Synthesis of the elements in stars: forty years of progress
George Wallerstein
Department of Astronomy, University of Washington, Seattle, Washington 98195
Icko Iben, Jr.
University of Illinois, 1002 West Green Street, Urbana, Illinois 61801
Peter Parker
Yale University, New Haven, Connecticut 06520-8124
Ann Merchant Boesgaard
Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, Hawaii 96822
Gerald M. Hale
Los Alamos National Laboratory, Los Alamos, New Mexico 87544
Arthur E. Champagne
University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27594
and Triangle Universities Nuclear Laboratory, Duke University, Durham, North Carolina
27706
Charles A. Barnes
California Institute of Technology, Pasadena, California 91125
Franz Ka
¨
ppeler
Forschungzentrum, Karlsruhe, D-76021, Germany
Verne V. Smith
University of Texas at El Paso, El Paso, Texas 79968-0515
Robert D. Hoffman
Steward Observatory, University of Arizona, Tucson, Arizona 85721
Frank X. Timmes
University of California at Santa Cruz, California 95064
Chris Sneden
University of Texas, Austin, Texas 78712
Richard N. Boyd
Ohio State University, Columbus, Ohio 43210
Bradley S. Meyer
Clemson University, Clemson, South Carolina 29630
David L. Lambert
University of Texas, Austin, Texas 78712
(Received 25 June 1997)
Forty years ago Burbidge, Burbidge, Fowler, and Hoyle combined what we would now call
fragmentary evidence from nuclear physics, stellar evolution and the abundances of elements and
isotopes in the solar system as well as a few stars into a synthesis of remarkable ingenuity. Their
review provided a foundation for forty years of research in all of the aspects of low energy nuclear
experiments and theory, stellar modeling over a wide range of mass and composition, and abundance
studies of many hundreds of stars, many of which have shown distinct evidence of the processes
suggested by B
2
FH. In this review we summarize progress in each of these fields with emphasis on the
most recent developments. [S0034-6861(97)00204-3]
995
Reviews of Modern Physics, Vol. 69, No. 4, October 1997 0034-6861/97/69(4)/995(90)/$23.50 © 1997 The American Physical Society
CONTENTS
I. Preface by E. Margaret Burbidge, Geoffrey R.
Burbidge, and Fred Hoyle 997
II. Introduction by George Wallerstein 998
A. The cosmological foundations of B
2
FH 998
B. The astronomical background in 1957 998
C. The eight processes 998
1. Hydrogen burning 998
2. Helium burning 999
3. The
a
process 999
4. The e process 999
5. The s process 999
6. The r process 999
7. The p process 999
8. The x process 999
D. Neutrino astrophysics 1000
1. The solar neutrino problem 1000
2. Other aspects of neutrino astrophysics 1000
E. Related reviews 1001
III. Stellar Evolution by Icko Iben, Jr. 1001
A. Historical preliminary 1001
B. Evolution of single stars that become white
dwarfs 1001
1. Overview 1001
2. Nucleosynthesis and dredge-up prior to the
AGB phase 1003
3. Nucleosynthesis and dredge-up during the
AGB phase 1004
4. The born-again AGB phenomenon 1006
5. Other mixing processes, and wind mass loss,
which affect surface composition 1007
C. Evolution of massive single stars that produce
neutron stars or black holes 1007
D. Close binary star evolution 1009
1. Modes of mass transfer and of orbital angular
momentum loss 1009
2. Scenario modeling 1009
a. Cataclysmic variables and novae 1010
b. White dwarf mergers: R CrB stars and
type Ia supernovae 1010
c. X ray binaries and pulsars 1012
IV. Hydrogen Burning in the pp Chain and CN Cycle
by Peter Parker 1013
A. The p(p,e
1
n
e
)d reaction 1013
B. The
3
He(
3
He,2p)
4
He reaction 1013
C. The
3
He(
a
,
g
)
7
Be reaction 1014
D. The
7
Be(p,
g
)
8
B reaction 1015
E. The
7
Li(n,
g
)
8
Li reaction 1015
F. The
14
N(p,
g
)
15
O reaction 1015
G. The
17
O(p,
a
)
14
N reaction 1016
H. The Hot CNO cycle 1016
V. The x Process by Ann Merchant Boesgaard 1016
A. Introduction and retrospective 1016
B. Abundances 1016
1. Lithium 1017
2. Beryllium 1018
3. Boron 1018
C. Nonlocal thermodynamic-equilibrium effects 1019
D. Production mechanisms 1019
1. Big Bang 1019
2. Spallation 1019
3. Asymptotic giant branch stars 1019
4. Supernovae 1020
VI. Helium Burning by Gerald M. Hale 1020
A. Triple-
a
capture 1020
B.
