...it dawned on me that if the impulse of a theory is very
strong, you need to have what I later call a 'don't worry hypothesis'.
In order to do this you have to have a hypothesis that will allow
you not of course to ignore facts, but to deal with what seem
to be difficulties later, rather than rejecting the hypothesis
out of hand as being impossible. ...you just say,' Well look, don't
worry about this. It will be resolved later. It's done with no
hands! How else would you expect it to be done.'
--------Sidney Brenner [My Life in Science].
Efforts to explain the origin of the elements prior to the 1950's
were strongly influenced by the notion of ``cosmical abundances.''
Astronomer's views of the origin of the elements is one of pendulum
swings.
Early in the 20
century, astronomers thought the stars had
very different chemical compositions. They thought, for example, that
the sun was made nearly entirely of iron. Sirius, the brightest star
in the sky, was mostly hydrogen. These ideas came directly from
spectroscopy, and the identification of absorption lines in stellar
spectra. Examples are shown in figure 5.1. We can see
that the star like Sirius (left) has strong hydrogen lines,
and the lines of other elements
are very weak. The solar-like star on the other hand, has a
spectrum dominated by iron lines.
Figure 5.1:
Spectra of Two Stars. The star on the left is like Sirius,
and has only a few strong lines, all of hydrogen.
Iron lines dominate the other spectrum, which resembles the sun.
The closer one looks, the more
iron lines one finds. It is no wonder early astronomers thought the
sun might be made mostly of glowing iron.
In the modern jargon of computing, people speak of WYSIWUG (pronounced
wiz-ee-wug), for ``what-you-see-is-what-you-get.'' In nature, your
eyes often fool you, and what you see distorts what is true. This turned
out to be the case with stellar abundances. The critical work was done
by an Indian astronomer M. N. Saha (1893-1956) whose important work is
not widely known. Every astronomer knows of him, however, because one of
the basic equations of astrophysics bears his name. The Saha equation
was published in 1920.
Saha showed how atoms can become ionized in a gas as the temperature
increases. We can show this for iron (Fe), by a chemical equation:
This shows that an iron atom can lose an electron and become an iron
ion--it becomes ionized. A free electron (
) is released.
The double headed arrow shows that the ``reaction'' can also go from right
to left, and an electron can combine with an ion to form a neutral iron
atom. In stars, there is an ionization equilibrium, and the number
of atoms of iron that are ionized per second is the same as the number
that recombine.
In the sun, the temperature is so high that almost all of the molecules
are dissociated. What we see is a glowing a gas of free atoms, ions,
and electrons. There is an equilibrium between Fe and Fe
, but with
enough neutral iron (Fe) to strongly absorb its characteristic
spectrum.
If the temperature
gets hot enough, the equilibrium shifts to the point where there are
practically no neutrals left, and iron is even beginning to lose
a second electron (
).
This is the situation that has occurred in the atmosphere of the
bright star Sirius.
Now it turns out that an ion has a completely different
spectrum from that of the corresponding neutral atom. The strongest
lines from Fe are in the ultraviolet, and not in the region
of the spectrum illustrated in figure 5.1. So the
neutral iron lines are almost entirely gone from the spectrum of Sirius.
If you
allow for ionization, there is about as much iron in the atmosphere
of Sirius as in the sun. To get this equality, you have to sum
the neutral atoms of iron and the ions. Saha's work explained how
this all happens.
The hydrogen lines are present in the solar spectrum, but
are relatively weak. They dominate the spectrum of Sirius. This time
the explanation is not one of ionization but merely excitation.
A spectral line is formed when the electrons in an atom jump from
one level of energy to another. These energy levels are characteristic
of each element, ion, and molecule.
In the case of hydrogen all of the jumps out of its lowest level
can only be made by relatively energetic photons--ones that occur in
the ultraviolet. The earth's atmosphere absorbs this part of the spectrum
and makes it unavailable to earthbound astronomers.
Lines from the ground level of hydrogen were only seen
by astronomers after the beginning of the space age.
Figure 5.2:
Energy Levels and Spectra of Hydrogen. The arrows indicate
quantum jumps made in the hydrogen atom as a result of absorbing
photons. All of the jumps out of the ground level require photons
in the ultraviolet. The jumps that cause absorption lines that can
be seen in figure 5.1.
Note how high the n=2 level is in energy.
The surface temperature of the sun is about 5800K, while that of
Sirius is 10000K. So it is not until the higher temperature
of the atmosphere
of Sirius that enough hydrogen atoms are in the 
level
to cause the strong absorption lines seen in the spectrum.
Following Saha's work in 1920, astronomers analyzed the atmospheres
of many stars, and reached the conclusion that all of them had just about
the same abundances.
There were a few stars whose atmospheres were clearly not
the same in composition as the majority. These were set aside, perhaps as
``exceptions that proved the rule,'' and astronomers and geochemists
began to speak of universal, or ``cosmical'' abundances.
Cosmical Nucleosynthesis-History
If the abundances of the elements were more or less universal, it
was entirely reasonable to imagine that they had all been created in one
major event, perhaps at the beginning of the history of the universe.
It was well known by the 1930's that the most distant galaxies are moving
away from us. It is a small mental jump from there to imagine that
at some time in the past, matter was highly compacted in some primeval
fireball. A Belgian Jesuit Georges Lemaitre (1894-1966) wrote a book
about this called The Primeval Atom.
Some of the best minds in physics have tried their hands at
a theory that would
account for the origin of the chemical elements by some cosmic event.
The most colorful of these was George Gamow (1904-1968).
Gamow was born in Russia, but came to the US in the 1930's. He was
one of the glorious ones of physics, and was at Göttingen
in 1928 along with the founders of quantum mechanics and Maria
Mayer.
Gamow's delight at doing physics is reflected in many popular books.
Three that I enjoyed as an undergraduate in the 1950's were
Birth and Death of the Sun (1940), Biography of the Earth (1946),
and One, Two, Three, ... Infinity (1948).
The illustrations in these books were informative,
and often very funny. While
many fine popularizations of science have been written, no one has surpassed
Gamow for insight and pure fun.
Gamow tried very hard to make the chemical elements in the early
universe. However, there was a formidable difficulty that neither he
nor anyone else has been able to get around. There is no stable nucleus
at either masses 5 or 8. This means that any process that starts with
either protons or neutrons must somehow jump over those gaps. It is not
so hard to imagine that the very light nuclei might be built up. Indeed,
we now think most of the helium and deuterium in the universe was synthesized
shortly after the big bang. But stars can do something the big bang
can't, and that is make carbon out of helium.
We shall see later that important nucleosynthesis does take place
in the very early history of the universe. Mostly helium and a few light
nuclides emerge from this epoch. To see how heavier nuclei are made,
we must discuss what goes on in stellar interiors.
The Source of Stellar Energy
Before Einstein's 
the source of the sun's energy was a great
puzzle. In the late 1800's it was thought that the sun 's energy came from
gravitational contraction. As the matter of the sun slipped deeper into its
own gravitational potential well, its atoms would get hotter and hotter, and
could radiate this away.
The problem with gravitational energy is that it is possible to calculate
how much of it has been spent in order for the sun to reach its present size.
We can also calculate how long it would take for the sun to radiate away that
much energy, given its current output, and that time is relatively short--only
about 10 million years. On the other hand, there is geological evidence that
the earth is much older than that. Early in the present century it
became possible to date rocks by the method of radioactive decay, and those
dates showed that some rocks were as much as a billion (
) years old.
So an age for the sun of 
or even 
years just wouldn't do.
Astronomers knew there had to be some additional energy source in the sun
and many speculated correctly that it was by conversion of mass by Einstein's
formula.
Just how this conversion took place, however, wasn't known until
the late 1930's. Hans Bethe showed that hydrogen could be converted to
helium by a cyclical process involving nuclei of light elements. It
was for this work that Bethe won the Nobel prize for physics in 1967.
We will write the nuclear reactions using a chemist's notation.
The mass number is written as a pre-superscript before the symbol
for the element. Thus, 
C means a nucleus of carbon with
mass number 12, and 
is the nucleus of a hydrogen atom, a proton.
We use 
for a gamma ray, and 
for a neutrino. The
symbol 
is used for a positron.
The celebrated Bethe carbon-nitrogen cycle went as follows:
A C nucleus collides with a proton, creating an excited
N nucleus, which jumps to the ground level by emitting a
-ray. This N is unstable. It has too many protons.
Consequently, the nucleus relaxes by emitting a positive electron
and a neutrino in a form of 
-decay (Section 4.2). The
C formed in this way absorbs another proton to give
N, and so on. In the last step of the cycle, a helium
nucleus is released. The net result of Bethe's cycle is not to
make helium out of four protons. The energy difference corresponding
to the mass of four protons and a helium nucleus can power a star.
Deep in the solar interior, where these reactions take place, most
electrons have been stripped by the high pressures and temperatures, so
the nuclei collide like billiard balls. However, the nuclei are all positively
charged, and repel one another. That repulsion must be overcome by
having the nuclei move fast enough, and for this the temperature must
be high.
Interestingly, the temperature at the center of the sun is not quite
high enough for it to derive most of its energy from the Bethe cycle.
Instead, it comes from the simple combination of protons in a fusion
reaction. Essentially, the reactions are these:
Two protons combine to form a deuterium (or heavy hydrogen) nucleus.
The deuteron adds a proton to become an isotope of helium, with
two protons but only one neutron. The 
He nucleus is formed in
an excited state, and it drops to the ground level with the emission
of a -ray. Finally, two of the He nuclei combine to give
a 
He nucleus and two protons. This scheme is called the 
.
The net result of this process is essentially the same as that of
the Bethe cycle, four hydrogen nuclei are converted to one helium
nucleus, with the production of energy (and the emission of neutrinos).
The positrons that are emitted, are quickly annihilated when they come
in contact with ordinary electrons, and the result supplies heat to the
solar interior. The neutrinos, however, escape from the sun completely,
carrying their energy with them. These neutrons have been detected
at the earth, though there have been fewer detections than were
expected.
Today, few astronomers doubt that the major source of stellar energy
is the conversion of hydrogen to helium. Most stars are busily doing this,
and while this process is taking place, the stars lie along the main
sequence of figure 3-4
Gamow's Notion of Tunneling
In an earlier section we mentioned that the wave function for a
nucleon did not have a zero point, or node exactly at the edge of a
well such as that shown in figure 4-7.
If the energy of
the nucleon corresponds to a value near the top of the well, something
very interesting happens. The little tail of the wave may persist
long enough within the region of the well that it may get outside the
well with a finite amplitude.
Figure 5.3:
Escape or Capture of a Nucleon by Tunneling. A quantum
particle can penetrate the potential ``barrier'' in a way that is
forbidden to a classical particle.
The plot
on the left corresponds to an energy that is not one of the allowed
energies of a nucleon. On the right, the energy of the incoming particle
is the same as that of an allowed nuclear level. In this case the
probability of capture is greatly enhanced.
Conservation of energy would forbid a classical particle from
being inside the ``forbidden'' region of the potential well, which
we have shown in the figure by shading. For example, if you have a
ball rolling in a bowl, the ball can't penetrate the walls of the
bowl.
Quantum particles are fuzzy, though, and may violate certain
classical laws. In particular, the conservation of energy may be
violated for a brief time. If the particle is close to the top of
the well, this time may nevertheless be enough for the particle to
sneak through the ``barrier'' that would stop a classical particle.
George Gamow clarified this phenomena, which became known as
tunneling in the early days of nuclear physics.
Just as it is possible for a nucleon to leak out of a nuclear
potential well by tunneling, it is also possible for one to sneak
in. Indeed, all of the reactions involving charged particles that
we have discussed in the previous section take place
primarily by this process. There is an interesting story that goes
with this.
In the 1920's quantum mechanics was in its infancy, and Gamow's
notion of tunneling lay in the future. Astronomers were aware, however,
that stellar lifetimes were sufficiently long that some powerful, but
still unknown source of energy was required to power them. The British
astronomer Sir Arthur Eddington (1882-1944),
a pioneer in the theory of the structure
of stars, speculated on this energy source in one of his popular books
Stars and Atoms. He argued that the most likely energy source was
the conversion of hydrogen into helium.
But Eddington's own work on the structure of stars gave reasonable
estimates for their central temperatures. From these temperatures,
one may calculate the energy of the protons--that energy is directly
proportional to the temperature. One could ask if the energies in
stars was sufficient to enable protons to get close enough to the nuclei
that reactions such as those in the above section could take place.
The answer given by experimental physicists in the 1920's was no.
It is straightforward to see the argument if we think of the potential
well, and the barrier that it presents to incoming particles. To get
into the well, to have enough energy for the nuclear forces to come into
play, a classical particle would have to get to the top of the well.
Stellar temperatures were not hot enough for that.
Eddington responded to this argument with a marvelous retort. We
may assume he knew, with the insight of his genius, that hydrogen
had to be converted to helium. It merely remained to find out how it
was done. His critics, he said, could go and find a hotter place!!.
Eddington made use of Brenner's "Don't Worry Hypothesis."
Gamow's theory of tunneling resolved the dispute, and made it
possible for Bethe to clarify the reactions that provide source of
the energy of most stars.
There is one more wrinkle on this tunneling that we need to discuss.
The energy of an incoming proton might correspond to one of the
allowed energies in the nucleus. When this happens, the probability
of capture by tunneling is greatly enhanced. Physicists speak of such
capture as being resonant, in tune, so to speak, with the natural
vibrations of the nucleon inside the nucleus. We shall encounter
a reaction of this kind in the next section.
Helium Burns to Carbon
We may recall that Gamow had great difficulty creating all of the
chemical elements at the time of the birth of the universe. A major
problem was that there are no known stable isotopes with masses
either five or eight. Any scheme for the origin of the chemical elements
would have to bridge this gap somehow.
When the hydrogen supply is exhausted in the centers of stars the
remaining material is primarily helium. There will be a small fraction
of heavier elements too, that came from the gas that originally made
the star. These heavier elements are mostly unaffected by hydrogen
burning, because of the charge on their nuclei.
In order for two protons to come together they must have enough
energy to overcome the repulsion of the two positive charges. If they
can get close enough, then they may be subject to the nuclear
forces that allow the reaction scheme called the pp-chain to occur.
The hotter the gas, the more energetic the particles in it. Now
it takes more energy to get a proton close to a carbon or nitrogen
nucleus than it does to get it close to another proton. Why? Simply
because there is more electrical repulsion in the former cases.
This is why the Bethe cycle isn't the dominant source of energy
in the sun. In stars with central temperatures that are hotter than
the sun's, the CNO cycle dominates.
After the hydrogen in the center of stars is used up, there is
a central, spherical core of mostly helium. Hydrogen continues to burn
at the surface of this core, in what astronomers call a ``shell source.''
This shell works its way outward. What happens next depends on the
mass of the star, and for our purposes, we need not delve into the
details. Eventually, the temperature of the cores will rise to the
point where helium nuclei may fuse.
When two helium nuclei fuse, the nucleus that is made is 
Be
(beryllium-8). This is right in one of the famous gaps that gave Gamow
so much trouble. The half-life of Be is the incredibly short time
of about
seconds. It would seem an impossible gap
to bridge. Two factors allow stars to get beyond the gap. First,
the density of particles is very high, so that even though the Be
nuclei split apart very quickly, they are made at a rapid rate. This
means that at any given time there are a tiny number of Be nuclei
around to be hit by another helium nucleus. The product of a Be
nucleus and an 
-particle (helium) is the stable C nucleus.
Astronomers call this the triple- process.
When the rates of the reaction
were first calculated by physicists they were too slow. Fred Hoyle,
of 
-fame investigated what would happen if another
-particle were added to the freshly made C, and found
to his surprise, that under the conditions visualized in the stars,
that all of the C would be quickly converted to 
O.
This left the astronomers with no way to account for the ubiquitous
C of the universe--no organic chemistry, no life!
