Supernova Explosions and Cosmology

On June 4, 2002, at the American Astronomical Society meeting in Albuquerque, N.M., Michael Warren and Chris Fryer from Los Alamos National Laboratory presented the results of one of several projects in this collaboration, the first 3D supernova explosion simulation, based on computation at NERSC (Figure 3). This research eliminates some of the doubts about earlier 2D modeling and paves the way for rapid advances on other questions about supernovae.

Figure 3   Computer visualization shows (left to right) three stages of a simulated supernova explosion over a period of 50 milliseconds, starting about 400 milliseconds after the core begins to collapse. The surfaces show the material which is flowing outward at a speed of 1,000 kilometers/second. Left is the initial spherical implosion. Center, as in-falling gas approaches the core, it is exposed to a higher and higher influx of neutrinos that heat the gas and make it buoyant. Right, as more cold gas sinks in, it is heated and rises, resulting in enough convective energy transfer to create an explosion.

Earlier one-dimensional simulations of core-collapse supernovae almost always failed to explode. Two-dimensional simulations were qualitatively different from 1D, leading to a robust explosion without fine-tuning of the star’s physical properties. They showed that the explosion process is critically dependent on convection, the mixing of the matter surrounding the iron core of the collapsing star. It was believed that the results could again be changed radically by adding a third dimension, but the 3D simulations turned out to be similar to the 2D results. The explosion energy, explosion time scale, and remnant neutron star mass do not differ by more than 10 percent between the 2D and 3D models. With these 3D results, researchers are ready to attack more exotic problems that involve rotation and non-symmetric accretion.

The 3D simulation used a parallel smooth particle hydrodynamics (SPH) code coupled with a flux-limited diffusion radiation transport. Supernova calculations are computationally demanding because many processes, involving all four fundamental forces of physics, must be modeled and followed for more than 100,000 time steps. Typical simulations (1 million particles) took about three months on the IBM SP at NERSC.

In the next five years, the Supernova Cosmology Project and the Nearby Supernova Factory experiments will increase both the quality and quantity of observational supernova data at low and high redshift by several orders of magnitude. The purpose of these experiments is to improve the use of supernovae as tools for cosmology by determining the underlying physics behind these catastrophic events and to utilize these tools to help us understand the dark energy that drives the acceleration of the universe. The only way to fully exploit the power of this amazing data set is to make a similar order-of-magnitude improvement in computational studies of supernovae, via spectrum synthesis and radiation hydrodynamics. The focus of the PHOENIX/SYNPOL collaboration’s portion of this project is to start the process of creating 3D spectrum synthesis models of supernovae (Figure 4) in order to constrain the observations and place limits on the explosion models and progenitors of supernovae using the full-physics 1D models as a guide.

Figure 4   A spectrum synthesis calculation of a supernova atmosphere surrounded by a toroid. The layout of the atmosphere is presented on the left, while at the right is a graph of the flux vs. wavelength vs. viewing angle. As the viewing angle shifts towards the toroid, the strength of the absorption increases dramatically. Data that confirm such a model would for the first time put strong constraints on the progenitors of Type Ia supernovae. Such flux features are seen in the spectrum of SN 2001el.

Currently two sets of spectrum synthesis codes, PHOENIX and SYNPOL, are used at NERSC to study the model atmospheres of supernovae. PHOENIX models astrophysical plasmas in one dimension under a variety of conditions, including differential expansion at relativistic velocities found in supernovae. The current version solves the fully relativistic radiative transport equation for a variety of spatial boundary conditions in both spherical and plane-parallel geometries for both continuum and line radiation simultaneously and self-consistently using an operator splitting technique. PHOENIX also solves the full multi-level non-local thermodynamic equilibrium (NLTE) transfer and rate equations for a large number of atomic species (with a total of more than 10,000 energy levels and more than 100,000 primary NLTE lines), including non-thermal processes. PHOENIX accurately solves the fully relativistic radiation transport equation along with the non-LTE rate equations (currently for ~150 ions) while ensuring radiative equilibrium (energy conservation).

SYNPOL is a 3D radiative transfer code to study the spectropolarimetry of supernovae. It is based on a Monte Carlo treatment of line formation via the Sobolev approximation and includes electron scattering. Because SYNPOL does not solve rate equations and does not do continuum transfer, it is not used for quantitative abundance determinations or for absolute flux calculations. Rather its value lies in establishing line identifications (the intervals of ejection velocity within which the presence of particular ions is detected) and in probing the geometry of the supernova and its ejecta. For a full 3D run, with signal-to-noise and resolution an order of magnitude greater than the observational data, approximately 10¹² photons are generated within a Cartesian grid of 300 per side. Due to the size of the atomic data—over 42 million lines whose strengths can vary at each cube in the grid—the memory requirements and the time it takes to process the scattering of such a large number of photons are quite large: 1 million CPU hours for a 3D simulation with simplified physics, and 10 GB input and 1 GB output per iteration, with 20 iterations per star model for 20 to 30 models.

NERSC provided a new 24-hour run queue to accommodate this simulation. Within the next two or three years, 100 times more CPUs will be needed to run 3D simulations with complex physics if there are no algorithmic improvements.

INVESTIGATORS
P. Nugent, D. Kasen, and S. Perlmutter, Lawrence Berkeley National Laboratory; S. Woosley and G. Glatzmaier, University of California, Santa Cruz; P. Hauschildt, J. Aufdenberg, C. Shore, A. Schweitz, and T. Barman, University of Georgia; E. Baron, University of Oklahoma; T. Clune, Goddard Space Flight Center; A. Burrows, S. Hariri, A. Hungerford, P. Pinto, H. Sarjoughian, and B. Ziegler, University of Arizona; T. Evans, C. Fryer, M. Gray, W. Miller, and M. Warren, Los Alamos National Laboratory; F. Dietrich and R. Hoffman, Lawrence Livermore National Laboratory.

PUBLICATIONS
C. L. Fryer and M. S. Warren, “Modeling core-collapse supernovae in three dimensions,” Astrophysical Journal 574, L65 (2002).
C. L. Fryer, D. E. Holz, and S. A. Hughes, “Gravitational wave emission from core collapse of massive stars,” Astrophysical Journal 565, 430 (2002).
D. N. Kasen, P. E. Nugent, L. Wang, and D. A. Howell, “Interpreting supernova polarization spectra,” Bulletin of the American Astronomical Society 33, 8409.

URLs
http://www.supersci.org/
http://www.lbl.gov/~nugent