EOS EOS
SN1987A Crab nebula (SN1054) A.K.Mann "Shadow of a Star" From http://hubblesite.org
重力崩壊型超新星爆発 中性子星 ブラックホールの誕生 重元素の起源 rプロセス 爆発的元素合成 銀河の進化 宇宙線 ガンマ線バースト 重力波 爆発メカニズムの解明 重力崩壊 コアバウンス 3 10 Explosion Dynamics Trapping, heating 2 10 ν νν ν Pt, Au 1 10 0 10 ν ν SUBAR U 10-1 10-2 10-3 100 150 200 http://subarutelescope.org/ Mass number Origin of Elements r-process, ν-process Super-Kamiokande ν http://www-sk.icrr.u-tokyo.ac.jp/ ν ν Dense Matter Astronomy Probe inside
Fe core ρ c ~10 10 g/cm 3 T c ~1 MeV ν ν- ρ c ~10 12 g/cm 3 T c ~2 MeV ν ν ν ν 1000 km ρ c ~3x10 14 g/cm 3 T c ~5 MeV ν ν ν ρ c ~4x10 14 g/cm 3 T c ~10 MeV ν ν ν Shockwave NS ~ 10 km NS T~0 MeV Y e <0.1
M Fe ~M NS ~ 1.4M solar, R Fe ~10 4 km R NS ~10 km ΔE Grav = GM 2 GM 2 ~ 10 53 erg R Fe R NS E exp ~ 10 51 erg E ν ~ 10 53 erg Macrophysics - - - Microphysics - - - 6
多次元流体力学計算 超新星爆発多次元流体計算の例 2D calc with rotation Shen-EOS 超新星爆発残骸 形状, 元素合成, 偏光 中性子星キック 非対称性 球対称:1D (非)軸対称:2D, 3D 回転, 磁場 流体力学的不安定性 対流, 組成混合 Jun. 2000 Wang 2002 Jan. 1997 7 Kotake et al. ApJ 595 (2003) 304
/ ν ν f(t,x,y,z,p x,p y,p z ) 6+1 ν ν ν ( ) / /
/ ν ν f(t,x,y,z,p x,p y,p z ) 6+1 ν ν f(e ν f ν (E ν ) ν ( ) 1.0 ρ c =10 14 g/cm 3 & 0.8 bounce 0.6 0.4 0.2 ρ c =10 12 / / ρ c =10 10-11 g/cm 3 0.0 1 10 MeV 100 MeV 1000 E ν [MeV] ν energy
9 SciDAC Review Spring 2006
ν (ρ, T, Y e ) : ε, p, S, µ n, µ p, X i, m *, ρ ν
: σ ~ A 2 ν / : e - + p ν + n e - + A ν + A e + + n ν + p : ν i + N ν i + N ν i + A ν i + A ν i + e ν i + e : e - + e + ν e + ν e γ ν i + ν i N + N N + N + ν i ν i i=e, µ, τ
Lattimer-Swesty EOS (1991) Skyrme-Hartree-Fock approach Relativistic EOS (Shen-Oyamatsu-Toki-Sumiyoshi, 1998) Relativistic Mean Field approach Hyperon EOS (Ishizuka-Ohnishi, 2006) Variational Approach (Kanzawa-Takano, 2005~) - 3D Skyrme Hartree-Fock EOS (Newton, Stone Mezzacappa, 2007) A=460 A=1400 (n b =0.08 fm -3, T=2.5 MeV, Y p =0.3) Fuller, Fowler & Newman, Bruenn (1989) Langanke-Pinedo (45<A<112) T. Otsuka & T. Suzuki, Fujita-RCNP Reddy, Horowitz, Yamada-Toki,
EOS n,p,e ρ ρ0 21pSA T=0 EOS
Approaches to obtain the EOS approach starts from ingredients Theory/Model empirical the parametrized EOS nuclear mass, size,... Phenomenological effective NN int. nuclear mass, size,... Liquid-Drop Model Droplet Model Thomas-Fermi Theory... Skyrme HF RMF AMD... many-body bare NN int. (AV18, Bonn, Paris,...) NN scattering,... Variational Calc. DBHF...
