The structure of
a proto-neutron star
Chung-Yeol Ryu
Hanyang University, Korea
C.Y.Ryu, T.Maruyama,T.Kajino, M.K.Cheoun, PRC2011.
C.Y.Ryu, T.Maruyama,T.Kajino, G.J.Mathews, M.K.Cheoun, PRC2012.
Outline
1. Introduction
2. Motivations
3. Models and conditions
4. Results
5. Summaries
1. Introduction
Vela pulsar
The structure of
neutron star
The depiction of a Shapiro Delay
The masses
of neutron stars
From A. Schwenk
2. Motivations
The depiction of a Shapiro Delay
Production of a proto-neutron star
The structure of
supernovae
The production of proto-neutron star
Supernovae explosion and PNS
A. Burrows(1995)
Motivation 1
Motivation 2
Isentropic process
Burrows&Lattimer APJ (1981), APJ(1987)
without convection
with convection
Motivation 3
S. Reddy et al. PRD(1998)
Motivation 4
S. Reddy et al. PRD(1998)
A. Burrows’ simulation
Idea
Beta equilibrium
n + νe
p + e-
:
Trapped ratio may depend on
densities and temperature.
3. Models and conditions
Many body theory in isolated system
Microscopic
model:
Hamiltonian or
Lagangian
Grand partition
function Z
Thermodynamic
potential Ω
- Minimum condition
• Chemical potential
• Chemical equilibrium for given reaction
- Minimum of Gibbs free energy
• Equation of state
- Energy density, Pressure, Temperature
• Observables (mass and radius for neutron star) from EoS
Constraints from experiment
Neutron star
Nuclear matter properties
at saturation density

Saturation density
0 = 0.15 - 0.17 fm-3

Binding energy
B/A =-(ε/ρ – m
N
)= 16 MeV

Effective mass of a nucleon
m N*/m N = 0.7 - 0.8 (이론)

Compression modulus
K-1 = 200 - 300 MeV

Symmetry energy
asym= 30 - 35 MeV
Equation of state
from
heavy ion collision
Symmetry energy from HIC and finite nuclei
Symmetry energy
Energy per nucleon
Energy per nucleon
in symmetric matter
in asymmetric
matter
Relativistic mean field model
Nucleons (Dirac equation)
+
meson fields (Klein-Gordon equation)
Meson fields  mean fields (no transition)
Mean fields theory : σ-ω-ρ model
Long range attraction (σ meson)
+
Short range repulsion (ω meson)
+
Isospin force : ρ meson
N
N
Other mesons are neglected !!
pion : (-) parity, other mesons : small effects, simplicity
QHD and QMC models
Hadronic degrees of freedom :
Quantum Hadrodynamics (QHD)
σ, ω, ρ
Quark degrees of freedom :
Quark-meson coupling (QMC) model
σ, ω, ρ
The Lagrangian of QMC model
σ, ω, ρ
Eq. of state and entropy
Isentropic process : S = 2 (S : entropy per a baryon)
The conditions in neutron star
1) Baryon number conservation :
2) Charge neutrality :
3) chemical equilibrium (Λ, Σ, Ξ)
- μνe
4) Fixed YL =? or other condition
where x is trapped ratio.
TOV equation
(Mass and radius)
• 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 :
• Microscopic part – Strong interaction model
• equation of state (pressure, energy density)
The moment of inertia
• Metric tensor
• Kepler frequency
• The moment of inertia in slow rotating approx.
Our picture
QHD & QMC models
-Eq. of motion
•
• Baryon number conservation
• Charge neutrality
• Beta equilibrium with neutrinos
Equation of state
- Energy density, Pressure, Temperature
• Mass, radius and the moment of inertia
Trapped ratio depends on
densities
4. Results
Cold neutron star (QMC)
Populations
Populations of neutrinos(S=2)
Our result
A. Burrows’simulation
Temperature
Equation of state
Mass and radius
Cold NS(T=0)
Proto-NS(S=2)
The moment of inertia
Summaries
1. Proto-neutron star : After supernovae
explosion, the initial state of NS is called
PNS.
2. YL = 0.4 condition is not enough to
explain trapped neutrino ratio.
3. So, we introduce that the trapped ratio
may depend on the baryon densities.
- The results agree with simulation.
4. The moment of inertia : PNS  CNS
- Pulsar rotation may depend on the mass.