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Asymmetric Neutrino Emission from Strongly Magnetized Neutron Star (強磁性中性子星からの非対称ニュートリノ放出). Tomoyuki MARUYAMA BRS, Nihon Univ. (Japan). Collaborators Toshitaka KAJINO Nao, Univ. of Tokyo (Japan) Nobutoshi YASUTAKE INFN, Catania (Italy)
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Asymmetric Neutrino Emission fromStrongly Magnetized Neutron Star(強磁性中性子星からの非対称ニュートリノ放出) Tomoyuki MARUYAMA BRS, Nihon Univ. (Japan) Collaborators ToshitakaKAJINONao, Univ. of Tokyo (Japan) NobutoshiYASUTAKEINFN, Catania (Italy) Myung-kiCHEOUNSoongs Univ.(Korea) Chung-YeolRYU Soongs Univ. (Korea) Jun HIDAKA Nao (Japan) G.J. MATHEWS Univ. of Notre Dome(USA) + Takami KURODA Nao (Japan) 1
Structure of Proto-Neutron Stars:Strange Matter, Ferromagnetism Observable Information ‥‥Neutrino Emissions S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 #013009 (1998) Influence from Hyperons Λ,∑ Ferromagnetism → Large Asymmetry? P. Arras and D. Lai, P.R.D60, #043001 (1999) S. Ando, P.R.D68 #063002 (2003) Magnetar 1015G in surface 1017-19G inside (?) Our Works ⇒ Neutrino Reactions on High Density Matter with with Strong Mag. Fields in the Relativistic Mean-Field (RMF) Approach TM et al., PRD83, 081303(R) (2011) Neutrino Scattering & Absorption in Surface Region §1. Introduction 4
Pulsar Kick CasA A.G.Lyne, D.R.Lomier, Nature 369, 127 (94) Asymmetry of Supernova Explosion kick and translate Pulsar with Kick Velocity: Average … 400km/s, Highest … 1500km/s Explosion Energy ~ 1053 erg (almost Neutrino Emissions) 1% Asymmetry are sufficient to explain the Pulsar Kick http://chandra.harvard.edu/photo/ 2004/casa/casa_xray.jpg Present Work ‥ Neutrino Scattering and Absorption In Hot and Dense Neutron-Star-Matter Estimating Kick Velocity and Spin of NS 8
Baryon B & L – Mag. Lepton §2. Formulation Magnetic Field : • Proto-Nuetron-Star (PNS) Matter without Mag. Field • Baryon Wave Function under Mag. Field in Perturbative Way • Cross-Sections for n reactions Weak Interaction e+ B→ e + B : scattering e+ B→ e-+ B’ : absorption S.Reddy, M.Prakash and J.M. Lattimer, P.R.D58 #013009 (1998)
EOS of PM1-1 T.M, H. Shin, H. Fujii, & T. Tatsumi, Prog. Theo. Phys. Vol.102, P809
EOS of Proto Neutron-Star-Matter Charge Neuttral ( ) & Lepton Fraction : Yp = 0.4
§2-2 Dirac Equation under Magnetic Fields Magnetic Part of Lagrangian Dirac Eq. NB << εF (Chem. Pot) →Bcan be treated perturbatively Landau Level can be ignored ~1017 G
3 negligibly small Dirac Spinor Spin Vector 14
Fermi Distribution Momentum Distr. of Major Part is deformed as oblate • Relativistic Effects of Magnetic Contributions • Momentum Dependent of Spin Vector • Deformation of Fermi Distribution 15
Landau Level Electron When B → 0 , the wave function → plane wave
§2-3 The Cross-Section of ν-B Fermi Distribution Deformed Distribution Perturbative Treatment Magnetic Part Non-Magnetic Part 17
The Cross-Section of Lepton-Baryon Scattering with Spin-independent part
Electron Contribution Single Particle Energy Sum of Landau Level Expectation Value of Quantity A Perturbation Spin vector
§3 Results of Cross-Sections No magnetic field
Differential Cross-Sections in Magnetic Field 3% difference
Increasing in Dir. parallel to B Magnetic parts of Cross-Sections Scat. Integrating over the initial angle Absorp. Integrating over the final angle 25
Neutrino Mean-Free Paths scattering absorption
EOS of Neutron-Star-Matter with p, n Λ in RMF Appraoch • Cross-Sections of Neutrino Scattering and Absorption under Strong Magnetic Field, calculated in Perturbative Way • Neutrinos are More Scattered and Less Absorbed in Direction Parallel to Magnetic Field ⇒ More Neutrinos are Emitted in Arctic Area Scattering 1.7 % Absorption 2.2 % at ρB=3ρ0 and T = 20 MeV 30
