Asymmetric Neutrino Reaction in Magnetized Proto-Neutron Stars in Fully Relativistic Approach Tomoyuki Maruyama BRS, Nihon Univ. (Japan) Tomoyuki Maruyama BRS, Nihon Univ. (Japan) Toshitaka Kajino NAO & Univ. of Tokyo (Japan) Toshitaka Kajino NAO & Univ. of Tokyo (Japan) Nobutoshi Yasutake NAO (Japan) Nobutoshi Yasutake NAO (Japan) Myung-ki Cheoun Myung-ki Cheoun Soongs Univ. (Korea) Chung-Yeol Ryu Chung-Yeol Ryu Soongs Univ. (Korea) Tomoyuki Maruyama BRS, Nihon Univ. (Japan) Tomoyuki Maruyama BRS, Nihon Univ. (Japan) Toshitaka Kajino NAO & Univ. of Tokyo (Japan) Toshitaka Kajino NAO & Univ. of Tokyo (Japan) Nobutoshi Yasutake NAO (Japan) Nobutoshi Yasutake NAO (Japan) Myung-ki Cheoun Myung-ki Cheoun Soongs Univ. (Korea) Chung-Yeol Ryu Chung-Yeol Ryu Soongs Univ. (Korea) 1 TM et al., arXiv: , Phys. ReV. D (2011) in press

High Density Matter Study ⇒ Exotic Phases ⇒ Exotic Phases : Strange Matter, Ferromagnetism Meson Condensation, Quark matter, CSC, … Meson Condensation, Quark matter, CSC, … They may exist inside Neutron Stars (NSs) Observable Information Observable Information ‥ Neutrino Emissions from Proto-NS S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 # (1998) Influence from Hyperons Λ ， ∑ Magnetar G in surface G inside (?) Magnetic Field → Large Asymmetry ？ P. Arras and D. Lai, P.R.D60, # (1999) S. Ando, P.R.D68 # (2003) Neutrino Scattering & Absorption in Surface Region 2 §1. Introduction

Pulsar Kick Pulsar Kick

4 Pulsar Kick Asymmetry of Supernova Explosion kick and translate Pulsar with Kick Velocity: Average … 400km/s ， Highest … 1500km/s Explosion Energy ~ erg ( almost Neutrino Emissions) 1% Asymmetry are sufficient to explain the Pulsar Kick /casa/casa_xray.jpg CasA A.G.Lyne, D.R.Lomier, Nature 369, 127 (94) Present Work ‥ Neutrino Scattering and Absorption In Hot and Dense Neutron-Star-Matter Estimating Kick Velocity

5 §2. Formulation Magnetic Field : Baryon Lepton B & L – Mag. Weak Interaction e + B → e + B : scattering e + B → e - + B’ : absorption

§2-1 Neutron-Star Matter in RMF Approach RMF Lagrangian, N, 

Charge Neutral （ ） & Lepton Fraction : Y L = 0.4 EOS of Proto Neutron-Star-Matter PM1-L1 T.M, H. Shin, H. Fujii, & T. Tatsumi, PTP. 102, P809 7

§2-2 Dirac Equation under Magnetic Fields  N B << ε F (Chem. Pot) → B can be treated perturbatively Landau Level can be ignored Dirac Eq. ~ G Magnetic Part of Lagrangian

Spin Vector Dirac Spinor

Fermi Distribution Momentum Distribution of Major Part is deformed as oblate

The Cross-Section of Lepton-Baryon Scattering Perturbative Treatment Noraml PartMagnetic Part

Spin-indep. part Spin-dep. Part

§3 Results 3% difference

14 Magnetic parts of Cross-Sections Increasing to Arctic Dir. Scat. Absorp.

Elements of Absorption Cross-Sections Contribution from Λ is small 15

§4 Neutrino Absorption in Proto Neutron Star Neutrino Propagation ⇒ Boltzmann Eq. Neutrino Phase Space Distribution Function Equib. PartNon-Equib. Part Solution ⇒

\ θ Neutrino Propagation 1)Neutrinos propagate on the straight lines 2) Neutrino are created and absorbed at all positions on the lines Mean-Free path : σ ab /V

