Equation of state in supernova core & neutrinos

K. Sumiyoshi

• Relativistic EOS table for supernova simulations• EOS effects on explosion mechanism and ν-reactions

• Neutrino bursts from black hole formation• Detection of BH, a probe of EOS

Numazu College of Technology &National Astronomical Observatory of Japan

RCNP, 2007. 3

SN1987A

Core-collapse supernova explosion

Collapseρc~1010 g/cm3

Tc~1 MeVYe~0.46

ν-trappingρc~1012 g/cm3

Tc~2 MeV

!! !

!

Core Bounceρc~3x1014 g/cm3

Tc~10 MeVYe~0.3

NS

!

!

10 km

R-process

Supernova ν

P NS

Explosionρc~6x1014 g/cm3

Tc~10 MeV

T~0 MeVYe<0.1

1000 km

Fe core

Shockwave

!!

!

!

e-capture

Roles of Equation of state (EOS)1. Pressure, stiffness,

– structure, core bounce,..2. Entropy, Temperature

– ν-energy, spectrum,..3. Composition

– e-capture, ν-interaction,..• Set of physical EOS for supernovae

– Lattimer-Swesty EOS (1991) Used so far uniquely– Relativistic (Shen) EOS (1998) NEW

ν

• Whether the explosion occurs or not with new EOS?• Properties of neutron star/black hole, supernova ν?

Relativistic equation of statefor supernova simulations

Relativistic equation of state for supernovae

• Relativistic Mean Field + Local-Density Approx.– Based on relativistic Brueckner Hartree-Fock (RBHF) theory– Checked by exp. data of n-rich unstable nuclei

• Nuclear structure: mass, charge radius, neutron skin,…

• EOS data table (~60MB) covers– Density: 105 ~ 1015.4 g/cm3

– Proton fraction: 0 ~ 0.56– Temperature: 0 ~ 100 MeV

• Extended studies on EOS table– RMF with hyperons (Ishizuka 2005, Tsubakihara-Ohnishi, 2006)– Variational calculation with N-N interaction (Kanzawa-Takano, 2006)

Shen, Toki, Oyamatsu & Sumiyoshi, 1998, NPA, PTP

cf. Lattimer-Swesty EOS (1991)- Extension of compressible liquid drop model: bulk EOS with Skyrme I’

Mixture ofn, p, α, nuclei

Relativistic Mean Field Theory - Effective Lagrangian

!

LRMF = " i#µ$µ %M % g&& % g'#µ'

µ % g(#µ) a(aµ % e#µA

µ 1% ) 32

*

+ , -

. / "

!

+1

2"µ#"

µ# $1

2m#

2# 2$1

3g2# 3

$1

4g3# 4

!

"1

4Hµ#H

µ# +1

2m$

2$µ$µ +

1

4c3$µ$

µ( )2

!

"1

4Gµ#

aG

aµ# +1

2m$

2$µ

a$aµ "1

4Fµ#F

µ#

Parameters determined by nuclear data (masses, radii)TM1:

Nuclear structure calculations EOS calculations

Serot, Walecka 1986

Sugahara, Toki Nucl. Phys. A 579 (1994) 557

Rel. Brueckner HF

Rn

Rp

Symbols: Exp. DataLines: RMF

T. Suzuki et al. PRL 75 (1995)

Neutron skins of Na isotopes

Rp, Rn[fm]

Radii of isotopes

208Pb: 0.27fm (cf. 0.16fm, SkX)

Sugahara, Toki NPA 579 (1994)

0.2fm Ska 0.16fm SkX, by A. Brown0.13fm SIII

Interaction determined by masses and radii: TM1

150

100

50

0

sym

met

ry e

ner

gy [

MeV

]

100

50

0

ener

gy p

er b

aryon [

MeV

]

0.60.50.40.30.20.10.0

baryon density [fm-3

]

K=281 MeV

K=180 MeV

Asym=36.9 MeV

Asym=29.3 MeV

LS-EOSShen-EOS

n0

2.5

2.0

1.5

1.0

0.5

0.0M

g [

Mso

lar]

1014

1015

!c [g/cm3]

Mmax=2.2Msol

Mmax=1.8Msol

Sumiyoshi et al. NPA730 (2004)

•Density dependence of Asym

cold NS

•Symmetry energy effect is large• Checked by unstable nuclei• Difference of composition

- e-capture, ν-reaction rates

• Relativistic EOS is stiff cf. non-rel• Supernova dynamics• Proto-neutron star properties

Shen-EOS vs LS-EOS

1410 1286 Log10(ρB) g/cm3Density

Temperature

10

15

5

T [MeV]

n+p Boltzmann gas

n+p uniform matter

ρB=105~1015 g/cm3

T=0~100 MeVYp=0~0.5

Phase diagram of dense matter• Mixture of n, p, α, nuclei @ finite T• Uniform & non-uniform matter

n0

n+p+α gas

n+p+α+A gas

Yp=0.4

0

Numerical simulation of supernovae

– Solve hydrodynamics & ν-transfer at once• Standard ν-reaction rates (Bruenn) with some revised rates• Two sets of equation of state (Shen-EOS(new) vs LS-EOS)• Initial model (Fe core and Si-layer)

