Weak rates for ECSN progenitor evolution andnucleosynthesis
Gabriel Martínez Pinedo
Electron Capture Supernova & Super-AGB Star Workshop,Melbourne, February 1-6, 2016
Nuclear Astrophysics Virtual Institute
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Outline
1 Introduction
2 Weak rates for ONeMg core evolution
3 3D simulations oxygen deflagration (Jones et al)
4 nucleosynthesis in ECSN
5 Summary
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Stellar Evolution Intermediate mass stars
Stellar Cloudwith
Protostars
Low-mass StarRed Giant
Planetary Nebula
White Dwarf
Massive Star
Red SupergiantNeutron Star
Black Hole
Intermediate-mass Star
Supernova
CCSN
ECSN
AgeM
ass
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Core evolution (intermediate stars)
Jones et al., ApJ 772, 150 (2013)
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Threshold densities for electron capture
David Arnett, Supernovae and Nucleosynthesis
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Urca pairs: cooling vs heating
odd A
(odd,even)
(even,odd)
(odd,even)
Q1
Q2
even AQ1>Q2Q2>Q1
(even,even)
(odd,odd)
(even,even)
Q1
Q2
ec
β-
Urca cooling heating
ec
ec
Pairing
electron fermi energy:
mass parabola for isobaric chain
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Description electron capture and beta decay rates
Both rates are given by a thermal average over states in the initial nucleus:
λ =
∑i f (2Ji + 1)λi f e−Ei/(kT )∑
i(2Ji + 1)e−Ei/(kT )
Allowed approximation (Gamow-Teller transitions)
λi f =ln 2K
Bi f Φ(qi f , µe,T ), K = 6144 s
Bi f : transition matrix element. Most of the relevant transitions areexperimentally known. Shell-model calculations are possible.
Φ(qi f , µe,T ): “trivial” phase space integral that accounts for thestrong sensitivity of rates to temperature and density.Implementation in stellar evolution codes requires special care.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
What to include in a weak interaction rate table?
Directly the rates: Requires very fine grids in density and temperature toachieve accurate interpolations. Particularly relevant at the lowtemperatures relevant for ONeMg core evolution.
Instead of the rate tabulate an effective matrix element (Fuller, Fowler andNewmann 1985). For electron capture
λec =ln 2K
BeffΦec(qgs, µe,T ), qgs = Qgs/(mec2)
Phase space can be expressed via Fermi integrals:
Φec(Q, µe,T ) =
(kT
mec2
)5 {F4
(µe − Q
kT
)+ 2
QkT
F3
(µe − Q
kT
)+
( QkT
)2
F2
(µe − Q
kT
)}Allows to use approximate expressions for Fermi integrals: fast andaccurate up to 10-20%.
An extension to β− decay is necessary.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Example: Electron capture on 23Na
Rates from Oda et al (1994) tabulation.
−40
−30
−20
−10
0
log
10 [λ
ec (
s−1)]
8 9 10
log10 [ρYe (g cm−3)]
0
0.1
0.2
Bef
f
Direct interpolation in sparse density grid results in 1-2 orders ofmagnitude uncertainty.
Interpolation matrix element results in a maximum error of a factor 2.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
How to do better?
In general, all rates relevant for ONeMg core evolution are determined by a fewtransitions. It is possible to provide analytical expressions for each individualrate [GMP+, PRC 89, 045806 (2014)]
2+ 0.0 11.163 s
2
09F11
Q–(g.s . )=7024.538
0+ 0.0>10.5<0.001
2+ 1633.6744.969799.9913
Log f tIβ–
21
00Ne10
1+ 1.057
Low densities (all temperatures): Rate determined by 2+ → 2+
(Q = 5.902 MeV) transition (experimentally known from beta decay).
Intermediate densities (T < 0.9 GK): determined second forbiddentransition 0+ → 2+ (Q = 7.536 MeV) (only an experimental limit)
Higher densities: transition 0+ → 1+ (Q = 8.592 MeV determines rate(experimentally known from (p, n) charge exchange).
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Electron capture on 20Ne
9 9.2 9.4 9.6 9.8 10
log10 [ρYe (g cm−3)]
−35
−30
−25
−20
−15
−10
−5
0
log
10 [λ
ec (
s−1)]
Takahara et al.
2+ → 2+
2+ → 3+
0+ → 2+
0+ → 1+
Total
T = 0.4 GK
9 9.2 9.4 9.6 9.8 10
log10 [ρYe (g cm−3)]
−20
−15
−10
−5
0
log
10 [λ
ec (
s−1)]
Takahara et al.
