Metallicity-Dependent Isotopic Abundances and the Impact of Helium Rate Uncertainties in

216 Pages·2013·28.81 MB·English

Metallicity-Dependent Isotopic Abundances and the
Impact of Helium Rate Uncertainties in Massive Stars
A DISSERTATION
SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL
OF THE UNIVERSITY OF MINNESOTA
BY
Christopher West
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
Doctor of Philosophy
Alexander Heger
December, 2013
(cid:13)c Christopher West 2013
ALL RIGHTS RESERVED
Acknowledgements
I would like to first thank my adviser, Alexander Heger, for all his help and guidance
over these several years. I must express my appreciation to Yong-Zhong Qian for his
support, very useful discussions, and advice. I thank also all my other teachers who
contributed to my learning, within the classroom and without. They made this journey
possible, and revealed the true rewards along the way.
I am very grateful to my mother and fathers, who inspired in me a passion and drive
for learning. They have always supported my academic efforts, carrying my courage for
me in times of doubt, and being there in times of need.
Ithankmysister,Genevi`eveWest,forkeepingmehumble. Ithankmybrother,Louis
Teerlinck, for keeping me honest. Both of whom also provided the valuable service of
holding me intellectually accountable.
I thank Catherine Katt for helping me discover this journey, and sharing with me
the life of the spirit. I thank Kathy and LuLu Manus, for encouraging me to reach for
the stars, in many different ways, throughout my entire life.
A special thanks to Vince Froehlich for freely sharing the language of the heart, for
walking the path at eye level, and for other things left unstated.
Finally, I thank with all my heart, my sweet Jellybean. Her patience and sacrifice
through this process were so lovingly given. She is my inspiration, and always reminds
me to see also the Sun, when studying the stars.
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Dedication
To those who anonymously serve. May we all forever meet on the Broad Highway.
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Abstract
All stellar evolution models for nucleosynthesis require an initial isotopic abundance
set to use as a starting point, because nuclear reactions occur between isotopes. Gen-
erally, our knowledge of isotopic abundances of stars is fairly incomplete except for the
Solar System. We develop a first model for a complete average isotopic decomposition
as a function of metallicity. Our model is based on the underlying nuclear astrophysics
processes, and is fitted to observational data, rather than traditional forward galactic
chemical evolution modeling which integrates stellar yields beginning from big bang
nucleosynthesis. We first decompose the isotopic solar abundance pattern into contri-
butions from astrophysical sources. Each contribution is then assumed to scale as a
function of metallicity. The resulting total isotopic abundances are summed into ele-
mental abundances and fitted to available halo and disk stellar data to constrain the
model’s free parameter values. This procedure allows us to use available elemental ob-
servational data to reconstruct and constrain both the much needed complete isotopic
evolutionthatisnotaccessibletocurrentobservations,andtheunderlyingastrophysical
processes. Our model finds a best fit for Type Ia supernovae contributing (cid:39) 0.7 to the
solar Fe abundance, and Type Ia onset occurring at [Fe/H] (cid:39) −1.2, in agreement with
typical values. The completed model can be used in future nucleosynthesis studies.
We also perform a preliminary analysis to assess the impact of our isotopic scaling
model on the resulting nucleosynthesis of massive stars, compared to a linear inter-
polation method. Using these two input methods we compute a limited grid of stellar
models,andcomparethefinalnucleosynthesistoobservations. Thecompactnessparam-
eter was first used to assess which models would likely explode as successful supernovae,
and contribute explosive nucleosynthesis yields. We find a better agreement to solar
observations using the scaling model compared to the linear interpolation method, for
the six s-only isotopes along the weak s-process path.
As a second project, we study the sensitivity of presupernova evolution and super-
nova nucleosynthesis yields of massive stars to variations of the helium-burning reaction
rates within the range of their uncertainties. The current solar abundances from Lod-
ders (2010) are used for the initial stellar composition. We compute a grid of 12 initial
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stellar masses and 176 models per stellar mass to explore the effects of independently
varying the 12C(α,γ)16O and 3α reaction rates, denoted R and R , respectively.
α,12 3α
The production factors of both the intermediate-mass elements (A = 16−40) and the
s-only isotopes along the weak s-process path (70Ge, 76Se, 80Kr, 82Kr, 86Sr, and 87Sr)
were found to be in reasonable agreement with predictions for variations of R and
3α
R of ±25%; the s-only isotopes, however, tend to favor higher values of R than
α,12 3α
the intermediate-mass isotopes. The experimental uncertainty (one standard deviation)
in R (R ) is approximately ±10%(±25%). The results show that a more accurate
3α α,12
measurementofoneoftheserateswoulddecreasetheuncertaintyintheotherasinferred
from the present calculations. We also observe sharp changes in production factors and
standard deviations for small changes in the reaction rates, due to differences in the
convection structure of the star. The compactness parameter was used to assess which
models would likely explode as successful supernovae, and hence contribute explosive
nucleosynthesisyields. Wealsoprovidetheapproximateremnantmassesforeachmodel
and the carbon mass fractions at the end of core-helium burning as a key parameter for
later evolution stages.
