Nuclear Physics (and Astrophysics) of Core Collapse Supernovae

W.R. Hix (ORNL/ U. Tenn.) MSU Astrophysics Seminar, March 2008 

Nuclear Physics (and 

Astrophysics) of Core 

Collapse Supernovae 

Collaborators 

M. Baird (UTK), E. Lentz (UTK), O.E. B. Messer (ORNL), A. Mezzacappa (ORNL) 

K. Langanke(GSI), G. Martínez-Pinedo (GSI), A. Juodogalvis(Vilnius), J. Sampaio 

(Lisbon) 

H.-T. Janka (MPA), B. Müller (MPA), A. Marek (MPA) 

S.W. Bruenn (FAU), J. Blondin(NCSU), C.-T. Lee(UTK)


Microscopic Macroscopic 

Core Collapse Supernovae present an interesting 

Nuclear Physics problem in that physics at the 

femtometer scale drives (and is driven by) 

astrophysical processes at the kilometer scale, 

leading to explosions that 

spread debris over 

exameter scales.


Microscopic Macroscopic 

Core Collapse Supernovae present an interesting 

Nuclear Physics problem in that physics at the 

femtometer scale drives (and is driven by) 

astrophysical processes at the kilometer scale, 

leading to explosions that 

spread debris over 

exameter scales.


Textbook Supernova 

ν-Luminosity 

Matter Flow 

Heating 

_ ν e + n → p + e - 

ν e + p → n + e + 

Shock 

_ ν e + n ← p + e - 

ν e + p ← n + e + 

Cooling 

Gain Radius 

Proto-Neutron 

Star 

ν-Spheres

Supernova Nucleosynthesis 

W.R. Hix (ORNL/ U. Tenn.) MSU Astrophysics Seminar, March 2008


Examining Microphysics Effects 

Spherically symmetric collapse, bounce and shock 

stall simulations using AGILE-BOLTZTRAN 

Fully implicit, multi-group, 4-flavor Boltzmann 

neutrino transport 

• Most modern neutrino physics, LMSH electron capture rates (Hix et al. 2004, 

Langanke et al. 2003) or Bruenn 85 electron capture rates (Bruenn 1985) 

• Implicit, spherically symmetric 

hydrodynamics with an adaptive 

mesh. 

• Both general relativistic 

(including gravitational redshift) 

and Newtonian gravity. 

Liebendörfer, Messer, 

Mezzacappa, Bruenn, 

Cardall & Thielemann (2004) 

• Modular architecture allows 

use of multiple realistic equations 

of state.


History of Captures on Nuclei 

Entropy of iron core is low 

(S/k ~1) so few free 

nucleons are present. Thus 

e - and ν capture on heavy 

nuclei via 1 f 7/2 ⇔ 1 f 5/2 GT 

transition dominates. 

(Bethe,Brown, Applegate & Lattimer 1979) 

During collapse, average 

mass of nuclei increases, 

quenching e - capture (at 

N=40). 

Thermal unblocking and first 

forbidden were considered 

but rates too small. 

(Fuller 1982, Cooperstein & Wambach 1984) 

Implemented using average 

nucleus. Bruenn (1985)


New e - /ν Capture Rates 

Shell Model calculations 

are currently limited to 

A~65. 

Langanke, …, Hix, … (2003) 

Langanke et al (2003) 

employed a hybrid of 

shell model (SMMC) and 

RPA to calculate a 

scattering of rates for 

A


New e - /ν Capture Rates 

Shell Model calculations 

are currently limited to 

A~65. 

Langanke, …, Hix, … (2003) 

Langanke et al (2003) 

employed a hybrid of 

shell model (SMMC) and 

RPA to calculate a 

scattering of rates for 

A

The impact of EC with stellar mass 

15 M 25 M 

Higher mass cores have higher initial entropy. 

Effects of nuclear electron capture are reduced 

but comparable (1/2 to 2/3). 

W.R. Hix (ORNL/ U. Tenn.) MSU Astrophysics Seminar, March 2008


PNS Convection 

Fluid instabilities which 

drive convection result 

from complete neutrino 

radiation-hydrodynamic 

problem including 

nuclear interactions. 

