1
Nuclear physics and neutrino transferin supernovae and compact objects
K. ‘Sumi’yoshi
- Neutrino transfer: Solver of 6D Boltzmann equation- Equation of state: Composition of dense matter
Numazu College of TechnologyJapan
NPCSM2016@YITP, Kyoto, 2016/11/15
Crab nebula
hubblesite.org
Nuclei and neutrinos
Numazu near Mt. FujiWikipedia (trimmed)
n
~10 km
Core-collapse SNe: collapse, bounce and explosion
1000 km
Fe core Collapse n-trapping
e-capture
Core Bounce
νν ν
ν
Shockwaveνν
ν
ν
Explosion
NS
ν
ν
10 km
proto-
Neutron star
Supernova neutrinos
Massive star ~20Msun
difficult part!!
2
~6000 km
~50 km
1051 erg
1053 ergscattering
in 1 second
n
r > r0
Proto-NS
Explosions mechanism in 2D & 3D
- Convection, SASI, rotation, magnetic etc
3
neutrino-heating with hydro instabilities
n-heating
n
n
shockwave
Marek et al, ApJ (2009) Suwa et al. (2010) PASJ
Enough time for n-heating
Deformation of shock Convection
* Sloweraccretion
* Longer Falling time
Roberts ApJ (2016)
1D
3D
2D
100 km
Takiwaki (2015)
Shock radius
time
• Numerical simulations of core-collapse supernovae
• Equation of state• Neutrino reactions
at 105-1015 g/cm3, ~1011 K
• Hydrodynamics• Neutrino transfer• General Relativity
4
Nuclear Physics Astrophysics
Supercomputing technology
Huge supercomputing power is necessary
• Main trigger, 2D vs 3D, low explosion energy?• Evaluation of neutrino-heating• Dependence on nuclear physics
http://www.aics.riken.jp
Remaining issues of explosion mechanism
• To clarify the problem we need full simulations
K-Computer, Japan
5
Neutrino transfer in 2D/3D supernovae
From approximate to exactneutrino-radiation hydrodynamics
Nagakura et al., ApJS (2014, 2016)Sumiyoshi et al., ApJS (2012, 2015)
Neutrino heating mechanism for revival of shockHeating by neutrino absorption ne + n → e- + p,
ne + p → e+ + n
nn n
~100km
Proto-NS
heating
Shock
Fe core surface
n-heating
Delayed explosion
Eν−heat ~ 2×1051 ΔM0.1Msolar
$
%&
'
()
Δt0.1s$
%&
'
()erg
Transfer of energy from n
Shock position
time [s]
100ms after bounce
Neutrino energy/fluxfrom trapped neutrinos
Janka A&A (1996)
n
pTrapped neutrinos
“Legendary simulation” in 1980’s
Bethe & Wilson ApJ (1985)Liebendörfer et al. (2000)
Shock position
time [s]
No explosion by modern 1D simulations
6
Reaction/scatteringDiffusion
High T/r Shock wave
Free-streamingn n
nn
n
n
n-transfer to determine n-heating
• From diffusion to free-streaming– Intermediate regime is important
→ From approximate to exact
7
n-heating
n
50km 5000km100km
€
1c∂fν∂t
+ n ⋅ ∇ fν =
1cδfνδt
'
( )
*
+ ,
collision
Need to solve Boltzmann eq.
• Neutrino flux & heating– ν-trapping, emission, absorption
formidable so far
2D/3D hydrodynamics + neutrino heating
Proto-NS
n-heating
n
n
shockwave
New code solves 6D Boltzmann eq.
