Chapter 16 - Basic Properties of Stars
CHAPTER 16
BASIC PROPERTIES OF STARS
CHAPTER OUTLINE AND LECTURE NOTES
1. Star Names
One of the stories in astronomy teaching lore is about a university lecturer who had just
finished discussing parallaxes and the distance of the stars. A student came up to him and
asked “If the stars are so far away, how do we know their names?”.
2. The Distances of Stars
After years of Star Trek and Star Wars, students have the impression that interstellar travel,
while impossible now, is just a matter of time (no pun intended). I try to emphasize the
almost unfathomable distances to the stars by handing out packets of salt to the students
and asking them to imagine they are holding a handful of stars. I then ask them to imagine
the model of the galaxy described in the introduction to this chapter.
3. The Motions of the Stars
It might be a good idea to emphasize that the proper motions of the stars only show the
relative motions of the stars. I compare the actual motions of the local stars as they orbit
the galaxy to the motions of birds relative to one another in a flock that is moving more or
less together in a given direction.
4. The Brightnesses of Stars
Except for historical reasons and the fact that some of the references and further readings
use the magnitude scale, it should cause few difficulties to skip magnitudes entirely. In
later chapters I have almost always discussed brightness in terms of luminosity rather than
in terms of magnitude although Figure 16.5, the luminosity function of the nearby stars,
uses magnitude rather than luminosity.
5. Stellar Spectra
Although there are a few topics where it would have been helpful to have presented spectra
and atoms before discussing the solar system, I decided to postpone spectra and atoms until
this chapter, where knowledge of spectra and atoms is really essential. The main reason
was to avoid expanding the amount of physics the students need to learn before they begin
reading about the various astronomical bodies. One of the reviewers of this book correctly
pointed out that the Angstrom unit, though not a standard SI unit, has often been used to
describe wavelength in astronomical spectroscopy. To familiarize the students with
Angstrom units I have included a definition and example of the Angstrom unit in the
caption of Figure 16.10.
6. H-R Diagrams
In this section I present a very brief discussion of what H-R diagrams (Figures 16.19 and
16.20) tell us about the evolution of stars. This discussion is greatly amplified in Chapter
18, on stellar evolution.
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Chapter 16 - Basic Properties of Stars
7. Stellar Masses
Some of your students (certainly some of mine) may have trouble with non-integer
exponents such as those in the mass-luminosity relation (Figure 16.21). A reminder of the
meaning of non-integer exponents might be a good idea. Even if they have trouble with the
concept, however, they should be able to use most calculators to do problems involving the
use of non-integer exponents.
KEY TERMS
absolute magnitude — The apparent magnitude a star would have if it were at a distance of 10
parsecs.
absorption line — A dark line superimposed on a continuous spectrum when a gas absorbs
light from a continuous source that is hotter than the absorbing gas.
antapex — The direction in the sky away from which the Sun is moving. Because of the Sun’s
motion, nearby stars appear to converge toward the antapex.
apex — The direction in the sky toward which the Sun is moving. Because of the Sun’s
motion, nearby stars appear to diverge from the apex.
apparent brightness — The observed brightness of a celestial body.
apparent magnitude — The observed magnitude of a celestial body.
Balmer series — A series of absorption or emission lines of hydrogen seen in the visible part of
the spectrum.
brown dwarf — A star with too low a mass for nuclear fusion to begin in its core.
continuous spectrum — A spectrum containing neither emission nor absorption lines.
dwarf — A main sequence star.
emission line — A narrow, bright region of the spectrum. Emission lines are produced when
electrons in atoms jump from one energy level to a lower energy level.
energy level — Any of the many energy states that an atom may have. Different energy levels
correspond to different distances of the electron from the nucleus.
giant — A star larger and more luminous than a main sequence star (dwarf) of the same
temperature and spectral type.
ground state — The lowest energy level of an atom.
Hertzsprung-Russell diagram (H-R diagram) — A plot of luminosities of stars against their
temperatures. Magnitude may be used in place of luminosity and spectral type in place of
temperature.
ionization — The removal of one or more electrons from an atom.