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Contents
Acknowledgements i
Dedication ii
Abstract iii
List of Tables ix
List of Figures x
1 Stellar Evolution 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Stellar Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1 Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Stellar Evolution by Mass . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Stellar Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.1 The Basic Equations . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Convection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.3 Explosion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Nucleosynthesis 17
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Big-Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3 General Classification of Processes . . . . . . . . . . . . . . . . . . . . . 19
v
2.4 Light Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.1 Helium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.2 ν-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4.3 Galactic Cosmic Ray Spallation . . . . . . . . . . . . . . . . . . . 21
2.4.4 Classical Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.5 Low and Intermediate-Mass Star Contributions . . . . . . . . . . . . . . 22
2.6 Intermediate-Mass and Iron Group Isotopes . . . . . . . . . . . . . . . . 22
2.6.1 Hydrostatic Burning . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.6.2 Core Collapse Supernovae . . . . . . . . . . . . . . . . . . . . . . 26
2.6.3 Pair-Instability Supernovae . . . . . . . . . . . . . . . . . . . . . 26
2.6.4 Type Ia Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.7 Heavy Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7.1 The Main s-Process . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.7.2 The Weak s-Process . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7.3 The Strong s-Process . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7.4 Lighter Element Primary Process . . . . . . . . . . . . . . . . . . 33
2.7.5 The r-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7.6 The i-Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.7.7 p-Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.8 Galactic Chemical Evolution . . . . . . . . . . . . . . . . . . . . . . . . 38
3 Isotopic Scaling Model 41
3.1 Introduction and Motivation. . . . . . . . . . . . . . . . . . . . . . . . . 41
3.2 Solar Abundance Decomposition . . . . . . . . . . . . . . . . . . . . . . 46
3.2.1 Big-Bang Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . 46
3.2.2 Light Isotopes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2.3 Low and Intermediate-Mass Stars. . . . . . . . . . . . . . . . . . 48
3.2.4 Intermediate-Mass and Iron Group Isotopes . . . . . . . . . . . . 48
3.2.5 Heavy Isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.3.1 Massive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.3.2 Type Ia Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . 61
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3.3.3 Neutron Capture and p-Isotopes . . . . . . . . . . . . . . . . . . 63
3.3.4 Hydrogen Burning, Classical Novae, ν-Process, and Galactic Cos-
mic Ray Spallation . . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.4 Fitting Scaling Model to Observational Data . . . . . . . . . . . . . . . 65
3.4.1 SNe Type Ia Parameters . . . . . . . . . . . . . . . . . . . . . . . 66
3.4.2 r-Process and hs Parameters . . . . . . . . . . . . . . . . . . . . 68
3.4.3 Weak s-Process and ls Parameter. . . . . . . . . . . . . . . . . . 70
3.4.4 “Strong” s-Process Parameter. . . . . . . . . . . . . . . . . . . . 71
3.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4 The Impact of Helium-Burning Reaction Rates on Massive Star Evo-
lution and Nucleosynthesis 84
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.2 Stellar Models and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 86
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.3.1 Comparison of 12C(α,γ) 16O and 3α Reaction Rates . . . . . . . 89
4.3.2 Intermediate-Mass Isotopes . . . . . . . . . . . . . . . . . . . . . 90
4.3.3 Implications for Stellar Remnants . . . . . . . . . . . . . . . . . 98
4.3.4 Variations in Carbon Mass Fractions and Remnant Mass . . . . 107
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5 Dependence of Stellar Nucleosynthesis on Initial Composition 112
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2.1 Initial Compositions . . . . . . . . . . . . . . . . . . . . . . . . . 114
5.2.2 Stellar Models and Numerical Methods . . . . . . . . . . . . . . 115
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.3.1 Iron Production and Neutron-to-Seed Ratio . . . . . . . . . . . . 116
5.3.2 Weak s-Process Production . . . . . . . . . . . . . . . . . . . . . 118
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
6 Summary 122
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Bibliography 126
Appendix A. Fitting Algorithm 151
Appendix B. Tables 155
Appendix C. Solar Abundance Decomposition 173
Appendix D. Initial Composition Plots 183
Appendix E. Helium Reaction Rate Plots 197
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