a
1
12
C capture 1021
1. E1 capture 1021
a. Direct measurements 1021
b.
b
-delayed
a
spectrum from the decay of
16
N 1022
2. E2 capture 1022
3. Other analyses and recommended values 1023
VII. H Burning in the NeSi Region: Laboratory Studies
by Arthur E. Champagne 1024
A. Introduction 1024
B. Experimental approaches 1024
C. The neon-sodium cycle at low temperatures 1025
1. Reaction rates 1025
2. Network calculations 1026
D. The magnesium-aluminum cycle at low
temperatures 1027
1. Reaction rates 1027
2. Network calculations 1028
E. High-temperature behavior 1029
1. Reaction rates 1029
2. Network calculations 1029
F. Conclusion 1030
VIII. Observational Evidence of Hydrogen Burning by
George Wallerstein 1030
A. CN cycle and mixing 1031
B. O depletion and the enhancement of Na and Al 1032
C. Origin of the Na and Al enhancements 1033
IX. Carbon, Neon, Oxygen, and Silicon Burning by
Charles A. Barnes 1034
A. Introduction 1034
B. Carbon burning 1035
C. Neon burning 1036
D. Oxygen burning 1036
E. Silicon burning 1036
X. s Process: Laboratory Studies and Stellar Models by
Franz Ka
¨
ppeler 1038
A. The s process since B
2
FH 1038
B. Laboratory experiments 1038
1. Neutron capture cross sections 1038
2. Stellar
b
decay 1039
C. The canonical s process 1040
1. The
s
N curve 1040
2. Branchings 1041
XI. Observations of the s Process by Verne V. Smith 1042
A. Brief history 1042
B. Observations of nucleosynthesis and mixing in
CH, Ba, S, and C stars 1043
C. The s process as a function of metallicity 1043
D. Rubidium and the s-process neutron density 1045
E. Recent models: Radiative burning of
13
C during
the AGB interpulse phase 1046
XII. The r Process by Robert D. Hoffman and Frank X.
Timmes 1047
A. Introduction 1047
B. A search for the astrophysical site 1047
C. Early model results, from conflict to clarity 1048
D. Twisting in the wind 1049
E. Concluding remarks 1049
XIII. Observations of the r Process by Chris Sneden 1050
A. Defining the r-process elements 1050
B. Early r-process discoveries 1051
C. Recent r-process surveys 1051
D. Thorium and the age of the halo and disk 1053
E. Filling out the picture 1054
XIV. The p Process by Richard N. Boyd 1054
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: Synthesis of the elements
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A. The p process 1054
B. Early p-process models 1055
C. The
g
process 1055
D. The rp process 1057
E. The
n
process 1058
F. Recent developments 1058
G. Summary 1059
XV. The e Process and the Iron-Group Nuclei by
Bradley S. Meyer 1059
A. Energetics and equilibria 1059
B. Statistical equilibrium 1060
C. A brief history of the ideas of iron-group
element synthesis 1063
D. Significance for astrophysics 1065
XVI. Carbon Stars: Where Theory Meets Observations
by David L. Lambert 1066
A. Prologue 1066
B. Carbon stars—An observer’s view 1066
1. What is a carbon-rich star? 1066
2. What makes a carbon-rich star? 1067
3. The principal types of carbon-rich stars 1068
a. R-type carbon stars 1068
b. N-type carbon stars 1069
c. Barium and related stars 1070
C. Epilogue 1071
XVII. Conclusions 1071
Acknowledgments 1072
References 1072
I. PREFACE
It is curious that both the primordial and stellar theo-
ries of the origin of the elements should have been pub-
lished in the same year, 1946. Little notice was at first
taken of the stellar theory, attention being directed at
first overwhelmingly to Gamow’s suggestion of associat-
ing nucleosynthesis with the origin of the Universe.
