neutron stars swollen under strong magnetic fields
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/1.jpg)
Neutron stars swollen under strong magnetic fields
Chung-Yeol RyuSoongsil University, Seoul, Korea
Vela pulsar
![Page 2: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/2.jpg)
Outline1. 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
![Page 3: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/3.jpg)
Motivation I- Heavy ion collisions
and neutron stars
![Page 4: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/4.jpg)
Dense matter- Heavy ion collisions and neutron star
Neutron star
![Page 5: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/5.jpg)
Constraints- Heavy ion collisions and neutron stars
T. Klahn et al., Phys. Rev. C 74, 035802 (2006) : np
Heavy Ion Collisions Neutron stars
![Page 6: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/6.jpg)
The masses of neutron stars
![Page 7: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/7.jpg)
The structure of neutron star
![Page 8: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/8.jpg)
Theoretical calculations1) 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 mat-ter, kaon condensa-
tion) ruled out ?
![Page 9: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/9.jpg)
Motivation II- Magnetar
![Page 10: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/10.jpg)
The histroy of soft gamma repeater (Mag-netar)
![Page 11: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/11.jpg)
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 ~ 105 Be
c where Be
c is the electron critical field (4.414 x 10 13 G)
We need to investigate neutron star in strong magnetic fields with
strangeness.
![Page 12: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/12.jpg)
Models- Magnetic fields
- Baryons (QHD)
- Kaons
![Page 13: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/13.jpg)
The magnetic fields in neutron starMagnetic flux conservation : ФM = < B > R2
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.
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
B ∼ 2 x 108 (M/M⊙)(R⊙ /R)2
∼ 1018 G : the interior of the star
![Page 14: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/14.jpg)
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
![Page 15: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/15.jpg)
σ-ω-ρ model in nuclear matter
N N
Long range attraction (σ meson)+
Short range repulsion (ω me-son)
+ Isospin force : ρ meson
Other mesons are neglected !! pion : (-) parity, other mesons : small effects, simplic-ity
H
H
attraction (σ* meson) + repulsion (φ me-son)
![Page 16: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/16.jpg)
QHD Lagrangian in magnetic field
Hadronic phase in magnetic fields- Quantum hadrodynamics (QHD)
Baryon octet, leptons and five meson fields
![Page 17: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/17.jpg)
Energies for fermionsin strong magnetic fields
• Energy spectra for charged, neutral baryons and lep-tons
Here ν = n + ½ - sgn(q) s/2 = 0, 1, 2 … enumerates the Landau levels of charged fermions where s = +1 (↑) and s=-1 (↓).
![Page 18: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/18.jpg)
Kaon fields in magnetic fields
Kaons under magnetic fields
where covariant derivative is
And the effective mass of a kaon is
![Page 19: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/19.jpg)
The energy of an antikaon
Antikaon condensation under magnetic fields
S-wave condensation : ) )
![Page 20: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/20.jpg)
Equation of state in magnetic fields
The energy density :
The pressure :
where
+ εK
![Page 21: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/21.jpg)
The conditions in neutron star
1) Baryon number conservation :
2) Charge neutrality :
3) chemical equilibrium (Λ, Σ, Ξ)
μ n - μ p = μK
![Page 22: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/22.jpg)
TOV equation• Macroscopic part – General relativity
• Einstein field equa-tion :
Static and spherical symmetric neutron star (Schwarzschild metric)
Static perfect fluidDiag Tμν = (ε, p, p, p)
• TOV equation :
• equation of state (energy density, pressure)
![Page 23: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/23.jpg)
Density dependent magnetic fieldsMagnetic field from surface to interior in the star
B0 = B0* x Be
c
where
Bec = 4.414 x 10 13
G(electron critical magnetic field)
Thus, B0* is a free
parameter.
![Page 24: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/24.jpg)
3. Results
![Page 25: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/25.jpg)
Baryon octet (npH)
![Page 26: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/26.jpg)
Populations of particles (npH)
![Page 27: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/27.jpg)
Populations of particles (npH)
![Page 28: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/28.jpg)
Populations of particles (npH)
![Page 29: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/29.jpg)
Equation of state (npH)
![Page 30: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/30.jpg)
Mass-radius relation (npH)
![Page 31: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/31.jpg)
Baryon octet +
kaon condnesation (npHK-)
![Page 32: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/32.jpg)
Populations of particles (npHK)
![Page 33: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/33.jpg)
Populations of particles (npHK)
![Page 34: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/34.jpg)
Populations of particles (npHK)
![Page 35: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/35.jpg)
Equation of state (npHK)
![Page 36: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/36.jpg)
Mass-radius relation (npHK)
In preparation
![Page 37: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/37.jpg)
4. Summaries I1. The large masses (M > 2 M solar) of neutron stars in observa-
tions : Are all exotic phases like hyperons and kaon conden-sation ruled out ?
2. But we can explain them with exotic phases by considering very strong magnetic fields B ~ 1018 G .
3. We assume very strong magnetic fields due to scalar virial theorem.
4. Strong magnetic fields cause the Landau quantization of charged particles.
5. Hyperons and kaon condensation with strong magnetic fields can explain around 2 M solar.
![Page 38: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/38.jpg)
Summaries II
6. If strong magnetic fields are possible in the center of a neu-tron star ,
proto-neutron stars may have strong magnetic fields which can cause pulsar kick through the emission of neu-trinos shown in pre-vious talk by Maruyama san.
![Page 39: Neutron stars swollen under strong magnetic fields](https://reader036.vdocument.in/reader036/viewer/2022062323/568165ac550346895dd89651/html5/thumbnails/39.jpg)
Thank you for your attention !