Type II Supernovae: electro-weak processes and systematic ... - LUTH

Université Paris Sud 11 

IPN Orsay 

Type II Supernovae: 

Università degli Studi di Milano 

Dipartimento di Fisica 

INFN, Sezione di Milano 

electro-weak processes and 

systematic thermal reduction 

of neutronization 

during core-collapse 

Anthea F. FANTINA 

Dr. E. Khan & Dr. J. Margueron (IPN Orsay) 

Dr. P. Blottiau, Dr. Ph. Mellor (CEA, DAM, DIF) 

Seminar at LUTH, Meudon, 2nd April 2009 

Prof. P. Pizzochero & Dr. P. Donati 

(Univ. Milano & INFN)

Motivation 

Outline 

Introduction 

- Type II Supernova 

- Weak processes (Electron capture) 

Nucleon effective mass & symmetry energy 

Results 

- One zone code 

- 1D Newtonian code 

Conclusions & Outlook 

Anthea F. Fantina - Seminar @ LUTH, Meudon, 2nd April 2009

Motivation 

Outline 

Introduction 




Results 





Motivation 

• Simulations VS nature: what’s missing? 

• Nucleosynthesis of heavy elements 

• Neutrino physics 

• GW signal 

Microphysics Macrophysics 

Anthea F. Fantina - Seminar @ LUTH, Meudon, 2nd April 2009 

hydrodynamics 

nuclear physics

Motivation 

Outline 

Introduction 




Results 





Type II SN – Overview 


1. Infall epoch: 

compression of the 

core to nuclear 

density 

(electron capture) 

1. Core bounce 

and formation 

of shock wave 

1. Explosion: 

propagation of 

shock wave, 

possible explosion

Chandrasekhar 

mass 

shock formation 

at the edge of 

homologous core 

( from Janka H.-Th. et al., 

Phys. Rep. 442, 38 (2007) ) 

SNII – picture of gravitational collapse 


Nuclear inputs: 

electron capture rates 

Hydrodynamics: 

We investigate … 

… electro-weak processes 

in core collapse supernova 

nucleon effective masses 

EoS 

→ one-zone code ( Fantina A.F. et al., arXiv:0811.0456 [astro-ph] ) 

→ 1D Newtonian code ( Blottiau P., PhD thesis (1989) ) 

→ 1D Relativistic code ( Romero J. et al., Astroph. J. 462, 839 (1996) ) 


Electron capture (1/3) 


μ p 

on free protons 

on nuclei 

Determine lepton fraction evolution position of formation of the shock 

before BBAL ( Bethe H.A. et al., Nucl. Phys. A324, 487 (1979) ) 

electron capture on free protons 

BBAL 

( Bethe H.A. et al., Nucl. Phys. A324, 487 (1979) ) 

Low Xp capture on nuclei (A = 60 – 80 ) 

Statistical model at T = 0 

Δ N ≈ 3 MeV 

μ n


Fuller ( Fuller G.M., Astrophys. J. 252, 741 (1982) ) 

FFN ( Fuller G.M. et al., Astrophys. J. 293, 1 (1982) 

Fuller G.M. et al., Astrophys. J. Suppl. 48, 279 (1982)) 

Capture on free protons dominates 

Two-level transition at T ≠ 0 

IPM; Pauli blocking effects for Z < 20, N ≥ 40 

x γ 2 

matrix element! 



on nuclei 

In Bruenn parametrization ( good for multigroup calculation! ) 

( Bruenn S.W., Astrophys. J. Suppl. 58, 771 (1985) )




on nuclei 

Cooperstein & Wambach 

( Cooperstein J. and Wambach J., Nucl. Phys. A420, 591 (1984) 

Capture on nuclei with N ≥ 40 can compete with capture on free protons 

RPA calculations at finite T ( T ~ 1.5 MeV ) unblocking 

Langanke et al. 

( Langanke K. et al., Phys. Rev. C66, 45802 (2001) ) 

Capture on nuclei dominates 

“Hybrid model” at T ≠ 0: 

- SMMC calculation (occupation number) 

- RPA calculation (capture rates) 

??? 

… we run collapse for different capture rates (on nuclei)!

Motivation 

Outline 

Introduction 




Results 





Nucleon effective mass in nuclei (1/3) 

Interacting particle IPM (mean field) 

Σ(k) : mean field (ex. Skyrme) 

m*(k) < m 

Results: ok for single-particle energy, 

but not for level density! 

beyond IPM energy dependence of Σ 



Beyond IPM particle-vibration coupling 

m* related to the group velocity 

m* related to level density (a from experiments!!!) 

k – mass 


ω – mass T - dependence!

Physical interpretation 


IPM: nucleon has a well defined energy 

spectral function S(k,ω) is a delta function 

beyond IPM: collisions taken into account 

spread in ω 

( Mahaux et al., Phys. Rep. 120, 1 (1985) ) 

Ζ(k) : quasiparticle strenght 

probability amplitude 

that 1p (or 1h) excitation 

with momentum k 

propagates with energy ε(k) 

and lifetime τ 


sym 

T-dependence of m* and E 

Theoretical studies on influence 

of T-dependence of nuclear symmetry energy 

on collapse trajectory: 

Donati P. et al, Phys. Rev. Lett. 72, 2835 (1994) 

study of m*(T): 98 Mo, 64 Zn, 64 Ni in the range 0 < T < 2 MeV (QRPA) 

decrease of m*(T) in the range 0 < T < 2 MeV 

increase of E sym (~ 8%) 

effects on gravitational collapse not negligible 

Dean D.J. et al, Phys. Rev. C66, 31801 (2002) 

study of E sym (T): A = 56-66 in the range 0.33 < T < 1.23 MeV (SMMC) 

increase of E sym (~ 6%) consistent with Donati et al. 