In one of those classic flashes of insight, Hoyle realized that the
rate at which C is made had to be speeded up, and he proposed
that the structure of the nucleus had to be changed. He therefore
postulated the existence of an energy level in the C nucleus
that would make the triple- reaction go much more quickly.
Hoyle predicted that the triple- reaction would be resonant
as discussed in the previous section.
With a resonant reaction, there would then be too
much C made for all of it to be destroyed
by the addition of another . William Fowler, the nuclear
astrophysicist and member of the team set out to see if
Hoyle's prediction was correct. He found the predicted level just
where Hoyle said it had to be.
It remains to explain why this process can't happen in the Big
Bang. Certainly it was hot enough--take your pick of times, and the
temperature can be as hot as you need. It was also dense enough.
Again depending on how old the universe was, it could be as dense
as you need.
We think we know the conditions in
the Big Bang reasonably well. If that seems a little smug, then
allow us to say that we know the conditions in our models
quite well. These conditions tell us that temperature and
the density were not right at the same time. When the temperature
was about right for the
triple- process, the densities weren't high enough. A tiny
bit of C was made, but it just wasn't enough to account
for what we have today.
Alpha Nuclides
Much of the carbon that is produced in the triple- process
burned to O, which in principle could be converted into
Ne, 
Mg,
Si, and 
S. Indeed, if the temperatures were high enough
the process could go on to include
A and 
Ca. These isotopes are all simple
multiples of -particles, so the number of protons and neutrons
is equal. As more protons get into the nucleus, the electrical repulsion
becomes more and more effective relative to the strong nuclear force.
We know from the nuclide chart that the way the nucleus accommodates
a lot of charge is to mix in a few more neutrons than protons. This is
why the plot of Z vs. N, figure 4-8
bends down from the
original 45-degree slope. But all of the -elements we have
discussed have equal numbers of protons and neutrons. How big can
the nuclei get with 
before extra neutrons have to be added?
The answer is that Ca is the last abundant ``''-nuclide.
This isotope is said to be doubly magic because both 
and
have the magic number 20.
There is another doubly magic isotope of calcium, 
Ca.
Calcium has six stable isotopes, all stretching from the doubly magic
Ca to the heavy, doubly magic Ca. No element lighter
than Ca has this many stable isotopes. It is not until one
reaches rather heavy nuclei of the element selenium (Z = 34) that
one finds six or more stable isotopes.
In the region of calcium, the even- elements have three or four
stable isotopes. At calcium, the valley of beta
stability runs between the neutron-magic numbers 20 and 28.
Probably neither Ca nor Ca would be stable if it were
not for the extra binding these nuclei get by having magic numbers
of neutrons (as well as protons).
If an is added to Ca, the result is 
Ti,
which has a half-life of only about 70 years. It decays by emitting
particles through Sc to the stable Ca. At
this point another may be added to reach the stable
Ti. Now Ti is by far the most abundant of the titanium
isotopes, so it is tempting that it was reached in this way, by
successive additions of 's. What astronomers think actually
happens is a bit more complicated.
The abundance curves show a deep trough at 
Sc, so it is
reasonable to assume that the nature of the synthesis of the elements
changes from the classical () -process that we have
been describing.
Stellar Evolution
After stars exhaust hydrogen in their cores, they leave the main
sequence (figure 3-4),
and move to the red giant region. Hydrogen
continues to burn, but in a shell. As the
size of the shell grows, the mass within it increases. For a time, the
entire core within the shell is maintained at the temperature of the
hydrogen burning, and astronomers speak of an isothermal core.
As the shell works its way out, the energy
coming from the shell is not enough to power the star. The core then
contracts, heats up, and helium burning starts by the triple-
process.
The helium burns mostly to C and O, but at the
temperatures where these processes occur, not much Ne can be
formed. Eventually, there is a mostly carbon-oxygen core, surrounded
this time by a helium-burning shell. What happens next depends critically
on the mass of the star. For stars that have about the same mass as
the sun or less, the core contracts, but never gets hot enough for the next
nuclear burning stage, which is called carbon burning.
In carbon burning, the C nuclei react with themselves.
Initially, a compound nucleus is formed in the merger. This
nucleus would have to have a mass number of 24, and 12 protons.
The nucleus is therefore Mg, but it is not in its ground
state. The Mg has a lot of excess energy as a result of the merging
of the two C's. There are several ways the highly excited
Mg nucleus can get rid of its energy. The most likely way
is for it to emit an , and become Ne, a nucleus that
might have been built up from O during helium burning if the
temperatures got hot enough.
While carbon is burning, it is also possible to have reactions
involving C plus O as well as O plus O.
The latter is sometimes called oxygen burning, and takes place
at temperatures a little higher than carbon burning, simply because
of the higher charge on the oxygen nuclei. The major product of
oxygen burning is not S (sulfur-32), although an excited,
compound S nucleus is formed. The major product of oxygen
burning is Si.
By the time oxygen burning is possible, the temperature has
risen to such high values that some of the photons in the hot gas
have high enough energies to cause nuclear reactions.
Take a look at some of the reactions listed for hydrogen burning
(Section 5.3). In a few cases you can see that after a proton has been
absorbed, the resulting nucleus will emit a gamma ray--an energetic
photon.
In the late stages of stellar evolution that we are now considering,
the inverse of this process can take place. A nucleus may absorb a
gamma ray, and emit a particle. If stars are massive enough, -rays
can react with the byproducts of oxygen burning to release both
protons and -particles. These, in turn, can react with ambient
nuclei, building successively heavier nuclei all the way to those in
the neighborhood of the iron peak. Initially, the doubly magic
Ni is produced rather than Fe. But the former is
unstable, and decays radioactively. First Co is formed.
This Co is formed in an excited state which decays by
emitting -rays.
The energy levels in the Co nucleus
are well known, so that the energies (or alternately, the wavelengths)
of the emitted -rays can be recognized. These wavelengths
have been sought--and found--in the spectra of exploding stars.
As early as the time of in the 1950's it was realized
that the synthesis of nuclides near the iron peak would require extreme
conditions of temperature and density. These conditions were most
likely to be found in the violent stellar explosions known as
supernovae.
Stars with sufficient mass--perhaps more than 8 times the mass
of the sun--can become supernovae at or near the end of their lifetimes.
The stars explode with massive outpourings of energy that sometimes
allow them to outshine an entire galaxy. Astronomers have studied
such phenomena for centuries, but the significance of these objects
for nucleosynthesis only became clear at the time of .
Modern calculations of these late stellar evolution stages treat
the hydrodynamics of the explosion as well as
all relevant nuclear reactions. The
abundances that emerge are rather closely fit by an approximate technique
used by Fowler and his collaborator David Bodansky in the late 1960's
which they called quasi-equilibrium. Later
calculations of these processes
were sometimes called explosive nucleosynthesis
because they had to occur in supernovae.
The quasi-equilibrium calculations showed two outcomes from
the rapid nuclear reactions leading up to the iron peak. On the one
hand, nearly all of the material could be processed into nuclei
with mass numbers near 56. This would happen at high temperatures
and densities. The quasi-equilibrium calculations were made without
a detailed stellar model. The workers merely asked what abundances
would result from nuclear processes at specified (high) temperatures
and densities.
At about the same time as Bodansky and Fowler's work on quasi-equilibrium,
the American astronomer David Arnett made one of the early attempts
to integrate calculations of a model star's late evolutionary phases.
He included a detailed ``network'' of nuclear reactions that would
occur in various zones of the star. Arnett's methods are the
ones that are followed today. They are more fundamental than
quasi-equilibrium because they are based on model stars and
explicit reactions.
Arnett found that the star completely exploded, leaving no remnant.
Most of the stellar mass was converted (eventually) to Fe.
This result became widely known. It was called
the carbon detonation model, because the onset of the stellar
explosion was caused by the violent ignition of carbon burning.
At the time of the calculation, astronomers believed that exploding
stars synthesized elements near the iron abundance peak
(see figures 4-4, and 4-5).
But the cosmic
abundance of iron was much too low for every supernova
to have processed so much material to the iron peak.
If the densities were somewhat lower during the quasi-equilibrium
processing of matter, virtually no iron would be produced, and the
net result would be a maximum abundance in the neighborhood of silicon.
Bodansky and Fowler therefore found an optimum choice of temperatures
and densities that led to abundances that matched those in the SAD
remarkably well.
Later workers could not arbitrarily choose a temperatures and densities
only to match the SAD because they were restricted to the conditions that
held in their exploding stellar models. They could, however, modify the
initial masses of their model supernovae, and for some time during the
1970's the goal was to find a stellar mass
that would reproduce most closely the
region of the SAD from nuclides somewhat lighter than silicon through
the iron peak.
Already in the 1970's astronomers began to explore an alternative
to the supernova involving a single kind of star. Today, the synthesis of
elements from carbon and oxygen through the iron peak is thought to
result from two distinct kinds of supernovae. On the one hand, a
single star could evolve burning hydrogen through helium, carbon,
and oxygen all the way to iron, more or less as we have described.
In the last stages, the star explodes as a supernova. A second
possibility involved evolution of stars in a binary system.
One member of a binary system might evolve through helium burning
so that its core contained mostly carbon and oxygen. If this star were
sufficiently massive, it could lose the overlying hydrogen
and helium-rich as a result of what are called stellar winds.
The resultant core could evolve into the white dwarf region,
until its companion swells toward the red giant phase, due to
its own evolution. In a binary system, what may happen is that
mass can be transferred to the white dwarf.
White dwarfs have a property that was first explained by the
Indian-American astronomer S. Chandrasekhar (1910-1995). If their
mass exceeds a limit slightly larger than a solar mass pressure
is incapable of supporting them, and they must collapse. This limit
is now known by astronomers as the Chandrasekhar limit, and
for this work, Chandrasekhar was awarded a Nobel Prize.
If enough mass is transferred in a binary system to a carbon-oxygen
white dwarf, it may exceed the Chandrasekhar limit and collapse. This
collapse, however, can initiate explosive carbon and oxygen burning, and
lead to the synthesis of heavy elements, just as was the case with a
single star. Ironically, supernovae that result from the evolution
of a single star are called Type II, while those involving binaries
are called Type I's or more recently Type Ia's. These types derive
from the appearance of the spectra of exploding stars. In the past,
astronomers also assigned types by the shape of plots of the supernovae
brightness as a function of time, plots often referred to as light curves. These observations had nothing to do with
models of supernovae--single or binary--and it is just an unfortunate
historical accident that the terminology does not fit the models.
Summary
We have seen how the nuclides belonging to helium through elements
on the iron peak can be synthesized in the interiors of stars.
thought it possible the universe began with pure hydrogen, with all
elements synthesized in the interiors of stars. We shall see in the
next chapter that galaxies probably began their history with nearly
their current helium contents and a few light nuclides. Apart from
these, the sequence of chemical reactions discussed in the present chapter
have shown how the chemical elements and most isotopes could be
synthesized in stars.
The entire sequence of reactions, from hydrogen and helium burning
through the explosive synthesis of the iron peak represents a slide
toward the most stable nuclei, in the neighborhood of iron. During
these processes, energy is extracted from the reactions. In the next
chapter we shall take up processes that can push past the most stable
nuclei to produce elements beyond the iron peak.
Chapter 6: Synthesis of Heavy Nuclei, Beyond the Iron Peak
The reactions that we considered in detail in the last chapter
would be called exothermic by a chemist--they release energy.
The energy could be used as fuel by the stars. We calculate the
energy that is released in a reaction, such as
by subtracting the masses on the right from those on the left, and
multiplying by 
, using Einstein's . Other kinds
of reactions take place in nature that are called endothermic.
In these reactions, it is necessary to supply energy somehow, in
order for the reaction to go to completion. This is the situation
for the synthesis of all of the chemical elements and their isotopes
beyond the iron peak.
All nuclei beyond the iron peak are unstable, and in principle,
if they were left alone in a laboratory, they
would decompose and form iron. Don't hold your breath! At normal
temperatures and pressures the radioactive
the half-lives of what we think of as stable nuclides along the valley
of beta stability are many, many times the age of the universe.
The direction of
a chemical (or a nuclear) reaction can be changed by the conditions
in the ambient medium. Both the temperature and the density of the
medium are relevant. This is true of chemical reactions, and it is
true for nuclear reactions as well.
For example, under high enough temperatures
(and low enough densities), the highly stable C nucleus would
dissociate into 3 -particles. Energy would have to be supplied
for this to happen, but if the energy were available, the reaction
would take place.
Similarly, with sufficiently
high densities, it is possible to create nuclides beyond the iron
peak.
George Gamow knew that the easiest way to make heavy elements
was to add neutrons to existing nuclei. This is because there is no
electrostatic repulsion between the positively charged nuclei and the
neutral neutrons. He thought that somehow masses 5 and 8 were
bridged at the beginning of the universe, and neutrons could than be
added to make heavy elements.
used this method too, but they and
their competitor A. G. W. Cameron used the interiors of stars as
the site of the neutron addition.
These founders of the modern theory of nucleosynthesis realized
that the isotopic abundances of the SAD could be explained by two
quite different neutron processes. On the one hand, there was evidence
that neutrons were added very slowly. This process eventually became
known as the 
-process. There was also evidence of a rapid neutron
addition, or 
-process. Interestingly, there was little evidence
of neutron addition at intermediate rates. In the next two sections,
we shall explore the - and -processes in detail.
In stars that have passed through core hydrogen and helium burning,
there will be a stage where a helium is burning in a shell. Within
the shell will be mostly C.
Outside the helium-burning shell there is a region of nearly pure
helium, and beyond that, a region of unburned hydrogen. There may
or may not be a hydrogen-burning shell between the helium and hydrogen
rich zones. Such a star would be a red giant, and its outer envelope
would be subject to hydrodynamical currents that help to carry
energy from the interior to the surface. These currents could cause
some mixing of the material of the three zones that are hydrogen,
helium, and carbon rich.
If protons could be mixed into the carbon-rich zones, these protons
could react to produce first N, which would decay to C.
The scheme occurs at the top of the ``Bethe'' cycle of hydrogen burning.
The 
-nucleus is highly likely to accept an -particle (4He),
and emit a neutron (n):
4He + 13C ----> 16O + n
Because
the protons have been mixed into a helium, or -rich environment,
this reaction is more likely than the addition of another proton to form
N, as in the Bethe cycle.
Another possibility often discussed that could produce free neutrons
assumes that N is created, or present in the inner zone to which
's are mixed. The following reactions might then occur:
Neutrons that have been freed by either of these schemes may react with
ambient heavy nuclei. Suppose the number of neutrons per cubic centimeter is
not very large. Then the time between captures of a neutron would be
relatively long, and the process of addition would be slow.
In the process pictured by , the -process starts with
Fe, and neutrons are added one-by-one.
Figure 6.1:
The Early s-process. Neutrons are added to
seed nuclei, in this case taken to be Fe. In
reality, all nuclides present at the time of neutron addition
would be subject to reactions similar to the ones shown.
The beginning of the -process is shown in figure 6.2.
The stable iron isotopes 
Fe and 
Fe are first made. Addition
of another neutron results in the unstable 
Fe, which -decays
to the stable Co. When Co adds a neutron, the unstable
Co is formed, and it -decays to the stable Ni.
The next two heavier nickel isotopes could then be made, leading
to the 
Ni, which has a 100 year half-life. In the classical
-process, neutron additions occurred on the order of one every
10,000 years, so the Ni would have time to decay to Cu.
By a sequence of reactions of this kind, successive nuclides are
formed that follow the valley of beta stability. The basic assumption
is that whenever an isotope is made with too many neutrons for stability,
there is time for a -decay to a stable nuclide. Mostly it
is a -decay that occurs, but in some cases, as in the circuitous
route from Cu to 
Cu, a -decay can occur.
The -process path is not unique for at least two reasons.
Even if there were an infinite amount of time for -decay, there
are some isotopes on the path that can either - or
a 
-particle. This is illustrated for 
Eu, which can
decay to either Sm or Gd.
