Asymmetric Neutrino Emission fromAsymmetric Neutrino Emission fromStrongly Magnetized Neutron StarStrongly Magnetized Neutron Star
(強磁性中性子星からの非対称ニュートリノ放出)(強磁性中性子星からの非対称ニュートリノ放出)
Asymmetric Neutrino Emission fromAsymmetric Neutrino Emission fromStrongly Magnetized Neutron StarStrongly Magnetized Neutron Star
(強磁性中性子星からの非対称ニュートリノ放出)(強磁性中性子星からの非対称ニュートリノ放出)
1
Collaborators
ToshitakaToshitaka KAJINOKAJINO Nao, Univ. of Tokyo Nao, Univ. of Tokyo
(Japan)(Japan)
NobutoshiNobutoshi YASUTAKEYASUTAKE INFN, Catania INFN, Catania (Italy)(Italy)
Myung-kiMyung-ki CHEOUNCHEOUN Soongs Univ. (Korea)
Chung-YeolChung-Yeol RYU RYU Soongs Univ. (Korea)
Jun HIDAKA Nao (Japan)
G.J. MATHEWS Univ. of Notre Dome (USA)
+
Takami KURODA Nao (Japan)
Collaborators
ToshitakaToshitaka KAJINOKAJINO Nao, Univ. of Tokyo Nao, Univ. of Tokyo
(Japan)(Japan)
NobutoshiNobutoshi YASUTAKEYASUTAKE INFN, Catania INFN, Catania (Italy)(Italy)
Myung-kiMyung-ki CHEOUNCHEOUN Soongs Univ. (Korea)
Chung-YeolChung-Yeol RYU RYU Soongs Univ. (Korea)
Jun HIDAKA Nao (Japan)
G.J. MATHEWS Univ. of Notre Dome (USA)
+
Takami KURODA Nao (Japan)
TomoyukiTomoyuki MARUYAMA MARUYAMA BRS, Nihon Univ. (Japan)BRS, Nihon Univ. (Japan)TomoyukiTomoyuki MARUYAMA MARUYAMA BRS, Nihon Univ. (Japan)BRS, Nihon Univ. (Japan)
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
4
§1. §1. IntroductionIntroduction§1. §1. IntroductionIntroduction
5
Birth of Proto-neutron StarBirth of Proto-neutron Star
core collapse
HHe
C+OSi
Fe
trapping core bounce
NSNS
shock propagation in coreshock in envelopeSN explosion
5
8
Pulsar KickPulsar KickPulsar KickPulsar Kick
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
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 and Spin of NS
9
§2. §2. FormulationFormulation§2. §2. FormulationFormulationMagnetic Field :
Baryon Lepton B & L – Mag.
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)
1. Proto-Nuetron-Star (PNS) Matter without Mag. Field
2. Baryon Wave Function under Mag. Field in Perturbative Way
3. Cross-Sections for reactions
§2-1§2-1 RMF Approach for Neutron-Star MattterRMF Approach for Neutron-Star Mattter
EOS of EOS of PM1-1PM1-1 -3
0* fm 0.17 at MeV 200 ,7.0/ MeV, 16 KMMBE NN
3/2
gg
gg
T.M, H. Shin, H. Fujii, & T. Tatsumi,
Prog. Theo. Phys. Vol.102, P809
EOS of Proto Neutron-Star-MatterEOS of Proto Neutron-Star-Matter
Charge Neuttral ( ) & Lepton Fraction : Yp =
0.4 ep
§2-2 Dirac Equation under Magnetic Fields§2-2 Dirac Equation under Magnetic Fields
N B << εF (Chem. Pot) → B can be treated perturbatively Landau Level can be ignored
Dirac Eq.
~ 1017 G
Magnetic Part
of Lagrangian
Spin VectorDirac Spinor
negligibly small
3
14
Fermi
Distribution
Momentum Distr. of Major Part
is deformed as oblate
Relativistic Effects of Magnetic Contributions
1)Momentum Dependent of Spin Vector
2)Deformation of Fermi Distribution
15
ElectronElectron
Landau Level
When B → 0 , the wave function → plane wave
§2-3 The Cross-Section of ν-B
0 BΔσΔσσσ Perturbative
Treatment
Non-Magnetic Part Magnetic Part
Fermi Distribution
Deformed Distribution
17
The Cross-Section of Lepton-Baryon The Cross-Section of Lepton-Baryon ScatteringScattering
with
Spin-independent part
Spin-dependent Spin-dependent PartPart
Electron ContributionElectron Contribution
Single Particle Energy
Sum of Landau Level
Expectation Value of Quantity A
Perturbation
Spin vector
Final electron contribution in Final electron contribution in ee →→ ee--
§3 Results of Cross-§3 Results of Cross-SectionsSections
No magnetic field
pot.) chem.-( ik
3% difference
0 andG102 , pot.) chem. (neutrino i17 Bki
Differential Cross-Sections in Magnetic Field Differential Cross-Sections in Magnetic Field
Initial Angle-DependenceInitial Angle-Dependence
0 andG102 , pot.) chem. (neutrino i17 Bki
25
f
eeiSc dΩ
ννdσdΩσ
f
efAb dΩ
eνdσdΩσ
Increasing in Dir. parallel to B
Scat.
