1 �

Numerical modeling of core-collapse supernovae���with progress in nuclear physics and supercomputing

K. Sumiyoshi

•  3D calculations of neutrino-transfer

(Numazu College of Technology)

Crab nebula

Bridge @Nara, 2012. 12. 16.

With H. Nagakura, S. Yamada, H. Matsufuru, A. Imakura, T. Sakurai

hubblesite.org

Talk mainly on:

Bridging nuclear, astrophysics by supercomputers

•  Simulations of supernovae - ν-radiation hydrodynamics

•  Quark, Nuclear Physics –  EOS, ν-reactions

Super-Kamiokande

SN1987A

ν

A01, A02

A03

Explosion mechanism Neutrino Astronomy

•  Supercomputing

2�

•  Massive Star Models –  Mass, Metallicities

A03

A04

ν

KEK YITP

Research products in 2008-2012 •  Equation of state (EOS) tables for supernovae

– Shen EOS tables + Hyperons, Quarks – Mixture of nuclei, neutrino reactions

•  Neutrino signals as probe of EOS – Neutrino bursts from proto-NS and BH – Dependence on massive stars, EOS

•  1D GR neutrino-radiation hydrodynamics

•  3D neutrino-transfer for supernovae – Solve Boltzmann eq. in 6D –  a new method for matrix solver

3 �

→ Togashi, Furusawa

→ Nakazato

→ Imakura

Phys. Rev x 3, ApJ x 2 JPG x 1

Phys. Rev x 2, ApJ x 4 PLB x 1

ApJS x 1, PTEP x 1 JSIAM x 1

16 papers

4 �

Neutrino-transfer is important�

Neutrino heating for explosion�

Role of neutrinos in supernova dynamics

1000 km

Fe core Collapse ν-trapping

e-capture

Core Bounce

νν ν

ν

Shockwaveνν

ν

ν

Explosion

NS

ν

ν

10 km

proto- Neutron star

Supernova neutrinos

Massive star

mean free path↓

ν-emission

5 �

neutrinos produced

Sumiyoshi et al. ApJ (2005)

No explosion in 1D (spherical calc.)

Problem: shockwave stalls on the way�

6 �

ν

Collapse

How to revive the shock propagation and trigger explosion?

Fe core

Core-bounce

•  Multi-dimensional effects •  Microphysics (EOS, ν-reactions) •  Neutrino heating mechanism

ν

Shockwave

ν

ν Explosion?

ν ν

ν ν ν

ν

ν

ν

~1% of neutrinos is used for explosion

1053 erg

1051 erg

Neutrino heating mechanism for revival of shock

Heating by neutrino absorption

Bethe & Wilson ApJ (1985)

νe + n → e- + p, νe + p → e+ + n

ν ν ν

~200km

Proto-NS

heating

Shock

Fe core surface

7 �

ν-heating

Delayed explosion �

€

Eν −heat ~ 2.2 ×1051 ΔM0.1Msolar

⎛

⎝ ⎜

⎞

⎠ ⎟ Δt0.1s⎛

⎝ ⎜

⎞

⎠ ⎟ erg

Transfer of energy from ν

Shock position

time [s]

100ms after bounce

Depends on neutrino energy/flux targets

Janka A&A (1996)

n

p

ν-heating occurs in the intermediate region

shockwave

ν-sphere

free-streaming

diffusion

ν

heating region

€

Qνi ≈110 MeV

s⋅ NLν Eν

2

R72 < µ >

Xi

⎛

⎝ ⎜

⎞

⎠ ⎟

€

< µ >=< cosθν >= 0 ~ 1flux factor:

8�ν ν center

R

outside

between diffusion & free-streaming

ν-heating rate

θν

Need to solve neutrino-transfer for angle distribution �

€

f (Eν ,θν )

ex. Diffusion approximation is not enough

Janka A&A (1996)

even 10~20 % change of ν-heating may affect the outcome: explosion

average energy, flux: Eν, Lν

Numerical simulation of supernovae

•  Hydrodynamics

•  ν-transfer(Boltzmann eq.) 　 distribution: f(t, r, Eν, θν)