Kirchhoff’s laws — Three “laws” that describe how continuous, bright line, and dark line
spectra are produced.
light year — The distance that light travels in a year.
luminosity — The rate of total radiant energy output of a body.
luminosity class — The classification of a star’s spectrum according to luminosity for a given
spectral type. Luminosity class ranges from I for a supergiant to V for a dwarf (main
sequence star).
luminosity function — The distribution of stars or galaxies according to their luminosities. A
luminosity function is often expressed as the number of objects per unit volume of space
that are brighter than a given absolute magnitude or luminosity.
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Chapter 16 - Basic Properties of Stars
Lyman series — A series of absorption or emission lines of hydrogen lying in the ultraviolet
part of the spectrum.
magnitude — A number, based on a logarithmic scale, used to describe the brightness of a star
or other luminous body. Apparent magnitude describes the brightness of a star as we see it.
Absolute magnitude describes the intrinsic brightness of a star.
main sequence — The region in an H-R diagram occupied by stars that are fusing hydrogen
into helium in their cores. The main sequence runs from hot, luminous stars to cool, dim
stars.
mass–luminosity relation — The relationship between luminosity and mass for stars. More
massive stars have greater luminosities.
parsec — The distance at which a star has a parallax of 1 second of arc. At a distance of 1
parsec, an AU fills an angle of 1 second of arc.
proper motion — The rate at which a star appears to move across the celestial sphere with
respect to very distant objects.
radial velocity — The part of the velocity of a body that is directed toward or away from an
observer. The radial velocity of a body can be determined by the Doppler shift of its
spectral lines.
solar motion — The motion of the Sun with respect to the nearby stars.
spectral class — A categorization, based on the pattern of spectral lines of stars, that groups
stars according to their surface temperatures.
supergiant — An extremely luminous star of large size and mass.
white dwarf — A small, dense star that is supported against gravity by the degenerate pressure
of its electrons.
ANSWERS TO QUESTIONS AND PROBLEMS
Conceptual Questions
1. Because Sirius is brighter than Newton assumed it was, it must be more distant than he
calculated to have the apparent brightness it does.
2. Parallax shifts the direction of a star back and forth. Proper motion moves the star
progressively farther
with time.
3. The directions of the apex and antapex would stay the same. Nearby stars would have
larger proper motions because their directions relative to the Sun would change at a greater
rate. Suppose the two stars travel the same distance through space relative to the Sun. The
nearer star will move through a greater angle than the more distant star.
4. The photon absorbed when an atom moves from energy level A to energy level B has the
same energy and wavelength as the photon emitted when the atom moves from level B back
to level A.
5. For emission to occur, the electron must jump to a lower energy level. An electron in the
ground state can’t jump to a lower level.
6. The reader must supply his or her own answer.
7. Essentially all the hydrogen in an O star is in ionized rather than atomic form and only
hydrogen atoms can produce Balmer lines. In the cooler A star, there is more atomic
hydrogen.
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Chapter 16 - Basic Properties of Stars
8. The gas in the atmosphere of the G star is too cool for collisions to excite many hydrogen
atoms to the second energy level from which Balmer absorption must occur. In the hotter
A star more hydrogen is excited to the second energy level.
9. The radial velocity is 0 km/s.
10. (b)
11. Most stars spend most of their luminous lifetimes as main sequence stars.
12. The giant is brighter.
Problems
1. 0.025 seconds of arc
2. 5 parsecs
3. 37 years
4. 0.8 second of arc, 0.008 seconds of arc
5. 40 times as bright
6. 630 times as bright
7. 2.5 million times as bright
8. Star A is 250 times as bright
9. 4 magnitudes
10. 1600
11. 17
12. 1 parsec
13. 500.33 nm
14. 1330 km/s toward the Earth
15. The more massive star is 130 times as luminous
Figure-Based Questions
1. The energy of the Lyman  line is less than the energy of the Lyman  line, so the
wavelength of the Lyman  line is longer.
2. There are about one-quarter as many stars of absolute magnitude 6.
3. The energy of the Lyman  line is the same as the combined energies of the Lyman  and
Balmer  lines, so, because the energy of a photon is proportional to its frequency, the
frequency of the Lyman  line is equal to the sum of the frequencies of the Lyman  and
Balmer  lines.
4. The abundance of tin is about 1/1000 that of iron.
5. About 0.005, about 400
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