• Approximations used so far- 2D/3D: Diffusion, Ray-by-Ray method
(1D spherical: 1st principle calculations)
• Comparison with Ray-by-ray- Local ν-heating ~20% difference
n nn
Ray-by-ray method
Sumiyoshi & Yamada, ApJS (2012)
€
fν (r,θ,φ; εν ,θν ,φν ; t)
Sumiyoshi et al. ApJS (2015)
Time evolution+Advection=Collision
€
1c∂fν∂t
+ n ⋅ ∇ fν =
1cδfνδt
'
( )
*
+ ,
collision
Boltzmann eq. • Collision Term is tough- Energy, angle dependent- Stiff, non-linear- Frame dependent→ Huge computation
Background fix 8
Neutrino-transfer in 3D space: fixed profile
150 msec after bounceRshock~250-400km
From Takiwaki et al. ApJ (2012)
entropy density Ye
entropy
9
11.2Msun, 3D
Fix hydro. variables, solve time evolution by 6D Boltzmann eq.- Evaluate stationary state of the neutrino distributions in 6D- Study neutrino transfer in 3D, heating rates, angle moments
3D supernova core at 150ms
Sumiyoshi et al. ApJS (2015)
6D BoltzmannRay-by-ray: radial only
• Ray-by-ray- Only radial transfer- Anisotropy enhanced
10
View from side: f-slice
150msec
Comparison with approximation
ne density: color
• 6D Boltzmann- Non-radial transfer- Integrated values
from various directions
Z
Sumiyoshi et al. (2015)
Consistent with Ott-Brandt in 2D
Comparison: n-heating rateDeviation of RbRRay-by-ray: radial only 6D Boltzmann
δ =QRbR −Q6D
Q6D
11Red: heating, Blue: cooling 11Msun, 150msec
Z
Sumiyoshi et al. (2013,2014)
Neutrino-radiation hydrodynamics: 2D dynamics
• 6D Boltzmann solver + 2D Hydrodynamics + 2D gravity– Relativistic effects: Doppler, angle aberration, moving mesh– Neutrino transfer in fluid flow (from diffusion to free-streaming)
12
Nagakura et al.ApJS (2014, 2016)
Color:Ye, Arrow: Velocity Color:ν-density, Arrow:ν-flux
Convection inside proto-NS 50km
Non-radial neutrino flux in the whole region cf. Ray-by-ray approx.Figure by Iwakami
First results of core-collapse simulations
13
Color: entropy, Arrow: Velocity11.2Msun 15Msun
• Collapse, bounce and shock propagation of 2 modelsNagakura, Iwakami et al. (2016)
with Furusawa EOS table with NSE & GSI e-capture rates(RMF-TM1, “extended Shen EOS”)
http://www.aics.riken.jp K-Computer, Japan
2D dynamics depends r-profiles
No explosion found in 2D Hydro+Boltzmann• No revival of shock in 2 models
14Need further study: Nuclear physics, General Relativity?
11.2Msun 15MsunShock position Shock position
“Neutrino heating + Convection” “Oscillatory shock dynamics with SASI”
Nagakura, Iwakami et al. (2016)
but depends r-profiles
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Neutrino transfer in neutron star merger
Provide information for neutrino-radiation hydrodynamics
In collaboration with Fujibayashi, Sekiguchi
• Merger of binary NSs – 1.35M + 1.35M
• Rotating hot NS – M~2.6Msun
– Hempel DD2 EOS– Mmax~2.4Msun
16Sekiguchi et al. PRD (2015)Fujibayashi (2016)
Hyper-massive NS
Y[km]
X[km]
r [g/cm3]
T [MeV]
log10 r [g/cm3]
Neutrino emission from hyper massive neutron star• Study of 2D Neutrino transfer in deformed objects
T [MeV]
- Neutrino emission- Neutrino heating
via pair process- Electron fraction
of ejecta
Evaluation by 6D Boltzmann eq. solver• Describes full angle energy distributions
17
for emission mechanism of neutrinos from NS mergers
Neutrino density, flux Neutrino sphere
En=34 MeV
nenµ ne-
cf. Monte Carlo by Richers, M1 by Just, Adv. Leakage by Perego
Evaluation by 6D Boltzmann eq. solver• Can be used to validate approximate methods
18
for dynamical calculations in moment formalism with M1
Neutrino heating rate Eddington tensor Trr
by Fujibayashi
19
Equation of state in supernovae
effects on explosion?