•  Equation of state (EOS) (ρ, T, Ye)

•  ν-reaction rates (ρ, T, µi, Xi)

pressure

Nuclear Physics

absorb emit scatter

ν-heating, cooling, pressure

ρ, T, Ye profiles

Combination of hydrodynamics and neutrino transfer

9 �

Astrophysics

composition

10 �

3D Neutrino-transfer is a challenge�

Boltzmann equation in 6D�

Calculation of ν-radiation transfer

Equilibrium�

Low T/ρ →

Neutrino heating�

Surface� Free-streaming �

Non-equilibrium�

11�

•  Neutrino propagation from supernova core to outside with neutrino reactions in dense matter

Shock wave�

- Including non-equilibrium situation

- We cannot use Fermi-distributions

ν

neutrino energy distribution during collpase�

　ν energy 100 MeV

10 MeV

ρc=1012

ρc=1014 g/cm3

& bounce

ρc=1010-11 g/cm3

f(Eν)

Diffusion �←High T/ρ�

ν

ν ν proto-NS �

To solve neutrino transfer in 3D •  Work in 6D: 3D space + 3D momentum

–  Neutrino energy (εν), angle (θν, φν)

•  Time evolution of 6D-distribution

–  Left: Neutrino number change –  Right: Change by neutrino reactions

•  Energy, angle-dependent reactions –  Compositions by EOS tables

€

1c∂fν∂t

+ n ⋅ ∇ fν =

1cδfνδt

⎛

⎝ ⎜

⎞

⎠ ⎟

collision

€

fν (r,θ,φ; εν ,θν ,φν ; t)

ν

12�

x

y

z

θ

r

φ

ν

θν

φν

Boltzmann eq.

13�

Status of neutrino-transfer

•  1D: first principle calculations •  2D, 3D: approximate treatment –  Diffusion (with flux limiter)

Only good in central part –  Ray-by-ray (radial transport)

Neglect lateral transport

•  Need full 3D calculations - examine the approximations, to the grand challenge

•  New code to solve 3D neutrino-transfer •  For the first time in the world

1D-transport independently

Marek-Janka, ApJ 694 (2009)

Sumiyoshi & Yamada, ApJS (2012)

Ray-by-ray method

See Ott et al. ApJ(2008) for 2D Sn-method

Boltzmann eq. in spherical coordinate�

– Discrete in conservative form (Sn method) –  Implicit method in time

•  stability, time step, equilibrium – Collision term for ν-reactions

•  absorption, emission, scattering

€

1cδfνδt

⎛

⎝ ⎜

⎞

⎠ ⎟

collision

= jemission (1− fν ) −1

λabsoption

fν + Cinelastic[ fν∫ ( ʹ′ E ν , ʹ′ µ ν )d ʹ′ E ν ]

€

1c∂fν∂t

+µν

r2∂∂r(r2 fν ) +

1−µν2 cosφν

rsinθ∂∂θ(sinθfν ) +

1−µν2 sinφν

rsinθ∂fν∂φ

€

+1r∂∂µν

[(1−µν2 ) fν ]+

1−µν2 cosθ

rsinθ∂∂φν

(sinφν fν ) =1cδfνδt

⎛

⎝ ⎜

⎞

⎠ ⎟ collision

Eν,µν ν E´ν,µν´

€

µν = cosθν

14

Sumiyoshi & Yamada, ApJS (2012)

Energy, angle dependent

Neutrino reactions in collision term �

•  Emission & absorption:� � e- + p ↔ νe + n � �e- + A ↔ νe + A �́

� e+ + n ↔ νe + p •  Scattering: � � νi + N ↔ νi + N � �νi + A ↔ νi + A � •  Pair-process:�

�e- + e+ ↔ νi + νi � � � ���N + N ↔ N + N + νi +νi ��

15�

Bruenn (1985) +Shen

3 species: νe, νe, νµ

Basic sets for supernova simulations

Notes: iso-energetic scattering, linearize pair process Lorentz transformation being implemented

