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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

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slide1

The structure of

a proto-neutron star

Chung-YeolRyu

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.

slide2
Outline

1. Introduction

2. Motivations

3. Models and conditions

4. Results

5. Summaries

slide3
1. Introduction

Vela pulsar

slide11
2. Motivations

The depiction of a Shapiro Delay

production of a proto neutron star
Production of a proto-neutron star

The structure of supernovae

The production of proto-neutron star

motivation 2
Motivation 2

Isentropic process

Burrows&Lattimer APJ (1981), APJ(1987)

without convection with convection

motivation 3
Motivation 3

S. Reddy et al. PRD(1998)

motivation 4
Motivation 4

S. Reddy et al. PRD(1998) A. Burrows’ simulation

slide18
Idea

Beta equilibrium

n + νe p + e- :

  • Trapped ratio may depend on densities and temperature.
many body theory in isolated system
Many body theory in isolated system

Thermodynamic potential Ω

- Minimum condition

Microscopic model: Hamiltonian or Lagangian

Grand partition function Z

  • 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
slide22

Nuclear matter properties

at saturation density

  • Saturation density
  • 0 = 0.15 - 0.17fm-3
  • Binding energy
  • B/A =-(ε/ρ – m N)= 16MeV
  • Effective mass of a nucleon
  • m N*/m N = 0.7 - 0.8 (이론)
  • Compression modulus
  • K-1= 200 - 300MeV
  • Symmetry energy
  • asym= 30 - 35MeV
symmetry energy from hic and finite nuclei
Symmetry energy from HIC and finite nuclei

Symmetry energy

Energy per nucleon in symmetric matter

Energy per nucleon in asymmetric matter

relativistic mean field model
Relativistic mean field model

Nucleons (Dirac equation)

+

meson fields (Klein-Gordon equation)

Meson fields  mean fields (notransition)

mean fields theory model

N

N

Mean fields theory : σ-ω-ρmodel

Long range attraction(σ meson)

+

Short range repulsion(ω meson)

+

Isospin force : ρ meson

Other mesons are neglected !!

pion : (-) parity, other mesons : small effects, simplicity

qhd and qmc models

σ, ω, ρ

QHD and QMC models

Hadronic degrees of freedom :

Quantum Hadrodynamics (QHD)

Quark degrees of freedom :

Quark-meson coupling (QMC) model

σ, ω, ρ

eq of state and entropy
Eq. of state and entropy

Isentropic process : S = 2 (S : entropy per a baryon)

the conditions in neutron star
The conditions in neutron star
  • Baryon number conservation :
  • Charge neutrality :
  • chemical equilibrium (Λ, Σ, Ξ)
  • Fixed YL =? or other condition

- μνe

where x is trapped ratio.

tov equation mass and radius
TOV equation(Mass and radius)
  • Macroscopic part – General relativity
  • Microscopic part – Strong interaction model
  • 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 (pressure, energy density)
the moment of inertia
The moment of inertia
  • Metric tensor
  • Kepler frequency
  • The moment of inertia in slow rotating approx.
our picture
Our picture

Conditions

Models

QHD & QMC models

-Eq. of motion

  • Baryon number conservation
  • Charge neutrality
  • Beta equilibrium with neutrinos
  • Trapped ratio depends on densities
  • Equation of state
  • - Energy density, Pressure, Temperature
  • Mass, radius and the moment of inertia
populations of neutrinos s 2
Populations of neutrinos(S=2)
  • Our result A. Burrows’simulation
mass and radius
Mass and radius

Cold NS(T=0) Proto-NS(S=2)

slide42
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.