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Neutron stars swollen under strong magnetic fields

Neutron stars swollen under strong magnetic fields. Vela pulsar. Chung- Yeol Ryu Soongsil University, Seoul, Korea. Outline 1 . Motivations - Equation of state from Heavy ion collisions and neutron stars

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Neutron stars swollen under strong magnetic fields

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  1. Neutron stars swollen under strong magnetic fields Vela pulsar Chung-YeolRyu Soongsil University, Seoul, Korea

  2. Outline 1. Motivations - Equation of state from Heavy ion collisions and neutron stars - Magnetar (neutron star with strong B fields) 2. Model for neutron star in strong magnetic fields - Baryons (QHD) - Kaons and kaon condensation 3. Results 4. Summaries

  3. Motivation I • Heavy ion collisions and neutron stars

  4. Dense matter- Heavy ion collisions and neutron star Neutron star

  5. Constraints- Heavy ion collisions and neutron stars Heavy Ion Collisions Neutron stars T. Klahn et al., Phys. Rev. C 74, 035802 (2006) : np

  6. The masses of neutron stars

  7. The structure of neutron star

  8. Theoretical calculations 1) No strangeness : 2-3 M๏ 2) Strangeness : 1-2 M๏ - hyperons(Λ, Σ, Ξ) - kaon condensation - quark matter(u, d, s) The masses of neutron stars are very large. Are all exotic phases (hyperons, quark matter, kaon condensation) ruled out ?

  9. Motivation II • Magnetar

  10. The histroy of soft gamma repeater (Magnetar)

  11. The observed magnetars and candidates C.Y.Cardall, M. Prakash, J.M.Lattimer, Astrophys. Jl. 554, 322 (2001) Surface magnetic field of neutron star : B ~ 10 14 – 10 15 G Interior magnetic field from scalar virial theorem : B ~ 10 18 G ~ 105Bec where Bec is the electron critical field (4.414 x 10 13 G) We need to investigate neutron star in strong magnetic fields with strangeness.

  12. Models • Magnetic fields • Baryons (QHD) • Kaons

  13. The magnetic fields in neutron star Magnetic flux conservation : ФM = < B > R2 A core of superonvae with B = 104 G and R = R⊙ A neutron star with B = 1014 G for R = 10 km – surface magnetic field Scalar virial theorem for non-rotating star : T + W + 3П + M = 0 Where T : Kinetic energy, W : Gravitational potential, П : Internal energy, M : magnetic energy. B ∼ 2 x 108 (M/M⊙)(R⊙ /R)2 ∼ 1018 G : the interior of the star

  14. Landau quantization under strong magnetic fields Lorentz force In quantum mechanics, the orbits of charged particles are quantized and then charged particles can be confined in strong magnetic fields.  Landau quantization

  15. N H N H σ-ω-ρmodel in nuclear matter Long range attraction(σ meson) + Short range repulsion(ω meson) + Isospin force : ρ meson attraction(σ* meson) +repulsion(φmeson) Other mesons are neglected !! pion : (-) parity, other mesons : small effects, simplicity

  16. Hadronic phase in magnetic fields - Quantum hadrodynamics (QHD) QHD Lagrangianin magnetic field Baryon octet, leptons and five meson fields

  17. Energies for fermions in strong magnetic fields • Energy spectra for charged, neutral baryons and leptons Here ν = n + ½ - sgn(q) s/2 = 0, 1, 2 … enumerates the Landau levels of charged fermions where s = +1 (↑) and s=-1 (↓).

  18. Kaons under magnetic fields Kaon fields in magnetic fields • where covariant derivative is • And the effective mass of a kaon is

  19. Antikaon condensation under magnetic fields The energy of an antikaon • S-wave condensation : ) )

  20. Equation of state in magnetic fields + εK The energy density : The pressure : where

  21. The conditions in neutron star • Baryon number conservation : • Charge neutrality : • chemical equilibrium (Λ, Σ, Ξ) μn - μp = μK

  22. TOV equation • Macroscopic part – General relativity • Einstein field equation : Static and spherical symmetric neutron star (Schwarzschild metric) Static perfect fluid Diag Tμν = (ε, p, p, p) • TOV equation : • equation of state (energy density, pressure)

  23. Density dependent magnetic fields Magnetic field from surface to interior in the star B0 = B0* x Bec where Bec = 4.414 x 10 13 G (electron critical magnetic field) Thus, B0* is a free parameter.

  24. 3. Results

  25. Baryon octet (npH)

  26. Populations of particles (npH)

  27. Populations of particles (npH)

  28. Populations of particles (npH)

  29. Equation of state (npH)

  30. Mass-radius relation (npH)

  31. Baryon octet + kaoncondnesation (npHK-)

  32. Populations of particles (npHK)

  33. Populations of particles (npHK)

  34. Populations of particles (npHK)

  35. Equation of state (npHK)

  36. Mass-radius relation (npHK) In preparation

  37. 4. Summaries I The large masses (M > 2 M solar) of neutron stars in observations : Are all exotic phases like hyperons and kaon condensation ruled out ? But we can explain them with exotic phases by considering very strong magnetic fields B ~ 1018 G . We assume very strong magnetic fields due to scalar virial theorem. Strong magnetic fields cause the Landau quantization of charged particles. Hyperons and kaon condensation with strong magnetic fields can explain around 2 M solar.

  38. Summaries II If strong magnetic fields are possible in the center of a neutron star , proto-neutron stars may have strong magnetic fields which can cause pulsar kick through the emission of neutrinos shown in previous talk by Maruyama san.

  39. Thank you for your attention !

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