In addition to ordinary stars like our Sun, the universe also contains other types of stars whose structures may differ because they exist in a multiple‐star system or they produce variable energy in their cores. Some of these different types of stars include binary stars and variable stars.
There are many single or isolated stars like the Sun, but about half of all stars in the sky are found in multiple systems. Of the 25 nearest star systems within 4 pc (13 ly) of the Sun, 8 actually are multiple systems (7 binaries and 1 triple system). Binary systems are of special interest, because analysis of their orbital characteristics by use of Kepler's Third Law yields a direct measure of stellar masses. Such stars that are well separated are known as visual binaries, but others may be detected only via the Doppler Effect and hence are known as spectroscopic binaries. If the orientation of the orbit is such that the stars alternatively pass in front of each other, then an eclipsing binary is observed; analysis of the light curves yields information directly about stellar sizes.
Other phenomena are found in close binary systems. Very close stars may have their spherical structures altered by the gravitational effects of their companions. If the stars are close enough, this process may result in the near sides of the stars touching as contact binaries. As one or the other of the stars in a pair evolves, there may result mass exchange between the two stars that alters the course of evolution for both stars. The most dramatic examples of mass exchange are represented by the novae and x‐ray binary stars. Given the large range of stellar properties, an extremely great variety of pair types and interactions is possible.
Stars whose luminosity changes in a periodic or non‐periodic fashion are known as variable stars. There are dozens of different types of variables known. Among the more important are very young stars (T Tauri variables) that are in the process of establishing stable thermonuclear energy production as main sequence stars; pulsating variables whose outer layers literally swell and contract; and several types of red giant stars. The variability of any star yields clues to its internal properties (in the same fashion that differences in vibration clearly distinguish a small, lightweight snare drum from a large, heavy kettle drum), but specific types of variables are of intense interest because they can be used as distance tools.
Instability strip. A number of types of variables are known as pulsating variables as their outer layers swell and shrink in a regular, cyclic pattern. When distended, the pressure in the outer layers is not adequate to balance gravitation, and thus gravity will reverse their expansion. When compressed, pressure can overbalance gravity and cause the star to re‐expand. Such a pulsation is analogous to a child on a swing set; energy must be continually added to the oscillation at the proper time in each cycle to maintain an unchanging pattern of swings. Without such an addition, the ordered energy of the pulsational cycle would die out as the energy is dissipated by frictional forces into random heat.
In a star the only energy that may be tapped to add into a pulsational cycle is the flow of energy outward. The ability to tap such energy depends upon how much energy is flowing and where in the outer envelope there exists a means of using that energy. If the means exists, but is too far out in the star, there is no star left to oscillate; if too deep in the star, then there is too much overlying star to affect. At temperatures and luminosities within a band that cuts diagonally upwards across the HR diagram (see Figure ), the instability strip, all the necessary factors are present to produce a stable cycle of oscillation. The energy‐tapping mechanism is the ionization of helium that already has lost one electron:
Variable stars in the HR Diagram—instability strip, miras, T Tauri variables.
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.