Core Collapse SNe

1
Core Collapse SNe
Inma Domínguez Marco Limongi
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• Evolution of Massive Stars
• Hydrostatic Nucleosynthesis
• Explosion Mechanism
• Explosive Nucleosynthesis
• Contribution to the Chemical Evolution

3
INTERPRETATION OF THE SOLAR SYSTEM ABUNDANCES
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
Type II SNe ? Chemical Evolution of the Galaxy
Type II SNe ? 16 lt A lt 50 and 60 lt A lt
90 16O 49Ti
60Ni 90Zr
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Evolutionary Properties of Massive Stars
Progenitors of CCSNe

• M gt 12 M?

CCSNe
Ignition of ALL Exothermic Nuclear Reactions

• Central Conditions (T,?)

• The stars is never in degenerate
• conditions along its evolution

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STELLAR EVOLUTION EQUATIONS
1 Dimension Lagrangian Hydrostatic
Mixing-length theory
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STELLAR EVOLUTION EQUATIONS
Chemical Evolution
Production Destruction
For each time step 1000 (zones) systems of
4N(isotopes) equations
High Computational Time
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HYDROGEN BURNING - PP
4H ? He
Proton-Proton Chain
1H 1H ? 2H e n 2H 1H ? 3He g
3He 4He ? 7Be g
PPI
3He 3He ? 4He 2 1H
PPII
PPIII
7Be e- ? 7Li n 7Li 1H ? 2 4He
7Be 1H ? 8B g 8B ? 8Be e n 8Be ? 2 4He
Depending on T the different branchings become
active. In all cases the result is 4 1H ? 1
4He
8
HYDROGEN BURNING CNO Cycle
When C and/or N and/or O are present ?
CNO
12C 1H ? 13N g 13N ? 13C e
n 13C 1H ? 14N g 14N 1H ? 15O g
15O ? 15N e n 15N 1H ? 12C 4He
(99)

16O g
(1)
CN
T ? 3 107 K
16O 1H ? 17F g 17F ? 17O e
n 17O 1H ? 14N 4He
NO
During the conversion of H into He through the
CNO cycle C and O are burnt and N is
produced
Products of CNO
C ? N ? O ?
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HYDROGEN BURNING ENERGY GENERATION
The CNO cycle is more efficient than he PP chain
over a certain Tcritica
CNO
PP
From Hydrostatic Equilibrium Eq
Central Temperatura scales with Total Mass
Massive stars H-burning CNO cycle
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HYDROGEN BURNING - CONVECTIVE CORE
The Energy generated by the CNO-cycle depends
strongly on T
High Energy Flux ? Increases Radiative Gradient
? A Convective core Develops
Masssive stars burn H within a Convective core
At high T the main contribution to the Opacity
comes from the Thomson Scattering
When the H decreases, the Opacity decreases and
the Convective Core receeds and finally, at
H-exhaustion, disappears
11
HYDROGEN BURNING Ne-Na, Mg-Al Cycles
If during the central convective H-burning T are
high enough log T7.5-7.8 ? Active Ne-Na e
Mg-Al cycles
Ne-Na Cycle
Mg-Al Cycle
20Ne 1H ? 21Na g 21Na ? 21Ne
e n 21Ne 1H ? 22Na g 22Na ?
22Ne e n 22Ne 1H ? 23Na g 23Na 1H
? 20Ne 4He
24Mg 1H ? 25Al g 25Al ? 25Mg
e n 25Mg 1H ? 26Al g 26Al ?
26Mg e n 26Mg 1H ? 27Al g 27Al 1H
? 24Mg 4He
Final results of the operation of these cycles
Na-Na e Mg-Al

• 21Na 25Mg practically burnt
• 22Ne is reduced by a factor 2
• 23Na 26Mg increase by a factor 6 2,
  respectively
• 26Al produced (10-7)
• 20Ne, 24Mg 27Al do not change

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STRUCTURE AT CENTRAL H-EXHAUSTION
The He-core is much more dense than the
H-envelope because the mean molecular weight for
4He is greater than for 1H ? Matter within the
He-core is more compact
The synthesis of heavier isotopes increases the
mean molecular weight and the structure becomes
more compact
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HYDROGEN SHELL BURNING