Hix, Messer, Mezzacappa, … 2003 

Updated nuclear 

e - /ν capture restricts 

PNS convection to 

smaller, deeper region.


Changes in Neutrino Emission 

ν e burst slightly delayed 

and prolonged. 

Other luminosities 

minimally affected (~1%). 

Hix, Messer, Mezzacappa, … 2003


Changes in Neutrino Emission 

ν e burst slightly delayed 

and prolonged. 

Other luminosities 

minimally affected (~1%). 

Mean ν Energy altered: 

Hix, Messer, Mezzacappa, … 2003 

1-2 MeV during collapse 

~1 MeV up to 50ms 

after bounce 

~.3 MeV at late time


What Rates are needed? 

Change in lepton 

abundance 

(Y l =Y e +Y ν ) occurs 

gradually up to 

~3x10 12 g/cm 3 . 

By 3x10 12 , rate of 

electron capture 

is determined 

largely by 

blocking. 

Y l 

,Y e 

0.4 

0.35 

0.3 

0.25 

N p 

*N h 

=0.1 

N p 

*N h 

=1.0 

N p 

*N h 

=10. 

0.05 M ȯ 

Yl 

Ye 

10 10 10 11 10 12 10 13 10 14 

Density (g/cm 3 )




abundance 



~3x10 12 g/cm 3 . 



is determined 

largely by 

blocking. 

Y l 

,Y e 

0.4 

0.35 

0.3 

0.25 

N p 

*N h 

=0.1 

N p 

*N h 

=1.0 

N p 

*N h 

=10. 

0.05 M ȯ 

Yl 

Ye 

10 10 10 11 10 12 10 13 10 14 

Density (g/cm 3 )




abundance 



~3x10 12 g/cm 3 . 



is determined 

largely by 

blocking. 

Average Nuclear 

Mass by 10 12 is 

100 or more with 

many nuclei 

contributing. 

Y l 

,Y e 

A, Z 

200 

A N p 

*N h 

=0.1 

0.4 

N p 

*N h 

=1.0 

N p 

*N h 

=10. 

150 

0.35 

0.05 M ȯ 

100 

0.3 

50 

0.25 

Ye 

10 10 10 11 density 10 [g/cm 12 ] 

10 13 10 14 

Density (g/cm 3 ) 

Yl 

0 

10 10 10 11 10 12 10 13 10 14 

Z




abundance 



~3x10 12 g/cm 3 . 



is determined 

largely by 

blocking. 




many nuclei 

contributing. 

Y l 

,Y e 

A, Z 

200 

A N p 

*N h 

=0.1 

0.4 

N p 

*N h 

=1.0 

N p 

*N h 

=10. 

150 

0.35 

0.05 M ȯ 

100 

0.3 

50 

0.25 

Ye 

10 10 10 11 density 10 [g/cm 12 ] 

10 13 10 14 


Yl 

0 

10 10 10 11 10 12 10 13 10 14 

Z




abundance 



~3x10 12 g/cm 3 . 



is determined 

largely by 

blocking. 




many nuclei 

contributing. 

Y l 

,Y e 

A, Z 

200 

0.4 

150 

0.35 

100 

0.3 

50 

0.25 

10 10 10 11 density 10 [g/cm 12 3 ] 

10 13 10 14 


N p 

*N h 

=0.1 

N p 

*N h 

=1.0 

N p 

*N h 

=10. 

0.05 M ȯ 

Yl 

Ye 

0 

10 10 10 11 10 12 10 13 10 14 

Need theory for the large number of 

reactions of interest and experiments 

to constrain this theory. 

A 

Z


What can RIBs say about e - /ν Capture? 

Charge Exchange Reactions, 

e.g. (n,p),(d, 2 He),(t, 3 He), 

also sample GT+ strength 

distribution, providing strong 

constraints on structure 

models. 

Baümer et al. PRC 68, 031303 (2003) 

Current Experiments, on 

stable nuclei, agree well with 

shell model calculations for 

A


Advertisement 

New tabulation of nuclear electron capture coming 

soon. 

