Towards Energy Saturation in 3D Core-Collapse Supernova Simulations Gauss Centre for Supercomputing e.V.


Towards Energy Saturation in 3D Core-Collapse Supernova Simulations

Principal Investigator:
Hans-Thomas Janka

Max Planck Institute for Astrophysics, Garching

Local Project ID:
pn69ho, pr53yi

HPC Platform used:
SuperMUC and SuperMUC-NG of LRZ

Date published:


This project explores the fundamental physical processes that cause and accompany the violent death of stars with at least nine times the mass of our Sun in so-called core-collapse supernova explosions [1]. Of particular interest are predictions of measurable signals such as neutrinos (elementary particles that interact with matter by the weak force) and gravitational waves (spacetime perturbations caused by asymmetric acceleration of masses). Both are emitted from the center of the explosion and can yield direct information of the processes there. Another aspect of great interest is the explanation of observed properties of supernovae and their gaseous and compact remnants, i.e., of neutron stars and black holes that are formed when the stellar iron cores collapse before the supernova blast expels the rest of the star into the circumstellar space. Moreover, the consequences of supernovae in our Universe are in the focus of intense research, for example connected to their ejection of life-enabling chemical elements such as carbon, oxygen, silicon, and iron, which are either forged by nuclear reactions over millions of years in those stars that finally explode, or which are freshly made by the supernova itself.

To address these important and timely questions of stellar astrophysics, it is crucial to develop a most detailed understanding of the physical mechanism that causes the stellar explosion. To this end and for the theoretical study of all of the mentioned problems, the most powerful available supercomputers are needed, because the involved processes are extremely complex, enormously diverse, and highly non-linear. These processes involve, tightly coupled, the hydrodynamics and thermodynamics of the stellar plasma, neutrino interactions and transport, nuclear reactions, as well as strong gravity to be described by Einstein’s theory of general relativity.

Results and Methods

With the support of computing resources on SuperMUC and SuperMUC-NG of LRZ over the past years, the Garching team has achieved to demonstrate, for the first time with modern numerical methods and state-of-the-art input physics, that energy transfer by neutrinos triggers the onset of the explosion and powers the supernova blast. Despite their weak interactions with matter, these particles are produced in huge numbers at the extreme densities (up to several times the density of atomic nuclei) and temperatures (up to nearly 1000 billion Kelvin) in the newly formed neutron star. While 99 percent of the neutrinos escape within a few seconds and thus carry away the gravitational binding energy that is released in the collapse of the stellar iron core, the remaining one percent gets stuck by particle interactions behind the supernova shock wave and powers the supernova explosion.

In this project the goal was to explain the observed properties of well studied, nearby, young supernovae and their remnants by neutrino-driven explosions. In particular, we focused on the supernova that blew up in the year 1054 and gave birth to the Crab Nebula with its rapidly spinning neutron star (a so-called “pulsar”), and, as a second target of interest, on Supernova 1987A, which exploded only 33 years ago and whose neutron star has been detected recently. The former object is thought to originate from the death of a low-mass star of about 9 to 10 solar masses, the latter case is connected to a star of 15 to 20 solar masses.

We therefore performed the first self-consistent 3D simulations that followed the evolution of such stars from the onset of stellar core collapse, through the neutrino-driven expansion of the supernova shock, to the time when the explosion energy reached its terminal value. In the cases of 8.8, 9.0, and 9.6 solar-mass stars, we continued until shock breakout from the stellar surface in order to determine the final asymmetry of the supernova and the final neutron star properties after the fallback of matter that does not become unbound in the explosion (Figure 1). In the case of a 19 solar-mass star it took already more than 7 seconds for the blast-wave energy to saturate (Figure 2). Thus we could demonstrate, for the first time by self-consistent models, that neutrino-driven explosions can explain the properties of the Crab supernova and its pulsar and of Supernova 1987A, i.e., their explosion energy, ejected mass of radioactive nickel, neutron star mass, kick velocity, and spin period [2,3].

