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WHERE did the chemical elements originate? Astronomers believe that
almost everything other than hydrogen and helium was produced in stars.
The most spectacular site of this so-called ‘nucleosynthesis’ is a supernova
explosion. But another kind of star is also busily producing various elements,
including the carbon essential to all life on Earth. These are the red giants.

Elements are produced deep within red giants, but occasionally a star
‘dredges up’ some of its interior gases to show us what is going on inside,
so we can check our theories. Some unusual red giants have carbon or exotic
metals at their surfaces. Others show signs of even rarer elements, such
as technetium.

Technetium is one of the few elements that does not have a stable isotope;
its longest-lived isotope has a half-life of two million years. The red
giant stars where we observe technetium, however, are thousands of millions
of years old, so the technetium cannot have been present when the star formed:
it must have been produced within the star.

A red giant is a star near the end of its life. All stars begin as vast
clouds of diffuse gas in the Galaxy. Gravity causes these clouds to contract,
reaching higher temperatures and densities, until hydrogen begins to fuse,
or ‘burn’, into helium. For the Sun, this contraction took about 30 million
years. The time that it takes a star to burn its hydrogen depends critically
on its mass. For example, our Sun will exhaust its core hydrogen supply
when it is some 10,000 million years old, whereas a star three times the
mass of the Sun would take only 20 million years. Our Sun is about 4500
million years old, and is thus about halfway through the phase of evolution
where it is burning hydrogen.

After all the hydrogen in the core has been converted into helium, the
core contracts and the envelope expands greatly. The star cools and so appears
redder. As the core contracts, regions rich in hydrogen reach temperatures
high enough to start hydrogen burning in a shell surrounding the helium
core. The total luminosity then rises. The star now possesses a core of
helium, and a very distended, cool, red envelope: it has become a red giant.

As the luminosity increases, there is extra energy to be carried through
the star. Yet there is a limit to the amount of energy that can be carried
by radiation. When this limit is exceeded, the material in the star must
carry the energy by the only other way it can: by physically moving about.
The gas bubbles like a pot of boiling water. Hot gas moves outward through
this convective region of the star, exchanging positions with cooler gas
from above it. One effect of this is to mix the convective region, so that
any variation in its composition is quickly removed.

As the star expands, a ‘wind’ of gas from its surface carries some of
its mass away into space. A similar process happens in the Sun, but the
solar wind is tiny in comparison to that streaming off red giants. During
the 100 million years that our Sun will spend as a red giant, it will lose
about 20 per cent of its mass. The material expelled into the Galaxy will
form the next generation of stars.

A star does not expand forever. By the time the star reaches about 2000
times the luminosity of the Sun, the central temperature rises high enough
for helium to ‘burn’ into carbon. Because the core of a red giant is extremely
dense, the helium burning spreads rapidly to produce a powerful ‘flash’
of energy. The helium flash may, for about an hour, generate more energy
than is produced by an entire galaxy, yet very little of this energy escapes
the star. It is absorbed in expanding the core and so lowering its density.

When calculations first suggested the helium flash, it seemed a miracle
that the star did not self-destruct. But many stars have passed through
this phase, so clearly the helium flash does not destroy them all. Recently,
Bob Deupree of the Los Alamos National Laboratory, in New Mexico in the
US, modelled the core flash with supercomputers. He found that the helium
flash may mix the star’s core, to produce some peculiar compositions, but
that most stars will survive.

Shell flashes

The star now settles down to a phase of helium burning in a core, surrounded
by a shell where hydrogen is burning (see Figure 1a). This is the second
major phase in the life of a star such as the Sun, and it lasts about 130
million years. The helium burning in the core initially produces carbon.
Later, some of the carbon nuclei capture helium nuclei to produce oxygen.
When the central supply of helium has been exhausted, therefore, the ashes
of the helium burning consist of a mixture of carbon and oxygen forming
a dense core. At this stage, the carbon-oxygen core is surrounded by a shell
where helium is still burning (see Figure 1b).

