Download 14.5 Yellow Giants and Pulsating Stars Variable Stars Not all stars

14.5 Yellow Giants and Pulsating Stars
Variable Stars
Not all stars have a constant luminosity. Stars that change in brightness are called variable stars, and
many of these are associated with stages in the evolution of a star. For example, the red giant star Mira
changes brightness over a regular period of 332 days (fig. 14.14). The T Tauri stars we discussed in
section 14.2 are irregular variables.
Figure 14.14
Two images of the star Mira in the constellation Cetus. Mira varies from an easily visible star to about
100 times fainter.
When stars are plotted on the H­R diagram, some lie between the hot, luminous, blue, main­sequence
stars and the red giants. Such stars are called “yellow giants.” The most luminous yellow giants are aging
high­mass stars. Less luminous yellow giants are old low­mass stars that have completed their first red­
giant stage and are burning helium in their cores. Regardless of their mass, many yellow giants have the
unusual property of swelling and shrinking rhythmically: they pulsate. As they change size, their
luminosity changes, and so astronomers refer to them “pulsating stars.”
Two particularly important types of pulsating stars are the RR Lyrae (pronounced lie­ree) and Cepheid
(pronounced sef­ee­id) variables. RR Lyrae stars have a mass comparable to the Sun's and are yellow­
white giants with about 40 times the Sun's luminosity. The time it takes them to complete a pulsation
cycle from bright to dim and back to bright is called their “period,” as illustrated in figure 14.15. RR
Lyrae variables have periods of about half a day and are named for RR Lyrae, a star in the constellation
Lyra, the harp, which was the first star of this type to be identified.
Figure 14.15
Brightness variations of various kinds of variable stars and their location in the H­R diagram. RR Lyrae
and Cepheid variables are usually yellow in color and lie along a narrow “instability strip” in the
diagram.
Page 375
Cepheid variables are yellow supergiants that are more massive than the Sun and range in luminosity
from several hundred times the Sun's luminosity to several tens of thousands times its luminosity. They
are named for the star Delta Cephei, and their periods can be as short as about 1 day or as long as about
70 days.
Giant stars pulsate because their atmospheres trap some of their radiated energy. This heats their outer
layers, raising the pressure and making the layers expand. The expanded gas cools, and the pressure
drops, so gravity pulls the layers downward and recompresses them. The recompressed gas begins once
more to absorb energy, leading to a new expansion. These stars continue alternately to trap and release
the energy, and so they continue to swell and shrink, as shown in figure 14.16.
Figure 14.16
Schematic view of a pulsating star.
Page 376
A covered pan of water boiling on a stove behaves similarly. The lid will trap the steam so that pressure
inside rises. Eventually, the pressure becomes strong enough to tip the lid, and steam escapes. The
pressure decreases, and the lid falls back. It again traps the steam, the pressure again builds up, and the
cycle is repeated.
A similar process occurs in pulsating stars, with the role of steam played by the star's radiation and the
role of the lid played by the star's atmosphere. For a star to trap radiation this way, its atmosphere must
have special absorbing properties—technically called “opacity”—that occur only if its surface
temperature and radius fall in a narrow range. That range, called the instability strip, is shown in the H­
R diagram shown in figure 14.15. In this region the star's opacity “puts a lid on” light coming out of the
star's core. The atmosphere then expands and cools until its opacity declines enough to let the light out.
The atmosphere compresses and heats, and the cycle repeats. A star that assumes these characteristics as
it evolves through the H­R diagram will begin to pulsate and will continue to pulsate until its temperature
or radius changes enough to remove it from the instability strip.
When a low­mass star crosses the region of the instability strip during its evolution as a red giant, it
becomes an RR Lyrae variable star. When a high­mass star crosses the instability strip in its red giant
phase, being more luminous it instead becomes a Cepheid variable. The amount of time a given star
spends in the instability strip depends on its mass. Massive stars such as the highly luminous Cepheids
evolve across the strip in less than 1 million years, but some cross the region several times as their
interior structures alter. Low­mass stars such as the RR Lyrae variables spend more time in the strip,
perhaps a few million years, but cross it less often. In either case, stars pulsate for only a brief portion of
their lives.
Astronomers have identified many other types of pulsating variables besides Cepheids and RR Lyrae
stars. For example, ZZ Ceti stars, a kind of pulsating white dwarf with periods as short as a few minutes
are found in the lower portion of the H­R diagram. There are many stars like Mira (known as Mira
variables) that have pulsation periods of about 1 year. These lie in the upper right of the H­R diagram.
The Sun will probably become a Mira variable near the end of its lifetime, as we will discuss in the
section 14.6.
The Period–Luminosity Relation
Many pulsating variable stars obey a law that relates their luminosity to their period—the time it takes
them to complete a pulsation. Observations (and theoretical calculations) show that the more slowly a
star pulsates, the more luminous it is (fig. 14.17). This so­called period–luminosity relation arises
because, other things being equal, more­luminous stars have a larger radius than less­luminous ones. This
follows simply from the fact that a bigger star has more surface, so it can emit more light (see section
13.2).
Figure 14.17
The period–luminosity relation. More­luminous stars tend to pulsate more slowly.
Q. What is the approximate luminosity of a Cepheid that has a 3­day period?
answer
Why, though, does the larger radius make the larger star pulsate more slowly? Again, the answer is
simple. Because an object's gravity weakens with increasing distance, other things being equal, a large­
radius star has a weaker surface gravity than a small­radius star. Hence, gravity pulls more feebly inward
for a large­radius star than for a small­radius one, so its pulsation takes longer. As a result, big (and
therefore bright) stars pulsate more slowly than small (and therefore dim) stars.
The period–luminosity relation gives astronomers a powerful tool for measuring distances. By measuring
the star's period and identifying the shape of its light curve with stars of the same class, astronomers can
find its luminosity. From its luminosity and apparent brightness, they find the star's distance, as discussed
in chapter 13. We will see in chapters 16 and 17 some specific applications of this method to measuring
the distances of galaxies.