While it is true that the one theory had to do with
cosmology, the other did not. The suggestion that stellar
nucleosynthesis had a connection to cosmology was an
invention of Robert Oppenheimer and it never had any
reality to it, since the first paper on stellar nucleosynthe-
sis appeared in 1946, two years before the steady-state
cosmological model was published. Nor were the objec-
tions to primordial synthesis by neutron addition by any
means confined to the well-known gaps at A5 5 and
A5 8, as is sometimes stated. There was always the
pragmatic objection that the elements were distributed
with too much spatial irregularity to be attributed to a
universal origin. And the well-known iron peak was an
obvious feature of solar system abundances, implying
that at least in some places matter had been able to
approach its most stable form.
For matter to approach its most stable form, tempera-
tures in stellar interiors would be needed of the order of
a hundred times those in main-sequence stars, a require-
ment that it would have been difficult to accept if the
beginnings of an understanding of supernovae had not
emerged in the early 1940s. In a rough kind of way it was
possible to compare supernovae with ordinary stars in
the same way that, in the mid 1940s, people were com-
paring nuclear weapons with chemical ones, this suggest-
ing that temperatures vastly higher than those that
seemed plausible in Eddington’s day might be possible.
The fact that primordial nucleosynthesis ran far ahead
of stellar nucleosynthesis in the years up to the early
1950s turned out to be advantageous to the eventual
emergence of the B
2
FH paper in 1957, because it per-
mitted facts to accumulate quietly without any frenzied
circus developing. In 1952, Salpeter discussed the stellar
formation of carbon from alpha particles, and a few
months later the relation of carbon synthesis to oxygen
synthesis was shown to require a state in the carbon
nucleus of about 7.65 MeV above ground level. When
this state was actually found, the laboratory discovery
carried a strong measure of conviction for all those who
were involved in it.
At the same time surveys of nearby stars by several
groups, including some of us, were showing variations of
metal abundances to hydrogen, the beginning of the
concept of metallicity, that seemed impossible to associ-
ate with some form of universal synthesis. We were also
puzzled by our 1953–54 analysis of high-dispersion spec-
tra obtained at McDonald Observatory, which showed
strange overabundances of some heavy elements and
seemed to indicate that neutrons were involved. And in
1953–54, carbon-burning and oxygen-burning were
found.
It was in the autumn of 1954 that the team of B
2
FH
came together in the quiet ambience of Cambridge, En-
gland, without, as mentioned above, any frenzied circus
developing.
During 1954–55 calculations involving neutron pro-
duction in the interiors of evolved stars with helium-
burning cores surrounded by a hydrogen-burning shell
were followed by calculations on neutron addition to
elements from neon to scandium. The process of neu-
tron addition was slow enough for each neutron capture
to be followed by beta decay (the origin of what we later
named the s process). In the same period, we became
aware that A.G.W. Cameron was working along similar
lines in Canada. These calculations showed the possibil-
ity of explaining the characteristic odd-even effect in
abundance ratios.
In the autumn of 1955 we all moved, or returned, to
Pasadena, where there was still a relatively peaceful set-
ting at both the Kellogg Radiation Laboratory at
Caltech and the Mount Wilson and Palomar offices at
813 Santa Barbara Street. We now also had the great
advantage of being at the home of the large telescopes.
