Core-collapse supernovae:Long-term effects of equation of state

K. “Sumi”yoshi*, H. Suzuki, H. Shen, H. Tokiand S. Yamada

• Relativistic equation of state (EOS) for supernovae• GR neutrino-radiation hydrodynamics (1D)

• Explosion or not?, Proto-neutron star, Supernova ν

* Numazu College of Technology, JapanSN1987A

05/03/05 @ CNS

No explosion: what is still missing?

Thompson et al. (2003) Rampp-Janka (2000)

• Macrophysics issues:– Hydrodynamics– ν-transfer– Convection, rotation, GR..

• Microphysics issues:– Equation of state– ν-reaction rates– e-capture rates,…

(Except Wilson)

Sumiyoshi et al. (2005)

Importance of microphysics• Unique set of microphysics has been used

– No explosion (shock stalled) so far with:– Lattimer-Swesty EOS, Bruenn’s weak rates (+improved)

Mezzacappa, Janka, Burrows(Except Wilson)

• Neutrino-heatingmechanism is sensitive

• Heating rate~LνEν

2 ~Tν6

• Neutrino-transferσν~Eν

2

• EOS, reactionsBethe-Wilson ApJ 295 (1985) 14

ν-heating

Delayed explosion in 0.5sec

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

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

– ν-energy, spectrum,..3. Composition (n, p, α, nuclei)

– e-capture, ν-interaction,..• Systematic studies by parameterized EOS

– Baron-Cooperstein, Takahara-Sato, Bruenn, Swesty,..• Set of physical EOS

– Wolff-Hillebrandt EOS (1985)– Lattimer-Swesty EOS (1991) Used so far– Relativistic (Shen) EOS (1998) NEW

ν

Physics of unstable nuclei• Recent advance of radioactive nuclear beam facilities provides

us with data on n-rich nuclei in Japan, US, Germany,…

From www.rarf.riken.go.jp

ex. RIKEN, GSI, RIA, …

• Relativistic EOS table is based on data of unstable nucleiShen et al. NPA, PTP (1998)

• We should examine supernova simulations in the light ofphysics of unstable nuclei

Stable

Dripline

Nuclear Chart 1993by Chiharu Tanihata

Unstable

820 28

50

82

126

8

20

28

50

82

65% for one page

4He

16O

40Ca

48Ni56Ni

100Sn

208Pb

N

Zneutron rich nuclei

New simulations with new microphysics– A new set of physical equation of state (EOS)

• Find out the fate of core collapse– Explosion or not?

• Evolution up to 1 sec after bounce (delayed explosion?)– Birth of proto-neutron star from supernova core

• Examine the effect of new EOS– Some hints on the explosion mechanism, prepare for 2D, 3D

• Within the exact treatment of ν-radiation hydrodynamicsin spherical symmetry– General relativistic neutrino-radiation hydrodynamics

• The first comparison of EOS effects beyond 300 msec– Most of simulations up to ~300 msec Sumiyoshi et al., submitted to ApJ (2005)

Sumiyoshi et al.

Equation of State for Supernovae

New equation of state for supernovae• Relativistic Mean Field + Local-Density Approx.

Shen, Toki, Oyamatsu & Sumiyoshi, 1998, NPA, PTP– Based on relativistic Brückner Hartree-Fock results

• Non-linear σ-ω + ρ TM1 parameter set– Checked by exp. data of n-rich unstable nuclei

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

• EOS data table (~60MB) covers– Density: 105 ~ 1015 g/cm3

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

• Extension with Hyperon (Ishizuka-Ohnishi, 2005)

• cf. Lattimer-Swesty EOS: former “standard” set

Comparison of EOSs

Yes---M*Yes---n-skinYes (incl. unstable)partlyNucl. DataMass, Rc, RnSaturationInteractionRMF (RBHF)“Skyrme”-likeBulk EOS

Rel. Mean Field +Local-Density Approx.

Compressibleliquid drop model

ModelShen-EOSLS-EOS

Neutron skins of Na isotopes

Rn

Rp

Symbols: Exp. DataLines: RMF

T. Suzuki et al. PRL 75 (1995) 3243

Local density approximation in cell

•Mix of:NeutronProtonAlphaNucleus

•Non-uniform&

Uniform

Shen et al. PTP (1998)

2.5

2.0

1.5

1.0

0.5

0.0

Mg [

Mso

lar]

1014 1015 1016

central baryon mass density [g/cm3]

Neutron star mass with Shen-EOS & LS-EOS

H. Suzuki (2004)

LS-EOS

Shen-EOS

K=180 MeV

K=281 MeV

Characteristics of new EOS1. Stiff in relativistic EOS not favorable

• Replusive at high density (relativistic many body theory)

2. Large symmetry energy favorable• Replusive in n-rich matter (neutron skins) cf. Non-rel.

– Difference of composition, chemical potential• Neutron Star: Yp=0.1~0.2 for rel-EOS• Small proton fraction → e-capture reduced → supernova dynamics

• Whether explosion occurs with new EOS?

