massive stars: presupernova evolution, explosion and nucleosynthesis marco limongi inaf –...
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MASSIVE STARS: PRESUPERNOVA EVOLUTION, EXPLOSION AND
NUCLEOSYNTHESIS
Marco LimongiINAF – Osservatorio Astronomico di Roma, ITALY
andCentre for Stellar and Planetary Astrophysics
Monash University – AUSTRALIAEmail: [email protected]
What is a Massive star ?
It is a star that goes through all the hydrostatic burnings in a quiescent way
from H to Si and eventually explodes as a core collapse supernova
Mup’ MPISN < Massive stars <
8 - 10 >120
Why are Massive stars important in the global evolution of our Universe?
Light up regions of stellar birth induce star formation
Production of most of the elements (those necessary to life)
Mixing (winds and radiation) of the ISM
Production of neutron stars and black holes
Cosmology (PopIII):
Reionization of the Universe at z>5
Massive Remnants (Black Holes) AGN progenitors
Pregalactic Chemical Enrichment
High Energy Astrophysics:
GRB progenitors
The understanding of these stars, is crucial for the interpretation of many astrophysical objects
Production of long-lived radioactive isotopes: (26Al, 56Co, 57Co, 44Ti, 60Fe)
-12-11-10
-9-8-7-6-5-4-3-2-1012
0 20 40 60 80 100 120 140 160 180 200
Atomic Weight
Lo
g M
as
s F
rac
tio
n
BB CR neut.Novae IMS SNIISNIa s-r
Le SNII contribuiscono in maniera rilevante all’evoluzione chimica della Galassia. Responsabili per la nucleosintesi degli elementi con 16<A<50 and 60<A<90
BB = Big Bang; CR = Cosmic Rays; neut. = n induced reactions in SNII;IMS = Intermediate Mass Stars; SNII = Core collapse supernovae;SNIa = Termonuclear supernovae; s-r = slow-rapid neutron captures
Computation of the Presupernova Evolution of Massive Stars 64Zn 66Zn 67Zn 68Zn65Zn
63Cu 65Cu
58Ni 59Ni 60Ni 61Ni 62Ni 63Ni 64Ni
54Fe 55Fe 56Fe 57Fe 58Fe 59Fe 60Fe
64Cu
58Co 59Co 60Co 61Co
54Mn 55Mn 56Mn
50Cr 51Cr 52Cr 53Cr 54Cr
49V 50V 51V
47Ti 48Ti 49Ti 50Ti 51Ti46Ti45Ti44Ti
51Mn 52Mn 53Mn
44Sc 45Sc 46Sc 47Sc 48Sc 49Sc41Sc 42Sc 43Sc
42Ca 43Ca 44Ca 45Ca 46Ca 47Ca 48Ca40Ca 41Ca
38K 39K 40K 41K 42K
48Cr 49Cr
37K
49Ca
38Ar 39Ar 40Ar 41Ar35Ar 36Ar 37Ar
38Cl35Cl 36Cl 37Cl33Cl 34Cl
58Cu 59Cu 60Cu 61Cu 62Cu
35S 36S 37S33S 34S32S31S
33P 34P32P31P30P
27Mg
27Si 33Si32Si31Si30Si28Si 29Si
27Al
26Mg24Mg 25Mg
23Na
22Ne20Ne 21Ne
19F
18O16O 17O
16N14N 15N
14C12C 13C
19O
17F 18F
13N
15O
20F
21Na 22Na
23Ne
24Na
25Al 26Al 28Al
47V 48V46V
52Fe 53Fe
54Co 55Co 56Co 57Co
29P
56Ni 57Ni
63Zn60Zn 61Zn 62Zn
65Ni
66Cu
52V
55Cr
61Fe
67Cu
22Na
26Al
44Ti
60Fe
60Co
44Sc
23Mg
45V
57Mn
50Sc
62Co
57Cu
11B10B
10Be8Be 9Be7Be
7Li6Li
4He3He
3H2H1H
n
(p,)
(,n) (,)
(,p)(p,n)
(p,)
(n,)
(n,p)
(n,)
(n)
(p)
()
1. Extended Network
Including a large number of isotopes and reactions(captures of light partcles, e± captures, β± decays)
Computation of the Presupernova Evolution of Massive Stars
),,(4
),,(),,(),,(
),,(4
14
2
2
4
i
igraviinuc
i
YTPPr
GmT
m
T
YTPYTPYTPm
L
YTPrm
rr
Gm
m
P
Ni
