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
under strong magnetic fields
Soongsil University, Seoul, Korea
- 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
Heavy Ion Collisions Neutron stars
T. Klahn et al., Phys. Rev. C 74, 035802 (2006) : np
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 ?
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.
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
In quantum mechanics,
the orbits of charged particles are quantized and then charged particles can be confined in strong magnetic fields.
- Quantum hadrodynamics (QHD)
QHD Lagrangianin magnetic field
Baryon octet, leptons and five meson fields
in strong magnetic fields
Here ν = n + ½ - sgn(q) s/2 = 0, 1, 2 … enumerates the Landau levels of charged fermions where s = +1 (↑) and s=-1 (↓).
Kaon fields in magnetic fields
The energy of an antikaon
The energy density :
The pressure :
μn - μp = μK
Static and spherical symmetric neutron star (Schwarzschild metric)
Static perfect fluid
Diag Tμν = (ε, p, p, p)
Magnetic field from surface to interior in the star
B0 = B0* x Bec
Bec = 4.414 x 10 13 G
(electron critical magnetic field)
Thus, B0* is a free parameter.
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.
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.
your attention !