“not significant changes for the collapse trajectory” 


lept,tr 

Effective mass Symmetry energy Y 

E symm (T) 

analogy with Fermi gas model 

Donati P. et al., Phys.Rev.Lett. 74 (1994) 

reduction of m ω with T ⇒ increase of E symm 

increase of 

less neutronization ⇒ larger values of Y lept at trapping 


Q-value!

lept,tr 

Y 

Shock wave energy 

Shock wave loses energy while crossing matter. 

dissociation energy: 

larger values of Y lept at trapping ⇒ less deleptonization 

⇒ less energy dissipated 

Stronger shock wave explosion 

m*(T) E sym Y l,tr Shock wave energy 


Brown G. et al, 

Nucl. Phys. A375, 481 (1982)

Motivation 

Outline 

Introduction 




Results 





Physical model – one-zone 

• One-zone code 

→ collapse of sphere with uniform density ρ 

• Matter made up by: 

- nuclei (A, Z), neutrons and free protons (C, NR) 

- electrons and neutrinos (Q, UR) 

⇒ EoS BBP (Bethe et al., Nucl. Phys. A175, 225 (1971) ) 

BBAL (Bethe et al., Nucl. Phys. A324, 487 (1979) ) 

• Thermal dissociation in α particle included (Saha eq.) 

Entropy: translational (nuclei, protons and free neutrons), 

excited states of nuclei, electrons and neutrinos (post trapping) 

• Electron capture on free+bound protons as 2-level transition at finite T 

( + backward reaction after trapping ), inclusion of γ 2 

• Trapping as a discontinuity ⇒ Yν = 0 if ρ < ρtr ( after neutrino trapping Ylept const! ) 


Numerical results of collapse simulation 

(one-zone code) 


γ 2 = 1 

Langanke K. et al., 

Phys. Rev. Lett. 90, 241102 (2003) 

γ 2 = 0.1 

Fuller G.M., 

Astroph. J. 252, 741 (1982)

Numerical results of collapse simulation 

(one-zone code) 


“Standard” 

parameters:

Physical model – 1D Newtonian 

• 1D code Newtonian ( Blottiau P., PhD thesis (1989) ) 

- sphere divided in 40 zone for core, total 100 zone 

- Lagrangian treatment, implicit scheme 

• Matter made up by: 

- nuclei (A, Z), neutrons and free protons (classical e non relativistic) 

- electrons and neutrinos (degenerate and ultra relativistic) 

⇒ EoS BBAL ( Bethe H.A. et al., Nucl. Phys. A324, 487 (1979) ) 

Fuller ( Fuller G.M., Astrophys. J. 252, 741 (1982) ) 

+ increasing of Γ to simulate stiffness of EoS 

• Hydro equation coupled to equation for electron fraction evolution 

and capture 

• Neutrino transport: multigroup, inclusion of different N p * N h 

( Bruenn S., Astrophys. J. Suppl. 58, 771 (1985) ) 

• Trapping comes out “automatically” 


Preliminary results of collapse simulation 

(1D Newtonian code) 


Motivation 

Outline 

Introduction 




Results 





Conclusions 

• Influence of T-dependence of E sym on the evolution of collapse 

→ systematic reduction of neutronization of the core 

(increasing of final lepton fraction) & less energy dissipated by shock wave 

- one zone model - 

→ position of shock wave formation: bigger homologous core 

- 1D Newtonian code - 

• Gain in shock wave dissociation energy if we consider m*(T) : 

δ T E diss ~ 0.4 foe (estimation with one-zone code, 

within reasonable physical ranges of parameters) 

and: K ~ 1 – 1.5 foe (Bethe H.A. & Pizzochero P., Astrophys. J. 350, L33 (1990)) 

⇒ even if no dramatic effect on dynamics of the collapse is expected 

(see fluid instabilities, SASI, magnetic field, …) 

effects are not negligible! 


Outlook 

Nuclear point of view: Microscopic calculation of nuclear inputs 

- Electron capture rates on nuclei 

→ γ 2 

- Calculation of m*(T) & E sym (T): 

→ systematic calculations on more nuclei 

→ level density parameter (experiments?!) 

→ dependence on ρ, A, Z, T 

Astrophysical point of view: Hydrodynamics 

- multizone / multi-D code → test in 1D 

- Newtonian & Relativistic 

- more accurate treatment of neutrinos 

and shock formation 

IPN Orsay (E.Khan) 

- EoS 

→ Lattimer & Swesty, Nucl. Phys. A535, 331 (1991), with 


Milan & IPN Orsay 

(P.Donati & J.Margueron) 

CEA Bruyères 

(P.Blottiau & Ph. Mellor) 

& 

LUTH Meudon 

(J. Novak & M.Oertel)

Thank you 

- Merci -

Type II Supernovae: electro-weak processes and systematic ... - LUTH

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