Towards Supernova Simulations with
Multi-Dimensional Boltzmann Transport～多次元ニュートリノ輻射流体コードの開発～
Hiroki Nagakura （長倉 洋樹）(HPCI researcher Kyoto Univ/Waseda Univ)
Collaborators:
Kohsuke Sumiyoshi (Numazu), Shoichi Yamada (Waseda)
Shun Furusawa (Waseda)
2011/12/3-5 素核宇 Workshop @ 合歓の郷Iseshima

Outline
1. Introduction
Standard Scenario for Core Collapse Supernova

2. Flow chart for developing numerical code
3. What I have done so far ?
Reconstruction of EOS table
Check the spherical collapse (Adiabatic calculation)
Sustaining the total energy conservation

4. Summary and Future WorkStandard Scenario for Core Collapse Supernovae（Delayed Explosion Scenario）
Detailed 1D spherical simulations failsupernova explosions.

Sumiyoshi et al. 2005 (Full Boltzmann Simulations in 1D )Catoon From Iwakami D thesis

Three-Dimensional Effect to Supernova
is still matter of debate.
Three-Dimensional Neutrino-Radiation (with Boltzmann Transport)
Hydrodynamics will give conclusive results of supernova physics.
Fe → 13 He + 4 n – 124 MeV
Neutrino Luminosity

Takiwaki et al. 2011

Nordhaus et al. 2010

Hanke et al. 2011

Approximate Neutrino Treatment (Methods differ from group to group.)
Hanke et al. 2011
Mass Accretion Rate
Nordhaus et al. 2010

200 – 300 km
Cartoon from Janka2. Flow chart for developing numerical code
Today’s talkMulti-Dimensional Hydrodynamic CodeHigh resolution central scheme
MICCG (Poisson solver for gravity)

Multi-Dimensional
Neutrino RadiationHydrodynamic CodeMulti-Dimensional Neutrino Transfer CodeDeveloped by K. Sumiyoshi

Some Important Assumptions
Neglect General Relativistic Effects
Neglect Magnetic Field Effects

Neglect Incoherent Neutrino Scattering Processes
Neglect Neutrino-Oscillations

Basic EquationsRad-Hydro Equations

Boltzmann Equation

Outline
1. Introduction
2. Flow chart for developing numerical code

3. What I have done so far ?
4. Summary and Future Work

3. What I have done so far ?
1. Reconstruction of EOS table
2. Check the spherical collapse(adiabatic calculation)

3. Sustaining the total energy conservation

Reconstruction of EOS Table
We employ Shen EOS in our simulations.
Low resolutions for direct tri-linear interpolations in simulations.
Reconstruction of EOS Table(Tri-Cubic Hermite Polynominal Interpolations)

Original TableT(Temperature)ε(internal energy)ρ (Density)

New Tableρ (Density)

Check the spherical collapse(Adiabatic calculation)
Density

Woosley 15 M_{sun}, M_{Fe} ～ 1.35 M_{sun}Velocity

Sustaining the total Energy Conservation
Difficulty of energy conservation
Iron Core

Dwarf
The explosion energy ofWhite
typicalSimilarisStructure
supernova
10^{51} erg.

E gra  1051 (erg )Eint  1051 (erg )NeutronStar

Etot  Ekin  Eint  E gra  1050 (erg )E gra  1053 (erg )The order of total energyis 0.1 % of gravitational(ineternal) energy of neutron stars.

Eint  1053 (erg )Energy Conservation
Standard Method
Muller Method
Muller +Adaptive Mesh

ここに数式を入力します。

Muller +Adaptive Mesh (high)Etot  Ekin  Eint  E graTime (s)The ratio of Gravitationalenergy for each mass shell

Proto Neutron Star| r  |The Adaptive Mesh2

Δ r (cm)

Radius (cm)Density＞
Gravitational Energy＜Radius (cm)Summary and Future work
The neutrino transport plays an crucial role for the delayed
explosion model.
I gave ad interim reports for developing Neutrino-Radiation
Hydrodynamic code.
The EOS table is reconstructed for satisfying thermodynamicrelation.
Our hydrodynamic code successfully simulates spherical corecollapse with good energy conservations.

Next steps
Multi-Dimensional Hydrodynamic Simulations.
Coupling with neutrino Boltzmann transport.

Work TableYe (Presupernova)
Ye (Liebendoerfer)

Ye 2
M ch  1.4( )0.5

Enclosed mass (M_{sun})Ye (Liebendoerfer)

Ye (constant)- Sound velocity

radialvelocity

Check the spherical collapse
Adiabatic Collapse (No coupling of neutrino)
Delayed Explosion
Scenario

Electron Capture (Ye )Fe → 13 He + 4 n – 124 MeV

Catoon From Iwakami D thesis