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

15

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

24

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