Baryon density in Proto-Neutron Star M = 1.68M solar Y L = 0.4 Calculating Neutrino Propagation above  B =  0

Mean-Free Path when B =0

Angular Dependence of Emitted Neutrino Direction of Emitted Neutrino

21 Kick Velocity p, n p, n,  Assuming Neutrino Energy ~ 3×10 53 erg D.Lai & Y.Z.Qian, Astrophys.J. 495 (1998) L103 p, n p, n,  T = 20 MeVT = 30 MeV

22 EOS of Neutron-Star-Matter with p, n Λ in RMF Appraoch EOS of Neutron-Star-Matter with p, n Λ in RMF Appraoch Cross-Sections of Neutrino Scattering and Absorption Cross-Sections of Neutrino Scattering and Absorption under Strong Magnetic Field, calculated in Perturbative Way under Strong Magnetic Field, calculated in Perturbative Way Neutrinos are More Scattered and Less Absorbed Neutrinos are More Scattered and Less Absorbed in Direction Parallel to Magnetic Field in Direction Parallel to Magnetic Field ⇒ More Neutrinos are Emitted in Arctic Area ⇒ More Neutrinos are Emitted in Arctic Area Scattering 1.7 % Scattering 1.7 % Absorption 2.2 % at ρ=3ρ Absorption 2.2 % at ρ B =3ρ 0 and T = 20 MeV ⇒ Convection, Pulsar-Kick §5 Summary

23 Estimating Pulsar Kick in Proto-Neutron-Star with Strong Magnetic Field with Strong Magnetic Field B = 2× G ⇒ Perturbative Calculations B = 2× G ⇒ Perturbative Calculations V kick = 300 km/s ( p,n ), 290 km/s (p,n,Λ ） at T = 20 MeV V kick = 300 km/s ( p,n ), 290 km/s (p,n,Λ ） at T = 20 MeV = 180 km/s ( p,n ), 77 km/s (p,n,Λ ） at T = 30 MeV = 180 km/s ( p,n ), 77 km/s (p,n,Λ ） at T = 30 MeV Antarctic Direction Antarctic Direction 400 km/s (Observed ）, 280km/s (Lai & Qian) 400 km/s (Observed ）, 280km/s (Lai & Qian) Future Plans Fixed Temp. ⇒ Constant Entropy Exact Solution of Dirac Eq. Exact Solution of Dirac Eq. Low Density Contribution is dominant Low Density Contribution is dominant → Landau Level at least for Electron → Landau Level at least for Electron Spin-Spin interaction Poloidal Mag. Field ⇒ Troidal Mag. Field

24 Birth of Proto-neutron Star 24

25 Structure of compact stars… nucleon pasta quark-hadron pasta 25 By D.Page

26 Temperature & lepton fraction in proto-neutron stars T = 40  5 MeV, Y L = 0.4  0.05 by A.Burrows et al. (1986)

Dirac Equation with Magnetic Fields

Dirac Spinor under the Magnetic Field

29 Stability of Magnetic Field in Compact Objects in Compact Objects (Braithwaite & Spruit 2004) Toroidal Magnetic Field is stable !!

EOS of PM1-1

31 §4 Summary EOS of Neutron-Star-Matter with p, n Λ in RMF Appraoch EOS of Neutron-Star-Matter with p, n Λ in RMF Appraoch Cross-Sections of Neutrino Scattering and Absorption Cross-Sections of Neutrino Scattering and Absorption under Strong Magnetic Field, calculated in Perturbative Way under Strong Magnetic Field, calculated in Perturbative Way Neutrinos are More Scattered and Less Absorbed Neutrinos are More Scattered and Less Absorbed in Direction Parallel to Magnetic Field in Direction Parallel to Magnetic Field ⇒ More Neutrinos are Emitted in Arctic Area ⇒ More Neutrinos are Emitted in Arctic Area Scattering 1.7 % Scattering 1.7 % Absorption 2.2 % at ρ=3ρ Absorption 2.2 % at ρ B =3ρ 0 and T = 20 MeV ⇒ Convection, Pulsar-Kick

Magnetic Parts of Scattering Cross-Sections 32

33 Magnetic Parts of Absorption Cross-Sections less absorp. Around θ i =0