SN-EOS for supernova simulations Empirical J.M. Lattimer, F.D. Swesty NPA535(1991). Phenomenological (RMF-TM1) H. Shen, H. Toki, K. Oyamatsu, K. Sumiyoshi, NPA637(1998), PTP100(1998). many-body (AV18) under construction (21pSA-11) H. Kanzawa, K. Oyamatsu, K. Sumiyoshi, M. Takano, NPA791(2007) Mukherjee, Pandharipande, Phys. Rev. C 75, 035802 (2007).
The Nuclear EOS for Supernova Simulations! based on the Realistic Nuclear Potential! H. Kanzawa a, K. Oyamatsu b, K. Sumiyoshi c and M. Takano a! a Waseda Univ., b Aichi Shukutoku Univ., c Numazu CT! 1) The uniform EOS: AV18+UIX,! Vatiational many-body calculations! 2) The Thomas-Fermi calculations for atomic nuclei reproduce their empirical data.! NPA791 (2007) 232! 3) The SN-EOS is under construction!
Hix (Proc. Nuclei in the Cosmos X to be published) Protoneutron star size 20% 200ms Shock location 20% lepton, entropy gradient 10 10 10 14 g/cm 3 BH neutrino 21pSA9,10
(flux, spectra) : (40M solar ) Sumiyoshi et al., PRL (2006) ν ν Shen EOS ν 50 ν cf. Hyperon WW95: 40M solar ν 40 ν e ν e ν µ < E ν > [MeV] 30 20 ν e ν e 10 Hyperon- 0.7 Shen- 1.3 ν 0 0.0 0.5 1.0 time after bounce [sec] 1.5 Sumiyoshi, Yamada & Suzuki ApJ (2007) Sumiyoshi et al. (2008) in preparation
(Prakash) 0.5 ρ0 ρ0 GDR ρ0 2-3 ρ0 Heavy Ion Collision Bao et al., Phys. Rep.(2008) in press.(arxiv: 0804.3580) ρ > 2-3 ρ0 Hyperon, Meson Condensate, Qurak Matter (
T=0 w n, x w 0 + K 0 18n 0 2 n n 0 2 + 1 2 x 2 S 0 + L 3n 0 n n 0 ds( n) L = 3n 0 dn n=n0 S 0 = S( n ) 0
L, K0 EOS K. Oyamatsu and K. Iida, PTP 109, 631-650, 2003.
Efforts being done Estimate L value from global behavior of nuclear mass and size in nuclear chart with Prof. Iida (Kouchi U.), Drs. Kohama(RIKEN), Koura(JAEA), Abu-Ibrahim(Cairo U.) For nuclear size, we need to directly compare calculations and cross section measurements. Kurotama (Black sphere) model(21asb7) Glauber calculation of cross sections Preliminary result from nuclear mass L value is relatively large. (closer to EOS C than to EOS G)
(Shen EOS) Wigner-Seitz cell free n, p, α Thomas-Fermi
arxiv:0708.3197v1 (astro-ph)
RMF calculation by Maruyama, Chiba, Tatsumi 12$&2($&*30&3*"$(%#(425"*!!"#$%&'()*+,-"$(%#(./(0"--! Pasta structures appear.! Y p =0.5! Y p =0.1!!!
QMD calculations by Sonoda, Watanabe, Sato, Takiwaki, Yasuoka, Ebisuzaki Pasta phases at zero temperature Cooling of Hot nuclear matter(~10 MeV) down to 0.1 MeV Snapshots calculated for model 2 Sphere Rod Slab 0.100! 0 0.200! 0 0.393! 0 Red!Proton Blue!Neutron! 0 =0.168 fm -3 "Nuclear density#! Rod-like Bubbles 0.490! 0 Spherical Bubbles 0.575! 0 14
Shen EOS table size log10 (T(MeV) ) 31 grids log10(yp) 0.25 71 grids log10(ρb (g/cm3)) 15.4 104 grids 31 71 104 228,904 data points
EOS L / GDR K0 Heavy ion collision Nuclear Statistical Equilibrium Hartree-Fock RMF
hyperons, meson condensate, quark matter,...
EOS T, ρ, Yp Mega Grids nucastrodata.org, bigbangonline.org