r-Process nucleosynthesis with SkyNetnpcsm/slides/4th/Lippuner.pdf · r-Process nucleosynthesis in...
Transcript of r-Process nucleosynthesis with SkyNetnpcsm/slides/4th/Lippuner.pdf · r-Process nucleosynthesis in...
r-Process nucleosynthesis in neutron star mergers with
SkyNet
Jonas Lippuner
Luke Roberts, Rodrigo Fernandez, Francois Foucart,
Matt Duez, Christian Ott
NPCSM 2016, YTIP, Kyoto University, Kyoto, Japan
November 9, 2016
Outline
1. r-Process recap
2. SkyNet
3. Parametrized r-process study
4. r-Process in accretion disk outflow
5. r-Process in NSBH dynamical ejecta (time permitting)
2 Jonas Lippuner
r-Process recap
τn ≪ τβ− ∼ 10 ms – 10 s
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
neutron drip lineclosed neutron shell
3 Jonas Lippuner
r-Process recap
τn ≪ τβ− ∼ 10 ms – 10 s
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
neutron drip lineclosed neutron shell
3 Jonas Lippuner
r-Process recap
s-process: τβ− ≪ τn ∼ 102 − 105 yr
r-process: τn ≪ τβ− ∼ 10 ms – 10 s
neutron drip line
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
closed neutron shell4 Jonas Lippuner
r-Process recap
s-process: τβ− ≪ τn ∼ 102 − 105 yr
r-process: τn ≪ τβ− ∼ 10 ms – 10 s
neutron drip line
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
closed neutron shell4 Jonas Lippuner
r-Process recap
s-process: τβ− ≪ τn ∼ 102 − 105 yr
r-process: τn ≪ τβ− ∼ 10 ms – 10 s
neutron drip line
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
closed neutron shell4 Jonas Lippuner
r-Process recap
s-process: τβ− ≪ τn ∼ 102 − 105 yr
r-process: τn ≪ τβ− ∼ 10 ms – 10 s
neutron drip line
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
closed neutron shell4 Jonas Lippuner
r-Process recap
s-process: τβ− ≪ τn ∼ 102 − 105 yr
r-process: τn ≪ τβ− ∼ 10 ms – 10 s
neutron drip line
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
closed neutron shell4 Jonas Lippuner
r-Process recap
s-process: τβ− ≪ τn ∼ 102 − 105 yr
r-process: τn ≪ τβ− ∼ 10 ms – 10 s
neutron drip line
65Cu
66Zn 67Zn 68Zn 70Zn
69Ga 71Ga
70Ge 72Ge 73Ge 74Ge 76Ge
75As
74Se 76Se 77Se 78Se 80Se 82Se
79Br 81Br
78Kr 80Kr 82Kr 83Kr 84Kr 86Kr
85Rb 87Rb
84Sr 86Sr 87Sr 88Sr
89Y
90Zr 91Zr 92Zr
closed neutron shell4 Jonas Lippuner
Solar system abundances
r sN = 50
r sN = 82
r sN = 126
logrelative
abundan
ce(Si=
106)
Mass number A
even A
odd A
iron-peak
−2
0
2
4
6
8
10
0 25 50 75 100 125 150 175 200 225
Data credit: Katharina Lodders, ApJ 591, 1220 (2003)
5 Jonas Lippuner
SkyNet
▸ General-purpose nuclear reaction network
▸ ∼8000 isotopes, ∼140,000 nuclear reactions
▸ Evolves temperature and entropy based on nuclear reactions
▸ Input: ρ(t), initial composition, initial entropy or temperature
▸ Open source (soon)
JL, Roberts 2016, in prep.