• At central H-exhaustion ? H-burning sets in a
  Shell outside the He-core.
• HR diagram the star moves to the red
• A convective envelope forms, the inner border of
  this envelope reachs zones chemically modified by
  he central H-burning.
• The 1st dredge-up occurs material processed by
  nuclear reactions is transported to the surface

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HELIUM BURNING 3?
At central H-exhaustion, the He core is mainly
composed by 4He (98) 14N (1) Withouth
Nuclear Energy generation within the core, it
contracts and Tc increases
When Tc 1.5 108 K ? Efficient He-burning
At the beginning 4He ? 8Be and 8Be rapidly decays
to 4He
4He 4He ? 8Be g 8Be ? 4He 4He
Later, at higher T and ? ? the equilibrium
abundance of 8Be increases and so increases the
probability of the reaction 8Be 4He producing
12C
4He 4He ? 8Be g 8Be ? 4He
4He 8Be 4He ? 12C g
3 4He ? 12C g
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HELIUM BURNING REACTIONS
Initially 4He in 12C But when 12C abundance is
significant and 4He abundance is reduced, it is
more likely that 4He is captured by 12C than by
4He
3 4He ? 12C g 12C 4He ? 12O g 16O 4He ?
20Ne g 20Ne 4He ? 24Mg g
The first 2 reactions are more efficient
3 4He Nuclear Cross Section depends markedly on T
Like H-burning (CNO cycle) He-burning occurs
within a convective core
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HELIUM BURNING s-process
14N produced by the CNO cycle
14N 4He ? 18F g 18F ? 18O e
n 18O 4He ? 22Ne g 22Ne 4He ? 25Mg n
78Rb
79Rb
80Rb
81Rb
82Rb
83Rb
85Rb
84Rb
86Kr
87Kr
88Kr
77Kr
78Kr
79Kr
80Kr
81Kr
82Kr
83Kr
84Kr
85Br
86Br
87Br
b-
76Br
77Br
78Br
79Br
80Br
81Br
82Br
83Br
84Se
85Se
86Se
b-
75Se
76Se
77Se
78Se
79Se
80Se
81Se
82Se
83As
84As
85As
b-
74As
75As
76As
77As
80As
81As
78As
79As
b?
73Ge
74Ge
75Ge
76Ge
80Ge
77Ge
79Ge
78Ge
n,g
72Ga
73Ga
79Ga
76Ga
77Ga
78Ga
74Ga
75Ga
In Massive ? during central He-burning, elements
heavier than Fe are synthesized by the s-process.
s-process depends on free neutrons and the
neutron abundance depends on Z ?
The final s-element abundances scale with initial
metallicity
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HELIUM EXHAUSTION
The most abundant isotopes at central
He-exhaustion
12C 16O 20Ne 25Mg 26Mg
The first three are produced by
3 4He ? 12C g 12C 4He ? 12O g 16O 4He ?
20Ne g
25Mg 26Mg come from the 14N-chain
14N 4He ? 18F g 18F ? 18O e
n 18O 4He ? 22Ne g 22Ne 4He ? 25Mg
n 22Ne 4He ? 26Mg g
12C, 16O, 20Ne, 25Mg 26Mg are the most
abundant isotopes and are produced by He-burning
with the surface abundance
12C/16O ratio depends on the 12C 4He ? 12O
g nuclear cross section that it is still NOT
well known at the energies of the He burning.
This ratio has a strong influence on the
subsequent evolution
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HELIUM EXHAUSTION s-process elements
The most abundant elements are
70Ge 74Se and 80Kr
Heavier nuclei, like 87Rb, 88Sr, 89Y, 90Zr are
not expected to be produced
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HELIUM SHELL BURNING CONVECTIVE SHELL
At central He exhaustion, He burning moves to a
shell just outside the CO core
The following evolution is characterized by the
development of a convective He-burning shell
limited by the CO core and by the H-burning
shell. The chemical composition of this shell,
that will be active till the collapse, tends to
get frozen because the evolution of the star is
more and more rapid at the advanced phases.
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STRUCTURE at He-exhaustion
At central H-exhaustion, the ? is composed by a
CO core, a He-shell and a rich H envelope
The two density gradients correspond to the
border of the He core ( 9 M?) and to the border
of the CO core ( 6 M ?)
This density profile is important for the
explosion properties
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ADVANCED EVOLUTIONARY PHASES NEUTRINO DOMINATED
Now the CO core, produced by the central
He-burning, contracts
During the contraction the ? and T within the
core favours the production of thermal neutrinos
produced by pair anhilation.
At Tgt109 K high energy photons produce ee- pairs
That suddenly recombine to produce a photon. BUT
once over 1019 times, ee- produces a
neutrino-antineutrino pair
This energy sink increases along the subsequent
phases up to the pre-collapse
phase
Advanced evolutionary phases of massive stars are
called neutrino dominated
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ADVANCED EVOLUTIONARY PHASES NEUTRINO LUMINOSITY
From now on the energy losses Photons from
the surface Neutrinos from the center
108