This phase of a star’s life has attracted a lot of attention in recent
years. Red giants are very cool, and therefore red, yet they are extremely
bright, with luminosities many thousands of times that of the Sun. In the
mid-1960s, Martin Schwarzschild and Richard Harm, at Princeton University,
and Alfred Weigert, of the Max Planck Institute for Physics and Astrophysics
in West Germany, made an exciting discovery. The output of energy of the
helium shell is unstable, so that it periodically produces enormous outbursts
of energy, called shell flashes .

After a shell flash, the convective region in the outer parts of the
star becomes deeper. If the bottom of the convective region goes down far
enough to make contact with the layers that are rich in carbon, it could
bring this carbon to the surface of the star. This process would provide
a natural explanation for the carbon stars, a rare kind of red giant with
a surface that is rich in carbon.

Because red giants are very cool, with a surface temperature below 3000
K (the Sun’s surface temperature is 5800 K), the atoms can combine to form
molecules. The spectra of many red giants, for example, show absorption
bands due to titanium oxide. Some peculiar red giants have bands caused
by other metal oxides, such as zirconium oxide. Not all the molecules are
oxides. The spectra of carbon stars show strong absorption due to a molecule
made of two carbon atoms.

The types of molecules that form in a red giant depend on the amount
of oxygen present. Carbon and oxygen atoms combine readily to form a molecule
of carbon monoxide. In ordinary red giants, oxygen atoms outnumber carbon
by three to two and all the carbon goes to form carbon monoxide (which is
difficult to detect directly). The oxygen atoms left over are free to form
the metal oxides that we see in these stars.

If, however, carbon atoms outnumber oxygen atoms, then all the oxygen
is locked into carbon monoxide molecules, and there is none left for the
formation of other oxides. The excess carbon appears as the dicarbon molecule.
So researchers believe that the carbon stars are simply red giants where
carbon is more abundant than oxygen. The ‘zirconium oxide’ stars seem to
be red giants that have roughly equal amounts of carbon and oxygen.

The first theorist to calculate the details of the way that a red giant
could dredge up some of its interior gasses was Icko Iben, of the University
of Illinois at Champaign-Urbana. Subsequent calculations by Iben and many
other astronomers in the US, Poland and Australia have confirmed this picture.

We must observe real stars to test the models, of course. Detailed observations
of star clusters in the two nearest galaxies, the Large and Small Magellanic
Clouds, have found that, with very few exceptions, the carbon stars in each
cluster are brighter than the other red giants in that cluster. This is
just what we would expect if carbon stars are produced by adding carbon
from the interior at succeeding shell flashes, which occur as the star grows
in luminosity.

During this part of a star’s life, two processes are eating away at
its large outer envelope of hydrogen. From the bottom, the shell of hydrogen
burning moves upwards turning the envelope’s hydrogen into helium. Meanwhile,
the stellar wind removes mass into space from the top of the envelope. For
the brighter stars, the loss of mass from the surface is the more important
effect. Don Faulkner of the Mount Stromlo Observatory in Australia and Bohdan
Paczynski and Detlef Schonberner at the University of Kiel, West Germany,
have calculated what happens after most of the envelope has wafted off into
space. The star remains about the same brightness, but becomes substantially
hotter. It produces ultraviolet radiation that eventually ionises the matter
previously expelled, to make it glow as a ‘planetary nebula’ – so-called
because it looks like a planet when seen in a small telescope. Soon afterwards,
the central star begins to cool, and becomes a white dwarf. This is the
end for the star, because it has exhausted all of its fuel.

These theoretical models explain in outline the evolution of red giants
– including the existence of carbon stars – in terms of the changes within
them. But the initial theory did not match the observations as well as we
would hope. For example, the original models predicted that carbon stars
would be twice as bright as we actually observe. This prompted Iben to write
a classic paper entitled ‘The Carbon Star Mystery: Why Do the Low Mass Ones
Become Such and Where Have All the High Mass Ones Gone?’. The existence
of the ‘carbon star mystery’ was based on calculations covering stars with
a limited range of masses, and with the same composition as stars in the
Milky Way. They did not include those of the masses and composition that
were being observed in the Magellanic Clouds.