YYYvNlkjc
YYvNkjcYjct
Y
lklkj
jlkjAi
kkj
jkjAij
jjii
,........,1
),,(
),()(
,,,,
22
,,
H/He burnings:),( ; ),(
; ),( ; ),( ; ),(
TPTP
TPTPTP
gravgrav
nucnuc
+
Decoupled
Adv. burnings: ),,( inucnuc YTP Coupled
2. Strong coupling between physical and chemical evolution:
Computation of the Presupernova Evolution of Massive Stars
3. Tratment of convection:
tmix
nucmix - Time dependent convection
- Interaction between Mixing and Local Burning
conv
i
nuc
ii
gravnuc
t
Y
t
Y
t
Y
Pr
GmT
m
Tm
L
rm
rr
Gm
m
P
2
2
4
4
4
14
m
YDr
mt
Y i
conv
i 24
D = Diffusion Coefficient
Core H burning
CNO Cycle
Convective Core
TR
MTP
3 4
2
R
MPc
R
MTc
FacTdr
dT
rad34
3
)1(2.0 HTh X
The Convective Core shrinks in mass
Massive Stars powered by the CNO Cycle
(T 3×107 K)
12C + 1H 13N +
13N 13C + e+ +
13C + 1H 14N +
14N + 1H 15O +
15O 15N + e+ +
15N + 1H 12C + 4He (99%)
16O + (1%)
16O + 1H 17F +
17F 17O + e+ +
17O + 1H 14N + 4He
CN-Cycle
C N O
i i
i
i i
i
A
X
A
X 0
CNO Cycle
NO-Cycle
CNO Processed Material
20Ne + 1H 21Na +
21Na 21Ne + e+ +
21Ne + 1H 22Na +
22Na 22Ne + e+ +
22Ne + 1H 23Na +
23Na + 1H 20Ne + 4He
Ne-Na Cycle
24Mg + 1H 25Al +
25Al 25Mg + e+ +
25Mg + 1H 26Al +
26Al 26Mg + e+ +
26Mg + 1H 27Al +
27Al + 1H 24Mg + 4He
Mg-Al Cycle
Ne-Na and Mg-Al Cycles
During Core H Burning the central temperature is high enough (3-7×107 K) that the Ne-Na and Mg-Al cycles
become efficient
21Na e 25Mg destroyed
22Ne slightly burnt
23Na e 26Mg increases
26Al (~10-7) produced
Evolutionary Properties of the Interior
t=6.8 106 yr
Evolutionary Properties of the Surface
Mmin(O) = 14 M
t(O)/t(H burning): 0.15 (14 M ) – 0.79 (120 M)
Core H
Burning
Models
Major Uncertainties in the computation of core H burning models:
Extension of the Convective Core (Overshooting, Semiconvection)
Mass Loss
Both influences the size of the He core that drives the following evolution
He Convective
Core
3+ 12C()16O
H burning shell
H exhausted core (He Core)
Core He burningK 105.1 8cT
4He + 4He 8Be +
8Be 4He + 4He
8Be + 4He 12C +
3 4He 12C +
ad
rad
Bordo iniziale
CC
Core Convettivo
He C,OMix He
The He convective core increases in mass
Nucleosynthesis during Core He burning
3 4He 12C +
12C + 4He 12O +
16O + 4He 20Ne +
20Ne + 4He 24Mg +
Chemical composition at core He exhaustion: mainly C/O
C/O ratio depends on:
1. Treatment of convection (late stages of core He burning)2. 12C()16O cross section
The C/O ratio is one the quantity that mainl affects the advanced evolution of Massive Stars (it determines the
composition of the CO core)
Nucleosynthesis during Core He burning14N, produced by H burning activates the sequence of reactions:
14N + 4He 18F +
18F 18O + e+ +
18O + 4He 22Ne +
22Ne + 4He 25Mg + n
For the CNO cycle:
XCNO(iniziale) X14N
i i
i
i i
i
A
X
A
X 0
For e Solar composition ),,,,,( 1036.9 17161514131240
OONNCCiA
X
i i
i
2414 103.1141036.9 X
For a Solat composition at core H exhaustion: X(14N) ~ ½ Z
In general: ZX2
114
The efficiency of the 14N reactions scales with the metallicity