6 Jonas Lippuner
SkyNet
Define abundance
Yi = ni
nB. (1)
Consider reaction
p + 7Li→ 2 4He (2)
with rate λ = λ(T , ρ). ThenY4He = 2λYpY7Li +⋯,Yp = −λYpY7Li +⋯,
Y7Li = −λYpY7Li +⋯ (3)
7 Jonas Lippuner
SkyNet reaction types
Strong
▸ Ordinary: n + 196Au → 197Au (REACLIB, Cyburt+10)
▸ Neutron induced fission: n + 235U → 118Pd + 118Pd (Panov+10,
Mamdouh+01, Wahl02)
▸ Spontaneous fission: 301Md → 121Ag + 180Xe (Frankel+47)
Weak
▸ Beta decays: 86Br → 86Kr + e− + νe (REACLIB, Fuller+82)
▸ Electron capture: 26Al + e− → 26Mg + νe (REACLIB, Fuller+82)
▸ Neutrino interactions and e−/e+ capture on free nucleons:n + νe → p + e− (Arcones+02)
▸ λνe ∝ ∫ ∞wecdE E2(E −Q)2(1 − fe)fνe
8 Jonas Lippuner
SkyNet additional features
Science
▸ Expanded Helmholtz equation of state
▸ Calculate nuclear statistical equilibrium (NSE)
▸ Calculate inverse rates from detailed balance to be consistent with NSE
▸ NSE evolution mode
▸ Implementing screening with chemical potential corrections
Code
▸ Adaptive time stepping
▸ Python bindings
▸ Extendible reaction class
▸ Make movie with chart of nuclides
9 Jonas Lippuner
Parametrized r-process study
10 Jonas Lippuner
Parametrized r-process
Lippuner & Roberts, 2015, ApJ, 815, 82, arXiv:1508.03133
Parameters
0.01 ≤ Ye ≤ 0.50 initial electron fraction
1kB baryon−1 ≤ s ≤ 100kB baryon−1 initial specific entropy
0.1ms ≤ τ ≤ 500ms expansion time scale
Density profile
ρ(t, τ) =⎧⎪⎪⎪⎨⎪⎪⎪⎩
ρ0e−t/τ
t ≤ 3τρ0 (3τ
te)3 t ≥ 3τ t
=3τ
Density
ρ/ρ 0
Time t/τ10−9
10−6
10−3
1
10−3 10−2 10−1 1 101 102 103
Initial conditions
▸ Choose initial temperature T0 = 6GK▸ Find ρ0 by solving for NSE at T0 and Ye that produces specified s
11 Jonas Lippuner
Movies
http://lippuner.ca/skynet/SkyNet_Ye_0.010_s_010.000_tau_007.100.mp4
http://lippuner.ca/skynet/SkyNet_Ye_0.250_s_010.000_tau_007.100.mp4
12 Jonas Lippuner
Final abundances vs. electron fraction
τ = 7.1mss = 10kB baryon−1
Relativefinal
abundan
ce
Mass number A
Ye = 0.01Ye = 0.19
Ye = 0.25Ye = 0.50
LanthanidesActinidesSolar r-process
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
0 50 100 150 200 250
13 Jonas Lippuner
Final abundances vs. entropy
τ = 7.1msYe = 0.19
Relativefinal
abundan
ce
Mass number A
skB = 1skB = 3.2
skB = 10skB = 100
LanthanidesActinidesSolar r-process
10−10
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
0 50 100 150 200 250
14 Jonas Lippuner
Impact of electron fraction
s = 10kB baryon−1
τ = 1ms
logX
Number
offissioncycles
Electron fraction Ye
XLa
XAc
XLa+Ac
Number of fission cycles
−5
−4
−3
−2
−1
0
0.0 0.1 0.2 0.3 0.4 0.50
1
2
3
4
5
6
7
8
9
10
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Example light curves
s = 10kB baryon−1
τ = 7.1ms
M = 0.01M⊙
Luminosity,heatingrate
[erg
s−1]
Time [day]
Ye = 0.01Ye = 0.13Ye = 0.25
LuminosityHeating rate
1039
1040
1041
1042
0 5 10 15
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r-Process in accretion disk outflow
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Ejecta mass
τττ [ms] MejMejMej [10−3
M⊙10−3 M⊙10−3M⊙] Mej,Ye≤0.25Mej,Ye≤0.25Mej,Ye≤0.25 [10−3 M⊙10−3 M⊙10−3 M⊙]
0 1.8 1.36
10 1.9 1.07
30 3.3 0.83
100 7.8 0.52
300 18.0 0.67
∞ 29.6 0.69
JL, Fernandez, Roberts, et al. 2016, in prep.