Baron (1985)

Bruenn (1989)

Sumiyoshi et al. NPA595 (1995)

36.929.3Asym [MeV]Shen-EOSLS-EOS

Numerical simulations of supernovae

Rel-EOS(new) vs LS-EOS

Numerical simulations• General relativistic hydrodynamics

» Yamada, ApJ 475 (1997) 720• General relativistic Boltzmann equation (ν-transfer)

» Yamada, Janka & Suzuki, A&A 344 (1999) 533– Fully implicit in time: advantageous to have long time steps

• Comparison by 2 sets of EOS– Relativistic EOS (Shen) vs Lattimer-Swesty EOS (LS)– Initial model: Fe core of 15Msolar– Standard weak rates (Bruenn) + ν-bremsstrahlung

(Woosley-Weaver, 1995)

(Bruenn 1985)

νν

ν

ν

Important factors during collapse• Initial shock energy↑~GMin

2/R~(lepton fraction)10/3

• Energy loss↓~Fe dissociation ~(Mout-Min )

• Softness↑– EOS

• Electron capture↓– on p, Nuclei (Z, N)

• Neutrino-trapping↑– neutrino-rate

• Explosion energy↑

Min

Mout

Bounce core

at core bounce

Fe core

lepton fraction

shock

40

35

30

25

20

Z

706050403020

N

40

35

30

25

20

Z

706050403020

N

Composition of dense matter during collapse: ρc=1011, 1012 g/cm3

Z, N of Nuclei

LS-EOSShen-EOS

Ref: Sumiyoshi et al. Nucl. Phys. A730 (2004) 227rhq05

N> 40 Blocked (Bruenn’s rate)

56Fe

Smaller e-capture larger bounce core

Velocity at bounce Free proton fraction during collapse

LS-EOSShen-EOS

-8x109

-6

-4

-2

0

2

velo

city

[cm

/s]

2.01.51.00.50.0Mb [Msolar]

10-5

10-4

10-3

10-2

10-1

100

X p

2.01.51.00.50.0Mb [Msolar]

ρc=1011 g/cm3

bounce

proto-neutron star

shock wave

collapse

No explosion even with new EOS (Shen)

Sumiyoshi et al. submitted to ApJ (2005); see also NIC8 proceedings in NPA (2004)

Fe-core of 15Msolar

Slower decrease of shock position in new EOS

LS-EOS

Shen-EOS

position of shock wave

150ms 1s

101

102

103

R sho

ck [k

m]

1.00.80.60.40.20.0time [sec]

νν

ν

1000kmRShock RFeRgain

~200km100km~80kmRν, RPNS

Proto-Neutron star

cooling

heating

Neutrino heating behind the shock after bounce

Shock position

Fe core surface νe + n e− + pνe + p e+ + n

Lower ν-heating

-1.0x1021

-0.5

0.0

0.5

1.0

heat

ing

rate

[erg

/g/s]

30025020015010050radius [km]

LS-EOSShen-EOS

Heating rate at tpb=150msShock dynamicssimilar up to 200 msec

• Lower heating rate

• Lower Lνν-energy, flux- lower T

• Cancels out

larger bounce core

Central density becomes different at late phase

Shen-EOS

0.5

0.4

0.3

0.2

0.1

0.0

bary

on d

ensit

y [fm

-3]

1.00.80.60.40.20.0time [sec]

LS-EOS

n0=0.17 fm-3

bounce

1011

1012

1013

1014

1015

dens

ity [g

/cm

3 ]

40302010radius [km]

LS: ρc=7.0×1014 g/cm3

SH: ρc=4.1×1014 g/cm3

Less compact object

Density at tpb=1sCentral PNS coreDifferent already at 1 s

• Central density lower: ρc↓Factor of ~2

• Larger radius: Rpns↑

• Stiff new EOS

• Lower T• Slower evolution

60

50

40

30

20

10

0te

mpe

ratu

re [M

eV]

2.01.51.00.50.0Mb [Msolar]

60

50

40

30

20

10

0

tem

pera

ture

[MeV

]

2.01.51.00.50.0Mb [Msolar]

Thermal evolution is different!Temperature profiles after bounce: tpb=20ms - 1s

LS-EOS Shen-EOSTpeak=53 MeV Tpeak=39 MeV

30

25

20

15

10

5

0

E ν [M

eV]

1.00.80.60.40.20.0time [sec]

30

25

20

15

10

5

0

E ν [M

eV]

1.00.80.60.40.20.0time [sec]

Properties of supernova neutrinos

Average energy is different!ΔEν=3~5 MeV

LS-EOSShen-EOS

νµ/τ

νe νe

30

25

20

15

10

5

0

E ν [M

eV]

1.00.80.60.40.20.0time [sec]

Summary• New simulations of supernovae

– Relativistic EOS table (cf. Lattimer-Swesty EOS)– Up to 1 sec after bounce

• The first comparison with two EOSs– No prompt/delayed explosion with new EOS

• Larger core size, lower luminosity: composition & stiffness– Difference after 300 msec: ρc by factor ~2

• Evolution of proto-neutron star: Release of Egrav• Signals of supernova ν: Terrestrial detection

• Further efforts toward successful explosion– e-capture, ν-reactions, extensions to 2D,…

• Size of core, Heating rate,…