Up to C central ignition the main energy losses
are due to photons and after are due to
neutrinos. As the nuclear energy gives the star
what is lossing, it follows first the luminosity
of photons, and after, the neutrino luminosity
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EVOLUTIONARY TIMES
Enuc is the energy per gram coming from nuclear
reactions, If this is the only energy source
in a star of mass M
Nuclear time scale
H burning 4 1H ? 4He
DM 4 x 1.0078 4.0026 0.0287 AMU 0.0287/4
AMU/nucleon 0.007 AMU/nucleon
Enuc 0.007 x 931.1 x 1.602 10-6 x 6.022 1023
6.44 1018 erg/g
1 AMU 931.1 MeV 1 MeV 1.602 10-6 erg
NA 6.022 1023 nucleon/g
He burning 4 4He ? 16O
DM 4 x 4.0026 15.9949 0.0115 AMU 0.0115/16
AMU/nucleon 0.0009 AMU/nucleon
Enuc 0.0009 x 931.1 x 1.602 10-6 x 6.022 1023
8.70 1017 erg/g
O burning 2 16O ? 32S
DM 2 x 15.9949 31.9720 0.0177 AMU
0.0177/32 AMU/nucleon 0.0005 AMU/nucleon
Enuc 0.0005 x 931.1 x 1.602 10-6 x 6.022 1023
4.98 1017 erg/g
For fix mass, Luminosity and amount of fuel
!
From models
The luminosity increases drastically due to
neutrino losses ? The evolutionary times are
drastically reduced
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Advanced burning stages
Neutrino losses play a dominant role in the
evolution of a massive star beyond core He burning
At high temperature (Tgt109 K) neutrino emission
from pair production start to become very
efficient
Evolutionary times reduce dramatically
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CARBON BURNING
Central C combustion stars 104 years after
central He-exhaustion Tc 7 108 K e ?c 1 105
g/cm3
C-burning depends on the 12C/16O ratio left
after central He burning, 12C(a,g)16O on the
amount of fuel
The formation of a Convective Core depends on the
existence of a positive energy flux
A Convective Core develops
enuc gt en
12C abundances determines the nuclear energy
generation rate
NO Convective Core
enuc lt en
In general, for a fix 12C(?,?)16O reaction
rate and mixing technics 12C abundance decreases
for higher initial masses
In the 25M? ? central carbon combustion occurs
in radiative conditions
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Synthesis of Heavy Elements
At high temperatures a larger number of nuclear
reactions are activated
Heavy nuclei start to be produced
C-burning
Ne-burning
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Synthesis of Heavy Elements
O-burning
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Synthesis of Heavy Elements
At Oxygen exhaustion
Balance between forward and reverse reactions for
increasing number of processes
a b
c d
At Oxygen exhaustion
At Si ignition
Sc
Si
Equilibrium
Equilibrium
Partial Eq.
Out of Eq.
Out of Equilibrium
56,57,58Fe, 52,53,54Cr, 55Mn, 59Co, 62Ni
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MATTER PROPERTIES AT HIGH TEMPERATURE NSE
The chemical composition of matter in NSE is a
function of T ? Ye
When the neutronization changes
The nuclei with that neutron excess are favoured
(with higher binding energies)
?0.000,Ye0.5000, 56Ni
?0.038,Ye0.481, 54Fe
?0.072,Ye0.464, 56Fe
?0.104,Ye0.448, 58Fe
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PRE-SUPERNOVA MODEL CHEMICAL COMPOSITION
Burning Site Main Products
Si Burning 54Fe, 56Fe, 55Fe, 58Ni, 53Mn
O Conv. Shell 28Si, 32S, 36Ar, 40Ca, 34S, 38Ar
C Conv. Shell 20Ne, 23Na, 24Mg,25Mg, 27Al s-process
He Centrale 16O, 12C s-process
He Shell 16O, 12C
H CentraleShell 14N, 13C, 17O
H Centrale
He Shell
C conv. Shell
He Centrale
H Shell
O conv. Shell
Si burning(Cent.Sehll)
4He
16O
1H
28Si
Fe
20Ne
12C
Studying the different isotope abundances in
detail is possible to know from which burning
phase they come from or the interior region of
the star where they were produced
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PRE-SUPERNOVA MODEL Fe-CORE STRUCTURE
16O
Fe
28Si
20Ne
12C
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EXPLOSION
The gravitational collapse of a stars with M ?
12 M? could liberate an energy of
Most of this energy increases the electron energy
and, after electron captures, is converted in
neutrino energy
Just a small fraction is used to eject (kinetic
energy) the envelope
So, the key question is to find a mechanism able
to transform a small fraction of the binding
energy left during the collapse in kinetic
energy of the envelope with the observed
velocities ( 104 km/s)
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Explosive Nucleosynthesis and Chemical Yields
Explosion Mechanism Still Uncertain
The explosion can be simulated by means of a
piston of initial velocity v0, located near the
edge of the iron core

