172 PART 2^ |^ THE STARS
The Deaths of Stars
Stars spend most of their lives fusing hydrogen into helium,
and, when the hydrogen is exhausted, they fuse helium into car-
bon. Th e more massive stars can fuse carbon into even heavier
atoms, but iron is the limit beyond which no star can go.
How long a star can live depends on its mass. Th e smallest
stars are very common, but they are not very luminous. Th ese
cool red dwarf stars are hardly massive enough to fuse hydrogen,
and they can survive for over 100 billion years. Th e sun, a
medium-mass star, will live a total of about 10 billion years. In
contrast, the most massive stars, up to almost 100 times the mass
of the sun, are tremendously luminous and fuse their fuels so
rapidly that they can live only a few million years.
Th is chapter tells the story of the birth and death of stars in
a few paragraphs, but modern astronomers know a great deal
about the lives of the stars. How could mere humans understand
the formation, development, and deaths of objects that can sur-
vive for millions or even billions of years? Th e answer is the math-
ematical model (How Do We Know? P-1). Astronomers
can express the physical laws that govern the gas and energy inside
a star as equations that can be solved in computer programs. Th e
resulting mathematical model describes the internal structure of a
star and allows astronomers to follow its evolution as it ages
(■ Figure P-3). Solving the mystery of the evolution of stars is one
of the greatest accomplishments of modern astronomy.
P-2 How a star dies depends on its mass. A medium-mass star
like the sun has enough hydrogen fuel to survive for billions of
years, but it must eventually exhaust its fuel, swell to become a
giant star, and then expel its outer layers in an expanding nebula
like that shown in the photograph that opens this chapter. Th ese
planetary nebulae were named for their planet-like appearance
in small telescopes, but they are, in fact, the remains of dying
stars. Once the outer layers of a star are ejected into space, the hot
core contracts to form a small, dense, cooling star—a white
dwarf.
Study The Formation of Planetary Nebulae on
pages 174–175 and notice four things:
First, you can understand what planetary nebulae are like by
using simple observational methods such as Kirchhoff ’s laws
and the Doppler eff ect.
Notice the model astronomers have developed to explain
planetary nebulae. Th e real nebulae are more complex
than the simple model of a slow wind and a fast wind, but
the model provides a way to organize the observed
phenomena.
Notice how oppositely directed jets and multiple shells pro-
duce many of the asymmetries seen in planetary nebulae.
Finally, notice the fate of the star itself; it must contract into
a white dwarf.1
2
3
4
How can scientists study aspects of nature
that cannot be observed directly? One of
the most powerful methods in science is the
mathematical model, a group of equations
carefully designed to mimic the behavior of
objects and processes that scientists want to
study. Astronomers build mathematical models
to study the structure hidden deep inside
stars. Models can speed up the slow evolution
of stars and slow down the rapid processes
that generate energy. Stellar models are based
on only four equations, but other models are
much more complicated and may require many
more equations.
For example, scientists and engineers
designing a new airplane don’t just build it,
cross their fi ngers, and ask a test pilot to try
it out. Long before any metal parts are made,
mathematical models are created to test
whether the wing design will generate enough
lift, whether the fuselage can support thestrain, and whether the rudder and ailerons
can safely control the plane during takeoff,
fl ight, and landing. Those mathematical
models are put through all kinds of tests: Can
a pilot fl y with one engine shut down? Can
the pilot recover from sudden turbulence? Can
the pilot land in a crosswind? By the time the
test pilot rolls the plane down the runway for
the fi rst time, the mathematical models have
“fl own” many thousands of miles.
Scientifi c models are only as good as the
assumptions that go into them and must
be compared with the real world at every
opportunity. If you are an engineer designing
a new airplane, you can test your mathemati-
cal models by making measurements in a wind
tunnel. Models of stars are much harder to
test against reality, but they do predict some
observable things. Stellar models predict the
existence of main sequence stars, the observed
numbers of giant and supergiant stars, andBefore any new airplane fl ies, engineers build
mathematical models to test its stability. (The
Boeing Company)P-1 Mathematical Models
the luminosities of stars of different masses.
Without mathematical models, astronomers
would know little about the lives of the stars,
and designing new airplanes would be a very
dangerous business.