Figure 6.2:
Nuclide Chart Near Europium. The Eu isotope can
emit either a or a , and this leads to a branching
of the -process path. The alternate paths merge again at
Eu. Note that 
Sm and 
Gd are not on the
-process path. These nuclides are made in the -process, to
be discussed below.
There is another process that can take place when a nucleus has
too many protons. In addition to -decay, some proton-rich
nuclei capture an electron from an inner shell. This process is called
electron capture, or EC. For our purposes, we really don't need to
make a distinction between electron capture and -decay.
Both processes result in a shift on the nuclide chart that is down
one unit in , and one unit to the right in .
There are considerable differences in the abilities of nuclides
to capture nuclei. At the lowest level of approximation, the probability
that a nucleus would capture a neutron would be proportional to the
area of the nucleus as seen by an incoming neutron. The bigger that
area, the bigger the probability the neutron will hit the nucleus.
Because of quantum mechanical effects, things are not so simple.
A neutron may bump into a nucleus, but not be absorbed.
There may be no easy way for the excited nucleus, that would momentarily
be formed, to get rid of the neutron's excess energy. So the neutron
would be quickly emitted, and it would look like it had just bounced
off. Physicists nevertheless speak of the neutron capture
cross section as a measure of the relative ability of nuclei
to absorb neutrons. The larger the cross section, the more frequent
the neutron captures, other things being equal.
Figure 6.3:
The Concept of a Cross Section. The decrease in the
intensity 
is related to the fraction of the area
that is blocked by the neutron absorbers.
Figure 6.3 shows schematically how one would
measure the neutron capture cross sections experimentally. A beam of
neutrons comes in on the left, and hits a slab with area and
thickness 
. If the initial beam has an intensity 
,
it decreases by an amount . This increases
directly with the number of neutron absorbers, and their cross
section, usually designated by the Greek letter sigma (
).
Physicists can arrange to have a known number of absorbers in the
slab. Then they can measure , and obtain .
For nuclides that are made through the -process, we expect
to find an inverse relation between the neutron capture cross section
and the abundance of the nuclide. The larger the , the more
likely a given species is to capture a neutron and become an isotope
with one more neutron.
Nuclides with very low neutron capture cross sections are likely
to increase in abundance relative to their neighbors. One or two of
the isotopes of a heavy element may be made almost entirely by the
-process. Examples are 
Ba and 
Ba. The isotope
between them, 
Ba is made by both the -process and the
-process. We will show in the following section how it is possible
to tell this from the nuclide chart. For the present, let us focus
on these two isotopes of barium.
Physicists have measured neutron cross sections for both isotopes,
and the cross section for Ba is 3.2 times larger than that
for Ba. The abundances are just the reverse. The isotope
Ba is 3.2 times as abundant as Ba. Enough examples
of this kind were found to convince and Cameron that
slow neutron addition played an important role in the synthesis of
heavy nuclides.
Those isotopes with magic numbers of neutrons have especially
small neutron capture cross sections. These ``neutron magic'' species
are the cause of the abundance peaks seen in figure 4-5,
and
marked with an `.' The three peaks result from the neutron magic
numbers 
, 82, and 126.
It is probable that neutron addition has played some role in the
synthesis of lighter species too, for example, the elements between
hydrogen and helium and the iron peak. However, the (SAD) abundances of these
species seem dominated by the processes we have discussed in the previous
chapter. These processes involved the fusion of light nuclei, or
the general trend toward the maximum nuclear binding which occurs at the
iron peak. Most of these reactions were exothermic, with the
addition of charged particles to previously existing nuclei.
For these reactions the neutron magic numbers are not as significant
as for the pure neutron addition of the -process.
Rapid Neutron Addition
We think the -process takes place slowly inside stars that are
in advanced evolutionary stages, but are still processing helium to carbon.
There is substantial evidence in the SAD abundance pattern that nuclides
were synthesized under the kinds of extreme conditions that would occur
in supernovae explosions. This evidence is seen on the abundance plots
of figure 4-5
in the form of the maxima labeled with 's.
Two of these maxima are readily seen, and occur at -values smaller
than those of the neutron magic, -process peaks for = 82 and 126.
The corresponding maximum ``behind'' the , -process peak is
mostly masked by the effects of the iron peak itself.
What could cause these strangely positioned abundance maxima?
Since there are -maxima associated with two and perhaps three
of the -process maxima, we might guess that somehow the neutron magic
numbers would play a role. In the -process, the special stability
of neutron-magic nuclei cause abundance maxima at these positions
but on the valley of beta stability. Let us now extrapolate
the -maxima from the valley of beta stability, where the species
now reside. We follow the opposite direction from that of -decays,
that is, down, and to the right on the nuclide chart.
We show this in figure 6.4 for the -peak near 
.
Figure 6.4:
Extrapolation to the -Process Path. Stable nuclides are shown
by the solid shading. The valley of beta stability is toward the upper
left corner of the diagram. The diagonal shading shows the -process
path explained in the next section. If nuclides reached
the region with
by -decay, they would have come from the direction
opposite the heavy arrows. The isotope 
Cd is neutron magic.
Neutron addition will slow down for the species with the magic value
, and nuclides will accumulate at this position. When they
-decay back to the valley of beta stability, the -process
maximum near will be formed.
Suppose there were some way to displace nuclides from
the valley of beta stability
shown in figure 4-8
right--to the neutron-rich side. We might still expect abundance maxima
at the neutron magic numbers, just as for the -process. If all of the
nuclides then decayed back to the valley, we would be left with maxima
just where they are found in the SAD. How could the nuclei be displaced
in this way?
Consider what would happen if stable nuclei in the valley were suddenly
bathed in a very dense sea of neutrons. Some of the neutrons would begin to
be captured. With many neutrons nearby, there would
not be time for the species to decay back to the valley before additional
neutrons would be added. All of the stable nuclides would be carried
onto the neutron-rich region of the nuclide chart. This is an example
of the process we speculated about in the above paragraph.
Now let us ask how far it would be possible to displace the
nuclides by this neutron addition. Consider what has happened. The
region of the nuclide chart that we have called the valley of beta
stability (figure 4-8)
might more generally called an
occupied region of the chart. It is occupied because it corresponds
to a local mass minimum, as shown in figure 4-9.
Just as marbles would gather in the bottom of a bowl, the nuclides
occupy the valley of beta stability. But this happens in the absence
of the neutron bath that we have postulated in the paragraph above. The
effect of this neutron bath is to push the nuclides up out of the valley.
We can picture what would happen with our analogy of marbles in the bowl.
Let the marbles that are originally in the bottom of the bowl be white.
Now imagine what would happen if we could put some black marbles in the
bowl that we could somehow supply energy to so they would be constantly
rolling back and forth in the bottom of the bowl. In this thought experiment
suppose the black marbles always had enough energy to roll up the side
of the bowl by as many as four inches, but never more.
The black marbles would push the white ones from the bottom of the
bowl. We imagine the white ones would lose energy by friction, so they
wouldn't quite get up as far as four inches, but if we put in a lot of
black marbles, the white ones would move completely out of the bottom
of the bowl.
The neutrons in the bath that we have considered would act like the
black marbles, and the nuclides from the valley would be the white ones.
The limit of how far the white ones could be pushed is set by the energy
of the black ones. The more energy we give them, the further up we can
push the white ones. It would be the same way with the nuclides. For
a given temperature and number of neutrons per cubic centimeter, the
``occupied'' region of the nuclide chart would be displaced just so far.
The more neutrons there are flying about, the further from the
valley the occupied region would be.
Eventually, the neutron bath would create an occupied path displaced
to the right of the valley of beta stability. The energy necessary to
do this would have to come from some external source. We can imagine that
a stellar explosion would supply the energy. As the nuclides are displaced
more and more from the valley, eventually the basic process of neutron
addition would come into equilibrium.
We have encountered the notion of equilibrium in section 5.1. In
that case, we considered the ``chemical'' reaction
. At a given temperature, there is a relation among the
amounts of iron, ionized iron, and electrons per cubic centimeter of material.
The higher the temperature, the more Fe.
A similar situation will hold for the neutron addition. We have the
same kind of situation with our neutron addition. The only difference
is that we deal with a nuclear reaction.
Let us consider a specific nuclide that has come into equilibrium
on the neutron-rich side of the valley of beta stability. We consider
Ru, an isotope of the element ruthenium,
which has a mass number of 116.
The relevant reaction is then
In equilibrium, the rate of destruction of 
Ru by
-ray photons would be equal to the rate of creation of
Ru by neutron addition. Physicists call such reactions
reactions. The inverse process is called a 
reaction.
Even though the creation and destruction rates of Ru
are the same, the relative amounts of the two ruthenium isotopes can
vary. If there are more neutrons, the reaction will be pushed to
the right, and the Ru to Ru ratio will increase.
If there are more
's the ratio will shift to favor the lighter isotope, Ru.
The same situation holds for 
Ru and Ru, as well as
for Ru and 
Ru. In equilibrium, given a fixed number
of neutrons and a fixed number of -rays per cubic centimeter,
there be fixed fractions of all of these isotopes. However, the
total number of ruthenium isotopes will be dominated by one or two
of these isotopes. These one or two determine where the ``occupied''
part of the nuclide chart occurs at 
(ruthenium). In
figure 6.4, we have drawn the schematic path for a
maximum of abundances of the ruthenium isotopes at Ru and
Ru. At the time of the neutron bath, all other Ru isotopes
would be small or negligible compared to these two.
In the previous section, we have described a process in which
neutron-rich isotopes can be made by what we have called a neutron
bath. The process of adding neutrons and emitting -rays eventually
comes to an equilibrium, when the -rays begin to disintegrate
the neutron-heavy isotopes.
Actually, this is not a perfect equilibrium, because all of the
neutron-heavy isotopes are subject to -decay. This decay
takes a given isotope one step up, and to the left on the nuclide
chart. The resulting isotope is less neutron rich than its antecedent,
but it has the same mass. Because it has one more proton,
it is likely to accept another neutron, and increase its mass.
This is essentially what happens on the -process path, but the
entire process takes place well off the valley of beta stability.
Just as with the -process, we have a piling up of nuclides
near the neutron-magic numbers.
The near equilibrium - and -reactions
combined with the -decays populates a strip of the nuclide
chart that is displaced to the neutron-rich side. Neutrons are
constantly lost from the bath to make heavier and heavier nuclides.
It is not known for sure what supplies this bath, but it is probably
supplied during a supernova explosion.
At some point, the explosion is over and the bath will no longer exist.
The nuclides will then decay back to the valley of beta stability.
However, the neutron-magic numbers will leave their imprint on the
abundance pattern. The -process peaks that are found in the SAD
come from displaced, neutron-magic isotopes.
The three neutron-magic,
neutron-rich isotopes 
Ag, Cd, and 
In are shown
with heavy horizontal shading in figure 6.4. This is
to indicate an excess population of this region of the nuclide chart
during -processing as a result of the neutron shell closing.
Heavy arrows are used for the -decay paths from this region to
suggest a maximum of the 
nuclides on the beta-stability
valley after the neutron bath is gone.
While the neutrons are being added, the nuclei will run
along the -process path toward ever heavier species. Just how far can
they go? The most likely fate of very heavy neutron-rich isotopes
is fission. No experiments have been done on the relevant isotopes.
Their half-lives are all too short for laboratory studies. It is
known that fission can be induced by adding neutrons to heavy species,
such as uranium or thorium isotopes. These typically split into two
fragment nuclei of unequal size. Both fragments are initially neutron
rich, and move back toward the valley of beta stability by -decay.
If this kind of fission occurred in a neutron bath, the fragments
would help to define the neutron-rich -process path, so that a kind
of cycling process could occur in which heavier nuclides are produced by
neutron addition. Fission at the heavy end then feeds nuclei back toward
the lower end of the -process path. Because of the nature of fission,
if this cycling went on for a relatively long time, there would be few
nuclides with -values much smaller than about 110, because of the nature
of what are called fission yields.
When nuclei fission the fragments
have typical sizes that depend on what causes the fission.
Very small fragments are quite rare. Asymmetrical fission may divide
an original heavy nucleus with mass number A into two nuclides with
mass numbers near 
and 
For 
that would
give 
and 
. Negligibly few fragments
would be expected that are much smaller than 96.
There is another kind of -process that might occur. Suppose
nuclides all along the valley of beta stability were exposed to a rich
neutron bath, but only for a short time. Suppose there was time only
for about a dozen neutron additions. Then all species would be displaced to
the neutron-rich ``hillside'' of the nuclide chart, but when the bath
dissipated, the isotopes would decay back to the valley. If this sort
of process took place, the -process peaks would still be evident.
A general decline in abundance with would still be present, although
all nuclides would increase in mass number by about 12 mass units.
The original abundance decline (e.g. of the SAD) would still be
present after such a short, intense exposure. All species would just
be displaced to higher .
After -decay, the -process maxima would still be evident.
In figure 6.4, we can see the -process
path, running from 
Sb through 
Xe. Nuclides along
this path that may have contributions from either the - or
-process are labeled 
. Examples are Sb and 
Te.
On the other hand, there is no way for the -process to make a
contribution to nuclides such as 
Te, or 
Te. Such
isotopes are -only isotopes, and are marked . Neither
Xe nor Xe can be reached by either the -
or the -process. assigned them to the 
-process,
which we shall discuss briefly below.
The -process is considered to be much better understood than the
-process. Abundances of -only species have enabled nuclear
astrophysicists to determine the nature of the neutron exposures.
Models of the -process include temperatures and densities when the
slow neutrons were added, and these conditions are expected in highly
evolved, red giant stars. Thus we think we know not only the nature
of -processing, but also the astrophysical circumstances.
In the SAD, it is clear that there was no
single exposure. The pattern of abundances can only be matched if
it is assumed that a relatively small amount of material was exposed
to many neutrons, while the majority of material received a much
lower exposure. A ``typical'' chunk of material that formed the
SAD was hit with 20 to 40 slow neutrons. It is possible that pulsing
and mixing in red giants could provide the distribution of neutron
exposures that is needed. More likely, the SAD pattern is the result
of processing through several stars. Material from
one star was returned to the interstellar gas of the galaxy, to be
processed by the next stellar generation.
Predictions from our models agree with the observed abundances
as well as one could hope.
The goodness of the fits make it possible to disentangle the -
from the -process contributions of the -nuclides. We can then
make a plot of the individual - - and also the -contributions.
Such a plot is shown in figure 6.6.
Figure 6.5:
Abundances in SAD of - - and -Process Nuclides.
The general character of SAD abundances from all three processes
shows one remarkable similarity. All abundances decline with roughly
the same slope. One can make a rough prediction of the abundances from
two of the processes, given the abundances of one of them--provided the
vertical displacements are given.
Clearly there are many fewer -nuclides than either -
or -products. The latter two products are produced in roughly similar
amounts--provided one smooths over the peaks due to the neutron magic
numbers.
The distribution of -process abundances may be the easiest to
understand. What we need to do is figure out a way to make the -nuclides
from existing species. Suppose we take a small fraction of the existing
nuclides, let us say from the - + -process, and convert them to
proton-rich nuclides. Then the resulting abundances would have the same
overall shape if we plotted them versus A as the combined -abundances
would have. Take some specific cases. Suppose some process turned 1 nuclide in 20
of the nuclides made by the - and -processes near 
into
proton-rich species. At the same time, suppose the same process turned
worked near 
. Then the ratio of the new -nuclides near
would have the same ratio to the new -nuclides near
as the original + species had.
This is basically what people think must have happened. A -process
converted somewhere between 1 in 10 and 1 in 100 of nuclei beyond the
iron peak into proton-rich species. The rough shape of the -distribution
resembles that of the - and -process because it was derived from
preexisting nuclides that were made by the latter processes.
What processes might have converted this small fraction of -nuclei
into proton-rich species? Early speculation centered on reactions in
which a fast proton ejected a neutron or was simply captured. More recently
attention has focused on high temperature processes that might take place
in supernova explosions. It turns out that in models of the supernovae
of Type Ia, conditions are right for the ejection of neutrons by
-rays. These so-called -reactions move nuclei to
the left of the nuclide chart, where the -nuclides are located.
