ASTROPHYSICS

Introduction

After millions of years of stable evolution, the life of a massive star is abruptly terminated by a spectacular event that outshines the light of billions of stars for weeks and is called core-collapse supernova (CCSN). Such events are triggered when the core of the star, which consists mostly of iron, becomes gravitationally unstable and collapses to a neutron star within less than a second. The sudden halt of the implosion at the moment when the neutron star begins to form, which is called “core bounce”, creates a shock wave that ultimately expels the overlying stellar layers in the supernova explosion.

Neutron stars are among the most extraordinary objects in the Universe. With the diameter of a city like Munich they contain more mass than our Sun, compressed to densities higher than that of atomic nuclei. They start out as extremely hot objects with temperatures up to nearly 1000 billion Kelvin and emit huge numbers of neutrinos. These weakly interacting elementary particles carry away the gravitational binding energy that is released in the catastrophic collapse of the stellar core, 100 times more energy than is set free by the star’s explosion, and 10,000 times more energy than is radiated in the splendidly brilliant light of the supernova.

Enormous progress has been achieved over the past five years in our understanding of the physical mechanism that reverses the catastrophic collapse of the stellar core to the powerful supernova blast. Neutrinos have now been established as the crucial agent that transfers the power to the supernova blast, thus confirming a 50 year old hypothesis of a “neutrino-driven mechanism” first outlined in a paper by Colgate and White in 1966.

This breakthrough became possible because of decisive advances on three fronts simultaneously. First, neutrino interactions in high-density media, thermodynamic properties of hot nuclear matter, and hydrodynamic phenomena such as convective transport, shock-wave instabilities, and turbulence, all of them playing a crucial role in the new-born neutron star and starting explosion, have been explored in great depth. Second, computationally efficient and accurate numerical tools have been developed to solve the coupled system of hydrodynamics solver and energy-dependent neutrino transport in three spatial dimensions (3D) and with the modern microphysics taken into account. And, third, massively parallel supercomputers have become available to apply these tools to full-scale, self-consistent 3D supernova simulations.

Because of access to HPC system SuperMUC at LRZ, the CCSN group at MPA Garching was worldwide first to demonstrate the viability of the neutrino-driven mechanism with modern 3D models in 2015 [1]. After this confirmation in principle, the focus has now shifted to better qualitative and quantitative insights into the role of the initial conditions in the progenitor star, the spatial resolution of the numerical models, and so far disregarded aspects of the relevant physics.

Results and Methods

In the course of this project the MPA group has taken two major steps towards more realism of CCSN modeling. First, we have started to compute initial conditions of progenitor stars in 3D, simulating the latest stages of convective oxygen-shell burning over periods of several minutes prior to iron-core collapse. This creates a highly asymmetric distribution of the chemical elements (in this case of O, Ne, Si) with large-scale fluctuations of density and velocity in the stellar layers surrounding the iron core (Figure 1), replacing the traditionally employed spherically symmetric (1D) pre-collapse conditions provided from stellar evolution modeling. Second, we have included, for the first time and uniquely, the effects of muons in the thermodynamical description of the neutron-star plasma as well as neutrino-muon interactions in the neutrino transport. Muons are about 200 times heavier than electrons (105.66 MeV), for which reason they had been thought to be created in insufficient numbers to have any influence on supernovae. To take the corresponding physics into account, our Vertex neutrino transport code had to be generalized for a 6-species treatment with couplings between neutrinos and antineutrinos of the three lepton flavors across the whole energy-momentum space. This generalization increases the computational demand of the anyway expensive neutrino physics by another 30–50%.

In addition to studying these two novel aspects connected to the 3D progenitor structure and microphysics in hot, new-born neutron stars, we also performed corresponding 3D simulations with different angular resolutions for convergence tests: Besides 2-degree models as our default, we compared to 4-degree runs (Figure 2) and, without the expensive muon physics, also 1-degree runs. Our set of 16 simulations was done on 16800, 4992, and 27,072 cores, respectively, consumed about 190 million core hours over 3 years, and delivered roughly 3 PB of archived data for the science results.

Our findings contradict the traditional thinking that muons do not play a role. Temperature and electron degeneracy (scaling with the high density) in the neutron star interior become so huge that muons can be formed in neutrino-electron reactions and thermal processes. Their appearance converts internal energy to rest-mass energy, which does not contribute to the pressure. Therefore this so-called muonization process leads to a faster contraction of the hot neutron star, boosting the neutrino emission and thus the energy transfer to the supernova shock, strengthening the neutrino-driven mechanism. This accelerates the onset of the explosion and leads to a faster increase of the explosion energy (Figure 3).

We found that muon effects thus overcompensate the negative consequences of lower resolution, which tends to damp the growth of hydrodynamic instabilities (convection and turbulence) in the volume behind the shock due to enhanced numerical viscosity. Since these instabilities support the neutrino mechanism, the damping influence of numerical viscosity can delay the onset of the explosion (Figure 3).

None of our simulations that were started from the 1D progenitor model ended in a successful supernova explosion. This clearly emphasizes that more realistic 3D initial conditions, constructed by our own 3D simulations of convective oxygen-shell burning, are a crucial ingredient, because the large-amplitude and large-scale asymmetries in the pre-collapse star stimulate stronger postshock flows when falling through the shock.