The mystery solved

To be certain that the problem existed, I incorporated the latest physics,
along with the appropriate masses and compositions for stars in these galaxies.

Indeed, I made models of carbon stars that had the correct luminosity.
Arnold Boothroyd and Juliana Sackmann, both from the California Institute
of Technology, have made independent calculations that seem to confirm this
conclusion. Although there is still some concern over the details, we can
now make models of carbon stars with a low luminosity, and so solve half
of the carbon star mystery.

The other half concerns the scarcity of very bright stars at this stage
of evolution. Faulkner and Peter Wood, also from Mount Stromlo Observatory,
have found a process that prevents stars from reaching a luminosity higher
than 10,000 Suns – the maximum brightness for most red giants. They have
found that the intense burst of radiation from a shell flash in a star at
this luminosity is powerful enough to eject the star’s envelope altogether,
so ending its period as a red giant.

Wood and his colleagues, Mike Bessell and Matthew Fox, have discovered
a few very bright stars that survive this fate in the Magellanic Clouds.
They are more than three times as massive as the Sun. These red giants are
not only much rarer than we would expect, but they also contradict the theory
by not showing excess carbon, despite their high luminosity. They are probably
‘hot bottom burning’ stars. At the bottom of the convection zone of these
stars, the temperature is high enough for a carbon nucleus to capture a
proton and turn into a nitrogen nucleus. This hot bottom burning reduces
the amount of carbon that we would see in the star’s surface, changing it
from a carbon star to an ordinary – though very bright – red giant. These
stars probably end their lives as supernovae or white dwarfs, depending
on their initial mass and the rate of mass loss. Recent observations by
Verne Smith at the University of Texas have revealed that these stars are
also producing copious amounts of lithium, which is also formed by the hot
bottom burning process. We are, therefore, rather hopeful that recent ideas
may solve the carbon star mystery, although progress is slow because the
calculations require such large amounts of computer time. But our theories
of red giant stars must be able to explain not only the stars we see, but
also the abundance of different elements in the Universe that were not formed
in the big bang or supernovae.

The foundation of this line of research was a classic paper published
in 1957, in which Margaret and Geoffrey Burbidge, Willy Fowler and Fred
Hoyle, all then at Caltech, discussed how to make elements heavier than
iron. Iron has the most tightly bound nucleus of all the elements, and thus
it is the most stable. The nuclear fusion of elements cannot produce anything
heavier than iron. The only known way of producing heavier elements is by
adding neutrons to iron nuclei. This can happen in one of two ways: by adding
neutrons comparatively rapidly in the ‘r-process’, or by the slower ‘s-process’
(see ‘The birth of elements’, New ÐÓ°ÉÔ­´´, 16 December 1989). Many elements
can be formed by only one or other of these processes. We expect elements
formed by the r-process to be made in supernova explosions; the s-process
elements require much slower cooking. We now believe that this probably
happened inside red giants.

We can estimate the relative numbers of elements from the s-process
in the Universe by looking at meteorites, which we believe to be matter
left over from the formation of the Solar System. These can then provide
clues to the oven in which they were cooked. In 1965, Philip Seeger and
Willy Fowler, both from Caltech, and Don Clayton of Rice University in Texas
found that the distribution of s-process elements in meteorites requires
the iron nuclei in the red giant to be exposed to neutrons in a particular
way: a small amount of iron is exposed to a large number of neutrons, whereas
the majority of the iron see only small amounts of neutrons. The mathematical
description of this exposure is an exponential function.

In 1973, Roger Ulrich, an astronomer at the University of California
in Los Angeles, pointed out that such a distri bution in the numbers of
neutrons may occur naturally in red giants. If there is a source of neutrons
in the convective shell, then the succession of shell flashes would expose
iron nuclei to the neutrons in an exponential manner. But what could be
the source of the neutrons?