Absorp.
0 BΔσΔσσσ
Integrating over the initial angle
Integrating over the final angle
Magnetic parts of Cross-SectionsMagnetic parts of Cross-Sections
0 andG102 , pot.) chem. (neutrino i17 Bki
Magnetic Parts of Cross-SectionsMagnetic Parts of Cross-Sections
cos1 ,,0
,, fiASASAS S
Neutrino Mean-Free PathsNeutrino Mean-Free Paths
scattering absorption
)180()0(2
1
VV
Contribution of Each Element in Contribution of Each Element in Scattering PartScattering Part
Contribution of Each Element in Contribution of Each Element in Absorption PartAbsorption Part
30
EOS of Neutron-Star-Matter with p, n Λ in RMF AppraochEOS 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 Wayunder Strong Magnetic Field, calculated in Perturbative Way
Neutrinos are More Scattered and Less Absorbed Neutrinos are More Scattered and Less Absorbed
in Direction in Direction Parallel to Magnetic FieldParallel to Magnetic Field
⇒ ⇒ More Neutrinos are Emitted in Arctic AreaMore Neutrinos are Emitted in Arctic Area
Scattering 1.7 % Scattering 1.7 %
Absorption 2.2 % at Absorption 2.2 % at ρρB==33ρρ0 and T = 20 MeV
31
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
CasA
A.G.Lyne, D.R.Lomier, Nature 369, 127 (94)
Estimating Kick Velocity of PNS with T = 20 MeV and B B = 2× 10= 2× 1017GG
PoloidalPoloidal Magnetic Field Magnetic Field 2‐32‐3%% Asymmetry Asymmetry inin AbsorptionAbsorption
§4 Estimating Pulsar Kick §4 Estimating Pulsar Kick VelocitiesVelocities
of Proto-Neutron Star of Proto-Neutron Star
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
Neutrino Transportation Neutrino Transportation
, ),(),( ),(),( 00 V
σbΔfcbIΔfcfcfc ab
νcoll
rprpr
rpr
rpr
Neutrino Propagation ⇒ Boltzmann Eq.
Neutrino Phase Space Distribution Function
,z)(p,rfdz
d,z)(p,rf
zpz
yybd,x)(p,rfx
dxzΔf
TT
z
x
z
TTc
00
0 0
,ˆ
, )(exp ),,( 1
r
rp
/)(exp11),( , ),( ),(),( 00 TfΔfff prprprprp
Equil. Part Non-Equil. Part
Solution ⇒
Neutrinos Propagate on Strait Line only absorption
Other Pieces are equilibrium
Mean-Free Mean-Free PathsPaths
Scattering
Absorption 21in
10
0ρρB
AS
Magnetic Parts
cos1 ,0
fiAAA S
SA: fitting function
0,, / ASAS V
Baryon density in Proto-Neutron StarBaryon density in Proto-Neutron Star
Calculating Neutrino Propagation above B = 0
M = 1.68Msolar
YL = 0.4
Baryon density in Proto-Neutron Star
T = 20 MeV
M = 1.68 Msolar
YL = 0.4
Calculating
Neutrino Propagation above B = 0
\θ
Neutrino Neutrino PropagatioPropagatio
nn 1) 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 in Uniform Poloidal Mag. Field
[erg] 103
[g], 68.1
53
T
solarNS
E
MM
p, n
p, n,
T = 20 MeV
[km/s] 600 M
pv zkick
Observable Average … 400km/s ,
cos 10 PPp n
[G] 102 17B
2
2
0
1
1094.1
1076.1 3
-
-
T
z
PP
E
p
38
Stability of Magnetic Field in Compact ObjectsStability of Magnetic Field in Compact Objects
((Braithwaite & Spruit 2004Braithwaite & Spruit 2004))
Toroidal Magnetic Toroidal Magnetic Field is stable !!Field is stable !!
§5 Angular Deceleration in Toroidal §5 Angular Deceleration in Toroidal Magnetic FieldMagnetic Field
Mag. FieldParallel
to Baryonic Flow
Assym. of -Emit.must decelerate
PNS Spin
No poloidal Magnetic Field at the No poloidal Magnetic Field at the beginningbeginning
by T. Kuroda
Single Toroidal
Finite Polaidal Magnetic Field at the beginning
by 黒田Anti-paralleled Double Toroidal
Toroidal Magnetic
Field
φφe
rz
rzzG
rRr
rRrrG
ezGrGBzr
L
T
TTT
LTTT
)0,cos,sin(ˆ
/exp1
/exp)(
/)(exp1
/)(exp16)(
ˆ)()(),(
2
20
0
0
B
z = 0
T = 20MeV
r = 0.5 (km)
R0 = 8 (km) Mag.‐A
R0 = 5 (km) Mag.‐B
42
Angular DecelerationAngular DecelerationAngular DecelerationAngular Deceleration
zLLS
z pΔfdpddcdt
dLN
prnrnr ),,(
Neutrino Luminosity
(dET/dt) ~ 3×1052 erg/s
/
/11
dtdE
dtcdL
dt
dE
Idt
dL
I T
Z
NS
Z
NS
T
dt
d
68.1 solarNS MM Period P = 10s
Mag
Distr.Bary.