• Explosion 1D PPM Lagrangian Hydrocode (Collella
  Woodward 1984)

• Explosive Nucleosynthesis same nuclear network
  adopted in the hydrostatic evolutions

v0 is tuned in order to have a given amount of
56Ni ejected and/or a corresponding final kinetic
energy Ekin
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EXPLOSIVE NUCLEOSYNTHESIS
Passing through the envelope the Shock Wave
increases the density and temperature and
nuclear reactions occur
We may define the burning time-scales for the
available fuels
Si, O, Ne, C, He and H
These time scales are determined by the
corresponding destructive reactions
Assuming the explosion time 1s
Burning products are similar to those obtained
in hydrostatic burning
He-explosive burning is not efficient in SNII
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EXPLOSIVE NUCLEOSYNTHESIS
Analyzing the most eficient processes
Still out of NSE Products are similar to those
from hydrostatic burning
EXPLOSIVE CARBON BURNING
Products 20Ne, 23Na, 24Mg,25Mg, 26Mg
EXPLOSIVE NEON BURNING
Products 16O, 24Mg 27Al, 29Si, 30Si, 31P,
35Cl, 37Cl
Starting NSE (direct and inverse process)
EXPLOSIVE OXYGEN BURNING
2 clusters at quasi-NSE separated by A?44. No
connection between the 2 clusters
Products 28Si, 32S, 36Ar, 40Ca 34S, 38Ar
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EXPLOSIVE NUCLEOSYNTHESIS
EXPLOSIVE INCOMPLETE SILICON BURNING
At this T the 2 clusters connect at A?44. Most
of the matter Alt44 ? just part of 28Si reachs
the upper cluster
Products 36Ar, 40Ca 56Ni(56Fe), 54Fe,
52Fe(52Cr),51Cr(51V), 55Co(55Mn), 57Ni(57Fe), 58Ni
EXPLOSIVE COMPLETE SILICON BURNING
At this high temperature NSE !!!!!! All 28Si
is burnt to Fe-peak elements. Abundances depend
on neutronization !! For N?Z 56Ni is the most
abundant nuclei
Products Iron Peak Nuclei
37
EXPLOSIVE NUCLEOSYNTHESIS
Changes in T and r following expansion are
crucial for the nucleosynthesis
During the explosion Temperatures are very high
It could be assumed that matter behind the shock
is radiation dominated
Location and T of the shock
The shock propagates in all directions (sphere)
Each radial coordinate in the presupernova model
will reach a maximum temperature
38
EXPLOSIVE NUCLEOSYNTHESIS
For Eexpl1051 erg we could infer in the
presupernova model which regions (volumes)
experience each burning
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EXPLOSIVE NUCLEOSYNTHESIS PROGENITOR
Influence of the Progenitor
1) M-R RELATION ( density profile)
Fix the mass inside a certain volume
2) Ye (neutronization)
In those zones that reach NSE or QSE determines
the rate between protons and neutrons
T5 109 K, r 108 g/cm3, Ye0.50 ? 56Ni0.63
55Co0.11 52Fe0.07 57Ni0.06 54Fe0.05
T5 109 K, r 108 g/cm3, Ye0.49 ? 54Fe0.28
56Ni0.24 55Co0.16 58Ni0.11 57Ni0.08
3) Chemical Composition
For those zones that experience normal burnings
(ie. Explosive Carbon e Neon burnings) fix the
amount of fuel available.
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MASS CUT
The Mass Cut depends on the piston initial
velocity
During the explosion internal zones fall back.
At some point part of the matter is Expanding
and some Collapsing Depending on v compare to
vesc ? The mass coordinate at the bifurcation is
defined as the Mass Cut
In general, for greater initial velocities
Smaller Mass Cut Greater kinetic Energies
1.110
1.144
1.170
1.220
1.250
1.263
The lack of a explosion model makes the MASS CUT
and the KINETIC ENERGY quantities that depend on
parameters (initial energy or piston initial
velocity and place at which the explosion is
started)
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EXPLOSION PROPERTIES CHANGES IN CHEMESTRY
Ekin1.14 foe
v01.5550 109 cm/s
Mcut1.89 M?
Taken
Mass Cut

