Transcript Nuclear “Pasta” in Compact Stars

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
No successful simulation with realistic settings
Scenario
“Bounce” triggered by nuclear repulsive force
Just before bounce (just before nuclear matter phase)
Nonspherical nuclei --- “Pasta” phases
Possible key element
Neutrino transport in supernova cores
EOS of dense matter
Neutron Stars and Nuclear “Pasta”
Neutron Stars
Pasta phases in the deep inside inner crust
Outer Crust
Inner crust
Pasta Phases
Core
1 km
10 km
Solid of heavy nuclei
Transition region from
nuclei to nuclear matter
Liquid of nuclear matter
(quark matter, hyperons)
What is Nuclear “Pasta” ?
Nonspherical nuclei in dense matter ～1014g/cc
Sphere→
Rod → Slab → Rod-like Bubbles → Spherical Bubbles
→Uniform Nuclear Matter
(Ravenhall et al. 1983,Hashimoto et al.1984)
Meatball
Spaghetti
Lasagna
Anti-spaghetti
Cheese
→”Pasta” Phases
(K.Oyamatsu, Nucl.Phys.A561,431(1993))
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
QMD is suitable to answer the above question
No assumptions on nuclear shapes.
Nuclear system is treated in degrees of freedom of nucleons.
Thermal fluctuations are included.
Quantum Molecular Dynamics
Model Hamiltonian 1（Chikazumi et al Phys.Rev.C 63 024602(2001))
Kinetic Energy
Pauli Potential
Nuclear Force
Coulomb Energy
Model Hamiltonian 2（Maruyama et al Phys.Rev.C 57 655(1998))
Nucleons obey Equation of Motion of QMD
Hamiltonian is constructed to reproduce …
Saturation properties of symmetric nuclear matter
Binding energy and rms radius of stable nuclei
Simulation settings
Simulation Settings
2048 or 10976 nucleons in simulation box
Periodic boundary condition
Proton fraction x=0.3
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
Cooling of hot nuclear matter (~10 MeV) below 0.1 MeV
Rod
Sphere
0.100ρ
0
0.200ρ
Slab
0
0.393ρ
0
Red : Protons
Blue: Neutrons
ρ0 =0.168 fm-3
（Nuclear density）
Rod-like Bubbles 0.490ρ 0
Spherical Bubbles 0.575ρ
0
Sponge-like Structure
Between rod and slab, slab and rod-like bubbles
Multiply 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
(a)
Model 1
SP&C coexist.
SP
(S,CH)
C (C,S) S
CH,SH coexist.
CH
SH
Uniform
ρ/ρ０
0
(b)
0.1
0
0.3
0.1
0.4
0.5
C (C,S) S CH
0.2
0.6
0.7
0.8
0.9
（密度）
(S,CH)
SP&C共存
SP
Model 2
0.2
0.3
0.4
0.5
SH
0.6
Uniform
0.7
0.8
0.9
ρ/ρ０
（密度）
SP: sphere S: slab
SH: spherical hole
C: cylinder CH: cylindrical hole ( , ): intermediate
Sphere
→Rod → Slab → Rod-like bubbles → Spherical bubbles
→Uniform matter
Pasta at finite temperatures
0.393ρ0 (Slab nuclei at zero temperature)
T= 0 MeV
Slab Nuclei
T= 1 MeV
Evaporated Neutrons
Increasing dripped neutrons
Diffusive nuclear surface
T= 2 MeV
Connected Slab
Pasta at finite temperature
T=3MeV
Rodlike Bubblelike structure
T=5MeV
Cannot identify
nuclear surface
T=6MeV
Phase separation
disappears
Phase transition, Melting surface, Dripped protons,
Disappearance of phase separation
Phase diagram at finite temperatures
T (MeV)
Phase separation line (T=6 ~ 10 MeV) SP ： Sphere
C ： Cylinder
S ： Slab
CH ： C bubble
SH ： S bubble
10
9
8
7
6
( , ) ： Intermediate
Phase separation
5
4
Surface line
(T=4 ~ 6 MeV)
(C,S) (S,CH)
3
2
1
SP
C
0
0.1
0.2
0.3
S
CH
0.4
0.5
SH
0.6
0.7
0.8
ρ/ρ0
Thermal fluctuation increases volume fraction of nuclei
Above T= 4 ~ 6 MeV, cannot identify surface
At T= 6 ~ 10 MeV, Liquid-gas phase separation
Summary of Phase Diagram
• Performed simulation of nuclear matter at subnuclear 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
Neutrinos are trapped in collapsing phase
Lepton fraction affects EOS
How pasta phases change neutrino transport
in collapsing cores ?
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
Amplification factor
T=0 MeV・YL=0.3
Red: with Pasta
Black: without Pasta
Peak at 30~40 MeV
Peak monotonically decreases
Below 25 MeV incoherent
Energy of neutrino (MeV)
Existence of Pasta phases
increases peak energy, and
decreases opacity at lower energy
QMD results
Ye=0.3, ρ=0.0660fm-3 (Slab at T=0)
T= 1 MeV
T= 3 MeV
・Peak is lowered by increasing temp.
・Transition from slab to rod-like
bubbles dramatically changes
peak energy and peak height
Phase transitions can largely change neutrino
opacity 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