Neutrino radiation-hydrodynamics & equation of state	

K. Sumiyoshi	

Crab nebula	

(Numazu College of Technology / KEK)	

hubblesite.org	

With K. Nakazato, S. Yamada, C. Ishizuka, H. Suzuki,	

H. Matsufuru, A. Imakura, T. Sakurai,	

H. Nagakura, S. Furusawa	

Brief report on: 	KEK	YITP	• Progress of EOS tables in astrophysics	

• 3D neutrino-radiation hydrodynamics	

Bridge @Ise-Shima, 2011. 12. 4.	

1�Collaborations on supernova studies	• Quark, Nuclear Physics	

– EOS, ν-reactions	• Massive Star Models	– Mass, Metallicities	

A01, A02	

A03	

• Simulations of supernovae	

parallel computing	- ν-radiation hydrodynamics	

A04	

A03	

Nucleosynthesis	

Explosion mechanism	 Neutrino Astronomy	Abundance	

Super-Kamiokande	ν	SN1987A	

ν	2�

Progress of EOS tables in astrophysics!
→石塚 12/3	
• Web pages for EOS table�
• Nuclear Compositions in supernovae�
Furusawa et al. ApJ (2011)	

→古澤 12/4	

• Probe hyperon potential by neutrinos�
Nakazato et al. ApJ (2011) accepted	

• QCD critical point sweep�(中里, 大西)	

Ohnishi et al. Phys. Lett. B (2011)	

3�

Supernova EOS covering the wide range	

•

Tables of EOS frequently used	–

Lattimer-Swesty EOS (1991)	

•–LS-EOS	Skyrme-interaction	

H. Shen, Toki, Oyamatsu & Sumiyoshi EOS (1998)	

Shen-EOS	
•

Relativistic Mean Field (RMF) approach	

1. Extension to high densities (ρ > ρ0=0.17fm-3)	

–Hyperons, Quarks•

			Softening of EOS	Ishizuka, Nakazato, H. Shen	

2. Extension to low densities (ρ < ρ0)	–Mixture of nuclei•Furusawa				Neutrino reactions	– Nuclear interactions, many body theories	

•G. Shen et al. (2011), Hempel et al. (2011)	

→富樫 12/3	4�

More massive stars lead to black holes	

Fe-core of	~ 40Msun star	

Accretion, MPNS↑	ν	Black hole	Collapse	

Core bounce	massive	ν	No explosion	ν	t=0s	t~0.2s	fat Proto-	neutron star	t~1s	Super-Kamiokande	• Short duration of neutrino burst:		

- Shen EOS: 1.3s	

failed supernova ν 		- Hyperon EOS: shorter	4 ν	AGalacticcase:
10• Probe of exotic EOS at high ρ and T	

Sumiyoshi et al. PRL (2006), ApJ (2009)	

Nakazato et al. PRD (2010)	

5

Neutrino burst from failed supernovae	

• Probe EOS difference due to hyperon potential	

– Repulsive or attractive?: Σ-potential in matter	

Hyperon	Shen	
Neutrino luminosity	Neutrino average energy	
Attractive	Repulsive	

UΣΣ== +30-30 MeV	MeV	U
Repulsive	
Attractive	

Hyperon mixture	in proto-neutron star	

Nakazato et al. ApJ (2011) accepted	

6�

Probe of exotic phase during the collapse	• ρ & T sweep critical point / phase boundary	

Ohnishi et al. Phys. Lett. B (2011)	

7�

3D neutrino-radiation hydrodynamics!
• Code of 3D Neutrino transfer�Sumiyoshi & Yamada, submitted to ApJ (2011)	

• Code of Hydrodynamics�
• Iterative method for matrix�→長倉 12/5	
→今倉 12/4	

8�

Status of neutrino radiation-transfer	• Affect neutrino heating for explosion	• 1D: first principle calculations	• 2D, 3D: approximate treatment	

Marek-Janka, ApJ 694 (2009)	

– Ray-by-ray (Radial transport only)		

Neglect lateral transport 	

• Need full 3D calculations 	

Ray-by-ray method:	

Solve 1D-transport Independently	

• New code to solve 3D neutrino-transfer	

• For the first time in the world	– Applications to supernova cores 	

Sumiyoshi & Yamada,
submitted to ApJ(2011)	

9�

To solve Neutrino transfer in 3D	

• Time evolution of 6D-distribution	Boltzmann eq.	
1 ∂fν  1 ⎛ δfν ⎞+ n ⋅ ∇fν = ⎜ ⎟c ∂tc ⎝ δt ⎠ collision– Left: Neutrino number change	

– Right: Change by neutrino reactions	€ν	θν	z	fν (r,θ, φ; εν ,θν , φν ; t)θ	– Neutrino energy (εν), Neutrino angle (θν, φν)	– Neutrino reactions, EOS table	

• Code: finite differencing, implicit	

– Linear eq. with large sparse matrix	φν	r	• 3D in spherical symmetry (r, εν, θν)	€ν	y	x	φ	10�Axially symmetric supernova core	• Fix the ρ, T, Ye profile & Solve 3D ν-transfer	ρ[g/cm3]	

T [MeV]	

Z	S [kB]	

Ye	Sumiyoshi, Yamada ApJ (2011) submitted	

ref. 1D, 15Msun, tpb=100ms	

11�Axially symmetric supernova core�• From small densities, the time evolution until the stationary state�νe	density	νe	

Radial	flux	

(r)	

Sumiyoshi, Yamada ApJ (2011) submitted	

νe	density	νe	

Polar	

flux	(θ)	

t=0~10ms	

12�Accretion disk around BH in collapsar	

From Sekiguchi (2011)	

• Polar flux of thermal neutrinos from disk	νµ density & flux	 Sumiyoshi (2011)	
Temperature [MeV]	

Preliminary	13�3D supernova core after bounce� From Takiwaki (2011)	
• Fix the ρ, T, Ye profile & Solve 3D ν-transfer	

Iso-Surface	ρ[g/cm3]	

S [kB]	

~ 200 km	

t=197ms	

14�Time evolution of neutrino transfer in 3D	

• Emitted neutrinos diffuse out and propagate	νe	density	νe	density	

Iso-Surface	

t=0~0.2ms	

Preliminary	

15�Development of 3D ν-transfer hydro. code	• 3D-neutrino transfer code: completed	– Neutrino-reactions, EOS tables: implemented	

• Diffusion, free-streaming tests: checked	• 1D profile, 2D, 3D formal solution: checked	

• Study 3D neutrino-transfer for static profile	– Applications to 2D, 3D profiles	

• Polar, azimuthal fluxes, beyond diffusion	

• MPI parallel version: done by Matsufuru	• Matrix inversion improvement by Imakura	– Need further optimizations to large systems	

• Coupling with hydrodynamics by Nagakura	

16�Thanks for collaboration with	

• Supernova research	• Supercomputing	– S. Yamada	– K. Nakazato	– H. Suzuki	

– H. Kikuchi	– H. Matsufuru	– A. Imakura	– T. Sakurai	

• Numerical simulations	• RMF-EOS table	

– H. Shen	

– K. Oyamatsu	

– H. Toki	• Extension of EOS table	

– S. Furusawa	– C. Ishizuka	– A. Ohnishi	•– H. Nagakura	– T. Takiwaki	– K. Kotake	– Y. Sekiguchi	Many body theory	– M. Takano	– H. Togashi and others	

Supercomputing resources at KEK, YITP,UT, RCNP, NAOJ, JAEA	

Core-collapse supernovae is one of
the target simulations on K-computer	

17