### Abstract

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 a 15 M _{⊙} star and compare them with the results in the latter computation. We also demonstrate multi-dimensional 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.

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

Article number | 17 |

Journal | Astrophysical Journal, Supplement Series |

Volume | 199 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Mar |

### Fingerprint

### Keywords

- methods: numerical
- neutrinos
- radiative transfer
- stars: massive
- stars: neutron
- supernovae: general

### ASJC Scopus subject areas

- Space and Planetary Science
- Astronomy and Astrophysics

### Cite this

**Neutrino transfer in three dimensions for core-collapse supernovae. I. Static configurations.** / Sumiyoshi, K.; Yamada, Shoichi.

Research output: Contribution to journal › Article

*Astrophysical Journal, Supplement Series*, vol. 199, no. 1, 17. https://doi.org/10.1088/0067-0049/199/1/17

}

TY - JOUR

T1 - Neutrino transfer in three dimensions for core-collapse supernovae. I. Static configurations

AU - Sumiyoshi, K.

AU - Yamada, Shoichi

PY - 2012/3

Y1 - 2012/3

N2 - 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 a 15 M ⊙ star and compare them with the results in the latter computation. We also demonstrate multi-dimensional 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.

AB - 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 a 15 M ⊙ star and compare them with the results in the latter computation. We also demonstrate multi-dimensional 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.

KW - methods: numerical

KW - neutrinos

KW - radiative transfer

KW - stars: massive

KW - stars: neutron

KW - supernovae: general

UR - http://www.scopus.com/inward/record.url?scp=84857845398&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84857845398&partnerID=8YFLogxK

U2 - 10.1088/0067-0049/199/1/17

DO - 10.1088/0067-0049/199/1/17

M3 - Article

VL - 199

JO - Astrophysical Journal, Supplement Series

JF - Astrophysical Journal, Supplement Series

SN - 0067-0049

IS - 1

M1 - 17

ER -