In 1952 the process of neutron liberation and capture
had been clinched by Paul Merrill’s discovery of the un-
stable element technetium in S stars (evolved red gi-
ants), and we were able to obtain spectra with the
Mount Wilson 100-inch telescope of an evolved star of
the class known as ‘‘Barium II stars,’’ in which we deter-
mined the overabundances of just those heavy elements
that had at least one isotope with a magic neutron num-
ber.
One could not be in the same town as Walter Baade
without hearing a lot about his famous light curve of the
supernova in the galaxy IC 4182. With the interest of all
997
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et al.
: Synthesis of the elements
Rev. Mod. Phys., Vol. 69, No. 4, October 1997
four of us in supernovae as the spectacular death throes
of stars at the end of their active evolution and thermo-
nuclear energy production, we latched onto this. The
exponential decay of the energy output of this super-
nova immediately suggested radioactive decay, follow-
ing collapse, the release of a great burst of energy, neu-
trons, and neutrinos, and the formation of heavy
unstable nuclei.
Also in 1956, an improved solar-system abundance
curve became available from Suess and Urey. Values in
the upper half of the chart of the nuclides showed two
things: the association of magic neutron numbers with
abundance peaks, and a separation of peaks correspond-
ing to both slow and rapid neutron addition, the latter
being fast enough not to allow time for the beta-decay
involved in slow neutron addition. And released at that
time were hitherto classified data on (n,
g
) cross sections
for individual isotopes of elements, without which a
meaningful analysis of what in B
2
FH was called the s
process would not have been possible.
B
2
FH can be seen in retrospect to have been a highly
creative review article, putting together what the four
authors had done previously, together with the facts on
which the theory would now be based with considerable
confidence. We each brought ideas and data from very
different parts of physics to the table, and occasionally
we stopped arguing long enough to work things out and
write them down. There were a number of original con-
tributions, notably the calculations for the s and r pro-
cesses. The rest consisted of an extensive updating of
previous work. But one should not forget the introduc-
tion of a lettering notation for the various nuclear pro-
cesses:
a
, e, s, r, p, and x, which may have done
more for the development of the subject than almost
anything else!
II. INTRODUCTION
As of 1957 enough evidence had been assembled for a
review of what was known about nucleosynthesis in
stars. The data (which would now be called fragmentary,
though it then appeared to be spectacular) allowed Bur-
bridge, Burbridge, Fowler, and Hoyle, B
2
FH,
1
to com-
bine progress in stellar and solar system abundances
with laboratory nuclear physics data and stellar evolu-
tion calculations to show how stars can produce ele-
ments and their isotopes from helium to uranium. Their
paper provided a basis for nuclear astrophysics for the
decades that followed. How well did they do? In this
review we will first outline the basic processes that they
suggested to be the sources of elements heavier than
hydrogen and evaluate progress in confirming and ex-
tending their suggestion.
A. The cosmological foundations of B
2
FH
In 1957 there were two basic cosmological models,
though neither was sufficiently developed to deserve the
term ‘‘theory.’’ These were, of course, Big Bang and
steady state. The Big Bang obviously explained the ex-
pansion of the Universe but failed to predict the origin
of the elements beyond the lightest species. Steady state
provided for an understanding of the discrepancy be-
tween the expansion age and the apparent ages of the
globular clusters—a problem that is still with us—but
provided no physical basis for the continuous creation of
matter, the expansion, or the collection of diffusely cre-
ated matter into galaxies.
One of the strengths of the B
2
FH paper was its inde-
pendence of the cosmological models then under discus-
sion. The paper explained just how much stars could
contribute to the synthesis of nuclei heavier than hydro-
gen. Since they did not have the answers for D, Li, Be,
and B they relegated them to the ‘‘x process.’’ Almost
all other elements and isotopes could be produced in the
stellar environment by one of their eight processes (with
their ‘‘x process’’ included as number eight).