14N 22Ne during the initial stages of core He burning
ZX
X 21422 10222
14
During core He burning, 22Ne is reduced by a factor of ~2 by the nuclear reaction:
22Ne + 4He 25Mg + n
CNO (~1/2 Z) 14N (~1/2 Z) 22Ne (~Z)H burning He burning
ZX
X n 40
1106.4
222
1 422 Neutron Mass Fraction
s-process nucleosynthesis
Nucleosynthesis during Core He burning
84Se
85Br
86Kr
83As 84As 85As
85Se 86Se
86Br 87Br
87Kr 88Kr
73Ge 74Ge 75Ge 76Ge
74As 75As 76As
72Ga 73Ga
77As
75Se 76Se 77Se 78Se 79Se 80Se 81Se 82Se
76Br 77Br 78Br 79Br 80Br 81Br 82Br 83Br
77Kr 78Kr 79Kr 80Kr 81Kr 82Kr 83Kr 84Kr
80As 81As78As 79As
78Rb 79Rb 80Rb 81Rb 82Rb 83Rb 85Rb84Rb
80Ge77Ge 78Ge 79Ge
79Ga76Ga 77Ga 78Ga74Ga 75Ga
n,
b-
b-
b-
p
s
r
s,r
s-process during Core He burning
Both the neutron mass fraction and the seed nuclei abundances scale with the metallicity
The abundance of the s-process nuclei scales with the metallicity
Evolutionary Properties of the Interior
t=5.3 105 yr
WIND
Evolutionary Properties of the Surface
Core He
Burning
Models
Core He
Burning
Models
M ≤ 30 M RSG
M ≥ 35 M BSG
Major Uncertainties in the computation of core He burning models:
Extension of the Convective Core (Overshooting, Semiconvection)
Central 12C mass fraction (Treatment of Convection + 12C(,)16O cross section)
Mass Loss (determine which stars explode as RSG and which as BSG)
All these uncertainties affect the size of the CO core that drives the following
evolution
22Ne(,n)25Mg (main neutron source for s-process nucleosynthesis)
Advanced burning stages
Neutrino losses play a dominant role in the evolution of a massive star beyond core He burning
At high temperature (T>109 K~0.08 MeV) neutrino emission from pair production start to become very
efficient
eeee
H burning shell
H exhausted core (He Core)
He burning shell
He exhausted core (CO Core)
Core Burning
Advanced burning stages
Mt
EL
nuc
nuc L
MEt nucnuc
Evolutionary times of the advanced burning stages reduce dramatically
Evolutionary Properties of the Surface
M < 30 M Explode as RSG
M ≥ 30 M Explode as BSG
costL
LL 108 1010
After core He burning
Absolute Magnitude increases by ~25
At PreSN stage
Advanced Nuclear Burning Stages: Core C burning
H
He
CO
H burning shell
He burning shell
T~109 K
C-burning K 10~ 9T
Main Products of C burning
20Ne, 23Na, 24Mg, 27Al
MgnNe 2522 ),(
Scondary Products of C burning
s-process nuclesynthesis
Advanced Nuclear Burning Stages: C burning
At high tempreatures a larger number of nuclear reactions are activated
Heavy nuclei start to be produced
H
He
CO
H burning shell
He burning shell
T~1.3×109 K
NeO C burning shell
Advanced Nuclear Burning Stages: Core Ne burning
Ne-burning K 103.1~ 9T
Advanced Nuclear Burning Stages: Ne burning
Main Products of Ne burning
16O, 24Mg, 28Si
Scondary Products of Ne burning
29Si, 30Si, 32S
H
He
CO
H burning shell
He burning shell
T~2×109 K
NeO
C burning shell
Advanced Nuclear Burning Stages: Core O burning
O
Ne burning shell
Advanced Nuclear Burning Stages: O burning