2+ → 2+
2+ → 3+
0+ → 2+
0+ → 1+
Total
T = 1 GK
Mayor uncertainty is due to second forbidden transition.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Second forbidden calculation
λ =ln 2K
Φ2nd(q, µe,T )
Φ2nd(q, µe,T ) =
∫ ∞
qwp(q + w)2C(w)F(Z, w) fe(w, µe,T )dw
C(w) is the shape factor: Linear combination of matrix elementsand energy factors.
Relevant matrix elements (Behrens & Bühring 1971)
V F211 ∼[r ⊗ pi f
]2t+, pi f = (pi + pf )/2
V F220 ∼ r2Y2t+AF221 ∼ r2 [Y2 ⊗ σ]2 t+
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Shell-model calculations
sd-shell shell-model calculation using USDB interaction (Idini, Brown,Langanke, GMP, in preparation)
Harmonic Oscillator Wood–SaxonV F211 0. 0.0048V F220 0.8035 1.3353AF221 0.2423 0.3257
The beta-decay theoretical matrix element is B = 〈C(w)〉 = 1.36 × 10−7
using gA = 1.27 (1.11 × 10−7 for gA = 1.0).
The experimental upper limit is 1.94 × 10−7.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Impact on electron capture and beta decay
9 9.25 9.5 9.75 10
-4
-16
-10
Blue dashed: Experimental limitRed: Wood-Saxon wave functionsBlack: Harmonic oscillator wave functions
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Screening of weak interaction ratesThe pressence of a degenerate electron background can affect both beta-decaysand electron capture rates:
Correction to nuclear bindingenergy (DeWitt, Graboske, andCooper 1973; Hix and Thielemann1996, Bravo and García-Senz 1999,Juodagalvis et al. 2010). Q-valueincreases by 0.1–0.3 MeV.
Correction to electron energy(Itoh et al. 2002). Chemicalpotential reduced by0.02–0.05 MeV.
Net effect is a reduction ofelectron capture rate and anincrease of the beta-decay rate.
−14
−12
−10
−8
−6
−4
−2
0
log
10 [λ
(s−
1)]
e− capture (no scr.)
e− capture (scr.)
β decay (no scr.)
β decay (scr.)
9 9.2 9.4 9.6 9.8 10
log10 [ρYe (g cm−3)]
−14
−12
−10
−8
−6
−4
−2
log
10 [λ
(s−
1)]
Having an analytical scheme allows to consider screening corrections consistentwith the underlying EoS.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Impact evolution core
Based on ONeMg cores from Schwab, Quataert, and Bildsten 2015.Convection does not develop in the core.
9.5 9.6 9.7 9.8 9.9 10.0log ρc
8.4
8.6
8.8
9.0
9.2
9.4
logT
c
wo Ne20 2nd forbidden ECupper limit (GMP+ 2014, log fT = 9.8)
u.lim./1000 (log fT = 12.8)
How sensitive is this result to the set of nuclear reactions included?
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Larger network
Möller, Jones, GMP, in preparation
1 8 16 20 28N
1
8
16
20Zthis workSchwab+ (2015)
Increased to account for possible role of 20O(α, n)23Ne. This ratedominates over 20Ne(α, γ)24Mg during Neon burning.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Evolution larger network
9.5 9.6 9.7 9.8 9.9 10.0log ρc
8.4
8.6
8.8
9.0
9.2
9.4lo
gT
c
wo Ne20 2nd forbidden ECupper limit (GMP+ 2014, log fT = 9.8)u.lim./1000 (log fT = 12.8)
Convection does in fact develops in some of the models.
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Evolution larger network
9.90 9.92 9.94 9.96 9.98 10.00log ρc
8.4
8.6
8.8
9.0
9.2
9.4
logT
c
NACRE ratesREACLIB rates + O20(a,g)Ne24REACLIB + O20(a,g)Ne24*20REACLIB + O20(a,g)Ne24*400REACLIB + O20(a,g)Ne24*8000REACLIB + O20(a,g)Ne24/20
Evolution very sensitive to variations of 20O(α, n)23Ne rate. It may affectthe density at which oxygen deflagration initiates.
O DEFLAGRATIONMULTI-DIMENSIONAL SIMULATIONSJoes, Röpke, Pakmor, Seitenzahl, Ohlmann, Edelmann, arXiv:1602.05771 [astro-ph.SR]
LEAFS code (Reinecke+ 1999, Röpke & Hillebrandt 2005, Röpke 2005, 2006)
Isothermal ONe core/WD in HSE with a range of central (ignition) densities
Centrally-confined ignition: 300 'bubbles' within 50 km sphere, < 5 x 10-4 M☉ inside initial flame surface
In laminar regime, flame speeds from Timmes+ (1992); in turbulent regime, flame speeds from subgrid scale model of turbulence (Schmidt+ 2006)
Scale: 1500 kmTime: 0.7 s
56NiO
DEF
LAG
RA
TIO
N3D
4π
: 512
3
THER
MO
NU
CLE
AR
EX
PLO
SIO
N?