Modern calculations show that these reactions can account for the small
fraction heavy, proton-rich isotopes found in the SAD.
Some Unsolved Problems
It may be fair to say that the source of the neutrons is not known
for certain for either the - or the -process.
We are reasonably
sure the -process takes place in red giants because of the observation
of the unstable element technetium in the atmospheres of some of them.
There are no known stable isotopes of technetium, and the longest lived
isotope lasts only 4 million years--almost certainly much less than the
stellar lifetime. Moreover the same stars that show technetium in their
atmospheres also show an excess of those elements whose abundances are
dominated by neutron-magic isotopes, strontium (
Sr), and
barium (
Ba).
The -process is a different story. Monumental efforts
have been made to model the exploding stars that are probably the source
of both the -process and silicon burning toward the iron peak.
But the problems are formidable, and even the fastest computers are
not capable of including details that may be essential. Moreover,
observational constraints on supernovae are not very strong. We observe
mostly the ejected gas from these explosions, but the -processing
must take place deep down, in the invisible layers.
Experts have consistently said that the ``site'' of the -process
was uncertain. The supernovae explosions proposed by and
Cameron remain plausible. But Virginia Trimble, who has written
comprehensive reviews of nucleosynthesis, said in 1991 that several
other hypotheses were under active consideration. Of these, perhaps
the most audacious was that -process material might be releases if
a neutron star were torn apart by a black hole!
Neutron stars are objects that have been packed so closely by
gravitational forces that an entire solar mass of material is contained
in a sphere some 10 kilometers in radius. Within such an object,
the electrons have mostly been squeezed into the protons to form
neutrons. If such a star were to pass sufficiently close to a black
hole, it might be ripped apart, and some of its material released
to the interstellar medium. Why would this material show the -process
pattern?
Studies of the nuclear fragments that result from spontaneous fission
show a pattern closely resembling that of the -process. It is therefore
entirely plausible that ``neutronized'' matter, matter
from a neutron star, and therefore made mostly
of neutrons, would break up into similar fragments.
The entire concept of the -process pattern rests on the assumption
that the neutron-magic stability will be manifested in very neutron-rich
species (figure 6.4), far off the valley of beta stability.
While this still seems like a good bet, it remains to be proved. The
magic numbers have the particular values they do when the nuclei are
spherical. However, far from the valley of beta stability, they may
distort in shape, and if this were the case, the magic numbers might
shift or become ill defined.
We now turn to an insightful question raised by the cosmochemist
Hans Suess and his coworkers. The - and -nuclides are thought to be
made in vastly different sites--static red giants for the -process,
and most likely, exploding stars for the -process. Why, then
are the abundances of the two species so closely correlated?
If you smooth over the - and -peaks of figure 6.6,
the two curves would run nearly parallel to one another, and at nearly
the same values.
Hans Suess and Dieter Zeh suggested that this pattern could arise
if an -process abundance distribution were weakly exposed to (slow)
neutrons. Then a fraction of the -nuclides would be converted to
heavier species which would have the -process signature. This
hypothesis was never accepted by mainstream nuclear astrophysicists,
and remains as of this writing, apocryphal.
At a meeting in Belgium in 1978, several colleagues and I
spent an evening with William Fowler. Among those present was the German
astronomer Hartmut Holweger. I have known Hartmut since the beginning
of our careers because we both specialize in the determination of
stellar abundances. We both thought the question raised by Suess
needed more of an explanation than we had seen in the literature.
After several drinks, we
got the nerve to ask Fowler to comment on Suess's point about the - and
-abundance correlation. Fowler said he could not explain it,
but that there had to be some value for the ratio of the two.
He shook his head, and said that as far as he could see, a ratio
near unity was as plausible as any other--the correlation could
just be due to chance.
Nearly twenty years later, I still puzzle over this question.
The ``smoothed'' - and -abundances are not similar at only
one value of , but over the range shown in figure 6.6.
Until the site of the -process is clarified, I shall consider the
-abundance correlation an open question.
Perhaps the most remarkable aspect of the concept of rapid neutron
addition is that the general scheme suggested by nearly half
a century ago remains what it was originally. A plausible, coherent scheme.
Summary
Nuclei beyond the iron peak require endoergic reactions, they
need energy rather than provide it to power the stars.
Stars must supply this energy through
gravitational contraction. Most nuclei beyond the iron peak are made
by neutron addition under two vastly different sets of conditions.
In static red giant stars, neutrons are added slowly. The neutron
addition populates the valley of beta stability, with
abundance maxima on the at the neutron-magic values of , 82, and 126.
Rapid neutron addition can populate a band displaced to the right on
the neutron chart. Local abundance maxima are also created here at the
magic numbers 50, 82, and 126, but when the neutron bath dissipates,
the nuclei -decay (up, and to the left, figure 6.4),
creating -process peaks at smaller values of than the -peaks.
Proton-rich nuclei are relatively rare, and may be created from
a small fraction of the -species. The currently favored process for
this is ejection of neutrons by -rays.
Currently, the -process is understood better than either the
- or -process. For the former, we can observe stars that are almost
certainly mixing out the products of slow neutron addition as we observe
them. We have mentioned two plausible sources of the slow neutrons.
Probably both the - and -processes take place in stellar explosions.
In spite of intense efforts to understand these critical astrophysical
phenomena, the problems are formidable, and much remains to be learned.
A Universal Helium Abundance
The founders of nucleosynthesis thought it possible stellar
nucleosynthesis could account for all of the chemical elements beyond hydrogen.
According to their picture, the Galaxy would originally have been pure
hydrogen, and gradually become enriched in heavy elements as stellar
generations were born and died. Fred Hoyle, the `H' of
was a strong advocate of a theory (model) of the universe in which hydrogen
was spontaneously created out of nothing. This was the steady-state
theory, in which average properties of the universe did not change with
time. We mentioned this theory briefly in Chapter I.
George Gamow and his coworkers, of course, tried to make it plausible
that all of the chemical elements were manufactured in what Hoyle flippantly
called ``the Big Bang.'' They were unable to transcend the problem of
missing stable nuclides with masses of 5 and 8. During the time they struggled
to get past this difficulty, it became clear that there was no such thing
as a universal abundance pattern. While most stars, and gaseous nebulae
had quite similar abundances, some very old stars had markedly different
abundances from that of the sun. Moreover, the theory of stellar structure
and evolution had progressed to a stage where it was possible to say that
some very old stars were extremely metal poor.
This was just what one
would expect if the elements were synthesized in stars. The oldest stars
would have been formed from a gas that had not experienced much
enrichment from stellar nucleosynthesis. They would be metal poor.
Of course, we have to rule out the possibility that metals might have
been added to the old stars during their great lifetimes. As far as we
know, this possibility is not realized to any significant amount. Therefore,
astronomers interpret the abundances that they see on the surfaces of old
stars and pretty much indicative of their original compositions.
Helium itself is an element that is not easily analyzed in these old
stars. Therefore, for about a decade following the successful ideas of
and Cameron, it was thought that helium was probably about
as deficient in the old stars as some of the heavier metals. Then in
the mid 1960's it became more and more difficult to demonstrate that the
abundance of helium, anywhere in the universe, was significantly different
from its solar value, about one tenth that of hydrogen.
As far as helium was concerned, therefore, it appeared that the
abundance was universal. The theory to account for this was already in
place, as a result of the earlier work following Gamow. It is only
natural to try to explain a universal abundance by processes that took
place in the universe as a whole. The difference between the current
processes and those of Gamow and his colleagues is that the nucleosynthesis
was now confined to the very light nuclei. Mostly He, but a little
deuterium, He, and 
Li could be made in the Big Bang. Interestingly,
one of the early, post- writers on this topic was Fred Hoyle
himself.
The seminal paper on the early production of helium and the light
elements did not confine itself to what we now call cosmological production,
or Big-Bang nucleosynthesis. Robert V. Wagoner joined Fowler's laboratory
in 1963, and was soon at work with Fowler and Hoyle on the first extensive
calculations of nuclear reactions that could happen in the early universe.
But their 1967 paper was noncommittally entitled ``On the
Synthesis of the Elements at Very High Temperatures.'' The authors gave
considerable attention to the possibility that significant nucleosynthesis
might occur in an early generation of very massive stars.
The kinds of ``massive'' stars considered by these workers are ones
for which there is only the most fragile, circumstantial evidence.
Astronomers today know the masses of a number of stars very accurately
form their orbital motion about one another. The most massive of these
stars is no more than about 25 times the mass of the sun. There is
some evidence that a few peculiar objects could be as much as
several hundred times the solar mass, but even these objects are small compared to
the thousand or more solar mass stars considered by Wagoner, Fowler,
and Hoyle.
Everything we know about the structure of stars tells us that thousand
solar mass objects would not be stable. They would explode, or they
would collapse to form black holes. Either way, there would be nothing
left beyond their debris to say they ever lived and died. Wagoner, Fowler,
and Hoyle explored the possibility that some of their debris could be
the helium presently thought to be nearly universal in abundance. This
remains a possibility, but it is not one favored today.
Helium is made in stars from hydrogen,
mostly during the main sequence phase.
The amount of helium that is made in this way is considerably less than
that which is now thought to be the universal helium abundance. We have
an idea of how bright our own Galaxy is, and also, roughly, how old it is.
Therefore, we may ask how much hydrogen would have been burned into helium
to keep stars in the Galaxy shining--at the current rate, for its age.
This amount of helium is less than that in the SAD, which we now think is
nearly universal.
We might suppose the Galaxy was composed of much brighter stars
in the past. This might well be possible, but there is an additional
problem that in all of the stellar evolution schemes that we have explored,
the helium that is made inside the star is either burned to make carbon
and oxygen, or remains locked in very low mass stars that never explode
or return gas to the interstellar medium.
From a number of viewpoints, then, cosmological nucleosynthesis
of helium and a few light nuclei is currently attractive. Our Big Bang
models show that it is straightforward, we mostly believe now in the
Big Bang, and there are no alternate ways to account for the amount of
helium we now find.
The First Three Minutes
In 1965, Arno Penzias and Robert W. Wilson detected a universal
background of microwave radiation. This discovery has had an enormous
impact on modern ideas about cosmology and models of the universe. The
radiation itself is similar to the microwaves used in telephone and
computer-data transmissions. However, measurements show that it is
exquisitely matched to the radiation that would occur naturally in a
cavity with a uniform temperature. Such radiation is also called
``black body'' radiation. Penzias and Wilson measured it to be
about 
Kelvin.
A universal radiation had been predicted by the incomparable Gamow and his
collaborators, but their work had been largely forgotten by the time
it was actually discovered. This discovery may be the strongest factor
in the now general acceptance of the origin of the universe in a hot
Big Bang, and for it, Penzias and Wilson won the Nobel Prize for
physics in 1978.
The title of this section is from a very fine popular book on the
early universe by the American physicist Stephen Weinberg (1933--), also
a Nobel Laureate. Weinberg describes events in the history of the universe
from about the time the fundamental particles known as quarks combine
to form protons and neutrons until the time helium and a few other light
nuclides emerge with ``universal abundances.'' Weinberg's book
covers the universe from the time when its age is a few hundredths
of a second to somewhat over three minutes.
Physicists who are concerned with fundamental laws of
nature, have a deep interest in the history of the universe, even before
the starting point of Weinberg's book. We need not discuss this
topic here, as there are now many popular as well as technical books
that deal with the very early universe. We have listed a few of them
in an appendix.
It might come as a surprise to some that these early moments in
the history of our universe are considered to be rather well understood
by professionals. Can people seriously maintain they know anything about
what went on before the birth of the earth, the sun, or the Galaxy--at
a time when the entire universe was in a state of compression similar to
that at the center of stars? We have mentioned such audacities in an
earlier chapter. We told the reader that people who work on cosmological
problems are mostly dealing with the hypothetical properties of models.
All models represent simplifications of the ``reality'' they are designed
to represent. Scientists have models of stars, atoms, and planets.
Those scientists who do cosmology have models of the universe.
In the currently favored Big Bang models, the first three minutes
are generally thought to be well understood. Some writers who
discuss this period make no distinction between their models and ``the''
early universe. It is probable that many of them think their is no
important distinction to be made! Perhaps the reader will forgive
me if I follow this tradition, and simply speak of conditions in
the early history of the universe rather than in our models of it.
It is actually more important for the professional than the layman
to be aware of the difference between the model and reality.
Most models have what are called parameters--numbers whose
values should come from the real world. For example, when we make
a model of the sun, the mass of the model is a parameter that is fixed by
our knowledge of the mass of the real sun.
Density is a critical parameter that must be
chosen for models of the early universe. If the density is fixed at some
instant, when the temperature also has a given value,
then the models will determine their values at other times.
Both density and temperature decrease as the universe expands.
It turns out that the universal abundances of the light elements are
quite sensitive to the temperature and density in the early universe.
It is easier to make deuterium (
H) in the early universe than
in stars because neutrons are still available. When nucleons are first
formed from their parent quarks, neutrons are nearly as abundant as protons.
Eventually, they -decay, but with a half-life of 10.3 minutes,
longer than the ``Weinberg epoch.'' We might think it possible then
to make helium, He, by simple neutron addition: first H, then
tritium, or H, which would -decay to He. One more neutron
addition would lead us to an -particle, or He. The
problem here is the -decay of tritium, which has a half-life
of 12.3 years. There is not time for this in the early universe.
The synthesis of helium in the early universe therefore requires
some charged particle reactions. The reactions leading to helium are:
We have seen that high temperatures are necessary for charged-particle
reactions, because the incoming particle must climb the coulomb barrier.
On the other hand, high temperatures mean that energetic photons, or
-rays will be present. The deuterium nucleus is rather loosely
bound, and can be destroyed by 's.
The reactions above also go much faster when the
densities of the reactants are high. Once the nucleons appear, their
densities decrease with time as the universe expands. But the temperature
is also dropping with the expansion.
It therefore turns out that there is a critical balance between
the temperature and the density in these models if the observed
universal helium and abundances of the light elements are to be
explained.
If the density of the nucleons is high enough, all of the reactions
like the ones above go to completion, and there is no hydrogen or any of
the lighter species left. Since there is lots of hydrogen observed in stars,
such densities need not be considered. For lower nucleon densities, it
is still possible that all of the deuterium and He could be used up making
He. If we consider still lower densities of nucleons, then the amount
of He would be much less than the amount that appears to be observed
``universally.''
Actually, the experts think that the helium abundance may have
increased slightly as the universe aged. They have tried to find the
lowest helium abundance in the universe, and take that as the
amount that emerged from the Big Bang.
The theory of the early universe also gives the relative amounts of
deuterium, He, and Li produced in the Bang. The latter nuclide
is past the mass 5 gap, and only very small amounts of it come out of the
models. Nevertheless, observations of all of these light species might be
used to fix the nucleon density at a given time in the history of the
early universe.
A model that predicts the proper amounts of light nuclear species that
comes from the Big Bang also predicts the temperature while the relevant
reactions were taking place. This temperature may be directly related to
the number of photons per cubic centimeter. As the universe expands, this
number of photons decreases, just as the number of particles in a cubic
centimeter decreases. The ratio of particles to photons
in a cubic centimeter will therefore be constant as the universe expands.
The current density of nucleons in the universe may be estimated by
adding up all of the matter in stars and stellar systems.
We may combine our theory of the early universe with the observation of the
cosmic background radiation to provide an important check on this calculation.
The number of photons in a unit volume depends only on the temperature of
the radiation. Thus, we can calculate the present number of photons
per unit volume. Our theory of the early universe also provides values
of the temperature and the nucleon density at the time when the light
elements were created.
The ratio of the number of photons
to nucleons may be fixed by our models of primordial nucleosynthesis.
The same
ratio holds today. Since we know the number of photons per cubic centimeter
today from the cosmic background radiation, we can easily calculate
the corresponding number of nucleons. In this way, measurements of
abundances of light nuclei are directly related to conditions in the
early universe.
