek/AMRA/index.html or http://www.camk.edu.pl/~tomek/papers/ringberg98.uu ; to appear in W. Hillebrandt and E. Mueller, eds, Proceedings of the "Ninth workshop on Nuclear Astrophysics", held at Ringberg Castle, Germany, 23-27 March 1998. Revised version: Major text revision with new conclusions and figures; one reference added