§4 Estimating Pulsar Kick Velocities of Proto-Neutron Star CasA A.G.Lyne, D.R.Lomier, Nature 369, 127 (94) Asymmetry of Supernova Explosion kick and translate Pulsar with Kick Velocity: Average … 400km/s, Highest … 1500km/s http://chandra.harvard.edu/photo/ 2004/casa/casa_xray.jpg Explosion Energy ~ 1053 erg (almost Neutrino Emissions) 1% Asymmetry issufficient to explain the Pulsar Kick D.Lai & Y.Z.Qian, Astrophys.J. 495 (1998) L103 Estimating Kick Velocity of PNS with T = 20 MeV and B = 2× 1017G Poloidal Magnetic Field2‐3% AsymmetryinAbsorption 31
Neutrino Transportation Equil. Part Non-Equil. Part Neutrino Phase Space Distribution Function Other Pieces are equilibrium Neutrino Propagation ⇒ BoltzmannEq. only absorption Neutrinos Propagate on Strait Line Solution ⇒
Mean-Free Paths Magnetic Parts Scattering SA: fitting function Absorption
Baryon density in Proto-Neutron Star M = 1.68Msolar YL= 0.4 Calculating Neutrino Propagation above rB = r0
Baryon density in Proto-Neutron Star T = 20 MeV M = 1.68 Msolar YL= 0.4 Calculating Neutrino Propagation above rB = r0
θ \ Neutrino Propagation • Neutrinos • propagate on the straight lines • 2) Neutrino are created and absorbed at all positions on the lines • Mean-Free Path • : σab/V
Angular Dep.of Emitted Neutrinos inUniform Poloidal Mag. Field T = 20 MeV Observable Average … 400km/s, p, n p, n, L
§5 Angular Deceleration in Toroidal Magnetic Field Stability of Magnetic Field in Compact Objects (Braithwaite & Spruit 2004) Toroidal Magnetic Field is stable !! Mag. Field Parallel to Baryonic Flow Assym. of n-Emit. must decelerate PNS Spin 38
No poloidal Magnetic Field at the beginning Single Toroidal by T. Kuroda
Finite Polaidal Magnetic Field at the beginning Anti-paralleled Double Toroidal by黒田
Toroidal Magnetic Field T = 20MeV Dr = 0.5 (km) R0 = 8 (km) Mag.‐A R0 = 5 (km) Mag.‐B z = 0
Magnetic Dipole Rad. Angular Deceleration Neutrino Luminosity (dET/dt)n~3×1052 erg/s Period P = 10s In Early Stage (~10 s)n Asymmetric Emission must affect PNS Spin More Significantly than Magnetic Dipole g-Radiation 42
§5Summary 43 • EOS of Neutron-Star-Matter with p, n, Λ in RMF Approach • Exactly Solving Dirac Eq. with Magnetic Field in Perturbative Way • Cross-Sections of Neutrino Scattering and Absorption under Strong Magnetic Field, calculated in Perturbative Way • Neutrinos are More Scattered and Less Absorbed in Direction Parallel to Magnetic Field ⇒ More Neutrinos are Emitted in ArcticArea Scattering 1.7 % Absorption 2.2 % at ρB=3ρ0 and T = 20 MeV ⇒ Convection, Pulsar-Kick
Pulsar Kick in Poroidal Mag. Field B = 2× 1017G ⇒ Perturbative Cal. vkick = 580 km/s ( p,n ) , 610 km/s (p,n,Λ) at T = 20 MeV = 230 km/s ( p,n ) , 270 km/s (p,n,Λ) at T = 30 MeV 400 km/s (Average of Observed Values) Spin Deceleration in Toroidal Magnetic Field Asymmetric n-Emission plays an important role in PNS Spin in Early Time Future Plans n-Scattering Fixed Temp. ⇒ Constant Entropy Exact Solution of Dirac Eq. in Non-Perturbative Cal. → Landau Level at least for Electron Antarctic Dir. Reestimating when B = 1015G in the surface with r = r0 44
§2-1 Neutron-Star Matter in RMF Approach RMF Lagrangian, N, L, s, , r Dirac Eq. Scalar Field ⇒ Effective Mass
negligibly small Dirac Spinor Spin Vector
Spin-indep. part Spin-dep. Part
θ \ Neutrino Propagation • Neutrinos • propagate on the straight lines • 2) Neutrino are created and absorbed at all positions on the lines • Mean-Free Path • : σab/V
Absorption Mean-Free Path B = 0 30MeV SA: fitting function 50MeV 100MeV 200MeV 300MeV