Abundances of the Light Elements
A geochemist once called efforts to find the primordial composition
of the solar system a search for the Holy Grail. It seems astronomy
has more than one example. Another Holy Grail is the primordial abundance
set of the critical light nuclides, H, He, He, and Li.
Only He (the -particle) is a robust nucleus. The other
species are fragile, and can easily be destroyed in stars. In the sun
they would be consumed at temperatures that occur roughly halfway to
the center. It would not even be necessary for them to be in the
hydrogen-burning solar core.
Unfortunately, the more robust He is less sensitive to
likely conditions of the early universe than the more fragile light nuclides.
It is therefore necessary to know its abundance very accurately
be able to extract information from it about the
early universe. It is also necessary to choose the objects to be analyzed
with great care, because there is evidence of a net increase in the helium
abundance with the age of the system analyzed. Recent work has focused
on extragalactic emission-line regions with low abundances. Other
popular sources for abundances of light species are old stars, and absorption
line systems between us and quasars.
Experts in this field quote spectroscopically determined
helium abundances to three figures--more accuracy than is justified in
any other astrophysical spectroscopic abundance determination known to this
writer! Deuterium and lithium abundances are more sensitive to the
conditions in the early universe, but it is more difficult to interpret
observational results. Lithium is clearly destroyed in stars like
the sun, and it also is found in enhanced abundances in certain young
stars. Deuterium is difficult to observe in atomic form. It can
be observed in a variety of interstellar molecules, but the results
are not easy to interpret. In molecule formation, the behavior of
hydrogen and deuterium are significantly different. It is expected
that deuterium will be preferentially concentrated in the molecular form.
Probably the best observations of deuterium come from observations
of the atomic form in interstellar clouds. There is a wavelength shift
between the lines of deuterium and ordinary hydrogen that allows spectral
lines from two kinds of hydrogen atom to be seen separately. Measurements
have been made from clouds in our Galaxy as well as distant systems.
Most determinations of this kind give ``primordial''
deuterium to hydrogen in the range
of one part in 100,000, with an uncertainty that may be as large as
a factor of ten.
What these determinations of light element abundances show is
a consistency with the notion of cosmological nucleosynthesis.
Active work is devoted to improving the reliability of the determinations
in the hope of constraining the cosmological models. The observed
abundances, and the theory of early nucleosynthesis constrains the
current density of nucleons. This density is important for the history
of the universe.
If the density of matter in the universe exceeds a certain critical
value--about one nucleon in 100,000 cubic centimeters--it will eventually
cease its expansion and contract to another fireball. The best estimates
from primordial abundances of the light nuclei are generally consistent
with densities about one to ten per cent of the critical value.
We have already mentioned the plausible existence of
large amounts of ``dark'' matter in some
form other than protons and neutrons--forget the electrons they have
a small mass. As far as we know, this dark matter would not influence
any of the nuclear reactions in the early universe, so the abundances
of the light elements have nothing to say about this putative
material.
It is revealed by its gravitational effects
over large distance scales--galactic and extragalactic. Many cosmologists
believe there is just enough of this dark matter to give our
universe the critical density. Their reasons are more aesthetic
than scientific. They like models that require this critical density
and no other value. In this case, the universe would
``just'' expand forever--a tad more matter, and it would eventually
collapse.
Cosmic Rays
Cosmic rays are very diffuse, energetic particles.
They pervade the interstellar medium, but with numbers far lower than
those of ordinary interstellar hydrogen gas. In spite of their rarity,
their high energies make them important in astronomy.
These energies
are conveniently measured in a unit called the MeV, which stands for
a million electron volts. One MeV is a typical energy for -rays
from an atomic nucleus. By contrast, one `eV', one electron volt is
typical of the excitation of the electrons in an atom.
Violent activity on the surface of the sun is known to create cosmic
rays with energies up to perhaps 100 MeV. Beyond this limit, cosmic rays
originate from sources that are still uncertain, somewhere within the Galaxy.
Galactic cosmic rays are generated up to hugh energies--a plot of their
energies may show 
eV at the extreme end.
Ten of these particles have enough energy to light a 100 Watt bulb for a
second. The higher the energy,
the rarer the cosmic ray particles, of course. Typical measurements might
be made on particles with several thousand MeV per nucleon.
Measurements of abundances in cosmic rays have been made from balloons and
spacecraft. They show that the particles have an abundance pattern that
resembles that of the SAD in many ways. Most of the cosmic rays are protons,
and roughly 10 per cent are -particles. One of the significant
differences between cosmic rays and the SAD comes in the composition of
other light nuclei.
Figure 7.1:
Abundances in Cosmic Rays Compared with the SAD. The vertical
scales have been adjusted so that the carbon abundance is the same for
both the SAD and cosmic rays.
In the SAD, the abundances of deuterium and He
as well as of all isotopes of the elements of lithium, beryllium, and boron
fall in a trough between helium (He) and carbon. In the cosmic rays,
that trough is largely filled. A similar filling of the trough between
silicon and the iron peak occurs 7.4.
It is relatively straightforward to see how the SAD abundance troughs
might be filled in the cosmic rays. First, we may suppose that the
cosmic ray nuclei began with an SAD composition. The rays are all bare
nuclei, so unlike the corresponding atoms, they have an electrical charge
equal to that of the number of their protons. Because of this charge, the
motion of the cosmic rays are severely constrained by weak magnetic fields
that occur within our galaxy. We are not sure how these weak fields originate
but their presence is now well established.
Any charge that moves across magnetic field lines will experience
a force that is perpendicular to both the field and the direction of motion
of the charge. This is shown in figure 7.4. The component of
the charge's velocity parallel to the field is unaffected. Thus the
net motion of the charge must be in the direction of the field.
In the Galaxy, the magnetic field lines are sufficiently tangled that the
cosmic ray particles move along them like insects crawling along a tangled
ball of wire.
Figure 7.2:
A Charged Particle Spirals Around A Magnetic Field Line.
The most highly energetic cosmic rays may escape the Galaxy altogether,
but these particles are very rare, and we shall not discuss them here. Typical
cosmic ray particles, of the kind whose abundances are shown in
figure 7.4, travel about the Galaxy for a time that it turns
out to be possible to estimate.
The time a typical cosmic ray particle travels through the Galaxy is
obtained by dividing the length of the path by the velocity. The velocity
for these particles is just a little less than that of light. We may
assume the velocity is known, and see how it might be possible to estimate
the distance such particles travel.
We can get an estimate of the distance the cosmic rays travel in the
Galaxy from their composition--indeed, from the filling in of the abundance
troughs for the light elements and for the scandium low
(figure 7.4). Let us make the assumption that the cosmic
rays originally had something like the SAD abundance distribution.
Then they were accelerated, by a mechanism that is still uncertain, perhaps
by pulsars, perhaps by supernovae. The accelerated particles move swiftly
through the Galaxy along the lines of magnetic force, and collide with
material in the interstellar medium. The particles of the interstellar medium
are also mostly atomic hydrogen.
Consider now a nucleus of one of the relatively abundance SAD species,
carbon, nitrogen, or oxygen (or CNO). To one of these particles, a (stationary)
hydrogen atom looks like it is approaching with a velocity near that of
light. Indeed this approaching proton is capable of smashing into the
cosmic-ray nucleus, and fragmenting it. The reaction is different in nature
from the ones we have been considering in nucleosynthesis, where an excited
or compound nucleus is formed. Physicists call reactions with very fast
particles spallation, possibly from the middle english word
spalle, which meant ``a chip.''
These ``chips'' from the CNO particles are typically protons, and the
light nuclear species that fill in the light-element trough. It is possible
to make measurements of such spallation processes in modern physics
laboratories. What these measurements show is that in cosmic rays, we would
expect roughly equal amounts of chips of various kinds to be formed by
spallation. Moreover the observed number of chips in the cosmic rays would
occur if the typical lifetime of the cosmic rays of a few million years.
For lifetimes greater than this, more chips than are observed would be
produced; for shorter lifetimes, the number of light fragments would not
equal those observed in the cosmic rays.
Typical confinement times are also set by radioactive
nuclides, such as 
B that are observed in the cosmic rays. The
half-life of this isotope is 1.6 
years. The lifetime of
these nuclei would be increased by relativistic time dilation
in reasonable accord with the confinement times obtained from the
light nuclei production by spallation.
Table 7.1:
Isotopic Abundances of the Light Elements
| Element |
|
% Abundance |
Process |
Abundance |
| |
|
|
|
 |
 |
| H |
1 |
 |
|
 |
 |
| |
2 |
|
U? |
 |
 |
| He |
3 |
|
U? |
 |
 |
| |
4 |
|
U,H |
 |
 |
| Li |
6 |
7.5 |
 |
 |
4.3 |
| |
7 |
92.5 |
,H,U |
 |
52.8 |
| Be |
9 |
100. |
|
 |
0.73 |
| B |
10 |
19.6 |
|
 |
4.22 |
| |
11 |
80.4 |
|
 |
17.0 |
| C |
12 |
98.9 |
He |
 |
 |
| |
13 |
1.1 |
H |
 |
 |
Table 7.1 gives abundance in the SAD according to two
compilations. As of this writing, the 1989 compilation
by Anders and Grevesse is still regarded
as the definitive one by many workers. Edward Anders, now retired from the
University of Chicago, has been one of the premiere analytical cosmochemists
of our time. Largely through his efforts, a particular kind of meteorite
known as a carbonaceous chondrite of type `CI,' is now accepted as the
best source to use for the SAD. Nicholas Grevesse is a Belgian analytical
spectroscopist who has specialized in abundance determinations from the
solar spectrum.
The nuclear astrophysicist A. G. W. Cameron made numerous compilations
of the SAD. If we look at his 1982 compilation of abundances for isotopes
of Li, Be, and B, we see that one, Li stands out conspicuously. By
number, it is nearly eight times more abundant than its nearest rival,
B. This could be understood if most of the Li was made in the
big bang, and a much smaller fraction by cosmic rays. People had made
detailed calculations of the relative amount of Li, Be, and B that
could be generated by cosmic rays, and roughly speaking, could accommodate
all but the Li. The general picture of cosmic synthesis, plus
spallation in the cosmic rays held together nicely.
The present situation is a little less clear, largely because the
newer compilation has increased the boron abundance to the point that it
is difficult to account for all of B with the cosmic-ray mechanism.
Even though the abundance of Li has not significantly changed, our
understanding of its numerical value has problems of its own.
Stellar Lithium
The abundances of lithium in stars has been studied over the last
several decades by astronomers, primarily in the US and France.
Their determinations show that stellar abundances of lithium vary by
many orders of magnitude, so that it is difficult to choose an
observational value that we could associate with the Big Bang.
Some stars are enriched in lithium by a factor of 10 or more
with respect to the SAD.
Clearly
there must be some process that manufactures lithium, in addition
to the cosmic rays.
If the enhanced lithium were due to cosmic ray production, even
locally, near some ``super lithium-rich stars,'' there should also be
enhanced beryllium and boron, and there is little evidence to indicate
this. Also, the lithium isotopes should be produced in comparable
abundances.
Unfortunately, the stellar spectroscopic observations mostly
give only the combined 
Li plus Li.
It has been known since the work of the American astronomer George
Herbig in the 1960's that the abundance of lithium in stars
like the sun declines as they get older. These stars have hydrodynamical
processes that are capable of mixing material from their surfaces down
toward, but not completely to their centers. The temperatures, nevertheless
are readily shown to be high enough to destroy lithium. So our current
understanding is that the stars slowly ``cook'' their original lithium.
Figure 7.3:
Lithium Abundances in Metal-Poor Stars. Lithium abundances
are plotted as a function of the iron abundances in old stars.
The French husband and wife team of Monique and Francois Spite have
suggested that certain very old stars may indicate primordial lithium
abundances--in the sense of Big Bang production. These workers have
considered stars with steadily decreasing abundances of heavy elements
like iron. We astronomers know that stars with very low abundances are
also very old, so the Spites were studying stars that were both old
and metal poor. What they found in their sample was that the lithium
abundances declined, and then reached a plateau (figure 7.3).
This plateau has generally been interpreted as a floor set by
cosmological nucleosynthesis. The lithium content on this plateau
represents the values that emerged from the Big Bang. If we assume
that this is true, we get good agreement with the conditions in the
big bang that yield the currently observed number of protons and
neutrons in the universe relative to the number of photons. We discussed
how this works in Section 7.2.
Summary
attributed the origin of lithium, beryllium, and boron
to an unknown, or ``-process.'' Spallation processes by cosmic rays
may produce most of the SAD components of these elements. This mechanism
cannot produce enough Li, but for this isotope
there can be appreciable cosmological (Big Bang) production. The theory
of the production of light elements in the Big Bang is highly developed.
With an optimism that springs from ignorance, some may say
that the conditions in the Big Bang are very simple, and well understood.
This is certainly true of their models!
These models of the early universe make a direct connection between
the amount of light elements that can be produced and the cosmic background
radiation now observed. We can use ``cosmological'' abundances of the
of the light elements along with the current radiation to predict the
density of protons and neutrons in our present universe. Needless to
say, these values are in good agreement with one another, but there is
much more uncertainty than we would like to have. We need better
methods to be sure we are really using cosmological abundances, and we
sorely need more isotopic abundances for all of the light elements.
In spite of these shortcomings, the coherence of the overall picture
is one of the strongest indications that our universe began with a
big bang.
The World of Bart J. Bok
When I first became interested in astronomy in the 1950's there
were very few introductory books that a serious young person could use to get
started. One of my teachers suggested a series called The Harvard Books
on Astronomy. This was quite a good series of books covering most aspects
of astronomy as it was known in the 1940's and 50's. Of these books, one
of the best know was written by Bart Bok with his wife Priscilla. It was
called, simply, The Milky Way. It first appeared in 1941, and went
through five editions, the last one published in 1981. Bok died in
1983.
Bart Bok was one of the most popular of this century's astronomers.
He was never an intellectual leader like Hoyle or Fowler, but his warmth
and enthusiasm made him popular with astronomical students as well as
the general public. He was born in The Netherlands, a country that has
had more than it's share of excellent astronomers. While he came to the
US in 1929, he always had a heavy Dutch accent. The accent
added to his charm. His command of the English idiom was extensive
however, and his classes and audiences would delight in hearing some
astronomical point clarified with the help of an American slang expression
that would come out in a thick accent.
During his early days at Harvard, he once corrected a student about
a historical point. Copernicus was not burned at the stake, as the student
thought. He died comfortably in bed, having just seen his book that put
the sun at the center of the universe. ``It must be nice to pop off like
that," said Bok.
The earliest editions of The Milky Way were not very enthusiastic
about the idea that stars were forming at the present time. Interestingly,
Bok's first research efforts were devoted to finding The Distribution of
the Stars in Space--a monograph that he wrote in the 1930's.
This volume described how astronomers found out where the stars were, and
how densely packed they were at various places in the Galaxy.
Now, if there
were a lot of dark, opaque material between the stars, it would obscure
their spatial distribution. In these early days, Bok was optimistic that
such obscuration was relatively minor. His opinion on this question
changed dramatically as his career evolved, and eventually the focus of his
research and writing was on interstellar material and the role that it
played in star formation.
Why, in the 1940's, did Bok think there was little star formation
going on in the Galaxy? First, I suppose, there was still a lingering
notion that the matter between the star was a nuisance. It
prevented workers from finding the distribution of stars in space.
Second, astronomers were just beginning to come to grips with the
modern concepts of the nuclear fuel of stars and its effects on
stellar lifetimes. There is a fascinating chapter in the second edition
of Bok and Bok entitled ``How Old is the Milky Way?". In it, the
Bok's argue at one point for an age of 10 billion years--not far from
our present estimates. But later, they seem to fix on an age of
about 3 billion years, which is about what was obtained from measurements
of the expanding universe at that time. The Boks thought most of the Milky-Way
stars were born at about the same time, about 3 billion years back.