Scale: 2500 kmTime: 1.3 s
56NiO
DEF
LAG
RA
TIO
N3D
4π
: 512
3
THER
MO
NU
CLE
AR
EX
PLO
SIO
N?
Scale: 400,000 kmTime: 60 sO
DEF
LAG
RA
TIO
N3D
4π
: 512
3
THER
MO
NU
CLE
AR
EX
PLO
SIO
N?
56Ni
ρign = 109.9 g cm-3
THERMONUCLEAR EXPLOSION?
ρign = 1010.2 g cm-3
CORE COLLAPSE
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Heavy elements and metal-poor starsCowan & Sneden, Nature 440, 1151 (2006)
30 40 50 60 70 80 90Atomic Number
−8
−6
−4
−2
0
Rel
ativ
e lo
g ε
30 40 50 60 70 80 90−8
−6
−4
−2
0
Stars rich in heavy r-process elements (Z > 50)and poor in iron (r-II stars, [Eu/Fe] > 1.0).
Robust abundance patter for Z > 50,consistent with solar r-process abundance.
These abundances seem the result of eventsthat do not produce iron. [Qian & Wasserburg,Phys. Rept. 442, 237 (2007)]
Possible Astrophysical Scenario: Neutron starmergers.
Stars poor in heavy r-process elements butwith large abundances of light r-processelements (Sr, Y, Zr)
Production of light and heavy r-processelements is decoupled.
Astrophysical scenario: neutrino-drivenwinds from core-collapse supernova
40 50 60 70 80
Atomic Number (Z)
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
log ε
(Z
)
EuHD 122563 (Honda et al. 2006)
translated pattern of CS 22892-052 (Sneden et al. 2003)
Ag
Y
PdMo
Ru
Nb
SrZr
(b)
Honda et al, ApJ 643, 1180 (2006)
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Nucleosynthesis in neutrino-driven winds
Main processes:
νe + n� p + e−
ν̄e + p� n + e+
Neutrino interactions determine theproton to neutron ratio.
Neutron-rich ejecta:
〈Eν̄e 〉 − 〈Eνe 〉 > 4∆np −[
Lν̄eLνe− 1
] [〈Eν̄e 〉 − 2∆np
]
neutron-rich ejecta: r-process
proton-rich ejecta: νp-process
We need accurate knowledge of νe andν̄e spectra
α, n
α, p α, p, nuclei
α, n, nuclei
R in
km
102
103
104
105
Rν
31.4
He
Ni
Si
PNS
ORns ~10
Neutrino cooling and
Neutrino-driven wind
n, p
νp-process
r-process
M(r) in M
νe,µ,τ, νe,µ,τ
νe,µ,τ, νe,µ,τ –
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Weak rates in the decoupling regionNeutrino mean-free paths at high densities:
11121314
10−4
10−3
10−2
10−1
100
101
102
103
Baryon Density, log10
(ρ [g cm−3
])
νµ/τ
νµ/τ n→νµ/τ n
νµ/τ p→νµ/τ p
νµ/τ ν̄µ/τ →e−e+
νµ/τ ν̄µ/τ NN→NN
νµ/τ e± →νµ/τ e±
11121314
10−4
10−3
10−2
10−1
100
101
102
103
Baryon Density, log10
(ρ [g cm−3
])
ν̄e
ν̄e n→ ν̄e n
ν̄e p→ ν̄e p
ν̄e p→e+n
νeν̄e →e−e+
νeν̄e NN→NN
ν̄e e± → ν̄e e±
11121314
10−4
10−3
10−2
10−1
100
101
102
103
Baryon Density, log10
(ρ [g cm−3
])
1/λ
[km
−1]
νe
νen→νen
νep→νep
νen→e−p
νeν̄e →e−e+
νeν̄e NN→NN
νee± →νee
±
νe emission: mainly determined by charged-current νe + n� p + e−.Depends on equation of state properties.
ν̄e emission: strong sensitivity to the processes considered and equation ofstate properties.
GMP, Fischer, Huther, J. Phys. G 41, 044008 (2014)
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Neutrino interactions at high densitiesMost of Equations of State treat neutrons and protons as “non-interacting”(quasi)particles that move in a mean-field potential Un,p(ρ,T,Ye).
