Kaon-Kaon scattering with SU(3) linear sigma model

The structure of a proto-neutron starChung-Yeol RyuHanyang 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, PRC2012.1Outline

1. Introduction2. Motivations3. Models and conditions4. Results5. Summaries1. Introduction

Vela pulsar

The structure of neutron star

The depiction of a Shapiro Delay

The masses of neutron stars

From A. Schwenk2. Motivations

The depiction of a Shapiro DelayProduction of a proto-neutron star

The structure of supernovaeThe production of proto-neutron star

Supernovae explosion and PNS

A. Burrows(1995)Motivation 1

Isentropic processBurrows&Lattimer APJ (1981), APJ(1987)

without convection with convectionMotivation 2S. Reddy et al. PRD(1998) Motivation 3

S. Reddy et al. PRD(1998) A. Burrows simulationMotivation 4

Idea

Trapped ratio may depend on densities and temperature.Beta equilibrium

n + e p + e- :

3. Models and conditionsMany body theory in isolated systemMicroscopic model: Hamiltonian or LagangianGrand partition function Z Thermodynamic potential

- 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 EoSConstraints from experiment

Neutron star

Saturation density 0 = 0.15 - 0.17 fm-3

Binding energy B/A =-(/ m N )= 16 MeV

Effective mass of a nucleon m N*/m N = 0.7 - 0.8 ()

Compression modulus K-1 = 200 - 300 MeV

Symmetry energy asym= 30 - 35 MeVNuclear matter properties at saturation density

Equation of state from heavy ion collisionSymmetry energy from HIC and finite nuclei

Energy per nucleon in asymmetric matterEnergy per nucleon in symmetric matterSymmetry energy

Relativistic mean field modelNucleons (Dirac equation)+meson fields (Klein-Gordon equation)Meson fields mean fields (no transition)Mean fields theory : -- model N NLong range attraction ( meson)+ Short range repulsion ( meson)+ Isospin force : mesonOther mesons are neglected !! pion : (-) parity, other mesons : small effects, simplicity Hadronic degrees of freedom : Quantum Hadrodynamics (QHD)

Quark degrees of freedom : Quark-meson coupling (QMC) model , ,

, , QHD and QMC models27

, , The Lagrangian of QMC model

28Eq. of state and entropy

Isentropic process : S = 2 (S : entropy per a baryon)29The conditions in neutron star

Baryon number conservation :

Charge neutrality :

chemical equilibrium (, , )

Fixed YL =? or other condition

- e

where x is trapped ratio.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 fluidDiag T = (, p, p, p) TOV equation : equation of state (pressure, energy density)The moment of inertiaMetric tensor

Kepler frequency

The moment of inertia in slow rotating approx.

Our picture Equation of state - Energy density, Pressure, Temperature Mass, radius and the moment of inertia

Trapped ratio depends on densitiesQHD & QMC models-Eq. of motionModelsBaryon number conservationCharge neutralityBeta equilibrium with neutrinosConditions4. ResultsCold neutron star (QMC)

Populations

Populations of neutrinos(S=2)

Our result A. BurrowssimulationTemperature

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.