Strangely, they present arguments that show this could not possibly
be true! Astronomers have known since the early decades of the present
century that there exist stars whose brightnesses exceed that of the sun
by many orders of magnitude. Bok cites a figure of 10,000 for the
ratio of the luminous output of some of these stars to that of the sun.
Given that the available fuel of these stars could be no more than
100 times that available to the sun, we would expect their lifetimes
to be at least 100 times shorter than the solar lifetime.
Even if these supergiant stars were to use all of their available
hydrogen, a calculation made by the
Boks shows the most luminous of them could
burn that fuel in no more than a few hundred million years. In the 1941
edition of the Milky Way, the Boks argue that this calculation must
show that all stars in the Galaxy are very young. Somehow, they still
managed to conclude the Galaxy was about three billion years old.
In a special chapter written for the 1945 edition of their book,
the Boks called attention to work done by the Princeton astronomer
Lyman Spitzer in collaboration with Bok's Harvard colleague Fred
Whipple. These workers focused their attention on interstellar matter,
and concluded that there was ample material in the plane of the Galaxy
to account for the formation of stars. This idea became a part of
Bart Bok's general outlook, and he spent much of his later career
searching for and investigating regions in the Milky Way where stars
were being born.
If a modern astronomer were to play a word association game, the name
Bok might immediately suggest the word ``globule.'' These are dark
regions, often seen sharply silhouetted against the field of bright gas.
Typical sizes are the order of 0.01 to a few tenths of a parsec, and
they may contain some tens of solar masses of material. The later editions
of The Milky Way suggested these were protostars--stars in the process
of formation. Today, it is probably fair to say that globules may not
be accepted specifically as protostars, but it is generally believed they
are intimately related to the process of star formation. They may be
the birthplaces of stars rather than an individual star.
Figure 8.1:
Bok Globules. These are the dark areas silhouetted against
the bright nebulosity called IC 2944 by astronomers. It is found
in the southern constellation of Centaurus.
Figure courtesy
of the Anglo-Australian Telescope.
Bok's biographer entitled his book The Man Who Sold the Milky Way.
Certainly, his zeal was passed on to his students and
young associates. We know a great deal more about our Galaxy and the stars
that are in it because of Bart J. Bok.
Giant Molecular Clouds
Serious study of the interstellar medium has only been possible after
the full electromagnetic spectrum became available to astronomers. Good
progress with many aspects of stellar astronomy was possible before that
time because the sun is a typical star, and most of its light comes through
the visible atmospheric window. In the case of hotter and cooler stars,
astronomers could make allowances for the radiation that did not get
through the atmosphere.
Important studies of the interstellar medium were made, of course,
by ground-based photography. Ingenious analytical tools were developed
for the study of emission nebulosities in the 1920's and 1930's, and
the names of many famous astronomers are associated with that work:
Menzel, Baker, Aller, Goldberg, Spitzer, Zanstra, to name just a few.
However, most of the mass of interstellar material in the
plane of our Galaxy is relatively cold, and its detailed study began
after the availability of the radio window.
This window is a region of the electromagnetic spectrum used by
radio telescopes.
In the 1950's extensive
mapping began of neutral hydrogen gas using the radiation emitted at
21 centimeters when an electron reverses its direction of spin.
After some decades of study, microwave techniques became sufficiently
refined that they could be applied to astronomical investigations.
Microwaves are electromagnetic waves shorter than radio waves, but
longer than those of infrared and optical light.
The author was a graduate student at the University of Michigan in the
late 1950's when Alan Barrett predicted the possibility of detecting
lines from interstellar molecules. He presented his work at a symposium
called The Next Five Years of Radio Astronomy, and at the time,
his paper seemed speculative. However, within five years, Barrett had
moved to MIT, and made the first detection of interstellar OH molecule.
Soon thereafter, Nobel Laureate Charles Townes and his coworkers had
discovered interstellar ammonia (
), and water (
).
Real progress came after 1970 when the CO molecule could be
studied. Soon after its identification in the great nebula of the
constellation Orion, it became clear that the plane of the Galaxy
contains numerous Giant Molecular Clouds, or GMC's. These clouds
are huge objects, with masses 
to 
times that of the sun.
The large ones may be a few tens of parsecs in diameter.
About half of the mass of the disk of our Galaxy is in the form of these
clouds, and the other half is in the form of stars. In the halo,
or the galactic center, less of the mass is in this non-stellar form.
Most of the mass of the GMC's is not CO at all, or course, but
molecular hydrogen, 
. This molecule is very difficult to
observe at radio or microwave wavelengths, however, because it is
formed from two identical atoms. Physicists call such molecules
homonuclear.
In order for an interstellar molecule to interact with radiation,
to absorb or emit photons, it must have some net separation of electrical
charge. In a molecule like CO, the electrons tend to spend a little more
of the time near the carbon atom than the oxygen. The molecule is said
to be permanently polarized, that is, have a negative pole toward
the carbon and a positive pole toward the oxygen. It is this net separation
of charge, this polarization, that makes it possible for the CO molecule
to emit and absorb photons. All radiation originates in the motion of
electrical charges.
Homonuclear molecules have no permanent
charge separation because there is no reason for the charge to
prefer one of the identical atoms to the other.
Astronomers had observed lines from molecular hydrogen with the
help of the Copernicus satellite, launched in 1972 under the direction
of
the Princeton astronomer Lyman Spitzer--the same Spitzer whose early
work directed Bok's attention to regions of the Galaxy where stars might
be forming. Molecular hydrogen will interact strongly with radiation if
the photons are sufficiently energetic to cause excited states of the
electrons. In this case, the photons see one of the electrons as
an individual charge which can be set into motion, and the
symmetry of the molecule is no longer relevant.
Observations from the Copernicus satellite only sampled the
peripheries of the GMC's. That is because these clouds are also the
location of relatively large quantities of interstellar dust. It
is almost certain that the clouds could not exist
as they are now, without this dust. We are not too sure about the
composition of this dust or where it came from, but it is critical
for the existence of a molecular cloud.
The ultraviolet radiation studied by the Princeton group is
blocked by the dust of the GMC's. This same radiation, would destroy
molecules like CO and many other species that have been found within
these clouds. A CO molecule would hardly last more than a few thousand
years if exposed to ultraviolet radiation that is ``typical'' for
our region of the Galaxy. This is true for many of the impressive
variety of molecular species identified in these clouds.
Table 8.1 lists those found through 1992,
according to William Irvine, and astronomer at the University of
Massachusetts.
Table 8.1:
Interstellar Molecules. After Irvine (1991, 1992).
| Simple hydrides, oxides, sulfides, amides, and
related molecules |
H |
CO |
NaCl |
CC |
| HCl |
OCS |
AlCl |
CS |
| PN |
SO |
KCl |
SiS |
| HO |
SiO |
AlF |
SiH |
| HS |
NH |
CH |
HNO |
| Nitriles, acetylene derivatives, and related molecules |
| CCC |
HNC |
HCNC |
HN=C=O |
| CCCCC |
HCN |
HCCN |
HC CH CN |
| |
HC CCN |
HCCCCN |
|
| |
HC CHCN |
|
|
| CCCO |
H(CC)CN |
HCCCH |
|
| |
HNCS |
|
|
| CCCS |
H(CC) CN |
HC(CC)H |
CSi |
| HCCH |
H(CC) CN |
HC(CC)CN? |
|
| HCCCHO |
H(CC) CN |
HCCH |
|
| HCCC |
HCCCC |
HCCNC |
CCCNH |
| Aldehydes,
alcohols, ethers, ketones, amides, and related molecules |
| HCO |
HCOH |
HOCHO |
HCNH |
| HCS |
HCCHOH |
HCOCHO |
HCNH |
| HCCHO |
HCSH |
HCOCH |
HNCN |
| NHCHO |
HCCO |
(CH)CO? |
|
| Cyclic molecules |
| CH |
CH(cyclic) |
SiC |
|
| Ions |
| CH |
HCO |
HCNH |
HO |
HN |
HOCO |
SO |
HOC |
| |
HCS |
|
HD |
| Radicals |
| OH |
CH(linear) |
CN |
HCO |
| CH |
CH |
CN |
NO |
| CH |
C H |
HCCN |
SO |
CH |
C H |
CS |
NS |
| SiC |
HCCN |
CP |
NH |
| SiN |
CO |
|
|
In addition to shielding the molecules from ultraviolet radiation,
astronomers think that the dust plays an important role in forming the
dominant molecules. Interestingly, is thought to
form on dust particles--the dust acts as an important catalyst for the
reaction
. Many of the other molecules
can be formed by reactions in the gaseous phase, but the most common
molecule requires dust. What is the nature of this dust, and where
did it come from?
Dust
We know a lot about interstellar dust and--we don't understand
everything we know. We would like to know what the dust grains are made
of and how they are made. Strangely, it seems there is more agreement
about how they are made than what they are made of. So let's start with
that.
Almost all models of dust formation begin with the extended envelopes
of stars in late stages of their evolution. It is rarely suggested that
dust might form in the cores of GMC's. The reason traditionally given for
this is that the densities in these cores, or clumps is not high enough
for the dust to form. This may well be true for those regions where the
densities have been sampled, but as we shall see, there is every reason
to think that stars are being formed in these cores, and this means the
densities must reach much higher values than those cited by the pundits as
being too low.
The extended atmospheres of very cool stars can have temperatures
well below 2000 Kelvin, and at these temperatures solids will begin to form
out of the gaseous phase. The process is the opposite of what is called
sublimation, which is what happens to dry ice or solid CO.
It is possible to detect solid materials in the neighborhood of stars
in a variety of ways. One of the most common is simply to look at the
radiation that is emitted from the star. A star that is surrounded by
a dust envelope will emit much more radiation in the infrared than a
similar object without the surrounding dust. This is because the dust
absorbs the radiation that is coming from the star and then re-radiates
it. The radiation that comes from the dust has much more of its energy
in the infrared than the radiation coming from the star. The cooler
an object, the more it will radiate at longer (e.g. infrared) wavelengths,
and the dust is cooler than the stars.
Another way to investigate the dust is actually to look at the
shape of the spectrum for features that will identify the nature of the
solids. This method is similar to that used to identify atomic absorbers
in a stellar or solar spectrum (cf. figure 4-2).The main
difference is that in the infrared, the features are not so numerous, and
they tend to be broad. Workers in this field tend to be less certain
about the identification of specific materials than what are called
functional groups of atoms. These atoms could occur in a variety of
molecules, but they give rise to characteristic absorption or emission
features in the infrared. Typical examples of such groups are Si--O
or O--H. In both cases, the stretching of the molecular bond causes
absorptions or emission at specific ranges of infrared wavelengths.
Astronomers have known for decades that a critical factor in
the determination of the chemistry of cool stars was the ratio of the
abundance of the element carbon to that of oxygen.
This is because the CO molecule
is very tightly bound. Therefore, if there is more C than O,
most of the oxygen will go to form CO, leaving some C to form compounds
such as 
. It is more common for there to be more O than C,
and when this is the case, most of the C is tied up in CO, and there
is O left over.
Most stars have C/O ratios about 0.4, like the sun,
and the spectra of the cooler objects show very strong absorptions due
to the TiO molecule.
The much rarer carbon stars show features, and
very strong CN and CH. The infrared spectra of these two different
kinds of stars show characteristic features that one might expect.
For example, SiO features are seen in the spectra of oxygen-rich
stars, while SiC has been identified in carbon-star spectra.
Once the dust is made by the stars, it may be dispersed to the
general interstellar medium of the Galaxy. Observations show that it is
very highly concentrated to the galactic plane, but it is a ubiquitous
feature in the planes of all spiral galaxies
(cf. figure 3-2).It has been known for decades that
interstellar dust dims and reddens the light from distant stars.
It also causes
a small fraction of starlight to be polarized.
From the way that starlight interacts with the grains it is possible
to say something about typical grain sizes. Most are about a tenth
of a micron--
cm in radius--pretty small, but very effective
in dimming starlight.
We can tell from the spectra of certain stars what the composition
is of the gas between us and the stars. The analytical spectroscopy of
interstellar matter has a long history. It was recognized in the
first decade of the twentieth century that the certain lines in the
spectra of double stars behaved strangely. Since double stars orbit
one another, their spectra show radial velocity (Doppler) shifts that
oscillate, reflecting their orbital motion. In the 1904 edition of the
Astrophysical Journal, the German astronomer Hartmann called
attention to lines of ionized calcium whose wavelengths did not change
along with the lines from the star in Orion he was observing. He
properly attributed this absorption to an interstellar cloud between
the earth and this star.
In the 1930's it became known that certain interstellar lines
were due to diatomic molecules, such as CH and CN. The ionized
molecule, CH was also identified. The Nobel laureate Gerhard
Herzberg is a molecular physicist who has had a continuing interest
in astrophysical problems. Many astronomers have learned both
atomic and molecular physics from Herzberg's monographs. These books
are unbelievable in the amount of detail that they present. In
spite of the complexity of the subjects discussed in these volumes,
there have remained the authoritative sources for four or more decades.
Herzberg discussed interstellar molecules in the 1950 edition of
his book on diatomic molecules, and on page 496, he mentions that
the excitation of the CN molecule is 2.3 Kelvin. This temperature
is surely due to the cosmic microwave radiation, discussed in Section 7.2.
In some sense, Herzberg had confirmed Gamow's prediction of a background
radiation. The value that he found was better than Gamow's which
ranged from 5 to 28 Kelvin, depending on very uncertain assumptions
about the present age of the universe.
The current value of the temperature is securely fixed at 2.7 Kelvin.
The modern era of analytical work on interstellar matter was
begun by Spitzer and his colleagues at Princeton, with the help
of the Copernicus satellite. Their work showed that the gas
was depleted in most elements heavier than hydrogen and helium. They
soon concluded that the missing
elements must be in dust grains. It would be truly surprising if the
interstellar gas were really metal poor. We can observe and determine
the compositions of very young stars, that have, so to speak, ``just''
formed from the interstellar gas.
As far as we can tell, their compositions
are very similar to the SAD. How could such stars form from a metal-poor
gas? Surely the young stars form from gas and dust, and
the dust is vaporized and mixed inside the star. The spectrum therefore
shows a normal composition.
The chemical composition of the dust grains is presently uncertain,
but there are many ideas about what it might be. The depletions of the
interstellar gas tell us that the grains must be made of common, abundant
elements. Ideas therefore focus on some form of solid carbon and/or silicate
minerals. There is evidence for these chemicals in circumstellar
envelopes (as opposed to interstellar gas), so probably they are also
a part of the dust in clouds and in the general interstellar field.
Textbooks on astronomy describe a model in which carbon or silicate
grain cores have icy coatings, or mantles.
A great deal of effort has gone into the interpretation of what
astronomers call the ultraviolet extinction curve. This is a graph of
the relative amount of starlight that is dimmed in interstellar space,
mostly by dust grains. The absorption is plotted against the reciprocal
of the wavelength of the light. Wavelengths (in Angstrom units) are
indicated across the top of part (b) of the figure. Basically, the
shorter the wavelength, the greater the extinction or dimming. However,
there is a very prominent hump near 2200 Angstroms. Calculations and
experimental data suggest this hump may be due to some form of solid
carbon, for example, graphite, or soot.
Figure 8.2:
The Interstellar Extinction Curve.
The ``typical'' galactic extinction curve is shown as a solid line.
The hump near 2200 Angstroms resembles absorption by
graphite in laboratory measurements, but the interstellar
feature could be due to some other substance or a mixture
with graphite. Not all
interstellar absorption shows this hump so strongly.
Additional curves are shown for the Large (LMC) and Small Magellanic
Clouds (SMC) as well as for the direction to a star
named 30 Doradus.
New information
on interstellar grains has come from the analysis of very small fragments
of meteorites that are thought to have originated in interstellar space,
but never melted and mixed with the general material of the solar nebula.
