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Register a new userA Finite Difference Representation of Neutrino Radiation Hydrodynamics in Spherically Symmetric General Relativistic Space-Time
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Added by
Matthias Liebendoerfer
Publication date
2002
fields
Physics
and research's language is
English
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We present an implicit finite difference representation for general relativistic radiation hydrodynamics in spherical symmetry. Our code, Agile-Boltztran, solves the Boltzmann transport equation for the angular and spectral neutrino distribution functions in self-consistent simulations of stellar core collapse and postbounce evolution. It implements a dynamically adaptive grid in comoving coordinates. Most macroscopically interesting physical quantities are defined by expectation values of the distribution function. We optimize the finite differencing of the microscopic transport equation for a consistent evolution of important expectation values. We test our code in simulations launched from progenitor stars with 13 solar masses and 40 solar masses. ~0.5 s after core collapse and bounce, the protoneutron star in the latter case reaches its maximum mass and collapses further to form a black hole. When the hydrostatic gravitational contraction sets in, we find a transient increase in electron flavor neutrino luminosities due to a change in the accretion rate. The muon- and tauon-neutrino luminosities and rms energies, however, continue to rise because previously shock-heated material with a non-degenerate electron gas starts to replace the cool degenerate material at their production site. We demonstrate this by supplementing the concept of neutrinospheres with a more detailed statistical description of the origin of escaping neutrinos. We compare the evolution of the 13 solar mass progenitor star to simulations with the MGFLD approximation, based on a recently developed flux limiter. We find similar results in the postbounce phase and validate this MGFLD approach for the spherically symmetric case with standard input physics.
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Massive stars end their life in an explosion event with kinetic energies of the order 1 Bethe. Immediately after the explosion has been launched, a region of low density and high entropy forms behind the ejecta which is continuously subject to neutrino heating. The neutrinos emitted from the remnant at the center, the protoneutron star (PNS), heat the material above the PNS surface. This heat is partly converted into kinetic energy and the material accelerates to an outflow that is known as the neutrino driven wind. For the first time, we simulate the collapse, bounce, explosion and the neutrino driven wind phases consistently over more than 20 seconds. Our numerical model is based on spherically symmetric general relativistic radiation hydrodynamics using spectral three flavor Boltzmann neutrino transport. In simulations where no explosions are obtained naturally, we model neutrino driven explosions for low and intermediate mass Fe-core progenitor stars by enhancing the charged current reaction rates. In the case of a special progenitor star, the O-Ne-Mg-core, the explosion in spherical symmetry was obtained without enhanced opacities. The post explosion evolution is in qualitative agreement with static steady-state and parametrized dynamic models of the neutrino driven wind. On the other hand, we find generally smaller neutrino luminosities and mean neutrino energies as well as a different evolutionary behavior of the neutrino luminosities and mean neutrino energies. The neutrino driven wind is proton-rich for more than 10 seconds and the contraction of the PNS differs from the assumptions made for the conditions at the inner boundary in previous neutrino driven wind studies. Despite the moderately large entropies per baryon of about 100 and the fast expansion timescale, the conditions found in our model are unlikely to favor...
We report on a set of long-term general-relativistic three-dimensional (3D) multi-group (energy-dependent) neutrino-radiation hydrodynamics simulations of core-collapse supernovae. We employ a full 3D two-moment scheme with the local M1 closure, three neutrino species, and 12 energy groups per species. With this, we follow the post-core-bounce evolution of the core of a nonrotating $27$-$M_odot$ progenitor in full unconstrained 3D and in octant symmetry for $gtrsim$$ 380,mathrm{ms}$. We find the development of an asymmetric runaway explosion in our unconstrained simulation. We test the resolution dependence of our results and, in agreement with previous work, find that low resolution artificially aids explosion and leads to an earlier runaway expansion of the shock. At low resolution, the octant and full 3D dynamics are qualitatively very similar, but at high resolution, only the full 3D simulation exhibits the onset of explosion.
An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. Again the formalism requires the knowledge of only one function (instead of two) to generate all possible solutions. To illustrate the method some known cases are recovered.
We present an analysis of the general relativistic Boltzmann equation for radiation, appropriate to the case where particles and photons interact through Thomson scattering, and derive the radiation energy-momentum tensor in the diffusion limit, with viscous terms included. Contrary to relativistic generalizations of the viscous stress tensor that appear in the literature, we find that the stress tensor should contain a correction to the comoving energy density proportional to the divergence of the four-velocity, as well as a finite bulk viscosity. These modifications are consistent with the framework of radiation hydrodynamics in the limit of large optical depth, and do not depend on thermodynamic arguments such as the assignment of a temperature to the zeroth-order photon distribution. We perform a perturbation analysis on our equations and demonstrate that, as long as the wave numbers do not probe scales smaller than the mean free path of the radiation, the viscosity contributes only decaying, i.e., stable, corrections to the dispersion relations. The astrophysical applications of our equations, including jets launched from super-Eddington tidal disruption events and those from collapsars, are discussed and will be considered further in future papers.
We discuss the averaging problem in general relativity, using the form of the macroscopic gravity equations in the case of spherical symmetry in volume preserving coordinates. In particular, we calculate the form of the correlation tensor under some reasonable assumptions on the form for the inhomogeneous gravitational field and matter distribution. On cosmological scales, the correlation tensor in a Friedmann-Lema^{i}tre-Robertson-Walker (FLRW) background is found to be of the form of a spatial curvature. On astrophysical scales the correlation tensor can be interpreted as the sum of a spatial curvature and an anisotropic fluid. We briefly discuss the physical implications of these results.
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