Andreas Marek

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.

IS STRONG SASI ACTIVITY THE KEY TO SUCCESSFUL NEUTRINO-DRIVEN SUPERNOVA EXPLOSIONS?

Following a simulation approach of recent publications, we explore the viability of the neutrino-heating explosion mechanisms 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 not a good diagnostic quantity for the readiness to explode. Instead, mass, integrated entropy, total neutrino-heating rate, and non-radial kinetic energy in the gain layer are higher when models are closer to explosion. Coherent, large-scale 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 clearly explode 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.

A New Multi-dimensional General Relativistic Neutrino Hydrodynamics Code for Core-collapse Supernovae. II. Relativistic Explosion Models of Core-collapse Supernovae

We present the first two-dimensional general relativistic (GR) simulations of stellar core collapse and explosion with the CoCoNuT hydrodynamics code in combination with the Vertex solver for energy-dependent, three-flavor neutrino transport, using the extended conformal flatness condition for approximating the spacetime metric and a ray-by-ray-plus ansatz to tackle the multi-dimensionality of the transport. For both of the investigated 11.2 and 15M⊙ progenitors we obtain successful, though seemingly marginal, neutrino-driven supernova explosions. This outcome and the time evolution of the models basically agree with results previously obtained with the Prometheus hydro solver including an approximative treatment of relativistic effects by a modified Newtonian potential. However, GR models exhibit subtle differences in the neutrinospheric conditions compared to Newtonian and pseudo-Newtonian simulations. These differences lead to significantly higher luminosities and mean energies of the radiated electron neutrinos and antineutrinos and therefore to larger energy-deposition rates and heating efficiencies in the gain layer with favorable consequences for strong nonradial mass motions and ultimately for an explosion. Moreover, energy transfer to the stellar medium around the neutrinospheres through nucleon recoil in scattering reactions of heavy-lepton neutrinos also enhances the mentioned effects. Together with previous pseudo-Newtonian models the presented relativistic calculations suggest that the treatment of gravity and energy-exchanging neutrino interactions can make differences of even 50–100% in some quantities and is likely to contribute to a finally successful explosion mechanism on no minor level than hydrodynamical differences between different dimensions. Subject headings: supernovae: general—neutrinos—radiative transfer—hydrodynamics—relativity

SASI Activity in Three-Dimensional Neutrino-Hydrodynamics Simulations of Supernova Cores

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 one-dimensional and two-dimensional (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 three dimensions can exceed those of the corresponding 2D case during extended periods of the evolution. We also perform parameterized 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.

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.

Equation-of-state dependent features in shock-oscillation modulated neutrino and gravitational-wave signals from supernovae

We present two-dimensional (axisymmetric) neutrino-hydrodynamic simulations of the long-time accretion phase of a 15 Mprogen- itor star after core bounce and before the launch of a supernova explosion, when non-radial hydrodynamic instabilities like convection occur in different regions of the collapsing stellar core and the standing accretion shock instability (SASI) leads to large-amplitude os- cillations of the stalled shock with a period of tens of milliseconds. Our simulations were performed with the Prometheus-Vertex code, which includes a multi-flavor, energy-dependent neutrino transport scheme and employs an effective relativistic gravitational potential. Testing the influence of a stiff and a soft equation of state for hot neutron star matter, we find that the non-radial mass motions in the supernova core impose a time variability on the neutrino and gravitational-wave signals with larger amplitudes, as well as higher frequencies in the case of a more compact nascent neutron star. After the prompt shock-breakout burst of electron neutrinos, a more compact accreting remnant produces higher neutrino luminosities and higher mean neutrino energies. The observ- able neutrino emission in the SASI sloshing direction exhibits a modulation of several ten percent in the luminosities and around 1 MeV in the mean energies with most power at typical SASI frequencies between roughly 20 and 100 Hz. The modulation is caused by quasi-periodic variations in the mass accretion rate of the neutron star in each hemisphere. At times later than ∼50-100 ms after bounce, the gravitational-wave amplitude is dominated by the growing low-frequency (<200 Hz) signal associated with anisotropic neutrino emission. A high-frequency wave signal results from nonradial gas flows in the outer layers of the anisotropically accreting neutron star. Right after bounce such nonradial mass motions occur due to prompt post-shock convection in both considered cases and contribute mostly to the early wave production around 100 Hz. Later they are instigated by the SASI and by convective overturn that vigorously stir the neutrino-heating and cooling layers, and also by convective activity developing below the neutrinosphere. The gravitational-wave power then peaks at about 300-800 Hz, connected to changes in the mass quadrupole moment on a timescale of milliseconds. Distinctively higher spectral frequencies originate from the more compact and more rapidly contracting neutron star. Both the neutrino and gravitational-wave emission therefore carry information that is characteristic of the properties of the nuclear equation of state in the hot remnant. The detectability of the SASI effects in the neutrino and gravitational-wave signals is briefly discussed.