Improvements include: 

✦ 

Expanded range of nuclei in NSE 

✦ Partition functions exceeding 10 GK (Rauscher 2000) 

✦ Updated screening prescription in NSE 

✦ Screening of weak reactions 

✦ Expanded set of SMMC/RPA rates (250) 

✦ 

Finely tabulated spectra (.5 MeV) 

Sampaio, Juodogalvis, Langanke, Martínez-Pinedo & 

Hix (2008) ADNDT, in prep.


Inelastic Neutrino-Nucleus Scattering 

As with electron/neutrino capture, advances in nuclear 

structure physics are improving our understanding of 

other neutrino-nucleus interactions. 

While coherent, elastic ν-nucleus scattering has long 

been considered, inelastic ν-nucleus scattering (INNS) 

has often been ignored. The exception is Bruenn & 

Haxton (1991) which used INNS rate calculated for 56 Fe 

at T=0. 

Recently, Juodogalvis, Langake, Martinez-Pinedo, Hix, 

Dean & Sampaio (2005) calculated INNS for 40 isotopes of 

Mn, Fe, Co & Ni at finite temperature using a 

combination of shell model and RPA. A tabulation of NSEaveraged 

rates has been produced for use in supernova 

simulations.


Dynamical Effects of INNS? 

During collapse, INNS works like NES to equilibrate the neutrino 

distribution. However there is little effect from this addition. 

Müller, Janka (2008), 

priv. comm. 

After bounce, heating rate just above shock is boosted (2-3x). 

However, heating of supersonically infalling matter is ineffective, 

so dynamics are little effected.


Observable Effects of INNS 

Higher energy 

tail of ν 

spectra are 

strongly 

suppressed 

during this 

interval. 

Langanke, Martínez-Pinedo, 

Müller, Janka, Marek, Hix, 

Juodagalvis & Sampaio (2007) 

Has a surprisingly large 

effect on potential 

terrestrial ν detectors.


Summary for Nuclear Opacities 

Electron and neutrino captures on heavy nuclei play 

an important role during core collapse, affecting 

✦ the initial launching point of the shock by up to 

20% in mass. 

✦ the rate of collapse of the outer iron core 

✦ material gradients in the proto-neutron star. 

Inelastic scattering of neutrinos off heavy nuclei can 

have a large impact on the local heating rate just 

above the shock, however, the dynamic impact is 

small. 

A much larger impact is felt by the high energy tail of 

the supernova neutrino spectra, potentially impacting 

terrestrial detectors.


Role of the Equation of State 

In general, the equation of state closes the system 

of hydrodynamic equations by relating the pressure 

to the internal energy (or temperature or entropy), 

density and composition. 

For supernovae, it includes contributions from 

photons, degenerate electrons & positrons, and 

nuclei or nuclear matter. 

In regions where Nuclear Statistical Equilibrium can 

be assumed, the supernova EOS also provides the 

nuclear composition, usually in the form of mass 

fractions for free nucleons, alpha particles and a 

representative heavy nucleus.


Examining Equations of State 

✦ LS EoS (Lattimer-Swesty 1991) 

• Liquid drop model 

• Compressibility – 180 MeV 

• Complete EoS - Includes baryon, lepton and photon contributions 

• Alpha abundance error 

✦ STOS EOS (Shen, Toki, Oyamatsu & Sumiyoshi 1998) 

• Relativistic mean field theory 


• Tabular Nuclear EoS - Includes only nuclear contributions 

✦ Wilson EOS (Mayle & Wilson 1991, McAbee & Wilson 1994) 

• Empirical Relation of Baron, Cooperstein & Kahana (1985), constrained 

by relativistic Brueckner-Hartree-Fock calculations of Muther, Prakash 

& Ainsworth (1987). 


• Includes Pions at high density constrained by comparison of simulations 

of Pion production in heavy ion collisions with experimental data. 

• Tabular Complete EoS


Pressure 

for fixed thermodynamic conditions 

near bounce 

Baird, Lentz, Hix, Messer & Mezzacappa, in prep. 

Differences limited to nuclear matter. 

At lower density, electrons dominate pressure.


