Asymmetric Neutrino Emission from Strongly Magnetized Neutron Star (?????????????????????)

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Asymmetric Neutrino Emission fromStrongly
Magnetized Neutron Star(?????????????????????)
Tomoyuki MARUYAMA BRS, Nihon Univ.
(Japan)
Collaborators Toshitaka KAJINO Nao,
Univ. of Tokyo (Japan) Nobutoshi
YASUTAKE INFN, Catania
(Italy) Myung-ki CHEOUN Soongs
Univ. (Korea) Chung-Yeol
RYU Soongs Univ.
(Korea) Jun HIDAKA
Nao (Japan)
G.J. MATHEWS Univ. of Notre
Dome (USA) Takami KURODA
Nao (Japan)
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1. Introduction
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Birth of Proto-neutron Star
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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_x
ray.jpg
Present Work ? Neutrino Scattering and
Absorption In
Hot and Dense Neutron-Star-Matter
Estimating Kick Velocity and
Spin of NS
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2. Formulation
Magnetic Field

1. Proto-Nuetron-Star (PNS) Matter without Mag.
   Field
2. Baryon Wave Function under Mag. Field in
   Perturbative Way
3. 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)
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2-1 RMF Approach for Neutron-Star Mattter
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EOS of PM1-1
T.M, H. Shin, H. Fujii, T. Tatsumi, Prog.
Theo. Phys. Vol.102, P809
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EOS of Proto Neutron-Star-Matter
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2-2 Dirac Equation under Magnetic Fields
?N B ltlt eF (Chem. Pot) ? B can be treated
perturbatively
Landau Level can be ignored
1017 G
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negligibly small
Dirac Spinor
Spin Vector
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Momentum Distr. of Major Part is deformed as
oblate

• Relativistic Effects of Magnetic Contributions
• Momentum Dependent of Spin Vector
• Deformation of Fermi Distribution

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Electron
When B ? 0 , the wave function ? plane wave
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2-3 The Cross-Section of ?-B
Fermi Distribution
Deformed Distribution
Perturbative Treatment
Magnetic Part
Non-Magnetic Part
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The Cross-Section of Lepton-Baryon Scattering
Spin-independent part
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Spin-dependent Part
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Electron Contribution
Single Particle Energy
Sum of Landau Level
Expectation Value of Quantity A
Perturbation
Spin vector
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Final electron contribution in ne ? e-
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3 Results of Cross-Sections
No magnetic field
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Differential Cross-Sections in Magnetic Field
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Initial Angle-Dependence
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Magnetic parts of Cross-Sections
Scat.
Integrating over the initial angle
Absorp.
Integrating over the final angle
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Magnetic Parts of Cross-Sections
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Neutrino Mean-Free Paths
scattering
absorption
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Contribution of Each Element in Scattering Part
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Contribution of Each Element in Absorption Part
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CasA
4 Estimating Pulsar Kick Velocities of
Proto-Neutron Star
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_x
ray.jpg
Explosion Energy 1053 erg (almost
Neutrino Emissions) 1 Asymmetry is
sufficient 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 Field 2-3 Asymmetry in Absorption
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Neutrino Transportation
Neutrino Phase Space Distribution Function
Other Pieces are equilibrium
Neutrino Propagation ? Boltzmann Eq.
only absorption
Neutrinos Propagate on Strait Line
Solution ?
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Mean-Free Paths
Magnetic Parts
Scattering
SA fitting function
Absorption
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Baryon density in Proto-Neutron Star
M 1.68Msolar YL 0.4
Calculating Neutrino Propagation above rB r0
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Baryon density in Proto-Neutron Star
T 20 MeV M 1.68 Msolar YL 0.4
Calculating Neutrino Propagation above rB r0
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Neutrino Propagation

• Neutrinos
• propagate on the straight lines
• 2) Neutrino are created and absorbed at all
  positions on the lines
• Mean-Free Path
• sab/V

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Angular Dep. of Emitted Neutrinos in Uniform
Poloidal Mag. Field
p, n
p, n, L
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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
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No poloidal Magnetic Field at the beginning
Single Toroidal
by T. Kuroda
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Finite Polaidal Magnetic Field at the beginning
Anti-paralleled Double Toroidal
by ??
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Toroidal Magnetic Field
T 20MeV
Dr 0.5 (km) R0 8 (km) Mag.-A R0 5 (km)
Mag.-B
z 0
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Angular Deceleration
Neutrino Luminosity (dET/dt)n 31052 erg/s
Period P 10s
Mag Distr. Bary. B G at rB r0 (cm) (n emis.) (g rad.)
Mag-A p,n 1.01016 46.7 3.0210-2 4.8210-2 1.010-8
Mag-A p,n,L 1.61016 70.6 5.1910-2 8.2610-2 2.610-8
Mag-B p,n 2.61013 0.157 1.0110-4 1.6110-4 6.610-14
Mag-B p,n,L 4.21013 0.259 1.9010-4 3.0310-4 1.710-13
In Early Stage ( 10 s) n Asymmetric Emission
must affect PNS Spin More Significantly than
Magnetic Dipole g-Radiation
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5 Summary

• EOS of Neutron-Star-Matter with p, n, ? 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 Arctic Area
  
• Scattering 1.7
• Absorption 2.2 at ?B3?0 and T 20
  MeV
• ? Convection, Pulsar-Kick

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Pulsar Kick in Poroidal Mag. Field B 2
1017G ? Perturbative Cal. vkick 580 km/s (
p,n ) , 610 km/s (p,n,?) at T 20 MeV
230 km/s ( p,n ) , 270 km/s (p,n,?) 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.
Mag Distr. (P 10 s) (P 10 s)
Mag Distr. p,n p,n,L
Mag-A 4.810-3 5.210-3
Mag-B 6.110-3 7.210-3
Dpl. Rad. 9.810-11 9.810-11
Reestimating when B 1015G in the surface with
r r0
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EOS in Iso-Entropical Model
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2-1 Neutron-Star Matter in RMF Approach
RMF Lagrangian, N, L, s, ?, r
Dirac Eq.
Scalar Field ? Effective Mass
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negligibly small
Dirac Spinor
Spin Vector
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Neutrino Propagation

• Neutrinos
• propagate on the straight lines
• 2) Neutrino are created and absorbed at all
  positions on the lines
• Mean-Free Path
• sab/V

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Absorption Mean-Free Path
B 0
30MeV
SA fitting function
50MeV
100MeV
200MeV
300MeV
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3 Results
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Neutrino Mean-Free-Path at Energy equal to Chem.
Potential
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Magnetic Parts of Cross-Sections
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Magnetic Parts of Cross-Sections