### Abstract

We have coded a Boltzmann solver based on a finite difference scheme (S_{N} method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find good overall agreement between the two methods. This gives credibility to both methods which are based on completely different formulations. In particular, the number and energy fluxes and the mean energies of the neutrinos show remarkably good agreement, because these quantities are determined in a region where the angular distribution of the neutrinos is nearly isotropic and they are essentially frozen in later on. On the other hand, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to slightly underestimate the flux factor and the Eddington factor outside the (mean) "neutrinosphere" where the angular distribution of the neutrinos becomes highly anisotropic. As a result, the neutrino number (and energy) density is somewhat overestimated in this region. This fact suggests that the Boltzmann solver should be applied to calculations of the neutrino heating in the hot-bubble region with some caution because there might be a tendency to overestimate the energy deposition rate in disadvantageous situations. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. Employing three different flux limiters, we find that all of them lead to a significant underestimation of the neutrino energy density in the semitransparent regime, and thus must yield too low values for the net neutrino heating (heating minus cooling) in the hot-bubble region. The accuracy of the Boltzmann solver can be improved by using a variable angular mesh to increase the angular resolution in the region where the neutrino distribution becomes anisotropic.

Original language | English |
---|---|

Pages (from-to) | 533-550 |

Number of pages | 18 |

Journal | Astronomy and Astrophysics |

Volume | 344 |

Issue number | 2 |

Publication status | Published - 1999 |

Externally published | Yes |

### Fingerprint

### Keywords

- Elementary particles
- Methods: Numerical
- Radiative transfer
- Stars: Neutron
- Stars: Supernovae: General

### ASJC Scopus subject areas

- Space and Planetary Science

### Cite this

*Astronomy and Astrophysics*,

*344*(2), 533-550.

**Neutrino transport in type II supernovae : Boltzmann solver vs. Monte Carlo method.** / Yamada, Shoichi; Janka, Hans Thomas; Suzuki, Hideyuki.

Research output: Contribution to journal › Article

*Astronomy and Astrophysics*, vol. 344, no. 2, pp. 533-550.

}

TY - JOUR

T1 - Neutrino transport in type II supernovae

T2 - Boltzmann solver vs. Monte Carlo method

AU - Yamada, Shoichi

AU - Janka, Hans Thomas

AU - Suzuki, Hideyuki

PY - 1999

Y1 - 1999

N2 - We have coded a Boltzmann solver based on a finite difference scheme (SN method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find good overall agreement between the two methods. This gives credibility to both methods which are based on completely different formulations. In particular, the number and energy fluxes and the mean energies of the neutrinos show remarkably good agreement, because these quantities are determined in a region where the angular distribution of the neutrinos is nearly isotropic and they are essentially frozen in later on. On the other hand, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to slightly underestimate the flux factor and the Eddington factor outside the (mean) "neutrinosphere" where the angular distribution of the neutrinos becomes highly anisotropic. As a result, the neutrino number (and energy) density is somewhat overestimated in this region. This fact suggests that the Boltzmann solver should be applied to calculations of the neutrino heating in the hot-bubble region with some caution because there might be a tendency to overestimate the energy deposition rate in disadvantageous situations. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. Employing three different flux limiters, we find that all of them lead to a significant underestimation of the neutrino energy density in the semitransparent regime, and thus must yield too low values for the net neutrino heating (heating minus cooling) in the hot-bubble region. The accuracy of the Boltzmann solver can be improved by using a variable angular mesh to increase the angular resolution in the region where the neutrino distribution becomes anisotropic.

AB - We have coded a Boltzmann solver based on a finite difference scheme (SN method) aiming at calculations of neutrino transport in type II supernovae. Close comparison between the Boltzmann solver and a Monte Carlo transport code has been made for realistic atmospheres of post bounce core models under the assumption of a static background. We have also investigated in detail the dependence of the results on the numbers of radial, angular, and energy grid points and the way to discretize the spatial advection term which is used in the Boltzmann solver. A general relativistic calculation has been done for one of the models. We find good overall agreement between the two methods. This gives credibility to both methods which are based on completely different formulations. In particular, the number and energy fluxes and the mean energies of the neutrinos show remarkably good agreement, because these quantities are determined in a region where the angular distribution of the neutrinos is nearly isotropic and they are essentially frozen in later on. On the other hand, because of a relatively small number of angular grid points (which is inevitable due to limitations of the computation time) the Boltzmann solver tends to slightly underestimate the flux factor and the Eddington factor outside the (mean) "neutrinosphere" where the angular distribution of the neutrinos becomes highly anisotropic. As a result, the neutrino number (and energy) density is somewhat overestimated in this region. This fact suggests that the Boltzmann solver should be applied to calculations of the neutrino heating in the hot-bubble region with some caution because there might be a tendency to overestimate the energy deposition rate in disadvantageous situations. A comparison shows that this trend is opposite to the results obtained with a multi-group flux-limited diffusion approximation of neutrino transport. Employing three different flux limiters, we find that all of them lead to a significant underestimation of the neutrino energy density in the semitransparent regime, and thus must yield too low values for the net neutrino heating (heating minus cooling) in the hot-bubble region. The accuracy of the Boltzmann solver can be improved by using a variable angular mesh to increase the angular resolution in the region where the neutrino distribution becomes anisotropic.

KW - Elementary particles

KW - Methods: Numerical

KW - Radiative transfer

KW - Stars: Neutron

KW - Stars: Supernovae: General

UR - http://www.scopus.com/inward/record.url?scp=3943054851&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3943054851&partnerID=8YFLogxK

M3 - Article

VL - 344

SP - 533

EP - 550

JO - Astronomy and Astrophysics

JF - Astronomy and Astrophysics

SN - 0004-6361

IS - 2

ER -