– 15Msolar & 40Msolar, Woosley-Weaver, 50Msolar, Tominaga-Umeda-Nomoto

• GR Hydrodynamics

• GR ν-transfer (Ye-evolution)　distribution: f(t, r, Eν, cosθ)

• Equation of state (EOS) (ρ, T, Ye)

• ν-reaction rates ∝Eν2

(ρ, T, µi, Xi)

pressure

composition

absorbemitscatter

ν-heating, cooling, pressure

compression, expansion

Mstar

40Msolar

35Msolar

30Msolar

25Msolar

20Msolar

15Msolar

10Msolar

neutron star

Numerical simulation of supernova explosion

Shen-EOS vs LS-EOS

• Whether explosion occurs with new EOS?

bounce

proto-neutron star

shock wave

collapse

No explosion even with new EOS (Shen)

Fe-core of 15Msolar

Sumiyoshi et al. ApJ 629 (2005) 922

Electron capture↓ Initial shock position↑Difference in composition: less free protons during collapse

10-5

10-4

10-3

10-2

10-1

100

Xp

2.01.51.00.50.0

Mb [Msolar]

ρc=1011 g/cm3

!!

!

!

Min

Mout

ν-trapping

At core bounce

Fe coreShockwave

Symmetry energy (Shen): 37 MeV0.1Msolar ~ 1.6x1051 ergMass

fraction

Radius

LS-EOSShen-EOS

Sumiyoshi et al. ApJ 629 (2005) 922.

After bounce: ν-heating effect

-1.0x1021

-0.5

0.0

0.5

1.0

hea

ting r

ate

[erg

/g/s

]

30025020015010050

radius [km]

LS-EOSShen-EOS

ν-heating rate↓ at tpb=150ms

~200msec after bounce:Similar dynamics of shock ν-luminosity↓Temperature↓　ν-energy, flux

• Cancel out EOS effects

Heatingregion

νν ν

νe + n e− + pνe + p e+ + n

Stalled shockProto-neutron star

Fe core

np

Sumiyoshi et al. ApJ 629 (2005) 922.

Influences on explosion mechanism:composition and weak reactions

Electron capture on nuclei: e+A→νe+A´• e-capture rates updates

– Bruenn• GT: f7/2 → f5/2

• N>40 blocked

– Langanke, Pinedo• Shell Model + RPA• 45 < A < 112

• e+A may dominate• Hix et al.

at bounceS

Ye

Hix et al. PRL (2003)

ρ

v

Min:0.1Msolar↓

Electron-capture rates on different nuclei• N-rich nuclei up to drip

– In collapsing core• EOS difference

– Symmetry energy

• NSE-mixtures– Nuclear masses

• Large e-capture rateseven for small fractions

40

35

30

25

20

Z

706050403020

N

56Feρc=1011~1012 g/cm3

ρc=3x1011 g/cm3

LS-EOS

Shen-EOS

Hix (‘03)

Sumiyoshi (‘04)N

Z

Add ν-N heating *30, 50, 70%from tpb=100 msec

tpb=100 ms

Test Calculations

shockwave

70%50%

30%Dependence on ν-heating

ν-heating through nuclei (Haxton 1988)

ννν

1000kmRShock RFeRgain

~200km100km~80km

Rν, RPNS

Proto-neutron star

cooling

heating

Stalled shock

Fe core surface

Fe

FeHe

He

νi + A νi´ + A´ νi + A e+ + A´νi + A e− + A´

•Charged-current•Neutral-current(inelastic)

Ενe ≤ Ενe ≤ Ενµ

~100ms after bounce

• Nucleon

• Nuclei

• Average energy transfer x cross section

• Effects on explosion mechanism by ν-α heating

Estimate of ν-heating

!

Q"

N# 223 $

L" ,52E" ,15

2

R7

2Xi[MeV

s $ N]

!

"E# $A

%& E $ E0( )

'[10

$40MeVcm

2]

–Lνi,52: luminosity in 1052 erg/s–Eνi, 15: average ν-energy in 15MeV–R7: radial position in 107 cm–Xi: mass fraction

!

