Theory

# General Description

The ORNL theoretical astrophysics group has among its primary focuses the determination
of the core collapse supernova explosion mechanism. Core collapse supernovae
are extraordinary stellar explosions that mark the death throes of massive stars,
with mass greater than eight to ten times the mass of the Sun. Such explosions
are the dominant source of elements in the Universe between oxygen and iron and
are believed to be responsible for half of the elements heavier than iron. They
are a key link in the origin of life in the Universe.

Using three major codes developed by the ORNL group in collaboration with researchers
at the University of Basel, Florida Atlantic University, and the North Carolina
State University, core collapse supernova simulations have been performed in
one (spherical symmetry), two (axisymmetry), and three spatial dimensions. The
three main thrusts of ORNL's future simulations are: (1) To continue our one-dimensional
simulations to explore neutrino transport effects and the implications of improved
and additional weak interaction rates, and improved nuclear equations of state.
(2) To produce a compendium of two-dimensional models to span a wdie range of
stellar progenitors and progenitor characteristics and to complete our
understanding of the axisymmetric case. (3) To perform three-dimensional
simulations with the sophistication in the treatment of the neutrino
transport and gravity that is implemented in our one-dimensional models.

# Detailed Description

The collapse of the stellar core of a massive star, whether composed
initially of iron or oxygen-neon-magnesium, proceeds until super-nuclear
densities, larger than the densities inside atomic nuclei, are reached.
The inner core becomes incompressible under these extremes, bounces, and,
acting like a piston, launches a shock wave into the outer stellar core.
This shock wave will ultimately propagate through the stellar layers
beyond the core and disrupt the star in a core collapse supernova explosion.

However, the shock stalls in the outer core, losing energy as it plows
through it, and exactly how the shock is revived is unknown.
This is the central question in core-collapse supernova theory.
After core bounce, ~ 10^{53} ergs of energy in the form of neutrinos
and antineutrinos of all three flavors (electron, muon, and tau) is released
from the newly formed proto-neutron star (PNS) at the center of the explosion.
The observed kinetic energy of the supernova explosion is ~ 10^{51} ergs.
Past simulations demonstrate that energy in the form of neutrinos emerging
from the PNS can be deposited behind the shock and may revive it.
This is the so-called Wilson delayed-shock (neutrino-heating) mechanism
and is central to our modern understanding of core-collapse supernovae.

The neutrino heating may be aided by fluid instabilities (e.g., convection) in the PNS,
which may boost the luminosity of this central neutrino bulb. Convection directly b
eneath the shock fundamentally alters the nature of neutrino shock reheating
relative to the spherically symmetric case, allowing simultaneous down flows
that fuel the neutrino luminosities by accretion and up flows that bring
energy to the shock. A recently (ORNL collaboration) discovered
multidimensional instability of the shock wave itself, the Standing
Accretion Shock Instability (SASI), dramatically alters the shock and
explosion dynamics. Centrifugal effects in a rotating stellar core,
and other rotational effects, can change supernova dynamics quantitatively
and perhaps qualitatively. Stellar core magnetic fields, increased by
compression during collapse, convection (e.g., via a dynamo), and
rotation (through wrapping and shear; in the latter case the
magnetorotational instability (MRI) may), may alsoplay a significant role
in driving, and perhaps collimating, at least a subset of
core-collapse supernova explosions where rapid rotation is present. Nuclear
burning must also be included, as the energy released by burning in the
compressed and heated material near the shock wave helps to power the
explosion. Finally, the PNS is an extremely dense, compact object, and
its gravitational field is not well described by Newtonian gravity.
Rather, general relativity is required. It is, after all, the release
of gravitational binding energy as the core collapses and the PNS forms
that provides the energy in neutrinos, which we believe ultimately powers
the explosion.

The past several years have seen notable progress toward ascertaining the core-collapse
supernova explosion mechanism. Three independent groups worldwide (ORNL/FAU/NCSU, MPA, Tokyo/Basel)
have now reported neutrino-driven explosions using multi-frequency neutrino transport, for a
range of stellar progenitor masses from 11 to 25 Solar masses. In all three cases, the
SASI couples with neutrino shock reheating to power the explosions and thus plays a central
role. The SASI provides the missing link that renders the Wilson delayed-shock mechanism
effective in multidimensional models. However, the energetics of these models must be
fully explored and many more models are needed. More important, these models must be
extended to three dimensions.