µp
µen
µ
En =p2
n
2m∗n+ m∗n + Un
Q = m∗n − m∗p + Un − Up
Ep =p2
p
2m∗p+ m∗p + Up
Energy difference between neutrons and protons is directly related to nuclearsymmetry energy.
Symmetry energy enhances νe absorption and suppresses ν̄e absorption.
Symmetry energy determines the spectral differences between νe and ν̄e andconsequently the nucleosynthesis.
GMP, Fischer, Lohs, Huther, PRL 109, 251104 (2012)Roberts, Reddy, Shen, PRC 86, 065803 (2012)
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Constrains in the symmetry energy
Combination nuclear physics experiments and astronomicalobservations (Lattimer & Lim 2013)Isobaric Analog States (Danielewicz & Lee 2013)Chiral Effective Field Theory calculations (Drischler+ 2014)
0.01 0.1
nB (fm−3)
0
5
10
15
20
25
30
35
40
Esy
m (
MeV
)
χEFT (NN+3N), Drischler et al 2014
Danielewicz & Lee 2013 IASDanielewicz & Lee 2013 IAS + SkinsLattimer & Lim 2013DD2NL3TM1TMASFHoSFHxFSUgold
IUFSULS180LS220
Figure data from Matthias Hempel (Basel)
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Impact on neutrino luminosities and Ye evolution
1D Boltzmann transport radiation simulations (artificially induced explosion)for a 11.2 M� progenitor based on the DD2 EoS (Stefan Typel and MatthiasHempel).
0 2 4 6 8 10Time [s]
1050
1051
1052
Lum
inos
ity[e
rgs/
s]
0 2 4 6 8 10Time [s]
6789
10111213
〈Eν〉[
MeV
] νe
ν̄e
νx
0 2 4 6 8 10Time [s]
0.460.480.500.520.540.560.580.60
Ele
ctro
nfra
ctio
n
0 2 4 6 8 10Time [s]
2030405060708090
100
Ent
ropy
[kB
/bar
yon]
Ye is moderately neutron-rich at early times and later becomes proton-rich.GMP, Fischer, Huther, J. Phys. G 41, 044008 (2014).
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Nucleosynthesis
50 60 70 80 90 100 110Mass number A
10−410−310−210−1
100101102103104105106107
Rel
.ab
unda
nce 11.2
25 30 35 40 45 50 55Charge number Z
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
Ele
men
tala
bund
ance
HD 122563
Elements between Zn and Mo (A ∼ 90) are produced
Mainly neutron-deficient isotopes are produced
Uncertainties: Equation of State, neutrino reactions (mainly ν̄e), Neutrinooscillations(?).
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Neutron decay
The neutron-proton energy difference in the medium could be of the order ofseveral 10s MeV. Neutron decay is important for low energy neutrinos.
ν̄e + p� n + e+
ν̄e + e− + p� n
This is part of the direct URCA process in neutron stars [Lattimer et al, (1991)]
Νe + e-+ p ® n
Νe + p ® n + e+
0 10 20 30 400.001
0.01
0.1
1
10
Energy HMeVL
OpacityHkm-1L
0.5 1 2 3 5 10
5
6
7
8
9
⟨E ν⟩
[MeV
]
0.5 1 2 3 5 10
6
7
8
9
10
11
12
⟨E ν⟩
[MeV
]
20
no neutron decay channelincluding neutron−decay channel
νe
ν̄e
t − tbounce [s]Fischer, Lohs, GMP, Qian, in preparation
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Additional opacity channels for ν̄e
10−2
10−1
100
101
102
103
104
10 20 30 40 50 60 70 80 90 100
Opa
city
[1/k
m]
Energy [MeV]
ν̄e + p→ e+ + nν̄e + n→ ν̄e + nν̄e + p→ ν̄e + pν̄e + e− → ν̄e + e−
νe + ν̄e + NN → NNν̄e + e− + p→ nν̄e + e− + νµ → µ−ν̄e + e− → ν̄µ + µ−
Introduction Weak rates for ONeMg core evolution 3D simulations oxygen deflagration (Jones et al) nucleosynthesis in ECSN Summary
Summary
Most of the weak interaction rates relevant for ONeMg coresevolution are well constrained by experimental data.
Challenge: accurate and fast implementation of rates in stellarevolutionary codes.
Core evolution sensitive to weak rates and thermonuclear rates.
Final outcome sensitive to density of oxygen ignition. 3Dsimulations by Jones et al
Electron capture supernova constitute an ideal test ground toexplore the impact of neutrino opacities on heavy elementnucleosynthesis.
It is important to improve the description of ν̄e opacities intransport codes.