18 Jonas Lippuner
YYYeee distribution vs. HMNS lifetimeEjectamass[10−3M⊙]
Electron fraction Ye
τ = 0 ms
τ = 10 ms
τ = 30 ms
τ = 100 ms
τ = 300 ms
τ = ∞
0.0
0.5
1.0
1.5
2.0
2.5
0.1 0.2 0.3 0.4 0.5
19 Jonas Lippuner
Final abundances vs. HMNS lifetimeFinal
mass×a
bundan
ce(M
ejY
i)
Mass number A
τ = 0 msτ = 10 ms
τ = 30 msτ = 100 msτ = 300 msτ = ∞ msSolar r-process
10−6
10−5
10−4
10−3
10−2
10−1
0 50 100 150 200 250
20 Jonas Lippuner
τ = 300τ = 300τ = 300 ms ejecta properties
0.1 0.2 0.3 0.4 0.50
20
40
60
80
100
Ye,5GK
s5GK
[kBbaryon−1]
−3
−2
−1
logvfinal[c]
0
1
2
Mej,−3⊙
0.0
0.5
1.0
1.5 Mej,−
3⊙
t5GK [s]
−3 −2 −1
log vfinal [c]
0.51.01.52.0 M
ej,−
3⊙
0 2 4 6
Mej,−3⊙
0.03 0.1 1 30.3
21 Jonas Lippuner
r-Process in NSBH dynamical ejecta
22 Jonas Lippuner
Neutron star–black hole merger
1. Full GR simulation of NS–BH
Francois Foucart (LBL), Foucart+14
2. Ejecta in SPH code,
Matt Duez (WSU)
3. Nucleosynthesis with SkyNet and
varying neutrino luminosity
JL and Luke Roberts (Caltech)
Roberts, JL, Duez, et al. 2016, MNRAS in
press, arXiv:1601.07942
Figure credit: F. Foucart
23 Jonas Lippuner
BHNS: Final abundances vs. neutrino luminosityRelativefinal
abundan
ce
Mass number A
Lνe ,52 = 0.2Lνe ,52 = 1
Lνe ,52 = 25Solar r-process
10−8
10−7
10−6
10−5
10−4
10−3
10−2
0 50 100 150 200 250
24 Jonas Lippuner
BHNS: Electron fraction distributionMass[M⊙]
Electron fraction Ye
Lνe ,52 = 0.2Lνe ,52 = 1Lνe ,52 = 25
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.00 0.05 0.10 0.15 0.20 0.25 0.30
25 Jonas Lippuner
BHNS: New first peak production mechanism
▸ Original seeds: A ∼ 80 → full r-process
▸ With neutrinos:
▸ νe + n→ p + e−▸ 2p + 2n→ 4He▸ 3 4He + n→ 12C + n
▸ Additional low-mass seed nuclei → enhanced 1st peak
▸ No combination of complete and incomplete r-process
26 Jonas Lippuner
Summary
▸ SkyNet is a flexible reaction network that will be open source
▸ Ye ∼ 0.25 is the critical value for lanthanide production
▸ Heating rate is fairly uniform
▸ Disk outflow after neutron star merger produces 3rd peak regardless of τ ,
but 3rd peak under-produced for τ ≳ 10 ms
▸ Black hole-neutron star merger produces very strong 3rd peak
▸ Neutrino irradiation can enhance 1st peak via low-mass seed nuclei
27 Jonas Lippuner
Extra slides
28 Jonas Lippuner
YYYeee slices
0.1
1
10
100
500Ye = 0.01
τ[m
s]
Ye = 0.25 Ye = 0.50
1 10 1000.1
1
10
100
500
s [kB baryon−1]
τ[m
s]
1 10 100s [kB baryon−1]
1 10 100s [kB baryon−1]
10−5
10−4
10−3
10−2
10−1
0.3
finalX
La+Ac
1037
1038
1039
1040
1041
1042
Mǫat1day
[erg
s−1]
29 Jonas Lippuner
Nuclear reaction network
Consider reaction
[j] + [k]→ [m] (4)
cross section = σ = # of reactions per target [j] per second
flux of projectiles [k]
= R/(Vnj)nkv
= r
njnkv, (5)
and so
r = R
V= σvnjnk =# of reactions per second per volume, (6)
where
R =# of reactions per second,
V = volume,
nj,k = number density of species [j], [k],
v = relative speed between [j] and [k].
30 Jonas Lippuner
Nuclear reaction network
In general
rj,k = ∫ σ(∥v j − v k∥)∥v j − v k∥d3njd
3nk , (7)
using Boltzmann distribution
rj,k = njnk⟨σv⟩j,k = njnk ( 8
µπ)1/2 (kBT)−3/2 ∫
∞
0Eσ(E)e−E/(kBT)
dE , (8)
where
µ = reduced mass = mjmk
mj +mk
,
T = temperature,
kB = Boltzmann constant.