O-burning K 102~ 9T
28Si (~0.55) 32S (~0.24)
38Ar (~0.10)
34S (~0.07)36Ar (~0.02)
40Ca (~0.01)
Main Products of O burning
Secondary Products of O burning
Advanced Nuclear Burning Stages: O burning
During core O burning weak interactions become efficient
42Ca 43Ca 44Ca40Ca 41Ca
38K 39K 40K 41K 42K37K
38Ar 39Ar 40Ar 41Ar35Ar 36Ar 37Ar
38Cl35Cl 36Cl 37Cl33Cl 34Cl
35S 36S 37S33S 34S32S31S
33P 34P32P31P30P
27Si 33Si32Si31Si30Si28Si 29Si
27Al26Al 28Al
29P
Pro
ton
Nu
mb
er
(Z)
Neutron Number (N)
31S(+)31P 33S(e-,)33P 30P(e-,)30Si 37Ar(e-,)37Cl
Most efficient processes:
The electron fraction per nucleon 5.0i
ii
ie X
A
ZY
H
He
CONeO
Advanced Nuclear Burning Stages: Core Si burning
OSiS
H burning shell
He burning shell
T~2.5×109 K
C burning shell
Ne burning shell
O burning shell
jlik rr
),max()(
jlik
jlik
rr
rrij
0)( ij
Non equilibrium1)( ij
Full equilibrium
Advanced Nuclear Burning Stages: Si burning
At Oxygen exhaustion
K 105.2~ 9T Balance between forward and reverse (strong
interaction) reactions for increasing number of
processes
i + k j + l
A measure of the degree of equilibrium reached by a couple of forward and reverse processes
At Oxygen exhaustion
K 105.2~ 9T
Si
Sc
Equilibrium
At Si ignition
K 105.3~ 9T
Out of Equilibrium
Equilibrium
Partial Eq.
Out of Eq.
At Si ignition(panel a + panel b)
K 105.3~ 9T
A=44A=45
Eq. Clusters
28Si
56Fe
Advanced Nuclear Burning Stages: Si burning
1.0)( ij
1.0)( ij
01.0)( ij
1.0)(01.0 ij
1.0)( ij
1.0)( ij
Advanced Nuclear Burning Stages: Si burning
K 105.3~ 9T
56,57,58Fe, 52,53,54Cr, 55Mn, 59Co, 62Ni
NSE
1.0)( ijA=44
A=45
Clusters di equilibrio
28Si
56Fe
24Mg20Ne
16O12C
4He
Ca),(K
Sc),(Sc Ti),(Ca
Ti),(Ca Ti),(Sc
Ti),(Ti Ti),(Ca
Ti),(Ca Ca),(Sc
Sc),(Ca Ca),(Ca
4441
45444643
45414544
45444542
46424444
45424443
p
nn
p
nn
pn
pn
1. 28Si is burnt through a sequence of reactions
2. The two QSE clusters reajdust on the new equilibrium abundances of the light particles
3. The matter flows from the lower to the upper cluster through a sequence of non equilibirum reactions
Equilibrium Clusters
4. Ye is continuosuly decreased by the weak interactions (out of equilibrium)
H
He
CONeO
Pre-SuperNova Stage
OSiS
H burning shell
He burning shell
T~4.0×109 K
C burning shell
Ne burning shell
O burning shell
Si burning shell
Fe
Evolutionary Properties of the Interior
H burning shell
He burning shell
C burning shell
Ne burning shell
O burning shell
Si burning shell
Chemical Stratification at PreSN Stage
Each zone keeps track of the various central or shell burnings
14N, 13C, 17O14N, 13C, 17O
12C, 16O
12C, 16O s-proc
20Ne,23Na, 24Mg,25Mg, 27Al,s-proc
16O,24Mg, 28Si,29Si, 30Si
28Si,32S, 36Ar,40Ca, 34S, 38Ar
56,57,58Fe, 52,53,54Cr,
55Mn, 59Co, 62NiNSE
Fase Time (yr)
Lnuc L Mcc Tc c Mshell Fuel Main Prod.
Sec. Prod.
H 5.93(6) 12.8 3.7(7) 7.2 8.7 1H 4He 13C, 14N, 17O
He 6.8(5) 6.02 1.5(8) 4.7(2) 6 4He 12C, 16O 18O, 22Ne, s-proc.
C 9.7(2) 1.0(6)-5.0(7)
4.0(7)-1.0(9)
7.2(8) 1.2(5) 2.39 12C 20Ne, 23Na, 24Mg, 27Al
25Mg, s-proc.