Q"

A# 32 $

L" ,52

R7

2E" ,15

Xi%E

" &A[MeV

s $ N]

Ohnishi-Kotake-Yamada (‘06)

Haxton (‘88)

10-3

10-2

10-1

100

101

102

103

rate

[1

e-4

2 M

eV

cm

**2]

302520151050

Enu [MeV]

Fe

He

Mass fraction

p

n

α

nuclei

Composition around heating region:tpb=150ms Nuclear species

1.0

0.8

0.6

0.4

0.2

0.0

Xi

10 100 1000

radiusc [km]

40

35

30

25

20

Z

706050403020

N

LS-EOSShen-EOS

56Fe

• Need to study composition– NSE mixture

• ν-reaction rate: Fe-group– Implement into simulations

Shen-EOS vs LS-EOS

Mstar

40Msolar

35Msolar

30Msolar

25Msolar

20Msolar

15Msolar

10Msolar

black hole

Neutrino burstsfrom formation of black hole

From http://www.oso.chalmers.se/~duilia/sn.html

SN 1997D

Fe-corecollapse

bounce black holeproto-neutron starν

ν

ν

What is the fate of more massive star (ex. 40Msolar)?

Hypernovae

Faint supernovae

• >25Msolar: Fe core (~2Msolar) too massive• No explosion → black hole formation

Large Eexp

Small Eexp

• Re-collapse beyond the maximum mass, Mmax

• Sudden termination of neutrino burst

matter accretion

bounce

proto-neutron star

shock wave

collapse

Trajectories of collapse: Shen-EOS

Core of40Msolar

black hole

Accretion

Sumiyoshi et al., PRL 97 (2006) 091101

In baryon mass: 2.66Msolar

In gravitational mass: 2.38Msolar

recollapse

~0.1ms

At MPNS=2.6Msolar

50

40

30

20

10

0

< E

! >

[M

eV

]

1.51.00.50.0

time after bounce [sec]

2x1053

1

0lu

min

osi

ty [

erg/s

]

1.51.00.50.0

time after bounce [sec]

40Msolar

Neutrino bursts toward black hole formationν-average energy ν-luminosity

Sumiyoshi et al., Phys. Rev. Lett. 57 (2006) 091101

νe

νµνe

νe

νµ

νe

!

L" ~GM ˙ M

r

T↑

Shen-EOS

bounce

proto-neutron star

shock wave

collapse

Trajectories of collapse: LS-EOS

Black holeformation

Accretion of matter

time [sec]

At MPNS=2.1Msolar

Core of40Msolar

Sumiyoshi et al., Phys. Rev. Lett. 57 (2006) 091101

3.0

2.5

2.0

1.5

1.0

0.5

0.0

bar

yon m

ass

of

PN

S [

Mso

lar]

1.51.00.50.0

time after bounce [sec]

Increase of proto-neutron star mass

LS-EOS

Shen-EOS

Sumiyoshi et al., ApJ (2006) in preparation

0.6sBH:

2.1Msolar

1.3sBH:

2.6Msolar

bounce

Softer EOS leads to earliercollapse to black holehaving smaller Mmax

Different timing of supernova ν termination

LS-EOS

Average energy of supernova ν

Shen-EOS

νe

νµ

νe

νµνe

νe

Sumiyoshi et al., Phys. Rev. Lett. 57 (2006) 09110150

40

30

20

10

0

< E

! >

[M

eV]

1.51.00.50.0

time after bounce [sec]

2x1053

1

0

lum

inosi

ty [

erg/s

]

1.51.00.50.0

time after bounce [sec]

50

40

30

20

10

0

< E

! >

[M

eV]

1.51.00.50.0

time after bounce [sec]

2x1053

1

0

lum

inosi

ty [

erg/s

]

1.51.00.50.0

time after bounce [sec]

bounce bouncetime time [s]

• Sudden termination of ν-signal - Short in LS-EOS

• Increasing ν-energy and luminosities - Common feature

Signal of black holeformation

WW95: 40Msolar

1.3 sec 0.6 sec

Different Progenitor (50Msolar, Tominaga et al. (2007), Z=0)

νe

νµ

νe

lhr50t01: In baryon mass: 2.11MsolarIn gravitational mass: x.xxMsolar

LS-EOS

•40Msolar (Z=solar)•Hashimoto (1995)

–Calculating now

SH-EOS

νe

νµ

νe

bounce bouncetime time [s]

• Similar feature of ν-signal, EOS difference in duration

r�hr50t01: In baryon mass: 2.65MsolarIn gravitational mass: x.xxMsolar

Sumiyoshi et al., ApJ (2006) in preparation

Average energy of supernova ν50

40

30

20

10

0

< E

! >

[M

eV

]

1.51.00.50.0

time after bounce [sec]

50

40

30

20

10

0

< E

! >

[M

eV

]

1.51.00.50.0

time after bounce [sec]

TUN05: 50Msolar

1.5 sec 0.5 sec

Summary• Equation of state in core-colapse supernovae

– Relativistic EOS table based on unstable nuclei– Comparison of simulations with two EOS sets

• Influence of EOS on explosion mechanism + No explosion even with new EOS (15Msolar)

– Stiffness → central density– Compositional difference → weak reaction rates

• Neutrinos signals to detect black hole + Short neutrino bursts with increase of Eν (40Msolar)

– Constraints on EOS by duration of neutrino bursts