# Technical Description

While a prodigious amount of neutrino energy emerges from the PNS, the neutrinos are weakly coupled to the material directly below the shock. The neutrino heating is very sensitive to the distribution of neutrinos in energy (or, equivalently, frequency and direction of propagation (specified uniquely by two angles), at any given spatial point behind the shock. In turn, this ultimately requires multi-frequency, multi-angle (Boltzmann) neutrino transport in order to compute accurately the neutrino distributions in this region in frequency and angle. This renders the core-collapse supernova problem a truly multidimensional [six dimensional (space plus neutrino frequency and angles)], exascale problem. On petascale architectures an approach to this ultimate goal must be staged, beginning with 3D, multi-frequency moments models of the neutrino radiation field and progressing eventually to multi-frequency, multi-angle Boltzmann models. In these moments models, the neutrino distributions in angle are approximately represented by the lowest order angular moments of the neutrino distribution function: the neutrino energy density and three momentum densities (one for each spatial dimension), all as a function of neutrino frequency. While this is an approximation to the full Boltzmann treatment, moments models can be quite sophisticated and can describe well what would be obtained if the Boltzmann equation were solved directly. One such approach is known as multi-frequency flux-limited diffusion and is a ''one-moment'' model that solves for the neutrino energy density as a function of frequency. A second, more sophisticated, approach is to use a ''two-moment'' Variable Eddington Tensor (VET) model in which we solve for both the neutrino energy density and the three neutrino momentum densities as a function of frequency. The ORNL group has three major code lines: (1) Agile-BOLTZTRAN, which was the first supernova code to include exact general relativity and Boltzmann kinetic theory for the neutrino transport. (2) CHIMERA, which is our current production code for two- and three-dimensional simulations and includes approximate general relativity, multi-frequency neutrino transport in the ray-by-ray, multi-group flux-limited diffusion approximation, and state-of-the-art weak interaction and nuclear equation of state physics. (3) GenASiS, which is the ORNL collaboration's next-generation, supernova code. GenASiS will include all of the physics included in the CHIMERA code but will improve upon (a) the neutrino transport by introducing more sophisticated multi-frequency neutrino transport via the Variable Eddington Tensor method and, ultimately, multi-angle, multi-frequency Boltzmann neutrino kinetics, and not in the ray-by-ray approximation in either case, and (b) the treatment of gravity, first through the introduction of the Conformally Flat Approximation and finally through the implementation of the BSSNOK approach, the latter of which will enable singularity avoidance and the ability to treat cases in which black holes form at the center of the explosion. GenASiS also includes magnetic fields, which CHIMERA does not.

# Publications

• Endeve, E., Cardall, C.Y., Budiardja, R.D., Beck, S.W., Bejnood, A., Toedte, R.J.,
and Mezzacappa, A. 2012, Turbulent Magnetic Field Amplification from Spiral SASI Modes:
Implications for Core-Collapse Supernovae and Proto-Neutron Star Magnetization. Ap.J. 751, 26.

• Lentz, E.J., Mezzacappa, A., Messer, O.E.B., Liebendorfer, M., Hix, W.R.,
Bruenn, S.W. 2012. On the Requirements for Realistic Modeling of Neutrino Transport in
Simulations of Core-collapse Supernovae. Ap. J. 747, 73.

• Yakunin, K.N., Marronetti, P., Mezzacappa, A., Bruenn, S.W.,
Lee, C.-T., Chertkow, M.A., Hix, W.R., Blondin, J.M., Lentz, E.J., Messer,
O.E.B., and Yoshida, S. 2010. Gravitational Waves from Core Collapse Supernovae.
Class. Quant. Grav. 27, 194005.

• Endeve, E., Cardall, C. Y., Budiardja, R. D., and Mezzacappa, A. 2010.
Generation of Magnetic Fields by the Stationary Accretion Shock Instability. Ap.J. 713, 1219.

• Bruenn, S. W., Mezzacappa, A., Hix, W. R., Blondin, J. M., Marronetti, P., Messer,
O.E.B., Dirk, C. J., and Yoshida, S. 2009. 2D and 3D Core-Collapse Supernovae Simulation
Results Obtained with the CHIMERA Code, Journ. Phys. Conf. Ser. 180, 012018.

• Blondin, J. M. and Mezzacappa, A. 2007. Pulsar Spins from an Instability in the
Accretion Shock of Supernovae, Nature 445, 58.