Internal energy 


near bounce 


Moderate differences, with STOS having higher 

internal energies in the region of forming shock.


Entropy 


near bounce 


Noticable differences at center, even larger differences at 

lower density. 

Entropy is dominated by the nuclear contribution.


Composition 

Baird, Lentz, Hix, Messer 

& Mezzacappa, in prep. 

Composition of unshocked matter shows large differences.


Composition after bounce 

Baird, Lentz, Hix, Messer 

& Mezzacappa, in prep. 

Shocked compositions similar except Wilson near 

phase transition


Self-consistent Simulations 

Examined the 

impact of the EOS 

using Agile-Boltztran 

GR simulations of 

15 M progenitor. 

STOS 

LS 

Wilson 

10 2 Time After Bounce [s] 

Differences persist 

in spherically 

symmetric models 

for more than 200 

ms after bounce. 

Radius [km] 


10 1 

0 50 100 150 200 

STOS: Shock launches 

slowly and peaks near 50 

ms with smallest shock 

stall radius. 

Wilson: Shock launches 

strongly, peaking near 150 

ms with largest shock stall 

radius.


EOS Comparison w/Nuclear EC 

Y e 

(Electron Fraction) 

Entropy per baryon 

Density (g cm !3 ) 

0.55 

0.45 

0.35 

0.25 

10 8 

5 

4 

3 

2 

1 

10 14 

10 12 

10 10 

1 x 105 

STOS 

LS 

Wilson 

Velocity (km/s) 

0 


!1 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 

Enclosed Mass 

At bounce, Wilson shows larger core and faster collapsing outer core.


EOS Comparison w/Nuclear EC 

e 


Y (Electron Fraction) 

e 



Density Density (g (g cm cm !3 !3 ) ) 

0.55 

0.6 

0.5 

0.45 

0.4 

0.35 

0.25 

0.1 

145 

12 

4 

10 

83 

62 

41 

2 

0 

10 10 14 14 

10 10 12 12 

10 10 10 10 

10 10 88 

1 x 105 105 

STOS 

LS L!S 

Wilson STOS 

Wilson 

100 ms after bounce 



0 


!1 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 

Enclosed Mass 

At bounce, Wilson shows larger core and faster collapsing outer core. 

After bounce, Wilson and STOS show different Ye gradients.


EOS Comparison w/proton EC 

Y e 



Density (g cm !3 ) 

0.5 

0.4 

0.3 

0.2 

6 

4 

2 

0 

10 14 

10 12 

10 10 

10 8 

5 x 104 

STOS 

LS 

Wilson 


0 

!5 


!10 

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 

Enclosed Mass 

At bounce, shock location similar, but core Ye gradient stronger.


EOS Comparison w/proton EC 

Y (Electron e Fraction) 

Entropy per per baryon 

Density (g (g cm !3 !3 ) ) 

0.6 0.5 

0.5 

0.4 

0.4 

0.3 

0.3 

0.2 

0.1 0.2 

126 

10 

84 

6 

42 

2 

00 

10 10 14 14 

10 10 12 12 

10 10 10 10 

10 10 8 8 

15 x x 105 104 

L!S 

STOS 

WIlson LS 

Wilson 

100 ms after bounce 


0 

0 

!5 


!10 

00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 

Enclosed Mass 

At bounce, shock location similar, but core Ye gradient stronger. 

After bounce, Wilson and STOS still show different Ye gradients.


A Closer look at bounce with Wilson EoS… 

Lower Pressure 

results in higher 

bounce density. 

Ye decreases rapidly 

in the central core 

as Pions become 

important. 

Pions reduce proton 

chemical potential 

shifting detailed 

balance away from 

electrons and toward 

neutrinos. 

Baird, Lentz, Hix, Messer & Mezzacappa, 

in prep.


Interplay of EOS and Nuclear Electron Capture 


Composition provided by the EOS impacts relative 

strength of opacities. Thus statements about 

importance of opacities must be re-examined in 

light of progress on the EOS.


EOS effects 

Equations of State play a large role in collapse 

and drives the physics involved in post bounce 

evolution. 