3D Collapse of Rotating Stellar Iron Cores in General Relativity Including Deleptonization and a Nuclear Equation of State

We present 2D and 3D simulations of the collapse of rotating stellar iron cores in general relativity employing a nuclear equation of state and an approximate treatment of deleptonization. We compare fully general relativistic and conformally flat evolutions and find that the latter treatment is sufficiently accurate for the core-collapse supernova problem. We focus on gravitational wave (GW) emission from rotating collapse, bounce, and early postbounce phases. Our results indicate that the GW signature of these phases is much more generic than previously estimated. We also track the growth of a nonaxisymmetric instability in one model, leading to strong narrow-band GW emission.

Gravitational wave burst signal from core collapse of rotating stars

We present results from detailed general relativistic simulations of stellar core collapse to a proto-neutron star, using two different microphysical nonzero-temperature nuclear equations of state as well as an approximate description of deleptonization during the collapse phase. Investigating a wide variety of rotation rates and profiles as well as masses of the progenitor stars and both equations of state, we confirm in this very general setup the recent finding that a generic gravitational wave burst signal is associated with core bounce, already known as type I in the literature. The previously suggested type II (or “multiple-bounce”) waveform morphology does not occur. Despite this reduction to a single waveform type, we demonstrate that it is still possible to constrain the progenitor and postbounce rotation based on a combination of the maximum signal amplitude and the peak frequency of the emitted gravitational wave burst. Our models include to sufficient accuracy the currently known necessary physics for the collapse and bounce phase of core-collapse supernovae, yielding accurate and reliable gravitational wave signal templates for gravitational wave data analysis. In addition, we assess the possibility of nonaxisymmetric instabilities in rotating nascent proto-neutron stars. We find strong evidence that in an iron core-collapse event the postbounce core cannot reach sufficiently rapid rotation to become subject to a classical bar-mode instability. However, many of our postbounce core models exhibit sufficiently rapid and differential rotation to become subject to the recently discovered dynamical instability at low rotation rates.

Neutrino-driven supernova of a low-mass iron-core progenitor boosted by three-dimensional turbulent convection

We present the first successful simulation of a neutrino-driven supernova explosion in three dimensions (3D), using the Prometheus-Vertex code with an axis-free Yin-Yang grid and a sophisticated treatment of three-flavor, energy-dependent neutrino transport. The progenitor is a nonrotating, zero-metallicity 9.6 Msun star with an iron core. While in spherical symmetry outward shock acceleration sets in later than 300 ms after bounce, a successful explosion starts at ~130 ms postbounce in two dimensions (2D). The 3D model explodes at about the same time but with faster shock expansion than in 2D and a more quickly increasing and roughly 10 percent higher explosion energy of >10^50 erg. The more favorable explosion conditions in 3D are explained by lower temperatures and thus reduced neutrino emission in the cooling layer below the gain radius. This moves the gain radius inward and leads to a bigger mass in the gain layer, whose larger recombination energy boosts the explosion energy in 3D. These differences are caused by less coherent, less massive, and less rapid convective downdrafts associated with postshock convection in 3D. The less violent impact of these accretion downflows in the cooling layer produces less shock heating and therefore diminishes energy losses by neutrino emission. We thus have, for the first time, identified a reduced mass accretion rate, lower infall velocities, and a smaller surface filling factor of convective downdrafts as consequences of 3D postshock turbulence that facilitate neutrino-driven explosions and strengthen them compared to the 2D case.

Neutrino-driven Explosion of a 20 Solar-mass Star in Three Dimensions Enabled by Strange-quark Contributions to Neutrino–nucleon Scattering

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_sun progenitor star that a moderate strangeness-dependent contribution of g_a^s = -0.2 to the axial-vector coupling constant g_a = 1.26 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 neutrino-nucleon scattering. Our results demonstrate the close proximity to explosion of the previously published, unsuccessful 3D models of the Garching group.