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Asymmetric Neutrino Emission from Strongly Magnetized Neutron Stars - Understanding Pulsar Kicks

This research study investigates the phenomenon of asymmetric neutrino emission from strongly magnetized neutron stars and its potential connection to pulsar kicks. The study utilizes the Relativistic Mean-Field (RMF) approach to analyze the scattering and absorption of neutrinos in high-density matter with strong magnetic fields. The results provide insights into estimating the kick velocities of proto-neutron stars and understanding the mechanisms behind pulsar kicks.

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Asymmetric Neutrino Emission from Strongly Magnetized Neutron Stars - Understanding Pulsar Kicks

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  1. 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

  2. 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

  3. Birth of Proto-neutron Star 5 5

  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

  5. 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)

  6. §2-1RMF Approach for Neutron-Star Mattter

  7. EOS of PM1-1 T.M, H. Shin, H. Fujii, & T. Tatsumi, Prog. Theo. Phys. Vol.102, P809

  8. EOS of Proto Neutron-Star-Matter Charge Neuttral （ ） & Lepton Fraction : Yp = 0.4

  9. §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

  10. 3 negligibly small Dirac Spinor Spin Vector 14

  11. 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

  12. Landau Level Electron When B → 0 , the wave function → plane wave

  13. §2-3 The Cross-Section of ν-B Fermi Distribution Deformed Distribution Perturbative Treatment Magnetic Part Non-Magnetic Part 17

  14. The Cross-Section of Lepton-Baryon Scattering with Spin-independent part

  15. Spin-dependent Part

  16. Electron Contribution Single Particle Energy Sum of Landau Level Expectation Value of Quantity A Perturbation Spin vector

  17. Final electron contribution in ne→e-

  18. §3 Results of Cross-Sections No magnetic field

  19. Differential Cross-Sections in Magnetic Field 3% difference

  20. Initial Angle-Dependence

  21. Increasing  in Dir. parallel to B Magnetic parts of Cross-Sections Scat. Integrating over the initial angle Absorp. Integrating over the final angle 25

  22. Magnetic Parts of Cross-Sections

  23. Neutrino Mean-Free Paths scattering absorption

  24. Contribution of Each Element in Scattering Part

  25. Contribution of Each Element in Absorption Part

  26. 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

  27. §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

  28. 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 ⇒

  29. Mean-Free Paths Magnetic Parts Scattering SA: fitting function Absorption

  30. Baryon density in Proto-Neutron Star M = 1.68Msolar YL= 0.4 Calculating Neutrino Propagation above rB = r0

  31. Baryon density in Proto-Neutron Star T = 20 MeV M = 1.68 Msolar YL= 0.4 Calculating Neutrino Propagation above rB = r0

  32. 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

  33. Angular Dep.of Emitted Neutrinos inUniform Poloidal Mag. Field T = 20 MeV Observable Average … 400km/s， p, n p, n, L

  34. §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

  35. No poloidal Magnetic Field at the beginning Single Toroidal by T. Kuroda

  36. Finite Polaidal Magnetic Field at the beginning Anti-paralleled Double Toroidal by黒田

  37. Toroidal Magnetic Field T = 20MeV Dr = 0.5 (km) R0 = 8 (km) Mag.‐A R0 = 5 (km) Mag.‐B z = 0

  38. 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

  39. §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

  40. 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

  41. EOS in Iso-Entropical Model

  42. §2-1 Neutron-Star Matter in RMF Approach RMF Lagrangian, N, L, s, , r Dirac Eq. Scalar Field ⇒ Effective Mass

  43. negligibly small Dirac Spinor Spin Vector

  44. Spin-indep. part Spin-dep. Part

  45. 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

  46. Absorption Mean-Free Path B = 0 30MeV SA: fitting function 50MeV 100MeV 200MeV 300MeV

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