Stars
What is a star?
The Pleiades, a cluster of young
stars
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A star is a sphere of gas held together by its own gravity. The
force of gravity is continually trying to cause the star to collapse,
but this is counteracted by the pressure of hot gas and/or radiation
in the star's interior. This is called hydrostatic support. During most
of the lifetime of a star, the interior heat and radiation is provided
by nuclear reactions near the center, and this phase of the star's
life is called the main sequence. Before and after the main sequence,
the heat sources differ slightly. Before the main sequence, the star is
contracting and is not yet hot enough or dense enough in its interior
for the nuclear reactions to begin. During this phase, hydrostatic
support is provided by the heat generated during contraction. After the
main sequence, most of the nuclear fuel in the core has been used up.
The star now requires a series of less-efficient nuclear
reactions for internal heat. Eventually, when these reactions no longer
generate sufficient heat to support the star against its own gravity,
the star will collapse.
The Main Sequence
The properties of a main-sequence star can be understood by considering
the various physical processes occurring in the interior.
First is the hydrostatic balance, also called hydrostatic equilibrium.
This determines the density structure of the star as the internal
pressure gradient balances against the force of gravity. Another way of
thinking about this is to imagine the star as a large number of nested
thin spherical shells, resembling the structure of an onion. The inward
forces on each shell consist of the gravitational pull from all the
shells inside it, and the gas and radiation pressure on the outside of
the shell.
The only outward force on each shell is
the gas and radiation pressure on the inside of the shell. There is no
gravitational force from material outside the shell (in physics, this
is known as Gauss's law)
In hydrostatic equilibrium, the inward and outward forces must balance.
If they don't, the shell will either collapse or expand. The timescale
for this to occur is called the "free-fall timescale," and it is about
2,000 seconds for a
star like the Sun. Since we know the Sun has been essentially stable
over the age of Earth (several billion years), the hydrostatic balance
must be maintained to a very high level of accuracy. A consequence of
hydrostatic balance is that the pressure on each shell from material
outside it must be less than the pressure from material inside it. This
is because gravity
acts only in the inward direction. Thus, the pressure in the star must
decrease with increasing radius. This is an intuitively obvious result,
as the
pressure at the center of the star is greater than it is at the surface.
The second physical process to consider is the transport of energy from
the interior of the star to the surface. The interior of the star
is heated by nuclear reactions, while at the surface electromagnetic
radiation can escape
essentially freely into space. This situation is analogous to a pot of
water on a stove, in which heat is deposited at the bottom by the stove
burner, and is transported upward through the water to the surface
where it can escape. The rate at which the water on the stove can
transport the heat determines the temperature. A lid on the pot will
cause the temperature in the water
to be higher than it would be with no lid, since heat is impeded from
escaping the pot. In the case of a star,
the temperature of the gas determines the density structure via the
hydrostatic equilibrium condition, so understanding the transport
mechanism is important.
The transport can occur by either of two mechanisms: either the energy
is carried by radiation, or it is carried by convection. Radiation is
the mechanism by which Earth receives heat from the Sun, and its
efficiency depends on the opacity of the material that the radiation must
traverse. Opacity is a measure of the transparency of a gas, and it
depends on the gas temperature, density and elemental composition. Convection is analogous
to the turbulent motion in a pot of water as it boils. It involves
motion of the fluid in the pot (or the interior of the star) which
transports heat. The operation of convection depends on how easily the
gas can move, i.e., its viscosity, and any forces that tend to resist
the convective motion, such as gravity. In addition, convection
can only operate if it transports more heat than radiation.
This is important. When the opacity is high and radiation is
inefficient, convection takes over. The details of the efficiency of
convection are not well understood, and they are probably the major
source of uncertainty in the study of stellar structure and evolution.
A third energy
transport mechanism, conduction, is relatively unimportant in stellar
interiors.
Main sequence stars have zones
(in radius) that are convective, and zones that are radiative,
and the location of these zones depends on the behavior of the opacity,
in addition to the other properties of the star.
Massive stars, which are those greater than several solar
masses, are
convective deep in their cores, and are radiative in their outer
layers. Low mass stars, which have a mass comparable to or less than
the Sun, are convective in their outer layers and radiative in their
cores. Intermediate mass stars (spectral type A) may be radiative
throughout. Convection is likely to be important in determining other
properties of the star. The existence of a hot corona may be associated with active convection
in the outer layers, and the depth of the convective layer determines
the extent to which material from the deep interior of the star is
mixed into the outer layers. Since interior material is likely to have
undergone nuclear reactions, which
change the elemental abundances, this mixing affects the abundances in
the star's atmosphere.
These can be observed by studying stellar spectra. They may also be
ejected from the star in a stellar wind,
and so affect the composition of interstellar gas.
The final ingredient in determining the structure of a main sequence
star is the source of heat in the interior: nuclear reactions. There
are many of these events, but there is still some uncertainty about the
exact rate of reactions. This is because the fundamental particles
produced by nuclear reactions, called solar neutrinos,
react weakly with other particles. Most pass right through the planet,
making them extremely difficult to detect.
