2010 KEK (Japan) (Japan) (Japan) Cheoun, Myun -ki Soongsil (Korea) Ryu,, Chung-Yoe Soongsil (Korea)
1. S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 #013009 (1998) Magnetar : ~ 10 15 G ~ 10 17 19 G (?) P. Arras and D. Lai, P.R.D60, #043001 (1999) S. Ando, P.R.D68 #063002 (2003) 2
CasA 10 53 erg http://chandra.harvard.edu/photo/ 2004/casa/casa_xray.jpg ~ 10 15 G ~ 10 17 19 G (?) T = 20 40 MeV T.M., et al, arxiv:nucl-th/1009.0976 3
4 Birth of Proto-neutron Star core collapse trapping core bounce H He C+O Si Fe SN explosion shock in envelope shock propagation in core NS 4
2. Formulation 5 Magnetic Field : Baryon Lepton B & L Mag. Weak Interaction e + B e + B : scattering e + B e - + B : absorption
2-1 1 Neutron-Star Matter in RMF Approach + p-n Symmetry Force
EOS of PM1-1 BE = ρ * 16 MeV, M N / M N = 0.7, K = 200 MeV at 0 = 0.17 fm -3 g σ g Λ σ = g ω g Λ ω = 2 / 3 T.M, H. Shin, H. Fujii, & T. Tatsumi, PTP. 102, P809
EOS of Proto Neutron-Star Star-Matter at Finite Temperature 8 Charge Neutral ρ p = ρ e & Lepton Fraction : Y L = 0.4 2 g = g 3 Λ σ, ω σ, ω
2-2 2 Dirac Equation under Magnetic Fields µ N B << F (Chem. Pot) B ~ 10 17 G Perturbative calculation, Ignoring Landau Level Magnetic Part of Lagrangian Dirac Eq.
Fermi Distribution Spin Vector Dirac Spinor
The Cross-Section of Lepton-Baryon Scattering with σ = σ 0 + σ σ B
Spin-indep. part Spin-dep. Part
3 Results k i = (neutrino chem.pot.), B = 2 10 G and θ = ε 0 17 o i 3% difference
Magnetic Parts of Scattering Cross-Sections σ Sc = dω i dσ ( ) e dω f e 14 Neutrinos are more Scatterd in Arctic Area
Magnetic Parts of Absorption Cross-Sections σ Ab = dω f dσ ( e) e dω f 15 Neutrinos are less Absorbed in Arctic Area
Elements of 16 Scattering Cross-Sections at T = 20 MeV
Elements of Absorption Cross-Sections 17 Contribution from is small
4 Neutrino Absorption in Proto Neutron Star Neutrino Phase Space Distribution Function { 1+ exp [( p ε ) / ]} f ( p, r) f0( p, r) + f ( p, r), f0( p, r) = 1 T Equib. Part Non-Equib. Part Neutrino Propagation Boltzmann Eq. c d dx d f0( p, r) + c f ( p, r) = Icoll cb f ( p, r), b = dx σ V ab Solution f z 1 z ( p, rt, z) = dx f (p,rt,x) d yb y 0 0 exp x ( ) c x dε z = r pˆ, f0(p,rt,z) = f0(p,rt,z) z dz ε,
Baryon density in Proto-Neutron Star M = 1.68M solar T = 30 MeV Y L = 0.4 Calculating Neutrino Propagation above ρ B = ρ 0
Mean-Free Path when B =0 λ = ab 0 1 ab σ / V o σ = σ ab ab o ~ ( + σ cosθ ) 1 ab
Angular Dependence of Emitted Neutrino < p >= drdp ( p uˆ ) f ( p, r) Direction of Emitted Neutrino
< p θ Kick Velocity 2 4π 2 E T >= = 4πR P P 0 0 + P cosθ, 1 p z = 3 P 1 p E T z = P1 3P 0 = = 6. 0 10 2. 6 10-3 -3 p, n p, n, Λ Assuming Nuetrino Energy ~ 3 10 53 erg D.Lai & Y.Z.Qian, Astrophys.J. 495 (1998) L103 M v NS kick = 1.68M = p z M solar [g], E = 180[km/s] = 77 [km/s] T = 3 10 53 p, n p, n, Λ 22
4 Summary EOS RMF p,, n B 10 17 G 1.7 % 2.2 % at B = 3 and 0 T = 20 MeV B = 2 10 17 G B = 2 10 18 G 10% 1%, 23
EOS RMF p,, n, B = 2 2 10 17 G V kick = 180 km/s ( p,n ), 77 km/s (p,n(,n, 400 km/s ( (,, 280km/s (Lai & Qian) 1.7 % at ρ B = 3ρ 0, T = 20 MeV) T = 30 MeV 24