The neutron factory

The mixing that brings up carbon to the surface of a star may be responsible.
Iben and Aluro Renzini at the University of Bologna showed that it may also
pull small amounts of hydrogen downwards into regions that are rich in carbon-12.
These two elements then combine to form another isotope, carbon-13. During
the next ‘on’ phase of the cycle, convection mixes the carbon-13 into hot
regions rich in helium. Here the carbon-13 can capture a helium nucleus
to give oxygen and the required neutron.

To calculate in detail how these neutrons build up s-process elements
from iron, we must follow reactions between hundreds of species of nuclei
– a task for a supercomputer. Although we are still uncertain about the
rates of many of the reactions, astronomers at Caltech and in Italy, at
the University of Turin, have come up with a distribution of elements similar
to that found in the Solar System. Despite this general agreement between
models of the s-process in red giants and the proportion of elements in
meteorites, there are still problems. In particular, the models predict
that the flux of neutrons is many times higher than we need to account for
the elements actually produced.

We also have difficulties when we try to combine the model stars required
to produce s-process elements with the models we need to account for the
evolution of ordinary red giants and carbon stars. At present, the only
models that produce carbon stars near the correct luminosities are those
constructed by myself, and those by Boothroyd and Sackmann at Caltech. Yet
mine do not show the required kind of convection, while those of Boothroyd
and Sackmann show only an insignificant amount. In neither case do they
make s-process elements. So the models that make s-process elements do not
give rise to carbon stars, and the models that do lead to carbon stars do
not indicate the s-process. Yet we do observe carbon stars where s-process
elements have apparently come up to the surface.

One solution to this problem is even more radical. As I mentioned at
the beginning of this article, astronomers have taken the presence of technetium,
one of the elements produced by the s-process, as unambiguous proof that
the s-process has happened recently in the star’s interior. Not so, says
Robert Malaney, of the Lawrence Livermore National Laboratory. He has shown
that the hydrogen burning shell can produce energetic gamma-rays which,
if they hit any uranium or thorium originally present in the star, can break
up these elements to form technetium. The next ‘dredge-up’ phase brings
this technetium to the surface of the star. Although the amount of technetium
produced is small, it is very easy to detect, and thus we would see it in
many red giant stars. This mechanism cannot produce other s-process elements,
such as strontium, which we often observe in large amounts in red giants.
But it does mean that we can no longer take the presence of technetium as
conclusive proof that the s-process is happening.

There are even more complications. Most red giant stars are ‘variables’:
their output of light and their radius vary with time, typically completing
one period in about a year. Such stars are called ‘Mira variables’ after
the prototype, visible to the naked eye at its brightest, in the constellation
Cetus. Certainly we would expect these pulsations and the shell flashes
to interact, at least in determining the extent of dredge-up. The star’s
continual expansion and contraction should also affect the loss of mass
from its surface.

At present, we do not have estimates of how these different phenomenon
will interact, and affect the star’s evolution. But we can be certain that,
although we have learnt a lot about red giants, there is much more to come.

* * *

Anatomy of a shell flash

RED giant stars mix and cook their ingredients in a ‘shell flash’ that
we can divide into four phases. During the ‘on’ phase (see Figure 2a) the
helium shell is burning at about 10 million times the rate of our Sun. This
lasts for only a year. The shell generates more energy than can be carried
by photons of radiation, and a convective zone forms, where bubbles of hot
gas carry the energy upwards. The convection zone stretches from the centre
of the helium shell almost to the hydrogen shell. This mixing homogenises
the composition of the layers involved. The helium shell is making carbon,
so the convection carries this outward.

The helium flash generates an enormous amount of energy that makes the
star expand. Typically, its radius increases from its usual value of about
300 times that of the Sun to about 500 times. The expansion pushes the hydrogen-burning
shell out in radius by a factor of about 20, resulting in temperatures too
low for nuclear fusion, and so hydrogen burning ceases.

