Only for stars within the instability strip does this occur at the right time in the cycle. If a star like the Sun were to be disturbed (say, by distending it so that pressure no longer balanced gravitation), no stable oscillation would be produced because the energy of the disturbance would rapidly be converted into random motions within the stellar material.
Classical Cepheid variables. High‐mass stars, once they have exhausted their core hydrogen, evolve to the right in the HR diagram. When these stars have luminosities and surface temperatures that place them within the instability strip, they will develop pulsations that affect not only their size but their surface temperatures and luminosities. The light curves will have a characteristic form showing a steep increase in brightness followed by a slower decrease in brightness. Any variable with this form of light variation is termed a Cepheid variable, after the first star of this class, δ Cephei. More specifically, a young, massive star with solar metal abundance that has recently left the main sequence and moved into the yellow supergiant region of the HR diagram is termed a Classical or Type I Cepheid. The pole star, Polaris, is an example of this type of variable star.
These Cepheids typically have periods of variability from a few days to as long as 150 days. Their luminosities are high, with absolute magnitudes between –1 to –7, and a difference between maximum and minimum light, of amplitude, of up to 1.2 magnitudes (a factor of 4 in luminosity). A Cepheid is brightest when it is expanding most rapidly, and faintest when contracting the fastest.
W Virginis variables. Young massive stars are not the only stars that can move into the region of the instability strip during some stage of their evolution. A very old, low‐mass star that is between its horizontal branch stage and its planetary nebulae stage can achieve the right luminosity and surface temperature when its helium‐burning shell has collided from below with its hydrogen‐burning shell, temporarily ending both types of thermonuclear reactions. When this phenomenon occurs, the star undergoes a quick contraction with a rise in surface temperature that takes it leftwards across the HR diagram into the region of the instability strip. Such a star is a Type II Cepheid or W Virginis star. Typically, the periods of variability of W Virginis stars are between 12 and 20 days. Although such a star may have a luminosity and surface temperature identical to a Classical Cepheid, their periods will be different.
RR Lyrae variables. The third major class of variable with a Cepheid‐like light curve is the RR Lyrae variables (also called cluster variables, because they are common in the globular star clusters). These stars have short periods, between 1.5 hours to 24 hours. They are fainter than the Cepheids, with luminosities of about 40 times that of the Sun. Like the W Virginis stars, these are old, low‐mass stars, specifically horizontal branch stars (core helium‐burning stars) whose surface temperature places them within the bounds of the instability strip.
Period Luminosity Relationship. A fundamental importance of the Cepheids is the existence of a relationship between their period of pulsation and their intrinsic luminosity, originally discovered by Henrietta Leavitt from a study of these variable stars in the Large and Small Magellanic Clouds. The period luminosity relationship differs for the Classical Cepheids and the W Virginis stars, with the former being about four times more luminous at any given period. Determination of the period of variability for any star is fairly straightforward, and once that period is known, the intrinsic luminosity of the star may be deduced. Comparison with the apparent brightness of the star then yields the distance to the star. As these are intrinsically very bright stars, they can be identified at distances as great as 20,000,000 parsecs, making them an extremely valuable tool for obtaining distances to a large sample of nearby galaxies. Indeed, they are a critical key to getting the distance scale of the Universe.
Irregular, semi‐regular, and Mira variables. A second important class of variables is the red variables. These stars do not have a stable cycle of variability, but exhibit semi‐regular or irregular behavior with periods of a few months to about two years, again due to deep ionization regions. In the highly distended outer parts of these stars, energy absorbed and released by ionization can produce shock waves that dramatically affect the surface layers, producing strong stellar winds with mass loss up to 10 –5 solar masses per year. In addition, condensation of molecules into dust grains can further obscure the light coming from these stars.
A prime example is the star Mira (the name means “wondress”) whose visible light varies by a factor of 100 in a semi‐regular manner over an approximate 330‐day period. Its total luminosity variation is only a factor of 2, but the greater part of that radiation is in the invisible infrared part of the spectrum. The variation of temperature over its cycle, with the peak wavelength of its radiation in the infrared, results in a major change in visible brightness.