Note that ⟨σv⟩j,k = ⟨σv⟩j,k(T).
31 Jonas Lippuner
Nuclear reaction network
Define abundance
Yi = ni
nB= # of species [i]
# of baryons, (9)
where nB is baryon number density, then for [j] + [k]→ [m]
Ym = rj,kV
# of baryons= rj,k
nB= YjnBYknB⟨σv⟩j,k
nB= YjYkλj,k , (10)
where
λj,k = nB⟨σv⟩j,k = NAρ⟨σv⟩j,k(T) = λj,k(T , ρ), (11)
where NA is Avogadro’s number, and ρ is the mass density.
And, of course
Yj = Yk = −Ym. (12)
32 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = ´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = − λ4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = − λ4HeY4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = − λ4HeY4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
+ 2λp,7Li´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = − λ4HeY4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
+ 2λp,7LiYpY7Li´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = − λ4HeY4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
+ 2λp,7LiYpY7Li´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
− 2λn,p,2 4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
SkyNet
In general
Yi = ∑α
Nαi λα(T , ρ) ∏
m∈Rα
Y∣Nα
m ∣m , (13)
where
Yi = ni/nB = abundance of species [i],
α = index running over all reactions,
Nαi =# of species [i] destroyed/created in α,
λα = reaction rate,
Rα = set of reactants of α.Example:
Y4He = − λ4HeY4He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶decay
4He→ 2d
+ 2λp,7LiYpY7Li´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶producing reaction
p + 7Li→ 2 4He
− 2λn,p,2 4HeYnYpY24He´¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¸¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¹¶
destroying reaction
n + p + 2 4He → 7Li + 3He
+ ⋯ (14)
33 Jonas Lippuner
Time stepping method
inputs: ρ(t), initial T or s, initial Y
calculate ∆t from previous ∆Y
calculate reaction rates from T , ρ(t +∆t)
initial guess x0 → Y
calculate Y (xn), J(xn) for guess xn,
xn+1 → xn − J−1 ( xn−Y∆t− Y )
converged?n > 10?
Y → xn+1, calculate ∆s from ∆Y ,
s → s +∆s, T → EOS(s, ρ(t +∆t),Y )
t → t +∆t
∆t →∆t/2
yes
no
no
yes
34 Jonas Lippuner
τττ slices
1
10
100τ = 0.10ms
s[k
Bbaryon−1]
τ = 7.1ms τ = 500ms
0.01 0.1 0.2 0.3 0.4 0.51
10
100
Ye
s[k
Bbaryon−1]
0.01 0.1 0.2 0.3 0.4 0.5Ye
0.01 0.1 0.2 0.3 0.4 0.5Ye
10−5
10−4
10−3
10−2
10−1
0.3
finalX
La+Ac
1037
1038
1039
1040
1041
1042
Mǫat1day
[erg
s−1]
35 Jonas Lippuner
Light curves vs. electron fraction
s = 10kB baryon−1
τ = 1ms
6days
1day1600K
6000K
logX
La+Ac,tp/3−5
,T
eff/30
00−4
.5
logPeakluminosity
Electron fraction Ye
Lanthanide and actinide mass fraction XLa+Ac
Peak time tp [day]Peak effective temperature Teff [K]
Peak Luminosity [erg s−1]
−5
−4
−3
−2
−1
0
0.0 0.1 0.2 0.3 0.4 0.51038
1039
1040
1041
1042
36 Jonas Lippuner
Light curves vs. electron fraction
−5
−4
−3
−2
−1
0
logX
i,logtp,logTeff
0.0 0.1 0.2 0.3 0.4−5
−4
−3
−2
−1
0
Ye
logX
i,logtp,logTeff
0.5 0.0 0.1 0.2 0.3 0.4
Ye
0.5 0.0 0.1 0.2 0.3 0.4 0.5
Ye
skB= 10, τ = 0.1 ms
skB= 30, τ = 0.1 ms
skB= 10, τ = 1 ms
skB= 30, τ = 1 ms
37
38
39
40
41
42
logM
ǫ,logLp
skB= 10, τ = 10 ms
37
38
39
40
41
42
logM
ǫ,logLp
skB= 30, τ = 10 ms
final XLa+Ac
Xn at 10min
Mǫ at peak [erg s−1]
Lp [erg s−1]
log tp − 4 [day]
logTeff − 6 [K]
37 Jonas Lippuner