B. The astronomical background in 1957
Starting in the late 1940s and early 1950s astronomers
were assembling data to show that all stars did not have
the same chemical composition. For 80 years it had been
known that some red giants, referred to as carbon stars,
showed molecular bands of carbon molecules in their
spectra while the vast majority of cool stars showed ox-
ide bands. Due to blending of absorption lines and mo-
lecular bands a quantiative comparison of carbon and
oxygen red giants was not possible. More recently the
subdwarfs had been found to be metal-poor by factors
more than 10 (Chamberlain and Aller, 1951), and the
heavy element stars such as the Ba II stars and S stars
were known to show abundance excesses of certain spe-
cies by factors near 10 (Burbidge and Burbidge 1957).
Of great importance was the discovery of Tc in S stars
(Merrill, 1952) since the longest lived isotope of Tc has a
half-life of 43 10
6
years and Cameron (1955) had shown
that
99
Tc, with a half-life of only 33 10
5
years was the
most easily produced isotope. This proved beyond any
doubt that nucleosynthesis took place within stars and
that the products could reach the stellar surface, with
the help of mass loss and mixing.
C. The eight processes
In order to produce (almost) all known nuclear spe-
cies in stars B
2
FH suggested eight separate processes.
1. Hydrogen burning
Following the fundamental papers by Bethe and
Critchfield (1938) and Bethe (1939), B
2
FH described
the laboratory experiments and the derived reaction
rates of the various proton captures of the pp chain and
the CNO cycle. The details of the rates of the individual
reactions in the pp chain determine the energy spectrum
1
This was probably the first astronomical paper to be referred
to by the initials of its authors.
998
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: Synthesis of the elements
Rev. Mod. Phys., Vol. 69, No. 4, October 1997
of the resulting neutrinos, which is crucial in attempts to
understand the solar neutrino problem. In addition they
discussed the p capture by the neon isotopes to produce
23
Na (also mentioned in Bethe’s 1939 paper). In Secs.
IV and VII, Parker and Champagne bring us up to date
on the laboratory rates of hydrogen burning reactions
from the pp reaction through the CNO cycle, the NeNa
cycle and the MgAl cycle. In addition the hot CNO cycle
plays an important role in nova explosions, while the rp
process discussed by Boyd in Sec. XIII may be respon-
sible for the production of certain p-rich isotopes.
2. Helium burning
By the time of B
2
FH helium burning to produce
12
C
had been suggested by O
¨
pik (1951) and its rate esti-
mated by Salpeter (1952). In Sec. VI. G. Hale describes
the present state of the experiments that located and
measured the width of the vital 7.65 MeV level in
12
C
(predicted by Hoyle) and the complicated combination
of experiment and theory that is necessary to estimate
the rate of the
12
C(
a
,
g
)
16
O reaction. The rate of the
12
C(
a
,
g
)
16
O reaction relative to the 3-
a
process deter-
mines the carbon/oxygen ratio in massive stars, and this
is crucial for the later evolution of such a star and its
resulting nucleosynthesis. Unfortunately, 40 years after
B
2
FH, the rate of the
12
C(
a
,
g
)
16
O reaction is still not
well determined. Fortunately the material that is re-
turned to the interstellar medium by stars that are less
massive than 11M
(
and evolve into white drawfs has
been enriched by matter that has experienced only par-
tial helium burning, so the uncertainty in the ratio of
reaction rates plays a minor role.
3. The
a
process
B
2
FH suggested that further
a
captures could extend
nucleosynthesis beyond
16
Oto
20
Ne,
24
Mg, etc., up to
the very stable, doubly magic nucleus,
40
Ca. However,
after experiments showed that the
16
O(
a
,
g
)
20
Ne rate is
very slow in stellar interiors, it became evident that car-
bon and oxygen burning are responsible for the origin of
species from Ne to S, with the nuclei consisting of inte-
gral numbers of
a
particles dominating the abundance
curve in this region.
