Numerical modeling of core-collapse supernovae …1 Numerical modeling of core-collapse supernovae!...
Transcript of Numerical modeling of core-collapse supernovae …1 Numerical modeling of core-collapse supernovae!...
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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
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→ 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
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
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neutrinos produced
Sumiyoshi et al. ApJ (2005)
No explosion in 1D (spherical calc.)
Problem: shockwave stalls on the way�
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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
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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
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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
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Astrophysics
composition
Calculation of ν-radiation transfer
Equilibrium�
Low T/ρ →
Neutrino heating�
Surface� Free-streaming �
Non-equilibrium�
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• 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
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x
y
z
θ
r
φ
ν
θν
φν
Boltzmann eq.
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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
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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 ��
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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�
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• 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
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diffusion
equlibrium
Validation of 3D-neutrino transfer code�
Sumiyoshi & Yamada ApJ (2012)
utilizing 1D ν-radiation hydrodynamics (GR) by Sumiyoshi et al. ApJ (2005)
Axially symmetric supernova core • Fix the ρ, T, Ye profile & Solve 3D ν-transfer
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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 �
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Fr Fθ
Fr
Fθ
Sumiyoshi, Yamada ApJ (2012)
2D supernova core�• Check of ray-by-ray
too strong angle dependence �
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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
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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 �
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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
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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
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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