Study of core-collapse supernovae:Post-bounce evolution and EOS effects

K. ‘Sumi’yoshi, S. Yamada, H. Suzuki,H. Shen and H.Toki

04/07/28@INT

• Supernova simulations beyond 300 msec after bounce:- General relativistic neutrino-transfer hydrodynamics- Relativistic EOS vs Lattimer-Swesty EOS- EOS effects on stalled-shock & supernova cores

From hubblesite.org

Numazu College of Technology, Japan

Why supernova does not explode?, What is missing?

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

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

Both issues should be examined to clarify the explosionmechanism.

•We focus on microphysics by simulations of neutrino-transfer hydrodynamics•In spherical symmetry, neutrino-transfer can besolved, we can examine microphysics

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

us with data on n-rich nuclei: RIKEN, GSI, RIA, …

From www.rarf.riken.go.jp

ex. RIKEN-RI Beam Factory

• 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

Efforts on examining microphysics• No explosion (shock stalled) in 1D so far with:

– Lattimer-Swesty EOS, Bruenn’s weak rates– Improved neutrino-rates, electron capture rates– Different sets of EOS– ~300 msec after bounce

• Post-bounce evolution for a long period of ~1 sec?• EOS effects on shock dynamics and supernova cores?• A new numerical code for general relativistic

hydrodynamics with Boltzmann eq. for n– With relativistic EOS table

Mezzacappa, Janka, Burrows(Except Wilson)Langanke et al., Hix et al.Janka, astro-phLiebendorfer, astro-ph

Sumiyoshi, Yamada, Suzuki, Toki (2004)

Purpose of our studies• Within the exact treatment of n-transfer

hydrodynamics in spherical symmetry– Find out the fate of core collapse

• Explosion or not?– Long-term evolution of supernova core

• Up to ~1 sec after bounce– Examine the effect of new EOS

• Some hints on the explosion mechanism

• The first comparison of EOS effects beyond 300 msec– Core bounce, shock dynamics and n-heating mechanism– Evolution of proto-neutron star, supernova n

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

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

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

– e-capture, n-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

n

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

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

– Based on relativistic Brückner Hartree-Fock– Checked by exp. data of 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

Relativistic Mean Field Theory - Effective Lagrangian

†

LRMF = Y igm∂m - M - gs s - gwgmw

m - grgmt aram - egm Am 1- t 3

2È

Î Í ˘

˚ ˙ Y

†

+12

∂ms∂ms -12

ms2s 2 -

13

g2s3 -

14

g3s4

†

-14

Hmn H mn +12

mw2wmw

m +14

c3 wmwm( )

2

†

-14

Gmna Gamn +

12

mr2rm

aram -14

Fmn F mn

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

Nuclear structure calculations EOS calculations

Serot, Walecka 1986

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

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)

Comparison of EOSs (1)

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

Rel. Mean Field +Local-Density Approx.

Compressibleliquid drop model

ModelShen-EOSLS-EOS

Comparison of EOSs (2)

2.21.8, 2.0, 2.7Max. NS mass [Msol]36.929.3Asym [MeV]281180, 220, 375K [MeV]Shen-EOSLS-EOS

•Symmetry energy effect is large cf. non-rel.•Neutron Star: Yp=0.1~0.2 for rel-EOS

•Difference of composition, chemical potential•e-capture, n-scattering rates → supernova dynamics

Sumiyoshi et al. NPA595 (1995)

Numerical code• General relativistic hydrodynamics: lagrangian

• Shock tubes, point explosion, collapse tests» Yamada, ApJ 475 (1997) 720

• General relativistic Boltzmann eq. solver: SN-method• Comparisons with Monte-Carlo calculations

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

• Comparisons with Liebendörfer et al. (astro-ph/0310662)• Consistent up to ~200 msec

• Other applications (hydrodynamics + heating-cooling)– Explosion of a minimum neutron star: Sumiyoshi et al. A&A 1997– R-process in a prompt explosion: Sumiyoshi et al. ApJ 2001– R-process in neutrino-driven winds: Sumiyoshi et al. PASJ 2000

Boltzmann equation for n (GR, spherical)