B [G]
at B = 0 (cm) ( emis.) ( rad.)
Mag-A p,n 1.0×1016 46.7 3.02×10-2 4.82×10-21.0×10-8
p,n, 1.6×1016 70.6 5.19×10-2 8.26×10-22.6×10-8
Mag-B p,n 2.6×1013 0.157 1.01×10-4 1.61×10-46.6×10-14
p,n, 4.2×1013 0.259 1.90×10-4 3.03×10-4 1.7×10-13
/
/
dtdE
dtcdL
T
Z PPPP
In Early Stage ( ~ 10 s) Asymmetric Emission must affect PNS Spin
More Significantly than Magnetic Dipole -Radiation
Magnetic Dipole Rad. [G] 102.3 39 PPB
EOS of Neutron-Star-Matter with p, n, Λ in RMF ApproachEOS of Neutron-Star-Matter with p, n, Λ in RMF Approach
Exactly Solving Dirac Eq. with Magnetic Field in Perturbative WayExactly Solving Dirac Eq. with Magnetic Field in Perturbative Way
Cross-Sections of Neutrino Scattering and Absorption Cross-Sections of Neutrino Scattering and Absorption
under Strong Magnetic Field, calculated in Perturbative Wayunder Strong Magnetic Field, calculated in Perturbative Way
Neutrinos are More Scattered and Less Absorbed Neutrinos are More Scattered and Less Absorbed
in Direction in Direction Parallel to Parallel to
Magnetic FieldMagnetic Field
⇒ ⇒ More Neutrinos are Emitted in More Neutrinos are Emitted in ArcticArctic AreaArea
Scattering 1.7 % Scattering 1.7 %
Absorption 2.2 % at Absorption 2.2 % at ρρB==33ρρ0 and T = 20 MeV
⇒ Convection, Pulsar-Kick
43
§5§5 SummarySummary§5§5 SummarySummary
44
Pulsar Kick in Poroidal Mag. Field B = 2× 1017G ⇒ Perturbative Cal.
vvkickkick = 580 km/s ( p,n ) , 610 km/s (p,n, = 580 km/s ( p,n ) , 610 km/s (p,n,ΛΛ ) ) at at T T = 20 MeV= 20 MeV
= 230 km/s ( p,n ) , 270 km/s (p,n,= 230 km/s ( p,n ) , 270 km/s (p,n,ΛΛ ) ) at at TT = 30 MeV = 30 MeV
400 km/s400 km/s (Average of Observed Values (Average of Observed Values ) )
Spin Deceleration Spin Deceleration in in Toroidal Magnetic Field Magnetic Field
Asymmetric Asymmetric --Emission plays an important role in PNS Spin in Early Time Emission plays an important role in PNS Spin in Early Time
Future Plans Future Plans -Scattering-Scattering
Fixed Temp. Fixed Temp. ⇒⇒ Constant Entropy Constant Entropy
Exact Solution of Dirac Eq. in Non-Perturbative Cal.Exact Solution of Dirac Eq. in Non-Perturbative Cal.
→ → Landau LevelLandau Level at least for Electron at least for Electron
Antarctic Dir.
Mag
Distr.
(P = 10 s)
p,n p,n,
Mag-A 4.8×10-3 5.2×10-3
Mag-B 6.1×10-3 7.2×10-3
Dpl. Rad.
9.8×10-11
][s 1-PP
Reestimatingwhen B = 1015G
in the surface with = 0
EOS in Iso-Entropical ModelEOS in Iso-Entropical Model
§2-1 Neutron-Star Matter in RMF §2-1 Neutron-Star Matter in RMF ApproachApproach
RMF Lagrangian, N,
Dirac Eq.
Scalar Field ⇒ Effective Mass
Spin VectorDirac Spinor
negligibly small
Spin-indep. part
Spin-dep. Part
\θ
Neutrino Neutrino PropagatioPropagatio
nn 1) 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 PathAbsorption Mean-Free Path
cos1 ,0
fiAAA S
1/ VAA
B = 0
30MeV
50MeV
100MeV
200MeV
300MeV
SA: fitting function
0 andG102 , pot.) chem. (neutrino i17 Bki§3 Results§3 Results
3% difference
Neutrino Mean-Free-Path at Energy equal to Neutrino Mean-Free-Path at Energy equal to Chem. PotentialChem. Potential
Magnetic Parts of Cross-SectionsMagnetic Parts of Cross-Sections
Magnetic Parts of Cross-SectionsMagnetic Parts of Cross-Sections
cos1 ,,0
,, fiASASAS S