In spite of relatively small differences in the 

nuclear matter regime: 

•Initial proto-neutron star size different by 

almost 20% 

•20% differences in shock location after 200 ms 

•Altered lepton and entropy gradients 

Effects of EOS not limited to pressure but also 

include composition and therefore opacities.


Multi-Physics Supernova Models 

CHIMERA Building Blocks 

• “RbR-Plus” MGFLD Neutrino 

Transport 

• PPM Hydrodynamics 

• Lattimer-Swesty EOS 

• Nuclear (α) Network 

• Newtonian Gravity with 

Spherical GR Corrections 

• Neutrino Emissivities/Opacities 

Standard (Bruenn 1985) 

Elastic Scattering on Nucleons 

Nucleon–Nucleon Bremsstrahlung 

• Run for postbounce times > 400 ms. 

• Run on a 180 degree grid. 

Ray-by-Ray Approximation 

Radial transport allowed. 

Lateral transport suppressed. 

Cast: 

Bruenn, Blondin, Hix, 

Marronetti, Messer, 

Mezzacappa, Lentz, 

Budiardja, Lee, 

Yakunin, …


2D Results 

20 M GR 

Resolution 

r,θ: 256, 256 

ν energy: 20 

Instability behind the shock distorts and expands the shock, 

increasing neutrino heating. 

Explosion takes several hundred ms after bounce to develop.


Anatomy of Explosion 

Radius (km) 

20 M GR 

Resolution 

r,θ: 256, 256 

ν energy: 20 

Avg Atomic Mass 

Time (s)



Si Layer 

O Layer 

Radius (km) 

Iron 

Core 

20 M GR 

Resolution 

r,θ: 256, 256 

ν energy: 20 


Time (s)



Si Layer 

O Layer 

Radius (km) 

Iron 


20 M GR 

Resolution 

r,θ: 256, 256 

ν energy: 20 


Time (s)



Si Layer 

O Layer 

Shock 

Radius (km) 

Iron 


20 M GR 

Resolution 

r,θ: 256, 256 

ν energy: 20 


Time (s)


Effects of Nuclear Burning? 

11 M GR 

Resolution 

r,θ: 256, 128 

ν energy: 20


Effects of Nuclear Burning? 

11 M GR 

Resolution 

r,θ: 256, 128 

ν energy: 20 

Heat near the shock from O/Si 

burning helps boosts shock.


Need for 3D? 

Stationary Accretion Shock Instability (SASI) 

Shock wave unstable to nonradial perturbations. 

Blondin, Mezzacappa 

& DeMarino (2003) 

• SASI has axisymmetric and nonaxisymmetric modes that are 

both linearly unstable! 

– Blondin and Mezzacappa, Ap.J. 642, 401 (2006) 

– Blondin and Shaw, Ap.J. 656, 366 (2007)


Need for 3D? 

Stationary Accretion Shock Instability (SASI) 

Shock wave unstable to nonradial perturbations. 

Power in m=1 mode. 

Blondin, Mezzacappa 

& DeMarino (2003) 

Power in l=1 mode. 

• SASI has axisymmetric and nonaxisymmetric modes that are 

both linearly unstable! 

– Blondin and Mezzacappa, Ap.J. 642, 401 (2006) 

– Blondin and Shaw, Ap.J. 656, 366 (2007)


Summary for RBR models 

Multi-group transport, increased run 

times, improved neutrino emissivities & 

opacities, and the inclusion of nuclear 

burning(?) are all critical. 

With self-consistent explosions, we can 

examine use nucleosynthesis to further 

constrain models. 

3D may be necessary as hydro studies 

suggest that the outcomes in 3D may be 

fundamentally different than 2D. 

Impact of magnetic fields remains 

to be seen.


Summary 

1) Nuclear Physics provides vital ingredients, in 

the form of neutrino opacities, the equation of 

state and reaction rates relevant for 

nucleosynthesis, for supernova simulations. 

2) The interrelation of these microphysical 

ingredients, both with each other, and the 

macroscopic astrophysical environment makes 

ongoing examinations important. 

3) We are entering a very interesting period in 

core collapse supernova simulation.

Nuclear Physics (and Astrophysics) of Core Collapse Supernovae

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