Chapter 16--Properties of Stars

multiple star systems containing three or more stars. Most
are tiny, dim red stars such as Proxima Centauri—so dim
that we cannot see them with the naked eye, despite the
fact that they are relatively close. A few nearby stars, such
as Sirius (2.6 parsecs), Vega (8 parsecs), Altair (5 parsecs),
and Fomalhaut (7 parsecs), are white in color and bright
in our sky, but most of the brightest stars in the sky lie farther
away. Because so many nearby stars appear dim while
many more distant stars appear bright, their luminosities
must span a wide range.
The Magnitude System
Many amateur and professional astronomers describe stellar
brightness using the ancient magnitude system devised by
the Greek astronomer Hipparchus (c. 190–120 B.C.). The
magnitude system originally classified stars according to how
bright they look to our eyes—the only instruments available
in ancient times. The brightest stars received the designation
“first magnitude,” the next brightest “second magnitude,”
and so on. The faintest visible stars were magnitude 6.
We call these descriptions apparent magnitudes because
they compare how bright different stars appear in the sky.
Star charts (such as those in Appendix J) often use dots of
different sizes to represent the apparent magnitudes of stars.
In modern times, the magnitude system has been extended
and more precisely defined (see Mathematical Insight
16.3). As a result, stars can have fractional apparent
The modern magnitude system is defined so that each difference
of 5 magnitudes corresponds to a factor of exactly 100 in brightness.
For example, a magnitude 1 star is 100 times brighter than
a magnitude 6 star, and a magnitude 3 star is 100 times brighter
than a magnitude 8 star. Because 5 magnitudes corresponds to a
factor of 100 in brightness, a single magnitude corresponds to a
factor of (100) 1/5 2.512.
The following formula summarizes the relationship between
stars of different magnitudes:
apparent brightness of Star 1
apparent brightness of Star 2
526 part V • Stellar Alchemy
magnitudes, and a few bright stars have apparent magnitudes
less than 1—which means brighter than magnitude 1.
For example, the brightest star in the night sky, Sirius, has
an apparent magnitude of 1.46. Appendix F gives the apparent
magnitudes and solar luminosities for nearby stars
and the brightest stars.
The modern magnitude system also defines absolute
magnitudes as a way of describing stellar luminosities. A
star’s absolute magnitude is the apparent magnitude it
would have if it were at a distance of 10 parsecs from Earth.
For example, the Sun’s absolute magnitude is about 4.8,
meaning that the Sun would have an apparent magnitude
of 4.8 if it were 10 parsecs away from us—bright enough
to be visible, but not conspicuous, on a dark night.
Understanding the magnitude system is worthwhile
because it is still commonly used. However, for the calculations
in this book, it’s much easier to work with the
luminosity–distance formula, so we will avoid using
magnitude formulas in this book.
astronomyplace.com
The Hertzsprung–Russell Diagram Tutorial, Lessons 1–3
16.3 Stellar Surface Temperature
The second basic property of stars (besides luminosity)
needed for modern stellar classification is surface temperature.
Measuring a star’s surface temperature is somewhat
easier than measuring its luminosity because the measure-
Mathematical Insight 16.3 The Modern Magnitude Scale
(100 1/5 ) m 2 m 1
where m 1 and m 2 are the apparent magnitudes of Stars 1 and 2,
respectively. If we replace the apparent magnitudes with absolute
magnitudes (designated M instead of m), the same formula applies
to stellar luminosities:
luminosity of Star 1
luminosity of Star 2
(100 1/5 ) M 2 M 1
Example 1: On a clear night, stars dimmer than magnitude 5 are
quite difficult to see. Today, sensitive instruments on large telescopes
can detect objects as faint as magnitude 30. How much more
sensitive are such telescopes than the human eye?
Solution: We imagine that our eye sees “Star 1” with magnitude 5
and the telescope detects “Star 2” with magnitude 30. Then we
compare:
apparent brightness of Star 1
apparent brightness of Star 2
(100 1/5 ) 305 (100 1/5 ) 25
100 5 10 10
The magnitude 5 star is 10 10 ,or 10 billion, times brighter than the
magnitude 30 star, so the telescope is 10 billion times more sensitive
than the human eye.
Example 2: The Sun has an absolute magnitude of about 4.8.
Polaris, the North Star, has an absolute magnitude of 3.6.
How much more luminous is Polaris than the Sun?
Solution: We use Polaris as Star 1 and the Sun as Star 2:
luminosity of Polaris
luminosity of Sun
(100 1/5 ) 4.8(3.6) (100 1/5 ) 8.4
100 1.7 2,500
Polaris is about 2,500 times more luminous than the Sun.