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Chapter 21 - Binary Star Systems
CHAPTER 21
BINARY STAR SYSTEMS
CHAPTER OUTLINE AND LECTURE NOTES
1. The Kinds of Binary Stars
In most other introductory astronomy textbooks, binary stars are covered in a piecemeal
fashion in several different chapters. There are several reasons why I decided to cover
binary stars in a single coherent chapter. First, most stars are in binary or multiple systems,
so it isn’t reasonable to treat single stars as if they were ordinary and binary stars as if they
were unusual. Second, we now have a clear enough picture of the evolution of close binary
systems that it seemed important to present an organized discussion of the evolution of
close binary systems, which make up a significant fraction of all stars. Third, many of the
exotic phenomena discovered by ultraviolet, X ray, and gamma ray astronomers occur in
close binary systems with compact companions. In order to present these phenomena in a
coherent manner, a chapter on binary stars seemed needed.
2. The Formation of Binary Systems
3. Evolution of Close Binaries
Equipotentials are so important for understanding the flow of matter in binary stars systems
that I think the subject needs to be discussed even though it is a fairly hard concept. I’ve
worked hard to develop the concept of equipotentials using the analogy of geographical
contour maps (Figures 21.11 and 21.12). If a student understands what equipotentials in
binary systems tell us about how matter flows from one star to another and out of the binary
system and if they understand what Figure 21.15 tells about the effect that transferring
matter has on the separation of the stars in a binary system, then I think the student will find
it relatively easy to understand the evolutionary stages presented in Figures 21.17 and
21.18. The evolution of a low mass binary is also shown as an animation on the CD that
accompanies this textbook.
4. Binaries with Compact Objects
Accretion disks are first discussed in this section. They will be encountered again, in more
depth, in Chapter 24 on quasars.
KEY TERMS
accretion disk — A disk of gas and dust spiraling inward toward a star or the nucleus of a
galaxy.
binary star system – A pair of stars that orbit each other under their mutual gravitational
attraction.
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Chapter 21 - Binary Star Systems
close pair — A binary system in which the two stars are close enough together that they
transfer matter to one another during some stages of their evolution.
common envelope — A stage in the evolution of a close pair of stars in which matter shed by
one of the stars fills the region just outside the Roche lobes of the two stars.
conucleation — A possible explanation for the origin of a wide pair of stars in which the two
cloud fragments that become the stars are already in orbit about one another when they
form.
disk instability — A possible explanation for the origin of a close pair of stars in which one star
forms within the disk of gas and dust orbiting another, newly formed, star.
eclipsing binary — Binary star systems for which the orbital plane of the stars lies so nearly in
the line of sight that two stars alternately pass in front of one another, causing eclipses.
equipotential — A line or surface of equal potential energy. On the Earth, a line of equal
elevation is approximately an equipotential.
fission — A possible explanation for the origin of a close pair of stars in which a star splits into
two pieces, each of which becomes a star.
fragmentation — A possible explanation for the origin of a close pair of stars in which a
collapsing cloud breaks into several pieces, each of which becomes a star.
L1 — The point between two stars in a binary system where matter may flow from one star to
the other.
light curve — A plot of the brightness of a body versus time.
minimum — The time of minimum light in a light curve.
nova — An explosion on the surface of a white dwarf star in which hydrogen is abruptly
converted into helium.
recurrent nova — A binary system in which the white dwarf star undergoes repeated nova
outbursts.
Roche lobe — The region around a star in a binary system in which the gravity of that star
dominates.
spectroscopic binary — A pair of stars whose binary nature can be detected by observing the
periodic Doppler shifts of their spectral lines as they move about one another.
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Chapter 21 - Binary Star Systems
tidal capture — A possible explanation for the origin of a wide pair of stars in which two cloud
fragments tidally interact with and capture one another.
type Ia supernova — An extremely energetic explosion produced by the abrupt fusion of carbon
and oxygen in the interior of a collapsing white dwarf star.
visual binary star — A pair of stars orbiting a common center of mass in which the images of
the components can be distinguished using a telescope and which have detectable orbital
motion.
wide pair — A binary star system in which the components are so distant from one another that
they evolve independently.
X-ray burst — Sporadic burst of X rays originating in the rapid consumption of nuclear fuels
on the surface of the neutron star in a binary system.
X-ray pulsar — A neutron star from which periodic bursts of X rays are observed.
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. The stars in a wide pair are too far apart to exchange matter with each other. The stars in a
close pair are close enough together to do so.
2. Binaries with periods less than a few years are usually only a few AU apart. This is too
close together for their images to be separated so that they would be seen as a visual binary.
3. If the binary doesn’t appear to obey Kepler’s laws, the orbit must be tipped.
4. More widely separated stars orbit each other too slowly for their Doppler shifts to be easily
detected.
5. Primary and secondary minimum are equally deep if the two stars have the same
temperature.
6. Primary (deeper) minimum occurs when star B (the hotter star) is eclipsed.
7. If the minima have flat bottoms, the two stars have unequal sizes.
8. Normally, a 4 solar mass star should leave the main sequence before a 1 solar mass star that
formed at the same time. In a close binary system, a red giant star can shed enough mass
onto its main sequence companion to make the companion the more massive star. In a
wide binary, this can’t happen.
9. Water flows toward lower potentials, so there is little flow of water across a lake while
water flows rapidly in a river.
10. The Roche lobe is the region in which the gravity of the star dominates.
11. The blob can’t remain at L1. The tiniest push will send it one way or the other. Whether it
flows into star 1 or star 2 can’t be predicted.
12. After the star fills its Roche lobe, it will spill its matter through L1 into the Roche lobe of
the other star.
13. This will make the masses of the star more unequal so the separation of the two stars will
increase.
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Chapter 21 - Binary Star Systems
14. This would make the masses of the Sun and Jupiter more equal so the separation of the two
would decrease.
15. If the mass-losing star is more massive, the separation of the two stars decreases, and the
mass-losing star continues to fill its Roche lobe even as it loses mass.
16. They lose orbital energy through friction with gas in the common envelope.
17. The two stars can exceed escape velocity and go their separate ways or form a close binary
consisting of two compact objects (neutron stars or black holes).
18. The energy emitted is ultimately derived from the gravitational energy released as matter in
the disk spirals inward.
19. Friction in the disk causes matter to spiral inward.
20. At first, the gas in the shell is too cool for fusion. Temperature increases as more matter
accumulates. When fusion begins, the degenerate gas is heated but doesn’t expand so
hydrogen is consumed explosively.
21. A nova outburst can occur whenever enough fresh material is accumulated for fusion to
begin.
22. As matter accumulates rapidly on a white dwarf, the star becomes smaller and its core
becomes hotter. When the core temperature reaches 10 billion K, carbon fusion begins.
The energy released by carbon fusion triggers a series of nuclear reactions that blow the star
apart.
23. X-ray bursts occur whenever freshly accumulated gas becomes hot enough for helium
fusion to occur.
24. Both candidates are in binary systems. The distances and orbital speeds of the companions
of the candidates can be used in Kepler’s third law to show that the candidates are too
massive to be white dwarf stars or neutron stars.
Problems
1. 1.08 solar masses + 0.88 solar masses = 1.96 solar masses, 1.08 solar masses/0.88 solar
masses = 1.2
2. 1 solar mass
3. 5.6 years
4. 900,000 years
Figure-based Questions
1. If the more massive is six times as massive as its companion, the stars are 1.3 times as far
apart than if the more massive star is five times as massive as its companion.
2. 9.4 and 1.6 solar masses
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