Cosmochemists call these presolar grains, because they were probably
solidified before the formation of the solar nebula. The most characteristic
signature of presolar grains is an isotopic composition very different
from that of the SAD. One class of clearly identified presolar grains are
found in carbonaceous meteorites, and this supports the notion that
carbon in some form is an important constituent of interstellar dust.
Would dust grains last forever? The answer to this is surely ``no,''
but it isn't easy to give the kind of estimate that we can for a CO or
molecule. Grains appear to be pretty tough. They can be
found in regions where the interstellar gas is hot (
K)
as well as in the cool clouds. There is some very hot gas, though, that
has been heated by shock waves from stellar explosions. In this gas,
the heavy metal content is more nearly normal, and a reasonable
interpretation is that the grains have been evaporated.
Cloud Formation and Dissipation
The Soviet astronomer I. S. Shklovsky was a powerful intellect.
He flourished during the time of the Cold War, and died just about at its
end. Nevertheless, he was very well known to Western astronomers because
he wrote important books that were translated into english. One of his
later books was called Stars: Their Birth, Life, and Death. The
english edition appeared in 1978, when the interests in interstellar
molecular chemistry were rapidly accelerating.
Shklovsky's training was in radio astronomy. In the
1950's he had written a fine monograph entitled Cosmic Radio Waves.
At that time, and for many years thereafter the only star seriously studied
by radio techniques was the sun. In the mid 1960's Shklovsky had written
a book on the solar corona, and the Russian edition of his book on stars
was published about 10 years after that. Shklovsky showed that he had
mastered the literature and the vocabulary of stellar astronomy, not something
that is easy, especially for one no longer young. But Shklovsky was
exceptional. In addition to his very competent writing about stars, he
brought interesting new ideas.
Shklovsky thought GMC's might be made with the help of interstellar
magnetic fields. There is ample evidence for such fields. They are quite
weak, but they produce measurable effects, and have been extensively
investigated. The field lines lie primarily in the plane of the Galaxy,
mostly running parallel to the spiral arms. Shklovsky's idea was that
the interstellar material is sufficiently charged to ``cling'' to the
field lines (figure 7.4). Then, if there were a little
accumulation of the matter at some point, the gravity of the central
plane of the Galaxy would pull the matter toward, it, bending the field
lines even more. The more material accumulates, the stronger the gravitational
force builds up, pulling even more matter into the forming cloud.
Figure 8.3:
Shklovsky's Notion of the Formation of GMC's. In this figure,
the central plane of the Galaxy represents the bottom of the potential
well that the dust is, so to speak, sliding down. The mirror image of
what is shown could be happening from ``below.''
Shklovsky typifies the kind of intellect that adds spice to science.
He was like Hoyle in the respect that he was full of ideas, some of which
were brilliant and enormously useful, while others were never taken seriously.
It is interesting to contrast his approach to science with that of the
Princeton astronomer Lyman Spitzer. Spitzer has always been at the forefront,
but never over the edge. No one ever accused Spitzer of anything but
competence and reliability, and those who wish to avoid being wrong about
some astronomical point could do no better than to follow his lead.
We are fortunate to have both kinds of minds at work on astronomical
problems.
Spitzer has discussed a simple model for the formation of GMC's
through the constructive coalescence of smaller clouds. His idea is that
small clouds--possibly even some formed by Shklovsky's mechanism--would
collide with one another. Some of these collisions would be destructive
and others constructive. The constructive collisions would lead to
larger clouds, and in this way a population of GMC's might be built up.
A great deal has been written on the subject of cloud formation,
and we cannot do justice to the ideas of many of the workers in this
burgeoning field. Modern workers do not stress the role of the magnetic
field suggested by Shklovsky. They do emphasize of the
importance of the self gravitation as a cloud grows in size. The more
massive the cloud, the stronger it pulls in still more material.
What role might be played by dust? Molecular hydrogen,
will last only a short time in the general field between the stars. Its
efficient formation requires dust as a catalyst. So the clouds won't be
molecular in nature without dust. Should there be models that start
with an accumulation of dust?
Without question, these GMC's are the site of star formation.
The astronomer is now armed with impressive ways to probe these complex
locations. At visual wavelengths, the clouds are essentially opaque,
but in the infrared as well as with radio and microwave methods, it
is possible to look inside these clouds to see very young stars as
well as stars in the process of formation.
There is still a big gap in our understanding of how gas clouds form
into stars. We are sure that it happens, but we can't yet make convincing
models of what happens. Rather straightforward laws of physics tell us
that as these clouds contract, they must spin more and more rapidly. We
know that somehow, this rotational energy must be lost by the star. At
the present time, we are just not sure how. Observations tell us that these
young stars are surrounded by disk-like structures, not unlike our picture
of the solar nebula. Probably much of the rotational energy of the star
gets transferred to that disk, but we don't know what the mechanism is.
Figure 8.4:
Protoplanetary Disks Observed by the Hubble Space Telescope.
These disk like features were observed in the Orion Nebula. Each of
the images is about 1700 AU across, so the disks are several hundred
AU across, and are intermediate in size between the Kuiper and
Oort comet clouds.
Courtesy of M. J. McCaugrean, C. R. O'Dell, and NASA.
There is another aspect of the formation of young stars that is not
at all understood. At some point as the disk is forming about a young
object, jets form as though expelled from the rotational poles (axes)
of the stars. It would be very useful if we could learn that these jets
carry off the rotational energy of the star, but so far we don't know
how this could be. The jets seem to be an important aspect of the formation
of a new star, but we don't understand their function.
Once massive young stars begin to shine, they blow away the gas from
their birthsites. All massive young stars have violent winds. If they
rapidly run through their nuclear fuel and explode, they remove the gas
even more quickly. The gas--and dust--return to the general interstellar
medium, at least partially enriched in chemical elements synthesized in
the very stars that caused the death of the cloud.
Summary
Stars are born in interstellar clouds. We can observe these clouds
using the radiation emitted by interstellar molecules. The molecules are
shielded from the general background radiation of the galaxy by dust.
We are not sure of the composition of this dust, but much of it may be
some form of carbon, probably graphite. Dust is thought to be formed in
the atmospheres of very cool stars. There is something of a chicken and
egg problem in that dust is required to shield ultraviolet radiation that
would break up molecules, and also to form the most common molecule,
. Yet some of the cool stars formed in these clouds may be the
ideal sites for the formation of dust. Massive, hot stars may evolve
and dissipate the clouds, either by their strong winds, their radiant
energy, or by stellar explosions. Thus the clouds are dissipated, and
much of their material is returned to the general interstellar medium
in the form of gas and dust.
Thermodynamics and Chemical Equilibrium
One of the triumphs of nineteenth century science was the discipline
of thermodynamics. The name of the discipline indicates that it has something
to do with heat, or energy. One may take a broader view, and include such
diverse matters as information, but we shall not do so here. Instead of
attempting a general description of thermodynamics, we shall describe some
specific situations that illustrate its principles. Ultimately,
thermodynamics rests on laws, that is, postulates, which we may justify,
but not prove in a fundamental way.
Suppose you had two large boxes of gas. We might suppose the gas
is inert, like helium or argon. It is simplest if we think of an ideal
gas, a material that does not exist, but is approximated for many purposes
by inert gases. Let us suppose that both contain the same number of molecules
but that
one of the containers is hotter than the other. The pressure would then be
higher in the hotter container, too. We
could put the boxes in contact with one another, and open a door between them.
Molecules from the hot box would stream into the cold one. We could put a
paddle wheel in the stream, and use it to generate electricity, or wind
a weight, or do a variety of other things.
Eventually, the gas in both boxes would reach the same temperature,
pressure, and number of molecules. At this point, there would be no way
we could use a paddle wheel to do any of the things we mentioned above,
nor any other useful work. Although there would still be lots of energy
in the boxes that had reached an equilibrium, we couldn't do
any work with them.
The system with the two boxes at different temperatures has the ability
to do work, while after the temperature between them has equalized, this
capacity is no longer present. The German physicist Rudolph Claussius
(1822-1888) proposed that the inability of a system to do work could be
considered a property of the system. If we picture our system as
a box of gas, then familiar properties would be temperature, volume, and
density. Claussius's new property was given the name entropy,
according to the popular science writer Isaac Asimov, ``...for no
clear etymological reason''!
Entropy is measured in a funny way, that makes sense only after
some study. Since it measures the inability to do work, you might
expect it to be zero for the two-box gaseous system, after it has come to
temperature equilibrium. But it turns out that entropy is measured
in a way that it reaches a maximum for that temperature equilibrium.
So we measure the ability of a system to do work by considering how
far the its entropy is from its maximum value.
Ludwig Boltzmann (1844-1906) clarified the notion of entropy
by postulating that it was a measure of the probability of the
system. Consider our two boxes at different temperatures just after
we open the door between them. According to Boltzmann's ideas, the
configuration with a high temperature (
) in
one box and a low one (
) in the other would not be very probable.
Therefore, the initial entropy of the system would be relatively low.
Then the system would adjust until the gas in both boxes had the
same temperature. Boltzmann was able to show from the kinetic theory
of gases that the state with the temperatures equal was much more probable
than the original one. Then, the way entropy is defined, the entropy
was higher.
The Laws of Thermodynamics
We are now in a position to state the three laws of thermodynamics.
Laws one and three turn out to be much simpler to state than the second
law, sometimes known as the law of increase of entropy. Most of this
section will be spent with it.
The first law is sometimes called the conservation of energy. We can
state it in a useful way with the help of a specific example. Suppose
we dump some energy inside a balloon that is filled with an ideal gas.
The first law then states that the energy of the gas will increase, but
some of the energy must go into expanding the balloon. Therefore, at
the end of the energy transfer, the gas will not be as hot as it would
be if, for example, the gas were in an insulated box with a fixed volume.
Whenever energy is converted from one form to another, such as from
heat to work, the first law just says we must be careful to consider all
of the possible forms.
The second law deals with entropy. It says that all naturally occurring
processes cause the entropy of a (closed) system to increase. Consider
our two boxes of gas. Just before we open the door, there is a value
for the entropy of the box with temperature , and one for the box
with temperature . It turns out that the entropy of the hotter box
is higher than that of the cooler box, but we don't need to worry about
that here. The second law tells us that after we open the door, and the
temperature equalizes, the entropy of the two boxes is greater than the
sum of the initial entropies.
My introduction to thermodynamics was in 1953, when I took a course
in physical chemistry at the University of Virginia. My lab partner said
the second law was easy--it just said water ran downhill. While this
is a considerable simplification, it is also very useful. We need to
use the concept of potential energy, which we discussed in Section 4.8.
Water that is uphill has a potential energy that is converted into
kinetic energy as it flows downhill. Since this is a natural process,
the second law implies that ``downhill'' water is more probable than
``uphill'' water. This is entirely in line with what we would expect.
Suppose we placed a droplet of water at the lip of a bowl. We
would expect it to slide to the bottom, probably move uphill a little
but end up right at the bottom. If there were no friction between the
droplet and the bowl, the droplet would oscillate forever (assuming it
didn't evaporate). We know that friction is a part of the real world,
so the water would end up at the bottom of the bowl. The potential
energy the drop had at the top of the bowl would be converted into
heat, and the bowl would be just a little hotter than before the drop
did its thing.
According to the second law, the entropy of drop + bowl would be higher
at the end of this process than at the beginning. It shouldn't be
too difficult to convince oneself that of all the possible things that
might happen to a drop of water at the lip of a bowl, the most probable
is that the water flow downhill--as my lab partner said.
As far as we know, there is no violation of any law of the elementary
interaction of particles that says heat might be extracted from the molecules
in the bowl and deposited in a small puddle of water in just such a way
that the puddle would climb up the side of the bowl! Common sense tells
us that this would not happen. Thermodynamics tells us something a little
different. It says that it is over-, over-, over-, overwhelmingly more probable
that the drop will settle at the bottom of the bowl than that it would
spontaneously extract the kind of energy from the bowl to do the opposite
thing.
Very simple physical systems behave in a way that doesn't depend on the
direction of time. Consider the planets as just points, moving around
a featureless, smooth sun. This is a simple system. We could make a movie
of the system, and it would look natural whether we ran the film forward
or backward. When there are many particles interacting in a complex way,
we could tell immediately whether the film was being run forward or backward.
Consider the water drop and the bowl. The number of molecules involved
in both the drop and the bowl are many powers of ten. There would be
water molecules in the drop were one millimeter in
diameter. For matter involving large numbers of particles like this,
time does have a unique direction. Time goes forward in such a way
that the entropy of an isolated system will increase. Technically, this
direction for time has only statistical validity. Practically, it is
so overwhelmingly more probable that the entropy of a complex isolated system
will spontaneously increase. There is only one exception, when the
entropy has reached its maximum value. We couldn't use an isolated
system that had reached its maximum entropy to tell time. This does not
pose a problem for the world we live in.
Given our definition of entropy as a measure of the probability, we
now briefly state the third law. At absolute zero, the entropy of pure
crystalline substances is zero. This postulate allows chemists to
make calculations of the entropy of substances from thermochemical
measurements. With the zero point defined by the third law, such
entropies are called absolute entropies. Another way to calculate
them for simple systems is with the help of Boltzmann's definition
of entropy in terms of probability. In practice, absolute entropies
are often not needed because we can tell the ``downhill'' direction
from changes in entropy.
The Gibbs Energy and the Direction of Chemical Reactions
In astronomy, we often have a temperature and pressure that is
fixed by our model, and we want to know the relative amounts of chemicals
that could be present. Chemists often have a similar problem. They
mix two chemicals at the ambient temperature of their laboratory, and the
want to know if they will react. Under these circumstances, it turns
out to be more convenient to look at another thermodynamic property of
a system known as the Gibbs energy.
The Gibbs energy is related to the entropy, but there is a negative
sign. Consider a system with energy (
), volume (
), and entropy
(
). Let us suppose the pressure (
) and temperature (
) have
fixed values. Then the Gibbs energy (
) may be defined as
. Since we are trying to avoid equations in this book,
we shall only point out that the minus sign leads us to expect the
Gibbs energy to decrease for spontaneous processes, since the
entropy must increase by the second law.
The energy and 
-terms in the definition make it simpler
to use it than the entropy when a system might have to do work against
a constant pressure. We could show this explicitly with a few equations.
We will try to make this plausible below.
Consider a chemical reaction to form the simple diatomic radical
CN. It is convenient to think of the two atoms as well as the molecule
as being in the gas phase, (g).
In order to see if the reaction will proceed at a fixed temperature and
pressure, we calculate the Gibbs energies for the substances on both sides
of the arrow. We would do this for more complicated chemical equations too.
If the Gibbs energy of the products (on the right) is lower than the
Gibbs energy of the reactants (on the left), then the second law tells
us the reaction will go from left to right as long as the temperature and
pressure remain fixed.
On an atomic level, it is useful to look at the formation of this
molecule with the help of a potential curve, similar to the ones we have
used in looking at the behavior of nucleons (figure 9.3).
Figure 9.1:
Schematic Potential Curve for the Diatomic Molecule CN. The
vertical axis gives the potential energy as a function of the relative
separation of the two atoms. The minimum of the curve shows the most
probable separation of the atoms in a bound molecule, at low temperatures.
If we think of the potential curve of figure 9.3 as
representing a classical system, then a marble placed on the curve
would roll down the hill toward the minimum. We might think of the
minimum as the most stable position, as we did for the water drop in the
bowl. But the CN molecule is a very simple system, and as yet, we have
no analogue of friction. So the ball would roll out of the minimum,
toward even smaller separation, come to a halt at the same vertical
position it started with, and roll back the way it came.
For the CN
molecule to form, something must remove the relative energy with which
the two atoms approached one another. This energy could be removed by
the emission of a photon, or by a collision with a third atom, which
could take up the excess energy. Given that these possibilities exist,
we ask whether for a given temperature and pressure the CN would form.
The answer depends on the values of the temperature and pressure.
Intuition tells us that if the temperature is high, the molecule
is more likely to dissociate than form. The pressure is also relevant.