• Liebendorfer, M., Rampp, M., Janka, H.-Th., and Mezzacappa, A. 2005.
Supernova Simulations with Boltzmann Neutrino Transport: A Comparison of Methods,
Ap. J. 620, 840.

• Liebendorfer, M., Messer, O.E.B., Mezzacappa, A., Bruenn, S. W., Cardall,
C. Y., and Thielemann, F.-K. 2004. A Finite Difference Representation of Neutrino
Radiation Hydrodynamics for Spherically Symmetric General Relativistic Supernova
Simulations, Ap. J. Suppl. 150, 263.

• Hix, W. R., Messer, O.E.B., Mezzacappa, A., Sampaio, J., Langanke, K.,
Dean, D. J., and Martinez-Pinedo, G. 2003. The Consequences of Nuclear Electron
Capture in Core-Collapse Supernovae, Phys. Rev. Lett. 91, 201102.

• Langanke, K., Martinez-Pinedo, G., Sampaio, J. M., Dean, D. J., Hix, W. R.,
Messer, O.E.B., Mezzacappa, A., Liebendorfer, M., Janka, H.-T., and Rampp, M. 2003.
Electron Capture Rates on Nuclei and Implications for Stellar Core Collapse,
Phys. Rev. Lett. 90, 241102.

• Cardall, C. Y. and Mezzacappa, A. 2003. Conservative Formulations of
Relativistic Kinetic Theory, Phys. Rev. D68, 023006.

• Blondin, J. M., Mezzacappa, A., and DeMarino, C. 2003.
Stability of Standing Accretion Shocks, With an Eye Toward Core-Collapse
Supernovae, Ap. J. 584, 971.

• Bruenn, S. W., DeNisco, K. R., and Mezzacappa, A. 2001. General Relativistic
Effects in the Core-Collapse Supernova Mechanism, Ap. J. 560, 326.

• Liebendorfer, M., Mezzacappa, A., Thielemann, F.-K., Messer, O.E.B., Hix, W. R.,
and Bruenn, S. W. 2001. Probing the Gravitational Well: An Energetic Supernova Explosion
with Boltzmann Neutrino Transport in General Relativity, Phys. Rev. D63, 103004.

• Mezzacappa, A., Liebendorfer, M., Messer, O.E.B., Hix, W. R., Thielemann, F.-K.,
and Bruenn, S. W. 2001. Simulation of the Spherically Symmetric Stellar Core Collapse,
Bounce, and Postbounce Evolution of a Star of 13 Solar Masses with Boltzmann Neutrino
Transport, and Its Implications for the Supernova Mechanism, Phys. Rev. Lett. 86, 1935.

• Mezzacappa, A., Calder, A. C., Bruenn, S. W., Blondin, J. M., Guidry, M. W.,
Strayer, M. R., and Umar, A. S. 1998. An Investigation of Neutrino-driven Convection
and the Core-Collapse Supernova Mechanism Using Multigroup Neutrino Transport, Ap. J. 495, 911.

• Mezzacappa, A., Calder, A. C., Bruenn, S. W., Blondin, J. M., Guidry, M. W.,
Strayer, M. R., and Umar, A. S. 1998. The Interplay Between Proto-neutron Star
Convection and Neutrino Transport in Core-Collapse Supernovae, Ap. J. 493, 848.

• Mezzacappa, A. and Bruenn, S. W. 1993. Stellar Core Collapse:
A Boltzmann Treatment of Neutrino-Electron Scattering, Ap. J. 410, 740.

• Mezzacappa, A. and Bruenn, S. W. 1993. A Numerical Method for Solving the
Neutrino Boltzmann Equation Coupled to Spherically Symmetric Stellar Core Collapse,
Ap. J. 405, 669.

• Mezzacappa, A. and Bruenn, S. W. 1993. Type II Supernovae and Boltzmann
Neutrino Transport: The Infall Phase, Ap. J. 405, 637.

• Mezzacappa, A. and Matzner, R. A. 1989. Computer Simulation of Time-Dependent,
Spherically Symmetric Space Times Containing Radiating Fluids - Formalism and Code
Tests, Ap. J. 343, 853.

# Presentations

# For More Information

The following links will let you learn more about this topic:

• Computational Astrophysics at ORNL• Core Collapse Supernova Visualization

# Contacts

Raph Hix, raph at ornl.gov