• The changes in composition due to the explosion
  occur only at the most internal 3.1 M?
• Outside the chemical composition remains
  untouched. It is that from the hydrostatic
  burning
• The complete explosive Si burning and part ot
  the incomplete explosive Si burning fall back to
  the compact remant

42
MASS CUT CALIBRATION LIGHT CURVES
From the LC we obtain information for the Mcut
After an initial phase, different for the
different types of SNe, the LC is powered by the
photons produced by the radioactive decay
8.8
111
Based on the Bolometric LCs and on the distance,
we can deduce the amount of 56Ni produced
during the explosion
56Ni is produced in the most internal zone
depends critically on the Mass Cut ? The
Mass Cut may be choose to reproduce a certain
amount of 56Ni in agreement with the
observations.
The theoretical kinetic energy must be
compatible with the observed
43
MASS CUT CALIBRATION vs INITIAL MASS
From the observed initial mass of the progenitor
we may obtain an empirical relaction between
this mass and the 56Ni produced (or Mcut)
Hamuy et al. 2003
PROBLEMS !!!!

• Few estimations of the progenitor initial mass
  from the observations
• Similar masses give very different 56Ni masses

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CHOOSING A MASS CUT
1) FLAT Case All masses produce the same 56Ni
mass 0.05 M? ? For each model a different mass
cut is chosen in order to reproduce this amount
of Ni
2) TREND Case We adopt a relation between
Initial Mass and 56Ni Mass
Mi (M?) M(56Ni) (M?)
13 0.15
15 0.10
20 0.08
25 0.07
30 0.05
35 0.05
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PRODUCTION FACTORS
To compare with Solar Abundances we introduce the
Production Factor
Two isotopes with the same Production Factor
Same Rate as in the Sun
Oxygen is produced only by Type II SNe and is
the most abundant element produced by SNII ?
Oxygen Production Factor is a Good Metallicity
indicator
It is useful to normalize all PF to that of
Oxygen to show wich isotopes follow Oxygen (Z)
46
INTEGRATED YIELDS (Elements)
Yields from 13-35 M? Salpeter Mass Function It
is assumed that all masses produce the same
amount of 56Ni (FLAT)
We consider Solar Scaled with respect to O all
elements with a PF within a factor 2 of the O PF
The yields produced by a generation of massive
stars integrated by a Salpeter IMF depend
mainly on the yields coming from a 20-25 M? star
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Contribution of Type Ia SNe
Production of Fe ? the percentage of SNIa,
relative to SNII, has been fixed by requiring
that PFFePFO
Open circles No SNIa Filled circles 12 SNIa

