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Register a new userOn the Requirements for Realistic Modeling of Neutrino Transport in Simulations of Core-Collapse Supernovae
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We have conducted a series of numerical experiments with the spherically symmetric, general relativistic, neutrino radiation hydrodynamics code Agile-BOLTZTRAN to examine the effects of several approximations used in multidimensional core-collapse supernova simulations. Our code permits us to examine the effects of these approximations quantitatively by removing, or substituting for, the pieces of supernova physics of interest. These approximations include: (1) using Newtonian versus general relativistic gravity, hydrodynamics, and transport; (2) using a reduced set of weak interactions, including the omission of non-isoenergetic neutrino scattering, versus the current state-of-the-art; and (3) omitting the velocity-dependent terms, or observer corrections, from the neutrino Boltzmann kinetic equation. We demonstrate that each of these changes has noticeable effects on the outcomes of our simulations. Of these, we find that the omission of observer corrections is particularly detrimental to the potential for neutrino-driven explosions and exhibits a failure to conserve lepton number. Finally, we discuss the impact of these results on our understanding of current, and the requirements for future, multidimensional models.
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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.
The overwhelming evidence that the core collapse supernova mechanism is inherently multidimensional, the complexity of the physical processes involved, and the increasing evidence from simulations that the explosion is marginal presents great computational challenges for the realistic modeling of this event, particularly in 3 spatial dimensions. We have developed a code which is scalable to computations in 3 dimensions which couples PPM Lagrangian with remap hydrodynamics [1], multigroup, flux-limited diffusion neutrino transport [2], with many improvements), and a nuclear network [3]. The neutrino transport is performed in a ray-by-ray plus approximation wherein all the lateral effects of neutrinos are included (e.g., pressure, velocity corrections, advection) except the transport. A moving radial grid option permits the evolution to be carried out from initial core collapse with only modest demands on the number of radial zones. The inner part of the core is evolved after collapse along with the rest of the core and mantle by subcycling the lateral evolution near the center as demanded by the small Courant times. We present results of 2-D simulations of a symmetric and an asymmetric collapse of both a 15 and an 11 M progenitor. In each of these simulations we have discovered that once the oxygen rich material reaches the shock there is a synergistic interplay between the reduced ram pressure, the energy released by the burning of the shock heated oxygen rich material, and the neutrino energy deposition which leads to a revival of the shock and an explosion.
Theory holds that a star born with an initial mass between about 8 and 140 times the mass of the Sun will end its life through the catastrophic gravitational collapse of its iron core to a neutron star or black hole. This core collapse process is thought to usually be accompanied by the ejection of the stars envelope as a supernova. This established theory is now being tested observationally, with over three dozen core-collapse supernovae having had the properties of their progenitor stars directly measured through the examination of high-resolution images taken prior to the explosion. Here I review what has been learned from these studies and briefly examine the potential impact on stellar evolution theory, the existence of failed supernovae, and our understanding of the core-collapse explosion mechanism.
Bearing in mind the application to core-collapse supernovae, we study nonlinear properties of the magneto-rotational instability (MRI) by means of three- dimensional simulations in the framework of a local shearing box approximation. By changing systematically the shear rates that symbolize the degree of differential rotation in nascent proto-neutron stars (PNSs), we derive a scaling relation between the turbulent stress sustained by the MRI and the shear- vorticity ratio. Our parametric survey shows a power-law scaling between the turbulent stress ($<< w_{rm tot}>>$) and the shear- vorticity ratio ($g_q$) as $<<w_{rm tot}>> propto g_q^{delta}$ with its index $delta sim 0.5$. The MRI-amplified magnetic energy has a similar scaling relative to the turbulent stress, while the Maxwell stress has slightly smaller power-law index ($sim 0.36$). By modeling the effect of viscous heating rates due to the MRI turbulence, we show that the stronger magnetic fields or the larger shear rates initially imposed lead to the higher dissipation rates. For a rapidly rotating PNS with the spin period in milliseconds and with strong magnetic fields of $10^{15}$ G, the energy dissipation rate is estimated to exceed $10^{51} {rm erg sec^{-1}}$. Our results suggest that the conventional magnetohydrodynamic (MHD) mechanism of core-collapse supernovae is likely to be affected by the MRI-driven turbulence, which we speculate, on one hand, could harm the MHD-driven explosions due to the dissipation of the shear rotational energy at the PNS surface, on the other hand the energy deposition there might be potentially favorable for the working of the neutrino-heating mechanism.
We present self-consistent, axisymmetric core-collapse supernova simulations performed with the Prometheus-Vertex code for 18 pre-supernova models in the range of 11-28 solar masses, including progenitors recently investigated by other groups. All models develop explosions, but depending on the progenitor structure, they can be divided into two classes. With a steep density decline at the Si/Si-O interface, the arrival of this interface at the shock front leads to a sudden drop of the mass-accretion rate, triggering a rapid approach to explosion. With a more gradually decreasing accretion rate, it takes longer for the neutrino heating to overcome the accretion ram pressure and explosions set in later. Early explosions are facilitated by high mass-accretion rates after bounce and correspondingly high neutrino luminosities combined with a pronounced drop of the accretion rate and ram pressure at the Si/Si-O interface. Because of rapidly shrinking neutron star radii and receding shock fronts after the passage through their maxima, our models exhibit short advection time scales, which favor the efficient growth of the standing accretion-shock instability. The latter plays a supportive role at least for the initiation of the re-expansion of the stalled shock before runaway. Taking into account the effects of turbulent pressure in the gain layer, we derive a generalized condition for the critical neutrino luminosity that captures the explosion behavior of all models very well. We validate the robustness of our findings by testing the influence of stochasticity, numerical resolution, and approximations in some aspects of the microphysics.
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