Supercomputing aspects: matrix solver�

16 �

•  Linear equation

•  Neutrino distribution –  Nspace=nr x nθ x nφ –  Nν=nε x nθν x nφν Nvector~106 x 103

•  Iterative method pre-conditioner by Imakura larger time step is possible

~factor 10 faster

•  Memory size

€

A f ν = d

Nvector ~109

200

150

100

50

0

num

ber o

f ite

ratio

ns

10-7 10-6 10-5 10-4

Δt [sec]

Imakura et al. SIAM (2012)

•  by analytic solutions – Gauss packet, free space – Formal solution along path – Approach to equilibrium

•  by spherical solutions – Fixed backgroud

•  collapse, bounce stages –  density, flux, moments –  ν-reactions, m. f. path

17�

diffusion

equlibrium

Validation of 3D-neutrino transfer code�

Sumiyoshi & Yamada ApJ (2012)

utilizing 1D ν-radiation hydrodynamics (GR) by Sumiyoshi et al. ApJ (2005)

18 �

Applications to 2D/3D supernovae�

demonstration of 3D code�

Axially symmetric supernova core •  Fix the ρ, T, Ye profile & Solve 3D ν-transfer

19 �

ρ[g/cm3] T [MeV]

S [kB]

Ye

Sumiyoshi, Yamada ApJ (2012) ref. 1D, 15Msun, tpb=100ms

Z

Axially symmetric supernova core �

20 �Sumiyoshi, Yamada ApJ (2012)

νe density

νe density

νe Radial flux (r)

νe Polar flux (θ)

t=0~10ms

•  From small densities, the time evolution until the stationary state�

Advantage of 3D neutrino-transfer�

•  describes polar flux –  beyond ray-by-ray –  beyond diffusion �

21�

Fr Fθ

Fr

Fθ

Sumiyoshi, Yamada ApJ (2012)

2D supernova core�•  Check of ray-by-ray

too strong angle dependence �

22�

Ray-by-ray �

νe density distribution �

Preliminary

From Takiwaki (2011)

-

11.2Msun, 2D

100ms

3D Boltzmann

€

δ =nrbr − n3Dn3D

deviation

Study of 3D neutrino-transfer in supernova core

3D neutrino distributions, flux, spectrum beyond approximations to explore new effects

23�

νe density iso-surface

Red: heating, Blue: cooling

3D profile by Takiwaki (2011)

ν-heating/cooling rates in 3D

Preliminary

Coupling with hydrodynamics�

•  2D hydro code is ready � •  1D collapse test �

24 �

Nagakura

working on the code for 2D/3D neutrino-radiation hydrodynamics

Computational load and future�

•  We have MPI parallel code + Hitachi tuning •  Matrix solver costs ~M3N

•  working on KEK, planned on K-computer •  needs Exa-scale for full 3D supernovae

25 �

Matsufuru, Hashimoto

machine� space� neutrino� memory � operations �

Current� 256 x 32 x 64� 8 x 12 x 14� 2TB � 6 Tera-flop�

K-computer � 512 x 64 x 128� 12 x 24 x 20� 200TB � 2 Peta-flop�

Exascale � 512 x 128 x 256� 24 x 24 x 24� 3PB� 80 Peta-flop�

Kotake et al. PTEP (2012)

Summary�•  Neutrino-transfer in 3 dimensions is possible

– Code to solve Boltzmann eq. in 6D – Collaboration with computational scientists (A04)

•  Matrix solver, Parallel coding, Tuning

•  Applying to 2D/3D supernova cores – Unique feature: Non-radial fluxes – Examine the approximations used so far

•  Ready to test ν-transfer + hydro. code –  toward the grand challenge of 3D supernovae

26 �

Support from: - HPCI Strategic Program Field 5 - Grant-in-Aid for Scientific Research (20105004, 20105005, 22540296, 24244036) - Supercomputing resources at KEK, YITP, UT, RCNP, K-computer