†

e-f ∂c∂t

fn

rB

Ê

Ë Á

ˆ

¯ ˜ + 4pe-fm

∂ef r2 fn

∂m

+∂

∂m(1- m2) 2prB

∂r2

∂m+ me-f ∂ ln(rB r3)

c∂t- 4pr2rB

∂f∂m

È

Î Í

˘

˚ ˙

fn

rB

Ê

Ë Á

ˆ

¯ ˜

Ï Ì Ó

¸ ˝ ˛

+ m2e-f ∂ ln(rB r3)c∂t

- e-f ∂ ln rc∂t

- m4pr2rB∂f∂m

È

Î Í

˘

˚ ˙

∂∂ En

3 /3( )En

3 fn

rB

Ê

Ë Á

ˆ

¯ ˜

Ï Ì Ó

¸ ˝ ˛

=1

rB

e-f dfn

cdtÊ

Ë Á

ˆ

¯ ˜

collision

Lindquist, Castor 1972, Bruenn 1985

Mezzacappa-Bruenn 1993Finite differenced in (t, m, m)

Neutrino processes• Emission and absorption: e- + p ´ ne + n e- + A ´ ne + A´

e+ + n ´`ne + p• Scattering: ni + N ´ ni + N ni + A ´ ni + A ni + e ´ ni + e• Pair process:

e- + e+ ´ ne +`ne g* ´ ni +`niN + N ´ N + N + ni +`ni i=e, m, t

• Nucleon-Nucleon Bremsstrahlung

Bruenn ApJS, 1985

• Initial model: Fe core of 15Msolar– MFe=1.32Msolar,

• Mesh size: radial Nr=127,n-energy NE=14, angle Nq=6– n-distribution: f(t, m, En, m)

• n-species: ne,`ne, nm,`nm, (nt,`nt) (Nn=4)– ~120 hours on Fujitsu-vpp5000 (8PE)– Block tridiagonal matrix: cyclic reduction in parallel– Nr*(NE*Nq*Nn)3

rEnq

Woosley-Weaver ‘95

Set up of numerical simulations

Sumiyoshi, Parallel Computing, 1997

Set up of numerical simulations II• Follow up to ~1 sec

– More grids for outer layer to resolve accretions– Lower resolution for inner part– Will be improved by rezoning

• Using 2 EOS sets (Shen-EOS, LS-EOS)– Comparisons of collapse, bounce, shock propagation– Other settings (weak rates) are the same

• First comparison of post-bounce beyond 300 mseccf. Proceedings reports: Liebendörfer et al. astro-ph/0211329

Janka et al. astro-ph/0405289

Collapse phase in Shen-EOS case

• Stiffness– Less compression– rc(peak)=3.3¥1014 g/cm3 (LS:4.2¥1014 g/cm3)

• Composition– Less n-rich nuclei: large symmetry energy– Smaller free proton fraction: Xp↓, mp ↓

• Smaller e-capture rates– Size of bounce core

• e-capture on nuclei suppressed due to N>40 (Bruenn’s rate)cf. Bruenn 1989, Hix. et al. 2004

Difference from LS-EOS case

Composition of dense matter during collapse: rc=1011 g/cm3

Mass fraction

p

n

nuclei

a

10-5

10-4

10-3

10-2

10-1

100X i

2.01.51.00.50.0Mb [Msolar]

LS-EOSShen-EOS

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

40

35

30

25

20

Z

706050403020

N

40

35

30

25

20

Z

706050403020

N

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

Z, N of Nuclei

LS-EOSShen-EOS

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

0.5

0.4

0.3

0.2

0.1

0.0

Y n, Y

e, Y L

2.01.51.00.50.0Mb [Msolar]

-8x109

-6

-4

-2

0

2

velo

city

[cm

/s]

2.01.51.00.50.0Mb [Msolar]

Profiles at bounce:tpb=0ms

Ylepton

Ye

Yn

VelocityLepton fraction

LS-EOSShen-EOS

preliminary

100

101

102

103

104

radi

us [k

m]

1.00.80.60.40.20.0

time [sec]

Fe coresurface

bounce

proto-neutron star

shock wave

collapse

Trajectories of fluid elements (Shen-EOS)

preliminarySumiyoshi, Yamada, Suzuki, Toki (2004) in preparation; see also NIC8 proceedings in NPA (2004)