In elementary chemistry we learned a useful rule called the law of mass
action. That law said that if you stressed a system, the system would
try to remove the stress. For example, if you increased the pressure of
either C or N, the system would try to form the CN molecule to decrease
the pressure.
Conversely, if the pressure of C and/or N decreased, it would be more
likely that the CN would dissociate.
There is another way to look at the effect of pressure. Pressure
depends on both the temperature and the number density or the number of
particles per unit volume. So if we fix the temperature, the pressure
will increase or decrease directly with the number density. Clearly
at high number densities, the atoms of C and N will collide more frequently
with one another, and have the opportunity to form CN. This is
what we also concluded from the law of mass action.
If CN dissociates, it forms two atoms, so there are two particles
where previously there was only one. At a fixed temperature, which we
assume, the two atoms supply exactly twice the pressure of the molecule.
Since we also assume a constant pressure, the increase due to the extra
molecule must be removed in some way, and that is done by an expansion of
the gas. This is equivalent to doing work against pressure. When CN
dissociates, we need to consider this extra work in addition to the
energy it takes to roll the ball up the hill in figure 9.3.
It is this extra work that is properly figured in the Gibbs energy
for the constant temperature and pressure processes. Such conditions
usually turn out to
be of primary interest, both in laboratory chemistry, and astronomical
applications.
Chemical Equilibrium and Condensation
Suppose the differences in the Gibbs energies of the two sides of a
chemical equation is zero. The reaction can then proceed in either
direction with equal probability.
The influence of pressure that we discussed in the previous section
now plays a key role. With the pressure fixed, it turns out to be
possible to calculate the relative amounts of the reactants and products
in a chemical equation.
Let us consider an especially reaction, where iron in the gas
condenses, that is, becomes solid iron. We may write
where the `g' and `s' stand for gas and solid. The `reaction' is
really only a phase change, but the laws of thermodynamics still apply.
In this case, the pressure of gaseous iron is a function of the
temperature only. Note that this is what the chemists call the
partial pressure of iron, that is, the pressure that would hold
if iron were the only gaseous species. The total gas pressure is
the sum of all of the pressures of atoms and molecules in the gas
phase.
There will always be some iron in the gaseous phase, no matter
how low the temperature drops, but there is a relatively narrow temperature
range where the pressure in the gas phase drops very rapidly, and for
temperatures below this range, it is a good approximation to assume
that all of the iron has passed into the solid phase. Workers in this
field often take the temperature at which the partial pressure has
dropped to half of its original value, and call it a 50% condensation
temperature.
Figure 9.2:
Condensation of Iron from the Gaseous Phase. The vertical
axis gives the partial pressure of gaseous iron. Temperature is
plotted on the horizontal axis, increasing to the right. A straight
line divides regions of the plot where gaseous and solid iron
are the dominant phases.
We can make a plot of the vapor pressure of iron as a function of
temperature. For each value of the vapor pressure, there will be a
temperature where half of the original vapor has condensed. The plot
of figure 9.4 is made so that a straight line on the plot
divides the region where the iron is primarily in the gas phase from
the one where it is primarily solid. The figure shows that the
condensation temperature depends on the partial pressure of gaseous iron.
The law of mass action is a useful mnemonic here. If we consider a
fixed temperature, then we would expect a high gas pressure would
drive the ``reaction,''
to
the right. So the region where the solid phase dominates is above
the dividing line of figure 9.4.
Calculations of condensation temperatures have mostly been carried
out for cooling gases with the composition of the SAD. They show that
the first appreciable solids to form are oxides of aluminum, calcium,
and titanium. Two of these oxide are the minerals corundum
(
), and perovskite (
). Materials that form solids
at the highest temperatures are called refractory, while those
that do not enter the solid phase until the temperature is low are
said to be volatile. Corundum and perovskite are thus said to
be refractory oxides.
The temperature at which a chemical element comes out of the gaseous
phase depends critically on the compounds that it forms.
Few elements condense as pure species, as we have indicated for iron.
Detailed calculations show this is not a bad approximation for iron itself,
but for an elements like aluminum or calcium, the assumption would
be badly off. Both of these elements come out of the gas phase
at high temperatures because they form refractory oxides.
It has nevertheless been the custom of workers in this field to
assign condensation temperatures to elements with the understanding
that these values depend on the overall composition assumed for the
cooling gas.
History and Planetary Densities
Condensation schemes were calculated for the cooling solar nebula
beginning with the remarkable work of Nobel Laureate Harold Clayton
Urey (1893-1981). He simply applied the laws of thermodynamics
that we have discussed in the previous sections to a cooling
gas with the SAD composition.
We can simplify the outcome of his work as well
as modern improvements of it with the help of three of our four
``elements'' from Chapter 2. Thermodynamics tells us
the materials that condense from a gas with the SAD composition
as the temperature drops.
The first solids are metallic, with
a small admixture of refractory oxides. At lower temperatures, rocky
materials solidify, followed by the ices.
Urey thought the condensation sequences provided a theoretical
basis for understanding the densities of planets at various
distances from the sun as shown in table 2-1.
In his original theory, there would be a different density for
each distance from the sun. This density could be derived from the
pressures and temperatures in the solar nebula.
Urey
pointed out that the decompressed densities should be used in this
comparison, since the solids in the solar nebula formed first under
low pressures.
The basic condensation model dominated thinking about the early
chemistry of the planets--especially the terrestrial ones. It has
long been granted that the Jovian planets may have formed largely as
a result of their own gravitation. For Mercury through Mars, and
perhaps even for some asteroids, condensation seemed the ideal
tool to understand the bulk densities. There was a problem understanding
what happened to the matter that did not condense, but it was assumed
a vigorous wind from the young sun could remove the uncondensed
material.
Even as the most detailed condensation calculations were being carried
out evidence began to accumulate that seemed to contradict the notion.
Space probes were able to sample the atmospheres of Venus and Mars.
Certain meteorites were identified with reasonable probability as
being fragments of the planet Mars or the asteroid Vesta. Many of these
observations showed that there was no firm relation between the volatility
of material and its location in the solar system.
A pillar of the condensation theory has always been the relatively
high bulk density of Mercury. If this is not due to condensation at a
high temperature, how might it be explained? A popular idea
that persists since the 1980's is that Mercury once had a structure
and composition similar to that of the earth and Venus. These twin
planets have rocky mantles and metallic cores that start about halfway
down toward their centers. In the case of Mercury, it is possible that
much of the rocky mantle was blasted away by meteoroid impact.
We have known since the Mariner missions in the 1960's that meteoroid
impacts have scarred the faces of Mars and other solid planetary surfaces.
Geochemists realized that the earth must have grown by the accumulation of
relatively small solid bodies because of the absence of heavy noble gases
in its atmosphere. These gases, argon, krypton, and xenon are much too
heavy to have simply boiled off into interplanetary space.
Throughout
much of the twentieth century astronomical textbooks used this
mechanism--boiling off--to explain why the earth and terrestrial planets
did not have their SAD complements of hydrogen and helium. It is
rather easy to show that most of these two light gases would leave the
present
earth's atmosphere. But it was never very clear how such demonstrations
would apply to a hypothetical body that once had all of the hydrogen
and helium that would complement the earth's metal and rock. Recall
that about 2% by mass of the SAD is in elements other than hydrogen
and helium. Consequently, a protoearth might have been 50 times its
present mass, not as massive as Jupiter or Saturn, but more massive than
Uranus and Neptune. It is at least problematical whether such a
body might have lost its hydrogen and helium.
The geochemists had it right all along. The earth and terrestrial
planets never did have their full complement of hydrogen, helium, and
other volatiles from the SAD because they formed from small solid bodies
mostly of metal and rock. In the heyday of condensation, it was thought
the terrestrial planets had the composition of solids that could condense
at various distances from the sun. Now, it seems any given inner planet
might have been formed from meteoroids and planetesimals from a wide
range of radii, perhaps stretching to the ``snow line'' some 3 to 4
AU from the sun.
It is now possible to follow by computer the motions of a large
number of planetesimals. The American planetary scientist George
Wetherill has made steadily improving calculations of this kind.
He follows the paths of these bodies, and has plausible formulae to
decide when a collision will result in a larger object or smaller
fragments. He has made models of planetary systems that could form
from the coagulation and fragmentation of such bodies, and some
resemble the present solar system.
In the late 1970's two hypotheses involving the impact of a
meteoroid or planetesimal on the earth became well known. Possibly the
better known of these was for a relatively recent impact, some 65 million
years ago. The geologist Walter Alvarez and his father Louis
suggested that the extinction of the dinosaurs might be related to
the aftermath of the impact of a large meteoroid. This hypothesis
is now widely accepted, but with some reservations,
because the extinctions could
be shown to have taken place both before and after the impact.
A great deal has been written on dinosaur extinction, so we
need not pursue the matter here.
The astrophysicist A. G. W. Cameron has made many contributions to
modern astronomy, in addition to his work on nucleosynthesis. In 1976
he and a collaborator wrote a paper in which it was claimed that the
Moon formed from debris when a relatively large body, perhaps 0.1 earth masses,
collided with the earth. We shall have more to say about this theory
of the Moon in a later chapter. It is probably cited today as the
most likely of many theories for the origin of the Moon.
Today, meteoroid and planetesimal impacts are being explored
as relevant to the chemistry of planets in many ways that were
not mentioned several decades ago.
Perhaps a majority of planetary
astronomers now prefer the ``blasting of the mantle'' hypothesis over
condensation as the explanation to Mercury's high density.
Does this mean that Urey's idea was wrong?
Most workers have been unwilling to
abandon the notion completely. Surely
processes in the early solar system were more complex
than in the simplest equilibrium condensation model explored by Urey.
But the planetesimals that formed the terrestrial
planets were basically of metal and rocky compositions. And it is
very tempting to conclude the lack of icy (volatile) material was due
to condensation at a relatively high temperature.
Condensation Temperatures and Volatility
The University of Chicago has a long history of research on
cosmochemistry of the solar system. A prime goal of much of their work
was to determine the primitive composition of the solar nebula,
what we have called the SAD. Gordon Goles, a graduate of Chicago,
facetiously compared the attempt to find this primitive composition to
the quest for the Holy Grail. The Chicago geochemist Edward Anders
may have been the principal knight in this noble quest. Unlike some
of the legendary Grail hunters, Anders has had good success.
Most scientists accept his
judgement that the SAD is best represented by a special type of
meteorite.
There is a class of meteorites known as carbonaceous chondrites.
While they are similar in composition, they are not identical. All
are unusual in having some 10 to 100 times more carbon
present than found in other meteorites. Recent work has revealed
microscopic grains of diamond and silicon carbide that are ``presolar''
in their isotopic compositions. At the time Anders and his collaborators
focused on a specific subclass of the carbonaceous chondrites as the best
SAD emulators, the classification designations was slightly different
from the ones used today.
Anders and his coworkers considered the content of obvious volatile
substances in the three subclasses, called CI, CII, and CIII.
Water is the most important
volatile.
A well-publicized plot from this group showed ratios of various elements
in CII's and CIII's relative to the CI's. If the abundance of an element
was the same in all three elements, the ratios would be unity. If there
were less of an element than in the CI's the ratio would be less than
unity. Figure 9.6 is a plot similar to the ones made by Anders
and his coworkers, but with newer material.
Figure 9.3:
Carbonaceous Chondrite Compositions Indicate Volatilities.
In this diagram, CM meteorites are substituted for the CII's used
by Anders, while CV's play the role of the CIII's.
Elements with the same meteorite compositions as the volatile-rich
CI carbonaceous chondrites plot at unity on the y-axis. Thus fluorine
sulfur, chlorine, zinc, selenium, and bromine are among the more volatile
elements.
Scandium, titanium, iron, and lanthanum are involatile.
Let us grant that all of the volatiles should be greater in the CI's
because that is where we find the most moisture (water). Then we can classify
the relative volatility of various chemical elements by how far they
deviate from the CI's composition. In the plot, the most volatile elements
are displaced downward by the largest amounts. We might refer to the
classification of the volatility of elements in this way as an
empirical classification.
We can also compare our judgements of the volatility from
figure 9.6 with theoretical calculations of the condensation
temperatures for the elements.
This is done in the top part of the figure.
These temperatures were taken from
a book on meteorites and the early solar system
by the American cosmochemist John T. Wasson.
Certain of the most volatile elements are not shown.
Hydrogen itself,
carbon, oxygen, and nitrogen are strongly depleted in all of these
meteorites relative to the solar composition. We will call these
elements supervolatiles.
Elements with the lowest condensation temperatures are the
most volatile, by definition. Volatility as defined by calculation is
a theoretical classification.
What we see from figure 9.6 is that there is a good, but
though not perfect correspondences between the empirical and theoretical
measures of volatility. Perfect correspondence is not to be expected.
It is certain that the theoretical model does not and cannot take
into account the complexities by which volatiles are depleted in the
three classes of carbonaceous chondrites.
All meteorites have spent time as a part of larger
parent bodies, most probably in the asteroid belt. We know that
many underwent extensive heating and melting, but this
was not true for the CI meteorites. Geologists can tell this
by examining the texture of the materials under a special microscope.
The carbonaceous chondrites were subjected to minimal heating, and the CI's
least of all. We know
this because of the difference in volatile contents between the CI's and
the other classes.
All of the carbonaceous chondrites have lost supervolatiles.
This is obvious, because they don't have their SAD complements of
hydrogen and helium, not to mention carbon, oxygen, and nitrogen.
It seems
reasonable to attribute the volatile loss within the class of carbonaceous
chondrites to heating that took place on the parent bodies themselves,
or possibly within the solar nebula. The carbonaceous chondrites
other than the CI's contain small, often rounded inclusions
called chondrules. These chondrules do appear to be igneous in nature,
and their volatile content is low. Generally speaking, among the
carbonaceous meteorites, low overall volatile content is associated
with a high proportion of these chondrules.
Figure 9.4:
Logarithmic Abundances in the Sun and Type I Carbonaceous
Chondrites. Meteoritic abundances from J. T. Wasson. Solar
abundances from a tabulation by N. Grevesse.
The strongest support for Anders's selection of the Type I carbonaceous
chondrites ``as the Holy Grail'' comes from a comparison of their abundances
with determinations from the solar atmosphere. Figure 9.6
shows a plot of the logarithm of abundances determined in the sun and
in the CI carbonaceous chondrites. The most volatile
elements, carbon, nitrogen, oxygen, and the noble gases, are not plotted.
For the remainder, the correspondence is remarkably good. Deviations
from a straight line for only a few elements seems significant, and
these may be due to errors.
The importance of finding the meteoritic Holy Grail is that
the composition of these meteorites may be used to estimate SAD compositions
for elements whose abundances are not well known in the sun.
The CI's arguably provide the best values for SAD abundances of
elements that are not supervolatile. It is common among earth scientists
to assume that the nonvolatile composition of the mantles of the
terrestrial planets closely resembles that of CI meteorites.
Similarly, the cores of these planets are assumed to be chemically
similar to meteoritic nickel-iron alloys.
Summary
Thermodynamics provides a basis for understanding many of the
processes that take place in the early solar nebula. With the help
of this discipline, we have been able to predict sequences in which
solids would form from a gas with the SAD composition as the temperature
drops.
It is probable that the
temperature in the solar nebula decreased with distance from the sun.
Materials that would be able to solidify first from a nebula with
the SAD composition would be primarily metallic (first) and then
rocky. At greater distances from the sun, ices would condense.
The terrestrial planets undoubtedly owe their metallic and rocky
natures to the early condensation of refractory or involatile materials.
It is an open question whether the density decline from Mercury
through Mars can be explained primarily in terms of condensation
or if we have been fooled into thinking so by Mercury's high density.
Many now think Mercury has a high density because its rocky mantle
was blasted off by meteoroid impact.
A certain class of meteorites known as CI carbonaceous chondrites
provides us with the best estimates of nonvolatile chemical elements
in the sun. Most SAD abundances are based on analyses of these meteorites.
Planetary abundances often assumed to be similar to those in various
meteorites.
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