The next phase is ‘power-down’ (see Figure 2b): the expansion has cooled
the helium-burning shell enough to decrease its power output. Also during
this phase, the convective shell disappears as the energy passing through
the star decreases to values which can be carried by the photons. This phase
lasts for a few hundred years.

The cooling continues, with the result that more and more of the hydrogen-rich
envelope becomes convective, and thus mixed (see Figure 2c). The inner edge
of the mixed region reaches further and further inward. During later pulses
it may reach beyond the (now extinct) hydrogen shell, and mix the products
of hydrogen burning to the surface of the star. This is why this phase of
the flash cycle is called ‘dredge-up’. Indeed, the convective mixing can
even reach down into the layers which were in the convective shell during
the ‘on’ phase. This region contains about 25 per cent carbon. Thus the
‘dredge-up’ phase can draw carbon to the surface. The duration of this phase
is under 100 years.

The final, and longest, phase is the ‘off’ phase (see Figure 2d). The
star contracts and heats up again. The inner edge of the convective envelope
recedes outward. The hydrogen shell is re-ignited, to provide virtually
all the star’s energy during this period. The energy output from the helium
burning shell passes through a minimum and then begins to increase again,
resulting in another flash.

Peter Wood and Dominic Zarro, at the Mount Stromlo Observatory, have
looked for evidence that red giants do experience such shell flashes. During
a flash cycle, the total luminosity of a red giant does vary a little, although
much less than the variation in the output of the helium shell. Wood and
Zarro showed that this variation in luminosity would cause a variation in
the pulsation period of the star. They looked at observations of suitable
red giants stretching back over 100 years, and found slow changes in the
period of pulsation that matched the changes predicted to happen during
a shell flash.

* * *

2: The fate of the Sun: from red giant to white dwarf

OUR Sun probably began its life as a large diffuse gas cloud, which
collapsed under its own gravitation. The collapse halted when nuclear fusion
reactions began in the Sun’s centre. After about 10 billion years of fusing
hydrogen into helium, the central hydrogen supply will be exhausted. The
Sun will then expand and cool, becoming a red giant. Over a few hundred
million years, the Sun’s luminosity will increase to about 1000 times its
present value – destroying all life on Earth – while its surface temperature
will drop from its present value of 5800 K to about 3000 K. Our Sun will
no longer be yellow, but a deep red. Its radius will increase more than
100 times, so that it will engulf Mercury, which orbits 83 solar radii out
from the Sun. The Sun will extend halfway to the Earth, which lies at 215
solar radii. It would certainly be a spectacular sight.

During this first expansion, our Sun will lose about 20 per cent of
its mass as a wind blowing off into space. Eventually a helium flash in
its core (see main text) will end this phase. The Sun’s luminosity will
drop to about 80 times its present energy output. It will then spend about
150 million years burning helium into carbon (and oxygen) in a core surrounded
by a hydrogen-burning shell.

Once the core helium supply has gone, the Sun will again start to expand.
We expect it to experience the shell flashes described in Box 1, but it
may never become a carbon star. The continuing loss of mass from its surface
will terminate its evolution before much (if any) carbon is dredged up from
its interior. Towards the very end of its life, the Sun will probably start
to pulsate as a Mira variable star, oscillating in both luminosity and radius.
At this stage, its envelope will be so large it will easily engulf the Earth.
After the solar wind has removed the last of the Sun’s outer envelope, the
hot compact core will be exposed. Radiation from the core will ionise the
previously ejected matter, as a planetary nebula.

The nebula will stop glowing when what is left of our Sun, a dense white
dwarf of about 60 per cent of its present mass, finally cools and disappears
from the view of astronomers in some other solar system.

John Lattanzio is in the Institute of Geophysics and Planetary Physics
at the Lawrence Livermore National Laboratory in California.

Further Reading Stars and their Spectra, JB Kaler, Cambridge University
Press; Stellar Evolution, AJ Meadows, Pergamon Press.