Core-collapse supernovae are among the most energetic explosions in the Universe. As such they play a major role in many astrophysical phenomena, including galactic dynamics, nucleosynthesis, and neutron star and black hole formation. Furthermore, the combination of extreme energetics and densities make these explosions fascinating nuclear and particle physics laboratories. Hence, a solid theoretical framework for the explosion mechanism will greatly illuminate solutions to some of the most important questions in astrophysics and fundamental physics.

The purpose of this program was to advance our understanding of the explosion mechanism by fostering collaborations among the theorists, observers, and nuclear and particle physicists. After many years of intense research, SN theorists are starting to converge on viable solutions to the explosion mechanism. At the same time, electromagnetic observations are beginning to probe closer to the mechanism, and neutrino and gravitational wave dectectors are coming on line that can probe the mechanism directly. These multi-messenger observations promise to greatly constrain the theory. The time is ripe for these communities to share the latest results, define the next questions in SN research, and begin to constrain the physics of core-collapse supernovae.

With this goal in mind experts from a wide range of fields came together for the 5-week program that was organized around two topical workshops on "Nuclear and Neutrino Physics in Stellar Core Collapse" and "Probing the Supernova Mechanism by Observations". The areas of research represented included supernova and remnant observations, progenitor and explosion modeling, nuclear astrophysics of matter under extreme conditions, neutrino theory and detection, and gravitational-wave astrophysics.

Supernova modeling is presently facing the grand computational challenge of carrying the simulations to the third dimension. These efforts were already rewarded with the first successful explosion models in 3D, although the computations still used modest numerical resolution and considerable simplifications in the neutrino treatment, which fall behind the most sophisticated existing 2D models. As in 2D simulations, the explosions are triggered by neutrino-energy deposition behind the supernova shock and are supported by violent nonradial mass motions, which stretch the timescale that matter is exposed to neutrino heating. The nature of these nonradial mass motions and the underlying hydrodynamical instability --- convection and buoyancy or the so-called standing accretion shock instability (SASI) --- are still a matter of vivid discussion. It is also unclear whether large-scale asymmetries (with strong dipolar and quadrupolar components of the flow pattern) or turbulent energy redistribution are mainly responsible for differences between models in one, two, and three dimensions.

Figures 1a and 1b: Two snapshots of a three-dimensional explosion model of an 11.2 solar-mass star at about 350 and 420 milliseconds after core bounce. The transparent surfaces correspond to different entropy levels and the projections visualize the entropy distribution by color coding. Large asymmetries, which have grown from small random perturbations, are generically connected to the onset of the explosion in 2D and 3D simulations. (Courtesy of Kei Kotake)

Figure 2: Shallow-water analogue of the standing accretion shock instability (SASI). The radial water flow towards a central drain pipe and a hydraulic jump corresponds to the accretion flow and accretion shock in the supernova core. A spiral-mode pattern with characteristic, rotating triple point and angular momentum separation can spontaneously develop even without initial rotation in this experimental "SWASI" setup (left images). Hydrodynamical simulations reproduce the experimental findings (right panels). (T. Foglizzo et al., Phys. Rev. Lett. 108, 051103 (2012); copyright: American Physical Society)

Progress on the modeling front is counterparted by a growing pool of observational data. Supernovae whose progenitors can be identified on archival images help to constrain the masses and properties of the corresponding stars. Oxygen lines with multiple peaks as well as radiation polarization yield evidence of time dependent explosion asymmetries and suggest a wide range of deformation from globally anisotropic supernovae to cases with "clumpy" local inhomogeneities. X-ray, optical, and radio "tomography" of young supernova remnants begins to reveal features that can be traced back to the earliest moments of the blast. In particular the systematic observational dissection of the Cassiopeia A remnant has revealed a wealth of ring-like structures, which seem to originate from the bubbles and Rayleigh-Taylor mushrooms found to carry heavy elements, especially also radioactive nickel, from the supernova core to the stellar envelope in hydrodynamical explosion models. Measurements of neutrino and gravitational-wave signals in the lucky case of a future galactic supernova are likely to reveal correlated signal features that provide direct evidence of violent hydrodynamic instabilities in the first second of the explosion.

Figure 3a: The Cassiopeia A supernova remnant in optical light. The image was taken by NASA's Hubble Space Telescope. The picture reveals a complicated and asymmetric structure of the expanding fragments of a star that exploded only about 330 years ago. (Credit: NASA/ESA/Hubble Heritage (STScI/AURA))

Figure 3b: Visualization of different components of the ejecta of the Cassiopeia A remnant. Red represents sulfur and oxygen whose presence is deduced from optical radiation. Purple is X-ray emitting iron. The point in the center is the geometrical origin to which the expansion of the stellar fragments points back. The translucent sphere is a visual aid. (Courtesy of Robert Fesen and Dan Milisavljevic; using iron data taken from DeLaney et al. (2010))

First-principle models of core-collapse supernovae heavily rely on a reliable description of the microphysics that plays a role in the supernova core and nascent neutron star. In particular the equation of state of dense and hot matter and the neutrino interaction rates in plasma at extreme conditions determine the collapse and explosion dynamics and the nucleosynthesis conditions in neutrino-heated ejecta. Observational constraints like neutron star masses and radius estimates, as well as theoretical and experimental studies of nuclear matter, begin to set serious constraints on the properties of the high-density equation of state. Considerable efforts are being made for developing consistent new models that account for all of these constraints and that can be supplemented by a consistent description of the neutrino opacities. A new, forthcoming generation of supernova models based on this improved input will yield more reliable predictions of neutrino spectra and luminosities and may exhibit interesting new twists of the role of neutrino flavor transformations and neutrino-induced nucleosynthesis in supernovae.

Figure 4: Neutron star mass determinations and estimates for different types of binary systems. In particular the 1.97 solar-mass pulsar of Demorest et al. (2010) has ruled out a large variety of models for "soft" neutron star matter. Only few of the currently available nuclear equations of state for supernova simulations are compatible with both the mass and radius constraints deduced from astrophysical and experimental data. (Courtesy of James Lattimer)