4. The
e
process
At very high temperatures, about 4 or 5310
9
K, so
many reactions take place that the nuclei settle down to
statistical equilibrium dominated by the most tightly
bound nuclei around
56
Fe. Such conditions are reached
only in supernovae. The observation of
g
rays from
SN1987A due to the deexcitation of
56
Fe, resulting from
the
b
decay of
56
Ni, has demonstrated the importance of
the production of iron-peak species in supernova explo-
sions. Modern calculations of the iron-peak abundances
are discussed by Meyer in Sec. XV.
5. The
s
process
Beyond the iron-peak, utilizing neutrons produced by
reactions such as
13
C(
a
,n)
16
O and
22
Ne(
a
,n)
25
Mg, nu-
clei can be produced along or adjacent to the valley of
stability via a process in which sequential neutron cap-
tures take place on a time scale that is slow compared to
the beta-decay lifetime of these nuclei. This process can
continue all the way up to lead and bismuth; beyond
bismuth the resulting nuclei alpha decay back to Pb and
Tl isotopes. In Secs. X and XI Ka
¨
ppeler and Smith bring
us up to date on laboratory measurements, stellar mod-
els (also discussed in Sec. III by Iben), and abundance
studies of the s-process elements.
6. The
r
process
B
2
FH showed that, in addition to the s process, there
must be another neutron capture process in which the
sequential neutron captures take place on a time scale
which is much more rapid than the beta decay of the
resulting nuclei. This process produces the much more
neutron-rich progenitors that are required to account for
the second set of abundance peaks that are observed
about 10 mass units above the s-process abundance
peaks corresponding to the neutron magic numbers,
N5 50 and 82. Historically, the r process has been asso-
ciated with SN explosions, and in the past decade inter-
est has focused more specifically on the neutrino-heated
atmosphere surrounding the newly formed neutron star
as the r-process site. In Sec. XII Hoffman and Timmes
review both the physics and astrophysical scenario of
rapid neutron capture during the explosion of massive
supernovae.
7. The
p
process
There are some relatively rare proton-rich nuclei such
as
92
Mo that are impossible to produce by n capture
alone. They may be produced by p capture at high
enough temperatures to overcome the huge coulomb
barrier or by (
g
,n) reactions during supernova explo-
sions. Recent work on (p,
g
) and (
g
,n) reactions includ-
ing the rp process are reviewed by Boyd in Sec. XIV.
8. The
x
process
None of the above processes can produce D, Li, Be,
or B, all of which are burned by p capture at low tem-
peratures in stars but hardly ever (except for
7
Li) pro-
duced in stars. B
2
FH did not know how they were pro-
duced so they ascribed their synthesis to the x process.
Modern cosmological models of big bang nucleosynthe-
sis are tuned to produce D,
3
He,
4
He, and some
7
Li to
fit observations of these species in very metal-poor stars
and other astrophysical sources. The observations and
theories of production of
7
Li, Be, and B in stars are
reviewed by Boesgaard in Sec. V. For a brief review of
the production of D,
3
He,
4
He, and
7
Li in the early
universe with further references see Olive and Schramm
(1996).
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: Synthesis of the elements
Rev. Mod. Phys., Vol. 69, No. 4, October 1997
![FIG. 21. Mean relative abundance ratios of ‘‘light’’ s-process elements Sr, Y, and Zr (top panel), ‘‘heavy’’ s-process elements Ba, La, and Ce (middle panel), and r-process elements Sm, Eu, and Dy (bottom panel), as functions of stellar metallicity [Fe/H]. The relative abundances are defined as @A/B#[log10(NA /NB)star – log 10(NA /NB)( for elements A and B . In each panel the dotted horizontal lines represent the solar abundance ratios of these elements: filled circles, McWilliam et al. (1995); open circles, Gilroy et al. (1988); open squares, Ryan et al. (1996); plus signs, Ryan et al. (1992); filled circles, Gratton and Sneden (1994); filled triangles, Magain (1989), Zhao and Magain (1990, 1991); crosses, Edvardsson et al. (1993) in the top and middle panels, Woolf et al. (1995) in the lower panel.](/figures/fig-21-mean-relative-abundance-ratios-of-light-s-process-289gu39q.webp)