Trajectories of position of shock wave

LS-EOSShen-EOS

101

102

103

R sho

ck [k

m]

1.00.80.60.40.20.0time after bounce [sec]

preliminary

nn

n

1000kmRShock RFeRgain

~200km100km~80kmRn, RPNS

Proto-Neutron star

cooling

heating

Neutrino heating behind the shock after bounce

Shock position

Fe core surface ne + n e- + pne + p e+ + n

Post-bounce phase in Shen-EOS case

• Heating rate– Smaller due to lower luminosity & smaller Xp

• Shock recession to be checked by higher resolution

• Thermal evolution of central core– Lower temperature, lower central density– Effect of effective mass M* & stiffness

• Possible effects of EOS on– Neutrino-heating mechanism– Supernova n, proto-neutron star evolution

• Collapsar, black hole formation

Difference from LS-EOS case

Heating rate after bounce: tpb=100 ms~[MeV/s/N]

-1000x1018

-500

0

500he

atin

g ra

te [e

rg/g

/s]

10 100 1000radius [km]

LS-EOSShen-EOS

preliminary

Heating region

8x1052

6

4

2

0

lum

inos

ity [e

rg/s]

10 100 1000radius [km]

Mass fractionLuminosity

nm

ne

ne

p

n

a

nuclei1.0

0.8

0.6

0.4

0.2

0.0

X i

10 100 1000radius [km]

Profiles after bounce:tpb=100ms

LS-EOSShen-EOS

radius [km]preliminary

EntropyTemperature15

10

5

0

entro

py p

er b

aryo

n [k

B]

10 100 1000radius [km]

Profiles after bounce:tpb=100ms

LS-EOSShen-EOS

30

25

20

15

10

5

0

tem

pera

ture

[MeV

]

10 100 1000radius [km]

preliminary

Comparison of numerical results

20 km23 kmRshock 600ms

3.9¥1014 g/cm36.0¥1014 g/cm3rc at 600ms

37 MeV48 MeVTpeak 600ms

440 MeV938 MeVM*c 600ms

160 km164 kmRshock (max)

Shen-EOSLS-EOS

†

E ~ p2

2M*• M*(<M): increase of level density:→ Lower T to get the same entropy

• Less compression preliminary

50

40

30

20

10

0te

mpe

ratu

re [M

eV]

2.01.51.00.50.0Mb [Msolar]

Profiles after bounce:tpb=20-600 ms Temperature

50

40

30

20

10

0

tem

pera

ture

[MeV

]

2.01.51.00.50.0Mb [Msolar]

LS-EOS Shen-EOSTpeak~50 MeV Tpeak~40 MeV

preliminary

10

8

6

4

2

0

entro

py [k

B]

2.01.51.00.50.0Mb [Msolar]

Entropy

(Shen-EOS)Profiles after bounce:tpb=20-600 ms Lepton fraction

0.5

0.4

0.3

0.2

0.1

0.0

Y L

2.01.51.00.50.0Mb [Msolar]

preliminary

Properties of supernova neutrinos

30

25

20

15

10

5

0

<En>

[MeV

]

0.60.40.20.0time [sec]

200x1051

150

100

50

0

lum

inos

ity [e

rg/s]

0.60.40.20.0time [sec]

LS-EOSShen-EOS

nm

ne

ne

nm

nene

preliminary

Summary• Numerical simulations of supernovae

– General relativistic n-transport hydrodynamics inspherical symmetry

• New nuclear physics with unstable nuclei– Relativistic EOS table

• Long-term simulation beyond 300 msec– Stalled shock and supernova cores

• Comparisons with LS-EOS– No prompt/delayed explosion– Difference in composition & stiffness– Difference in thermal evolution of central core

• Follow up to tpb~1 sec and beyond– Continue to proto-neutron star cooling

• Accretion induced collapse, Neutrino-driven winds– More grids for inner core

» To check stalled shock» Adaptive rezoning

• Extension of relativistic EOS table– Include hyperons (Ishizuka-Ohinishi)

• Update electron capture, n-rates– Consistent with EOS

To be done