EOS table for supernova simulations• Consistent framework• Experiments of nuclei• Observations of neutron stars
20
• Data covers wide range– r :– Yp :– T :
105.1 ~ 1016 g/cm3
0 ~ 0.650 ~ 400 MeV
Models Framework ReferenceNucleonbenchmark
Skyrme Hatree-FockExtended Liquid-DropRelativistic Mean Field
Wolff-HillebrandtLattimer-SwestyShen
Nucleonupdates
Relativistic Mean FieldNuclear many body
G. Shen, Oertel, PeresTogashi, Constantinou
Nucleonupdates+NSE
Relativistic Mean FieldMixture of nuclei
Hempel, Steiner, FischerFurusawa
Nucleon+Hyperon
Relativistic Mean FieldHyperon interactions
IshizukaGulminelli, Oertel, Banik
Nucleon+Quark
Relativistic Mean FieldBag model
NakazatoSagert, Fischer
LS-EOSShen-EOS
Furusawa
Based on Oertel, Hempel, Klaehn & Typel (2016)
1990’s~
2000’s~
Comparison of EOS sets: benchmark
21
• Difference in stiffness & symmetry energyLS-EOS Shen-EOS
K [MeV] 180, 220, 375 281Asym [MeV] 29.3 36.9
- Two representatives
- Extremes in modern sense
180, 220: Frequently used for many simulations
Sumiyoshi (2004)
101
102
103
Rsh
ock [
km]
1.00.80.60.40.20.0
time [sec]
LS-EOS
Shen-EOS
Sumiyoshi et al. (2005)
Shock position
15Msolar
time
100km
2.5
2.0
1.5
1.0
0.5
0.0
Mg [
Mso
lar]
1014 1015ρc [g/cm3]
Mmax=2.2Msol
Mmax=1.8Msol
cold neutron stars
Comparison of EOS sets: more recent
22
Steiner et al. (2013)
100km
Shock position
time
• Choice of nuclear interaction (stiffness, radius, …)• No explosion with various EOS tables
11.2MsolarHempel (2012)
Supernova profiles at core bounce: tpb=0 ms
Ylepton
Yn
Electron (Proton) fraction0.5
0.4
0.3
0.2
0.1
0.0
Yν,
Ye,
YL
2.01.51.00.50.0Mb [Msolar]
Sumiyoshi et al. ApJ 629 (2005) 922.
Radius
Density
Ye~0.3
LS-EOSShen-EOS
Radiusin mass
r: just above r0, T~10 MeV, Yp: not so neuron-rich yet
r0=3x1014 g/cm3
(n0=0.17 fm-3)
23
400
300
200
100
K [M
eV]
4035302520
Asym [MeV]
Suwa et al. ApJ (2013)
EOS effects in multi-D: larger than 1D?Need more systematic studies
Explosion
No explosionShen
LS
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LS
Shen
Janka ARNPS (2012)
HW
Shen
LS
HW
Explosion
No explosion
In 3D, LS 220MeVso far
Takiwaki (2012), Hanke (2013), Bruenn (2014), Lentz, Melson (2015)Robert (2016)
2D
soft is better
2D
25
Equation of state in supernovae
Effect of composition
26
x
During collapse
Wide variety of nuclei
Shen-EOS Furusawa-EOS
N
Z
N
Z
91Sex
Mixture of nuclei in supernova EOS tablesShen-EOS
Neutron, proton, 4HeOne species of nuclei
approximation
Neutron, proton, d, t, 3He, 4He,…All of nuclei up to A~1000
In nuclear statistical equilibrium
Furusawa-EOS
A representative nuclei
r=1011 g/cm3
T=1 MeVYp=0.3
Furusawa, Yamada, Sumiyoshi & Suzuki ApJ (2011, 2013, 2016)
e-capture on mixed nuclei during collapse• Composition of nuclei
1-species & 4He → Mixture• Electron capture on nuclei
– Bruenn -> GSI rates– Single -> NSE average
27Hix et al. PRL (2003)
νν
ν
ν
Bounce core Fe core
Initial energy & loss
€
Eshock ~GMinner
2
Rinner
= several ×1051erg
←
Z
bounce & after
rc=3x1011 g/cm3
Nuclear statistical equilibrium
profile of core bounceN
€
Eloss ~ −1.6 ×1051 Mouter
0.1Msolar
$
% &
'
( ) erg
↓
28Magic numbers Slide From Furusawa
• Shell smearing– at finite temperature
• Shift of abundance peakaffects electron capture rates– ~30% with/without shell effect
Shell effect on mixture of nuclei in supernova core
Furusawa et al. PRC (2016) submitted
Full Shell Weak Shell
No Shell
29
Light clusters + 4He can appear after bounceMulti-compositions with p, n, d, 3H, 3He, 4He, nuclei
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Xi
10 100r [km]
Xn Xp Xd Xt X3He X4He XA shock
Sumiyoshi & RöpkePRC (2008)
d
pn4He
3He
A>5
Heating regionProto-neutron starAt tpb=150ms
• 4He abundant at r > 100km → heating/cooling rates• d, t, 3He abundant at r < 50km → n-emission, absorption
3H
See also Arcones et al. PRC (2008) for proto-NS
Mass fraction
radius [km]
neutrino-sphere
Absorption of neutrinos: neutrino heating• Nucleons: ~200MeV/s
30
nn
nRShock
tpb~100ms
~150kmRPNS
Fe
FeHe
Heheating
n
nn
RFe
n, p
n, p
Haxton PRL (1988)
ni + A ni´ + A´ni + A e+ + A´ni + A e- + A´
• Fe, 4He• Light nuclei (d, t, 3He)
ne + n → e- + p, ne + p → e+ + n
• Nuclei: 0~30MeV/s
depends on species!!