Such simulations are a challenging problem, which could not be tackled before. On the one hand, because the explicit time step of the hydrodynamics solver is as small as some 107 seconds, which means that more than a million time steps are needed. On the other hand, following the growth of the energy requires the inclusion of the computationally even more demanding neutrino physics. The simulations employed our Vertex-Prometheus neutrino-hydrodynamics supernova code, which includes a modern shock-capturing hydrodynamics scheme based on the piecewise parabolic method (PPM) proposed by Colella and Woodward, and a two-moment ray-by-ray-plus neutrino transport solver with Boltzmann closure. They became possible for several reasons. First, the code uses a hybrid OpenMP/MPI parallelisation model that allows perfect linear scaling for up to more than 200,000 cores, as demonstrated at a dedicated workshop, and it also uses rigorously optimized vectorization on SuperMUC-NG. Second, the neutrino transport is time-implicit with recently accelerated and improved convergence, numerical stability and accuracy, which now allows for time steps that are up to 100 times bigger than the hydrodynamics steps. Third, for long-time runs over many seconds and beyond, a computationally cheaper neutrino scheme was implemented in the course of this project. It is based on data obtained from 1D neutrino-cooling simulations of the nascent neutron star and allows for a seamless, basically transient-free continuation of the 3D explosion simulations (see appendix in [2]).

A typical supernova run was done with up to 1000 radial zones and 2-degree angular resolution on 16,800 cores (350 nodes), using several 10 million core-hours. For convergence tests and varied microphysics inputs, also runs with 4-degree and 1-degree resolution were performed on 4992 and 54,144 cores (1128 nodes), respectively, but because of unacceptably frequent node failures only a maximum of 27,072 cores could be used in production runs. The two projects pn69ho and pr53yi involved research of three PhD students, consumed nearly 224 million core hours over 3 years, delivered on the order of 10,000 files, needed up to 300 TB of continuous work storage, and produced about 3 PB of archived data for the science results.

On-going Research / Outlook

Data analysis of the results is still going on, also with collaborators, evaluating the outputs for the predicted neutrino and gravitational-wave signals, nucleosynthesis, as well as astrophysical implications such as supernova light curves and spectra. Moreover, the 19 solar-mass model has still to be continued from 7 seconds to several days in order to track the fallback and development of the final explosion geometry. Since supernova progenitors are diverse, more simulations of the presented kind for different stars will be needed in the future for comparison with observed supernovae and remnants. SuperMUC-NG will be indispensable for this forefront research.

References and Publications


[2] Stockinger, G., et al. 3D models of core-collapse supernovae from low-mass progenitors with implications for Crab, MNRAS 496, 2039 (2020); arXiv:2005.02420

[3] Bollig, R., et al. Self-consistent 3D supernova models from 7 minutes to +7 seconds: a 1-bethe explosion of a ~19 solar-mass progenitor. ApJ, submitted,

Research Team

Robert Bollig1, Hans-Thomas Janka(PI)1, Daniel Kresse1,2, Georg Stockinger1,2, Naveen Yadav1,3

1Max Planck Institute for Astrophysics, Karl-Schwarzschild-Str. 1, Garching
2Physik Department, Technische Universität München, James-Franck-Str. 1, Garching
3Excellence Cluster ORIGINS, Boltzmannstr. 2, Garching

Project Partners

Alexander Heger4, Bernhard Müller4, Ken’ichi Nomoto5

4Monash University, Melbourne, Australia
5University of Tokyo, Tokyo, Japan

Scientific Contact:

Prof. Dr. Hans-Thomas Janka
Max-Planck-Institut für Astrophysik, Garching
Karl-Schwarzschild-Straße 1
D-85748 Garching (Germany)
e-mail: thj [@] MPA-Garching.MPG.DE

Local project ID: pn69ho

November 2020

Tags: LRZ MPA Garching Astrophysics