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Register a new userNumerical modeling of core-collapse supernovae and compact objects
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K. Sumiyoshi
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Massive stars (M> 10Msun) end their lives with spectacular explosions due to gravitational collapse. The collapse turns the stars into compact objects such as neutron stars and black holes with the ejection of cosmic rays and heavy elements. Despite the importance of these astrophysical events, the mechanism of supernova explosions has been an unsolved issue in astrophysics. This is because clarification of the supernova dynamics requires the full knowledge of nuclear and neutrino physics at extreme conditions, and large-scale numerical simulations of neutrino radiation hydrodynamics in multi-dimensions. This article is a brief overview of the understanding (with difficulty) of the supernova mechanism through the recent advance of numerical modeling at supercomputing facilities. Numerical studies with the progress of nuclear physics are applied to follow the evolution of compact objects with neutrino emissions in order to reveal the birth of pulsars/black holes from the massive stars.
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The proposal that core collapse supernovae are neutrino driven is still the subject of active investigation more than fifty years after the seminal paper by Colgate and White. The modern version of this paradigm, which we owe to Wilson, proposes that the supernova shock wave is powered by neutrino heating, mediated by the absorption of electron-flavor neutrinos and antineutrinos emanating from the proto-neutron star surface, or neutrinosphere. Neutrino weak interactions with the stellar core fluid, the theory of which is still evolving, are flavor and energy dependent. The associated neutrino mean free paths extend over many orders of magnitude and are never always small relative to the stellar core radius. Thus, neutrinos are never always fluid like. Instead, a kinetic description of them in terms of distribution functions that determine the number density of neutrinos in the six-dimensional phase space of position, direction, and energy, for both neutrinos and antineutrinos of each flavor, or in terms of angular moments of these neutrino distributions that instead provide neutrino number densities in the four-dimensional phase-space subspace of position and energy, is needed. In turn, the computational challenge is twofold: (i) to map the kinetic equations governing the evolution of these distributions or moments onto discrete representations that are stable, accurate, and, perhaps most important, respect physical laws such as conservation of lepton number and energy and the Fermi--Dirac nature of neutrinos and (ii) to develop efficient, supercomputer-architecture-aware solution methods for the resultant nonlinear algebraic equations. In this review, we present the current state of the art in attempts to meet this challenge.
In this review article we discuss selected developments regarding the role of the equation of state (EOS) in simulations of core-collapse supernovae. There are no first-principle calculations of the state of matter under supernova conditions since a wide range of conditions is covered, in terms of density, temperature and isospin asymmetry. Instead, model EOS are commonly employed in supernova studies. These can be divided into regimes with intrinsically different degrees of freedom: heavy nuclei at low temperatures, inhomogeneous nuclear matter where light and heavy nuclei coexist together with unbound nucleons, and the transition to homogeneous matter at high densities and temperatures. In this article we discuss each of these phases with particular view on their role in supernova simulations.
We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino distributions by the discrete-ordinate (S_n) method with a fully implicit differencing for time advance. The Boltzmann equations are formulated in the inertial frame with collision terms being evaluated to the zeroth order of v/c. A basic set of neutrino reactions for three neutrino species is implemented together with a realistic equation of state of dense matter. The pair process is included approximately in order to keep the system linear. We present numerical results for a set of test problems to demonstrate the ability of the code. The numerical treatments of advection and collision terms are validated first in the diffusion and free streaming limits. Then we compute steady neutrino distributions for a background extracted from a spherically symmetric, general relativistic simulation of 15Msun star and compare them with the results in the latter computation. We also demonstrate multi-D capabilities of the 3D code solving neutrino transfers for artificially deformed supernova cores in 2D and 3D. Formal solutions along neutrino paths are utilized as exact solutions. We plan to apply this code to the 3D neutrino-radiation hydrodynamics simulations of supernovae. This is the first article in a series of reports on the development.
The impact of electron-capture (EC) cross sections on neutron-rich nuclei on the dynamics of core-collapse during infall and early post-bounce is studied performing spherically symmetric simulations in general relativity using a multigroup scheme for neutrino transport and full nuclear distributions in extended nuclear statistical equilibrium models. We thereby vary the prescription for EC rates on individual nuclei, the nuclear interaction for the EoS, the mass model for the nuclear statistical equilibrium distribution and the progenitor model. In agreement with previous works, we show that the individual EC rates are the most important source of uncertainty in the simulations, while the other inputs only marginally influence the results. A recently proposed analytic formula to extrapolate microscopic results on stable nuclei for EC rates to the neutron rich region, with a functional form motivated by nuclear-structure data and parameters fitted from large scale shell model calculations, is shown to lead to a sizable (16%) reduction of the electron fraction at bounce compared to more primitive prescriptions for the rates, leading to smaller inner core masses and slower shock propagation. We show that the EC process involves $approx$ 130 different nuclear species around 86 Kr mainly in the N = 50 shell closure region, and establish a list of the most important nuclei to be studied in order to constrain the global rates.
Core-collapse supernovae are among Natures most energetic events. They mark the end of massive star evolution and pollute the interstellar medium with the life-enabling ashes of thermonuclear burning. Despite their importance for the evolution of galaxies and life in the universe, the details of the core-collapse supernova explosion mechanism remain in the dark and pose a daunting computational challenge. We outline the multi-dimensional, multi-scale, and multi-physics nature of the core-collapse supernova problem and discuss computational strategies and requirements for its solution. Specifically, we highlight the axisymmetric (2D) radiation-MHD code VULCAN/2D and present results obtained from the first full-2D angle-dependent neutrino radiation-hydrodynamics simulations of the post-core-bounce supernova evolution. We then go on to discuss the new code Zelmani which is based on the open-source HPC Cactus framework and provides a scalable AMR approach for 3D fully general-relativistic modeling of stellar collapse, core-collapse supernovae and black hole formation on current and future massively-parallel HPC systems. We show Zelmanis scaling properties to more than 16,000 compute cores and discuss first 3D general-relativistic core-collapse results.
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