1. SNIa contribute only to the Solar System
   abundances of nuclei in the range Ti-Ni

1. The inclusion of SNIa brings 50Ti and 54Cr into
   the band of compatibility ? 50Ti and 54Cr become
   scaled solar compared to O

3) 14N and lot of heavy elements come
from AGB stars
48
CONCLUSIONS
with mass loss 11 -120 M?

• Massive Stars are responsible for producing
  elements from
• 12C (Z6) up to 90Zr (Z40)
• 
  r-elements

• Assuming a Salpeted IMF the efficiency of
  enriching the ISM with heavy elements is

For each solar mass of gas returned to the ISM
H decreased by f0.64 He increased by
f1.47 Metals increased by f6.84
Pre/Post SN models and explosive yields available
at http//www.mporzio.astro.it/limongi Alessandr
o Chieffi Marco Limongi (ApJ 1998-2007)
49
Uncertainties in the computation PreSN Models

• Extension of the Convective Core (Overshooting,
  Semiconvection)

• Mass Loss

Uncertainties in the computation of the Explosion
Models

• Explosion itself
• Piston
• Mass-cut - Mini
• 56Ni (LC)
• Energy (vexp)

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51
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Cósmico
Estrellas y planetas en un espacio infinito
Tiene sentido nuestra presencia en el Universo ?
Podemos ganar la liga de campeones ?
IDEAL ORCEMAN by C. Hernández
52
CHEMICAL ENRICHMENT BY A GENERATION OF MASSIVE
STARS
The 25 M? solar model could be considered as the
typical case, representative of stars from 13
to 35 M?
If we compute the YIELDS (ejected abundances in
solar masses) of the different isotopes produced
by a grid of models (13 to 35 M?), we could
compute the chemical contribution of a
generation of Massive Stars to the ISM
These YIEDS are ingredients in a Chemical
Evolution Model for the Galaxy, includes SFR,
IMF Infall
In principle, the chemical solar distribution is
a consequence of different generations of stars
with different initial compositions
The metallicity of the ISM is expected to increse
continously and with longer time-scales than the
evolutionary time of the stars that contributes
to the chemical enrichment
We expect that the YIELDS of a generation of
masive solar metallicity stars explain the solar
distribution
53
Integrated Yields adopting a different Mi-M(56Ni)
relation
13 15 20 25 30 35 M?
Flat 56Ni gt 0.05 M?
Trend 56Ni gt 0.150.100.075-0.070.050.05 M?
The only elements that vary between case Flat
and case Trend are Fe and Ni and, at a smaller
extent also Ti, Co and Zn (i.e. elements
produced in the deep layers of the exploding
mantle)
The majority of the elements have PFs compatible
with that of O ? show a scaled solar distribution
54
The Final Fate of a Massive Star with mass loss
11 -120 M?
Limongi Chieffi, 2007
55
Individual Yields
Different chemical composition of the ejecta for
different masses
56
Averaged Yields
Yields averaged over a Salpeter IMF
Global Properties
Initial Composition (Mass Fraction)
Final Composition (Mass Fraction)
Mrem0.186
X0.695 Y0.285 Z0.020
X0.444 (f0.64) Y0.420 (f1.47) Z0.136
(f6.84)
57
Observed MPro smaller than LC models predict
Li et al. Smartt et al. van Dyk et al.
58
Initial Mass Function
mu 100 M? ml 0.1 M?
mrem ? Stellar evolution
IMF Present Day MF for massive stars
IMF ...universal?
59
Definitions
AMU (atomic mass unit, mu) ? 1/12 mass of
12C muc2
931.478 MeV Cross section Probability per pair
of particles of occurrences of a reaction
? ? cm2
???? ? cm3 /s