THE ISOTROPIC DIFFUSION SOURCE APPROXIMATION FOR SUPERNOVA NEUTRINO TRANSPORT

By Mathias Liebendörfer, S. Whitehouse, Tobias Fischer. 2007

149 citations recorded by the source corpus.

Astrophysical observations originate from matter that interacts with radiation or transported particles. We develop a pragmatic approximation in order to enable multidimensional simulations with basic spectral radiative transfer when the available computational resources are not sufficient to solve the complete Boltzmann transport equation. The distribution function of the transported particles is decomposed into a trapped particle component and a streaming particle component. Their separate evolution equations are coupled by a source term that converts trapped particles into streaming particles. We determine this source term by requiring the correct diffusion limit for the evolution of the trapped particle component. For a smooth transition to the free streaming regime, this “diffusion source” is limited by the matter emissivity. The resulting streaming particle emission rates are integrated over space to obtain the streaming particle flux. Finally, a geometric estimate of the flux factor is used to convert the particle flux to the streaming particle density, which enters the evaluation of streaming particle–matter interactions. The efficiency of the scheme results from the freedom to use different approximations for each particle component. In supernovae, for example, reactions with trapped particles on fast timescales establish equilibria that reduce the number of primitive variables required to evolve the trapped particle component. On the other hand, a stationary-state approximation considerably facilitates the treatment of the streaming particle component. Different approximations may apply in applications to stellar atmospheres, star formation, or cosmological radiative transfer. We compare the isotropic diffusion source approximation with Boltzmann neutrino transport of electron flavor neutrinos in spherically symmetric supernova models and find good agreement. An extension of the scheme to the multidimensional case is also discussed.

Subfields: Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/69272729697895cc472e747a61299f3c926099be

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In Nuclear and High Energy Physics

Citations in the corpus

THREE-DIMENSIONAL HYDRODYNAMIC CORE-COLLAPSE SUPERNOVA SIMULATIONS FOR AN 11.2 M☉ STAR WITH SPECTRAL NEUTRINO TRANSPORT (2011, methodology): “…explosion is obtained for a rapidly rotating 13M⊙ progenitor of Nomoto & Mashimoto (1988) compared to the corresponding non-rotating model, in which the isotropic diffusion source approximation (IDSA) for the spectral neutrino transport (Liebendörfer et al. 2009) is implemented in the ZEUS code.”
AN OPEN-SOURCE NEUTRINO RADIATION HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE (2014, methodology): “More advanced leakage-like schemes which do actually transport neutrinos but are based on similar approximations as leakage schemes are include the work of Scheck et al. (2006) and the isotropic diffusion source approximation (IDSA) transport method Liebendörfer et al. (2009).”
A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE (2012, methodology): “Using yet another neutrino transport scheme, the “isotropic diffusion source approximation” (Liebendörfer et al. 2009) in the ray-by-ray-approximation and without νµ and ντ transport, an explosion has also been reported by Suwa et al. (2010) and Takiwaki et al. (2012) for an 11.2M⊙ and a 13M⊙…”
A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY (2010, methodology): “…this approach combine multi-dimensional Newtonian hydrodynamics with an up-todate treatment of the microphysics with multi-group neutrino transport methods of similar sophistication as in the onedimensional case (Livne et al. 2004; Buras et al. 2006b; Bruenn et al. 2006; Liebendörfer et al. 2009).”
Multiple physical elements to determine the gravitational-wave signatures of core-collapse supernovae (2011, methodology): “The IDSA scheme splits the neutrino distribu ion into two components (namely the streaming and trapped neutrinos), both of which are solved using separate numerical techniques (see, Liebendörfer et al. (2009) [90] for more details).”
A COMPARISON OF TWO- AND THREE-DIMENSIONAL NEUTRINO-HYDRODYNAMICS SIMULATIONS OF CORE-COLLAPSE SUPERNOVAE (2013, methodology): “In the original IDSA scheme, a steady-state approximation (∂f s/(∂t) = 0) is assumed.”