Nakamura et al. PRC (2009)
Fe nuclei → light nuclei → neutrons, protons
ex.
O’Connor et al. PRC (2007)
d
d
2D supernova simulations with light clusters• (d, 3He, t, 4He ) appear
31
Furusawa et al. ApJ (2013)
n, p d, 3He, t, 4HeAbundance
Shock radius[km]
time [ms]
• n-absorption (d, 3He, t)
• Possible effects on shock revival when it is marginal
Nucleon only
Full
After core bounce
Emission of neutrinos via light clusters• Deuterons
• Proton, neutrons
• Triton, 3He
32
ex.
• Modifications of - n-sphere, emissivity
Nasu et al. PRC (2015)
cf.
nn
nRShock
tpb~100ms
~80kmRPNS
Fe
FeHe
Heemission
n
nn
RFe
n, p
n, p
d
d
dd
n, p
light nuclei appear around proto-NS surface
O’Connor, Arcones PRC (2007, 2008)
2D supernova simulations with light clusters• With/without reactions via deuterons
– Using abundance of nuclei from Furusawa EOS
33
WW95, 15Msun
Takiwaki et al. (2016) in preparation
2D with reaction
2D without
1D without1D with reaction
Slide From Takiwaki
34
0
1
2
3
4
5
6
7
50 100 150 200 250 300
Neu
trino
Lum
inos
ity [1
052er
g/s]
Time after bounce [ms]
FYSS, wo reactionFYSS, w reaction
νe ν-e
tpb=100ms
Luminosity
with reaction
without
0.001
0.01
0.1
1
0 20 40 60 80 100 120 140 160 180 200
Xn+
Xp,
Xd
Radius [km]
n,pd
deuteron
neutron, proton
Mass fraction
with reaction
without
Luminosity
Time evolution1D case:
• Emission via deuteron affects– Increase of luminosity, – Modify cooling/heating– Shock radius in 1D/2D
• Reaction channels• Neutrino-transfer
Stiffness & Composition of EOS in multi-D
n
n
n
, En, LnM, R
StalledShock wave
heating
Proto-NS
After bounce
~100km
~100ms
cooling
n-cooling & heating in multi-D hydrodynamicsFavorable for explosion
Examine nuclear physics in multi-D simulations
• EOS softCompact, Inner r, T ↑n-luminosity, energy ↑
> r0
35
IF opposite, maybe weaken explosions
• More n-absorptionat heating region ~10-5 r0
composition & n-reactionsat proto-NS surface ~10-2 r0
• More n-emission
36
Summary: Nuclear physics and neutrino transferfor core-collapse supernovae and compact objects
• Applications of 6D Boltzmann eq. solver– Explosion mechanism of core-collapse supernovae
• Neutrino-radiation hydrodynamics in 2D– Neutrino transfer in compact objects
• Validation of approximate methods
• Tables of equation of state with mixture of nuclei– Modification of electron capture rates– Neutrino absorption & emission for explosions
• Toward 1st principle calculations of 3D supernovae• General relativistic neutrino-radiation hydrodynamics
– Exa-flops supercomputer by post-K project in Japan– Need reliable equation of state, neutrino reactions
37
Project in collaboration with• Numerical simulations
– H. Nagakura– W. Iwakami– H. Okawa– A. Harada– S. Yamada
• Supernova research– T. Takiwaki– K. Nakazato– K. Kotake– Y. Sekiguchi– S. Fujibayashi
• Supercomputing– H. Matsufuru– A. Imakura, T. Sakurai
• EOS tables & neutrino rates– H. Shen, K. Oyamatsu, H. Toki– C. Ishizuka, A. Ohnishi– S. Furusawa– S. X. Nakamura, T. Sato
Supported by- HPCI Strategic Program Field 5- MEXT and JICFuS- for K-computer and Post-K machine
- HPC resources at KEK, YITP, UT, RCNP- K-computer: hp160071, hp160211
Grant-in-Aid for Scientific Research (15K05093)http://www.aics.riken.jp
K-Computer, Japan