The basic reactions that operate on the main sequence are fusion
reactions, which convert hydrogen nuclei (protons) into helium
nuclei. These reactions require high temperatures (greater than 10
million degrees Celsius
and densities (greater than a few hundred grams per cubic
centimeter), and the rates are sensitive functions of temperature and
density. This is the factor that
ultimately determines the lifetime of a main sequence star. More
massive stars have greater central temperatures and densities,
and exhaust their nuclear fuel more rapidly (in spite of the fact
that they have more of it) than do lower-mass stars. It turns out that
the main sequence lifetime is a sensitive function of mass. For a star
like the Sun, the main-sequence stage lasts about 10 billion years,
whereas a star 10 times as massive will be 1,000 to 10,000 times as
bright but will only last about 20 million years. A star with 1/10 the
Sun's mass may only be 1/1,000 to 1/10,000 of its brightness, but will
last about 1 trillion years.
It is interesting to consider what would happen to the star if the
nuclear reactions were to turn off suddenly. The timescale required for
the energy from a photon released at the center of the star to
make its way to the surface is approximately 1 million years for a star
like the Sun. Along the way,
the original gamma-ray photon interacts with the gas in the star and
loses energy. Through multiple interactions like this, this energy
"random walks" its way out of the star, ultimately being emitted at the
surface as many photons in the ultraviolet and visual wavelengths. So,
if the nuclear reactions were to turn off today, the Sun's luminosity
would stay approximately constant for a long time by human standards.
We do have historical records that tell us that the
Sun's output has been approximately constant over the course of written
human history, so scientists are fairly confident that the nuclear reactions
are still operating. However, there is the possibility that nuclear energy
generation in the center of the Sun is not perfectly constant.
The three physical processes discussed so far — hydrostatic
equilibrium,
radiation transport, and nuclear energy generation — serve to
determine
the structure of a star. But the devil is in the details. The areas of
greatest uncertainty are the behavior of opacity and
convection, and these are active areas of scientific research.
A convenient way to characterize a star from observations is by its
luminosity, as well as its color, or temperature. It is customary to
plot these two quantities
in an x-y plot, called a Hertzsprung-Russell diagram. It turns out that
when this is done for main sequence stars with a range of masses, the
points tend to occupy a narrow band in the diagram. The location of a
main sequence star in the diagram depends only on its mass (see Figure
below).
The Hertzsprung-Russell Diagram
Stellar Evolution
The mass of the star determines what happens after the main sequence
phase.
Stars similar in mass to the Sun convert hydrogen into helium in their
centers
during the main-sequence phase, but eventually there is not enough
hydrogen left in the center for fusion to provide the necessary
radiation pressure to balance gravity. The center of the star
contracts until it is hot enough for helium to be fused into
carbon. The hydrogen in a shell continues to convert to helium, but
the outer layers of the star have to expand to conserve energy. This
makes the star appear brighter and cooler, and it becomes
a red giant.
During the red giant phase, a star often loses many outer layers, which
are blown away by the radiation coming from below. Eventually, in the
more massive stars of the group, the carbon may convert to even heavier
elements, but eventually the energy generation will fizzle out and the
star will collapse to a white dwarf.
Astronomers think that white dwarfs ultimately cool to become black dwarfs.
Stars having masses between 0.08 and 0.4 times that of the Sun can
have main sequence lifetimes greater
than the current age of the Universe. These are known as red dwarfs, and
are quite plentiful in the Universe.
There are very few stars with masses greater than five times the
mass of the Sun, but their evolution ends in a spectacular fashion.
They finish
their main sequence lifetime in a way similar to the lower-mass stars,
but become brighter and cooler on the outside and are called red
supergiants.
Carbon burning can develop at the star's center and a complex set of
element-burning shells can develop towards the end of the star's life.
During this stage, many different chemical elements will be produced in
the star and the central temperature will approach temperatures
between 100 million and 600 million K. During this stage, the
structure can resemble an onion skin with progressive layers (going
inward) dominated by elements with greater and greater atomic mass.
This process ends when the core is composed primarily of iron. For all
the elements up to iron, the addition of more nucleons to the nucleus
produces energy, and so yields a small contribution to the balance
inside the star
between gravity and radiation. To add more nucleons to the iron nucleus
requires an input of energy, and so, once the center of the star
consists of iron,
no more energy can be extracted. The star's core then has no resistance
to the
force of gravity, and once it starts to contract a very rapid collapse
will take place. The protons and electrons combine to give a core composed of
neutrons, and a vast amount of gravitational energy is released. This
energy is
sufficient to blow away all the outer parts of the star in a violent
explosion, and the star becomes a supernova.
The light of this
one star at its peak during the
explosion is then about as bright as the collective light from all the
other 100 billion stars in the host galaxy. During this explosive phase, all the
elements with atomic weights greater than iron are formed and, together
with the rest of the outer regions of the star, are blown out into
interstellar space. The central core of neutrons is left as a neutron
star. We may observe some neutron stars as pulsars.
This is remarkable, because in the early Universe
there were no elements heavier than helium. The first stars were
composed
almost entirely of hydrogen and helium and there was no oxygen,
nitrogen, iron,
or any of the other elements that are necessary for life. These were
all produced inside massive stars and were all spread throughout space
by
such supernovae events. We are made up of material that has been
processed at
least once inside stars.
Last Modified: December 2010
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