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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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Presentation Transcript
slide1

Neutron stars swollen

under strong magnetic fields

Vela pulsar

Chung-YeolRyu

Soongsil University, Seoul, Korea

slide2
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

slide3
Motivation I
  • Heavy ion collisions

and

neutron stars

constraints heavy ion collisions and neutron stars
Constraints- Heavy ion collisions and neutron stars

Heavy Ion Collisions Neutron stars

T. Klahn et al., Phys. Rev. C 74, 035802 (2006) : np

theoretical calculations
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 ?

the observed magnetars and candidates
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.

slide12
Models
  • Magnetic fields
  • Baryons (QHD)
  • Kaons
the magnetic fields in neutron star
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

landau quantization under strong magnetic fields
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

model in nuclear matter

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

slide16

Hadronic phase in magnetic fields

- Quantum hadrodynamics (QHD)

QHD Lagrangianin magnetic field

Baryon octet, leptons and five meson fields

slide17

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 (↓).

slide18

Kaons under magnetic fields

Kaon fields in magnetic fields

  • where covariant derivative is
  • And the effective mass of a kaon is
slide19

Antikaon condensation under magnetic fields

The energy of an antikaon

  • S-wave condensation : ) )
equation of state in magnetic fields
Equation of state in magnetic fields

+ εK

The energy density :

The pressure :

where

the conditions in neutron star
The conditions in neutron star
  • Baryon number conservation :
  • Charge neutrality :
  • chemical equilibrium (Λ, Σ, Ξ)

μn - μp = μK

tov equation
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)
slide23

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.

4 summaries i
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.

summaries ii
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.

slide39
Thank you for

your attention !