Ne 7.7(-1) (280 d)
7.0(9) 2.2(9) 0.62 1.2(9) 2.1(6) 2.39 20Ne 16Ne, 24Mg
29Si, 30Si
O 3.3(-1) (120 d)
5.0(10) 5.9(11)
4.0(10) 1.05 1.8(9) 4.0(6) 1.7 16O 28Si, 32S, 36Ar, 40Ca,
Cl, Ar, K, Ca
Si 2.1(-2) (7 d)
1.1(13) 1.0(12) 1.08 3.1(9) 7.5(7) 1.5 28Si 54Fe, 56Fe, 55Fe
Ti, V, Cr, Mn, Co, Ni
Main Properties of the PreSN Evolution
Evolution of More Massive Stars: Mass Loss
O-Type: 60000 > T(K) > 33000
• WNL: 10-5< Hsup <0.4 (H burning, CNO, products)
• WNE: Hsup<10-5 (No H)
• WN/WC: 0.1 < X(C)/X(N) < 10 (both H and He burning products, N and C)
• WC: X(C)/X(N) > 10 (He burning products)
Wolf-Rayet : Log10(Teff) > 4.0
Final Masses at the PreSN stage
No Mas
s Loss
Final Ma
ss
He-Cor
e Mass
He-CC Mass
CO-Core
Mass
Fe-Core Mass
WNLWNE
WC/WO
RSG
Radius
WIND
HEAVY ELEMENTS
Major Uncertainties in the computation of the advanced burning stages:
Treatment of Convection (interaction between mixing and local burning, stability criterion behavior of convective shells final M-R relation explosive nucleosynthesis)
Computation of Nuclear Energy Generation (minimum size of nuclear network and coupling to physical equations, NSE/QSE approximations)
Weak Interactions (determine Ye hydrostatic and explosive nucleosynthesis behavior of core collapse)
Nuclear Cross Sections (nucleosynthesis of all the heavy elements)
Neutrino Losses
Partition Functions (NSE distribution)
THE EVOLUTION UP TO THE IRON CORE COLLAPSE
The Iron Core is mainly composed by Iron Peak Isotopes at NSE
The following evolution leads to the collapse of the Iron Core:
The Fe core contracts to gain the energy necessary against
gravity
T, increase
nuc lowers becaus the matter is at NSE
The Fe core begins to degenerate
The Chandrasekhar Mass
MCh=5.85×(Ye)2 M is reached
A strong gravitational
contraction begins
The Fermi energy increasesthe electron
captures on both the free and bound protons incease
as well
Tc ~ 1010 K, c ~ 1010 K
Pe ~ 1028 dyne/cm2
Pi ~ 2×1026 dyne/cm2
Prad ~ 3×1025 dyne/cm2
The main source of pressure against gravity (electron
Pressure) lowers
The gravitational collapse begins
3g/cm 103 11
Fe Core
3g/cm 103 12 diffusion
Neutrino Trapping
npe e
3g/cm 1014
Core Bounce and Rebounce
Shock waveFe Core
Stalled ShockEenergy Losses2 x 1051 erg/0.1M
“Prompt”shocks eventually stall!
-sphere
Strong Shock vs Weak Shock
A strong shock propagates.Matter is ejected.
A weak shock stalls.
Matter falls back.
diffusiondiffusionn,p
ee ,p,n
e+,e-
heating
cooling
Gain RadiusRG=100-150 Km
Stalled ShockRS=200-300 Km
NeutrinosphereR=50-700 Km
Neutrino-driven explosions
Energy deposition behind the stalled shock wave due to
neutrino interactions:
eeee
ee ee
Shock Wave reheated
Explosion
Propatagiont of the shock wave through
the envelope
Explosive Nucleosynthesis
Compression and
Heating
Explosive Nucleosynthesi
s
Explosion Mechanism Still Uncertain
The explosive nucleosynthesis calculations for core collapse supernovae are still based on explosions induced by injecting an arbitrary amount of energy in a (also arbitrary) mass location of the presupernova model and then following the development of the blast wave by means of an hydro code.
• Piston
• Thermal Bomb
• Kinetic Bomb
Induced Explosion and Fallback
Injected Energy
Induced Shock
Compression and Heating
Induced Expansion and
Explosion
Initial Remnant
Matter Falling Back
Mass Cut
Initial Remnant
Final Remnant
Matter Ejected into the ISMEkin1051 erg
Composition of the ejecta
The Iron Peak elements are those mostly affected by the properties of the explosion, in particular the amount of
Fallback.
