nuclear “pasta” in compact stars
DESCRIPTION
Nuclear “Pasta” in Compact Stars. Hidetaka Sonoda. University of Tokyo Theoretical Astrophysics Group. Collaborators (G. Watanabe, K. Sato, K. Yasuoka, T. Ebisuzaki). Content. Introduction Quantum Molecular Dynamics (QMD) Pasta Phases at zero and finite temperatures - PowerPoint PPT PresentationTRANSCRIPT
Nuclear “Pasta” in Compact Stars
Hidetaka Sonoda
University of Tokyo Theoretical Astrophysics Group
Collaborators (G. Watanabe, K. Sato, K. Yasuoka, T. Ebisuzaki)
Content
• Introduction
• Quantum Molecular Dynamics (QMD)
• Pasta Phases at zero and finite temperatures
• Neutrino opacity of Pasta phases
• Summary
Supernovae and Nuclear “Pasta”
Core-collapse Supernova Explosion
Neutrino transport in supernova coresEOS of dense matter
No successful simulation with realistic settings
Nonspherical nuclei --- “Pasta” phases
Possible key element
“Bounce” triggered by nuclear repulsive force
Scenario
Just before bounce (just before nuclear matter phase)
Neutron Stars and Nuclear “Pasta”Neutron Stars
Pasta phases in the deep inside inner crust
Core
Outer Crust
Inner crust
Pasta Phases
10 km1 km
Solid of heavy nuclei
Liquid of nuclear matter(quark matter, hyperons)
Transition region from nuclei to nuclear matter
What is Nuclear “Pasta” ?
(K.Oyamatsu, Nucl.Phys.A561,431(1993))
Nonspherical nuclei in dense matter ~ 1014g/cc
Sphere→ Rod → Slab → Rod-like Bubbles → Spherical Bubbles →Uniform Nuclear Matter
MeatballSpaghettiLasagnaAnti-spaghettiCheese→”Pasta” Phases
(Ravenhall et al. 1983,Hashimoto et al.1984)
Phase Diagram of Pasta Phases
Motivation
How pasta phases appear in collapsing cores ?And in cooling neutron stars?How transition from sphere to uniform matter ?
Pasta phases are dynamically formed as equilibrium-state of hot dense matter in supernovae ? as ground-state in neutron stars ?
Why QMD ?
Quantum Molecular Dynamics (QMD) gives us a picture for
How nuclei are deformed into uniform nuclear matter
No assumptions on nuclear shapes.Nuclear system is treated in degrees of freedom of nucleons.Thermal fluctuations are included.
QMD is suitable to answer the above question
Quantum Molecular Dynamics
Model Hamiltonian 1( Chikazumi et al Phys.Rev.C 63 024602(2001))
Pauli Potential Nuclear Force Coulomb EnergyKinetic Energy
Nucleons obey Equation of Motion of QMD
Saturation properties of symmetric nuclear matterBinding energy and rms radius of stable nuclei
Hamiltonian is constructed to reproduce …
Model Hamiltonian 2( Maruyama et al Phys.Rev.C 57 655(1998))
Simulation settings
2048 or 10976 nucleons in simulation boxPeriodic boundary conditionProton fraction x=0.3
Simulation Settings
Ground state is obtained by cooling of hot matter
Equilibrium state at finite temperature is obtained by Nose-Hoover thermostat for MD pot.
Pasta at zero temperature
Sphere Rod Slab
Spherical Bubbles
0.100ρ 00.200ρ 0 0.393ρ 0
0.575ρ 000.490ρRod-like Bubbles
Red : ProtonsBlue: Neutrons
ρ =0.168 fm-3
( Nuclear density )
0
Cooling of hot nuclear matter (~10 MeV) below 0.1 MeV
Sponge-like StructureBetween rod and slab, slab and rod-like bubblesMultiply connected “Sponge-like” structure appears
10976 nucleons at 0.3ρ0
Between rod and slab
10976 nucleons at 0.45ρ0
Between slab and rod bubbles
These intermediate phases at least meta-stable
Phase diagram at zero temperature
Model 1
Model 2
SP
SP
C
C
S SH
SHS
CH
CH
SP: sphereC: cylinder
S: slabCH: cylindrical hole
SH: spherical hole
Uniform
Uniform
(C,S)
SP&C coexist. (S,CH) CH,SH coexist.
(C,S)
SP&C 共存 (S,CH)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
ρ/ρ 0
ρ/ρ 0
(a)
(b)
(密度)
(密度)
( , ): intermediateSphere→Rod → Slab → Rod-like bubbles → Spherical bubbles →Uniform matter
Pasta at finite temperatures
0.393ρ0 (Slab nuclei at zero temperature)
Evaporated Neutrons Connected Slab
T= 2 MeVT= 1 MeVT= 0 MeV
Slab Nuclei
Increasing dripped neutronsDiffusive nuclear surface
Pasta at finite temperature
Cannot identifynuclear surface
Phase separationdisappears
Rodlike Bubble-like structure
T=3MeV T=5MeV T=6MeV
Phase transition, Melting surface, Dripped protons,Disappearance of phase separation
Phase diagram at finite temperatures
SP
1
2
3
45
6
7
8
910
T (MeV)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80ρ/ρ0
SP : SphereC : CylinderS : SlabCH : C bubbleSH : S bubble( , ) : Intermediate
Phase separation line (T=6 ~ 10 MeV)
Surface line(T=4 ~ 6 MeV)
Thermal fluctuation increases volume fraction of nucleiAbove T= 4 ~ 6 MeV, cannot identify surfaceAt T= 6 ~ 10 MeV, Liquid-gas phase separation
SH
(C,S)
CS CH
(S,CH)
Phase separation
Summary of Phase Diagram
• Performed simulation of nuclear matter at sub-nuclear densities with QMD
• Pasta Phases are obtained by QMD Ground-state by cooling hot matter Equilibrium-state of hot matter• How structure of nuclear matter change in the
density-temperature plane is examined
Neutrino Opacity of Pasta Phases
Motivation
Neutrino transport --- a key element for success of supernovae
How pasta phases change neutrino transportin collapsing cores ?
Neutrinos are trapped in collapsing phaseLepton fraction affects EOS
Cross section of neutrino-Pasta
Cross section of neutrino-nucleon system coherent scattering
Neutrino-neutron cross section
Amplification factor(Static structure factor)
Total transport cross section
→Amplification factor by structure
Method
1. Comparison cases with and without pasta phases using BBP liquid drop model
2. Show the results obtained by QMD as realistic model
Prediction by Liquid Drop Model
Energy of neutrino (MeV)
Red: with PastaBlack: without Pasta
Peak at 30~40 MeVPeak monotonically decreasesBelow 25 MeV incoherent
T=0 MeV・ YL=0.3
Amplification factor
Existence of Pasta phases increases peak energy, and decreases opacity at lower energy
QMD resultsYe=0.3, ρ=0.0660fm-3 (Slab at T=0)
・ Peak is lowered by increasing temp.
・ Transition from slab to rod-like bubbles dramatically changes peak energy and peak height
T= 1 MeV T= 3 MeV
Phase transitions can largely change neutrinoopacity with low energy (~25-30 MeV)
Summary of neutrino opacity
• Pasta phases decrease neutrino opacity at low energy
• Phase transitions at finite temperatures complicate neutrino opacity
Summary
• Pasta phases appear with QMD simulation
• How nuclei are deformed into uniform nuclear matter has been examined
• Pasta phases decrease neutrino opacity at low energy side
• Phase transition at finite temperature complicate neutrino opacity