The structure of a proto-neutron star
description
Transcript of The structure of a proto-neutron star
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.