The Final Fate of a Massive Star
No Mas
s Loss
Final Ma
ss
He-Cor
e Mass
He-CC Mass
CO-Core Mass
Fe-Core Mass
WNLWNE
WC/WO
Remnant Mass
Neutron Star
Black Hole
SNII SNIb/c
Fallback
RSG
Z=Z
E=1051 erg
Initial Mass (M)
Mass (M)
Major Uncertainties in the simulation of the explosion (remnant mass – nucleosynyhesis):
Prompt vs Delayed Explosion (this may alter both the M-R relation and Ye of the presupernova model)
How to kick the blast wave:
Thermal Bomb – Kinetic Bomb – Piston
Mass Location where the energy is injected
How much energy to inject:
Thermal Bomb (Internal Energy)
Kinetic Bomb (Initial Velocity)
Piston (Initial velocity and trajectory)
How much kinetic energy at infinity (typically ~1051 erg)
Nuclear Cross Sections and Partition Functions
Chemical Enrichment due to Massive Stars
Mtot
Mcut
Suni
Mtot
Mcut
i
i
dmX
dmX
PF Different chemical composition of the ejecta for different masses
Chemical Enrichment due to Massive Stars
Yields of Massive Stars used for the interepretation of the chemical composition of the Galaxy
We can have information on the contribution of massive stars to the solar composition by looking at the PFs of solar
metallicity massive star models.
ASSUMPTIONS
The average metallicity Z grows slowly and continuously with respect to the evolutionary timescales of the stars
that contribute to the environment enrichment
Most of the solar system distribution is the result (as a first approximation) of the ejecta of ‘‘quasi ’’–solar-metallicity
stars.The PF of the chemical composition provided by a generation of solar metallicity stars should be flat
Chemical Enrichment due to Massive Stars
Mup
Mlow
itot
i dmmYY )( 2.35 kmm )(Yields averaged over a Salpeter IMF
Oxygen is produced predominantly by the core-collapse supernovae and is also the most abundant element
produced by these stars
Use PF(O) to represents the overall increase of the average ‘‘metallicity ’’ and to verify if the other nuclei follow or not its
behavior
Chemical Enrichment due to Massive Stars
Elements above the compatibility range may constitute a problem
Elements below the compatibility range produced by other sources
Secondary
Isotopes?
No room for other sources (AGB) Type Ia AGB
No room for AGB
process. Other sources
uncertain
Explosion?
Chemical Enrichment due to Massive Stars
Global Properties:
Initial Composition (Mass Fraction)
X=0.695Y=0.285Z=0.020
Final Composition (Mass Fraction)
X=0.444 (f=0.64)Y=0.420 (f=1.47)Z=0.136 (f=6.84)
NO DilutionMrem=0.186
1 M1 M
IMF: Salpeter
Averaged Yields: Relative Contributions
Stars with M>35 M (SNIb/c) contribute for ~20% at maximum (large fallback)
with few exceptions
(H,He burning)
CONCLUSIONS
Stars with M<30 M explode as RSG Stars with M≥30 M explode as BSG
The minimum masses for the formation of the various kind of Wolf-Rayet stars are:
WNL: 25-30 M
WNE: 30-35 M
WNC: 35-40 M
The final Fe core Masses range between:
MFe=1.20-1.45 M for M ≤ 40 M
MFe=1.45-1.80 M for M > 40 M
The limiting mass between SNII and SNIb/c is :
30-35 M
SNII SNIb/c
22.0/
SNII
cSNIbSalpeter IMF
The limiting mass between NS and BH formation is:
25-30 M
NS BH
(uncertainties on mass loss, simulated explosion, etc.)
CONCLUSIONS
Assuming a Salpeted IMF the efficiency of enriching the ISM with heavy elements is:
H: decreased by f=0.64He: increased by f=1.47Metals: increased by f=6.84
For each solar mass of gas
returned to the ISM
Massive Stars are responsible for producing elements with 4<Z<38
SNIb/c contribute for ~20% to the majority of the elements (large fallback)
SNIb/c contribute for ~40% to the elements produced by H and He burning that survive to fallback
Depends on:Simulated expl.Mass LossBinary Systems..............
Pre/Post SN models and explosive yields available at http://www.mporzio.astro.it/~limongi