Variable stars were not widely known before the 17th century. One of the earliest variable stars to be discovered was Algol, or β Persei, which was noted by Geminiano Montanari in 1669. The name Algol may have been contributed by early Arab astronomers, who may have called the regularly dimming star "Al-Ghul," meaning the Devil or the Mischief Maker; the star also has been given colorful names in other languages. Compared to other variable stars, Algol is relatively easy to notice by visual observation. It is a bright star (2.12 magnitude), and it changes in brightness significantly as it is eclipsed (down to 3.40 magnitude at minimum). Significantly, this change in brightness happens over a relatively short period, which means that its variation can be noticed during a few days of study.
In 1782, over a century after Montanari's research, John Goodricke confirmed that Algol had a regular period of just less than 3 days, and went on to explain that this variability was caused by an eclipse - that two stars were locked in a binary system, close enough to each other to appear as a single star from our vantage point on Earth, and occasionally blocking out each other's light. Goodricke's research established the periodicity of Algol by looking at its light curve - the magnitude of the star over time.
During the 18th and 19th centuries, the only tool available to astronomers to discover variable stars was the star chart. Astronomers such as Argelander carefully mapped the sky and noted each star's position and magnitude; researchers could examine these charts year by year and compare magnitude numbers, a tedious task that limited the number of variable stars discovered. With the introduction of photographic plates towards the end of the 19th century, it became possible to compare magnitudes in large star fields at a single glance, and the number of known variable stars began to steadily increase.
These newly discovered variable stars are classified in a few basic categories: Pulsating or eruptive variables, where the star itself changes in brightness due to changes in its internal composition; and eclipsing or rotating variables, where the star's brightness changes because of external factors. Pulsating binary stars, such as Cepheid variable stars, have strongly predictable cycles of oscillation. Eruptive variable stars, for example novae, may change permanently and have a limited number of cycles. Eclipsing binary stars, like Algol, can be identified by two regular dips in brightness as each star in the binary system is eclipsed.
For most eclipsing binaries, these two dimming events (referred to as the primary and secondary minima) differ greatly in their magnitude since one star in the system is often brighter than the other. Some stars, such as ζ Aurigae, have such a great difference in brightness and size that the eclipse should be more properly called a transit - one star is a K5 orange supergiant that is large and dim, and the other is a tiny B9 star. The period of this variable star is so long that it is possible to observe the B9 star shining through the chromosphere of the K5 supergiant, which causes an emission spectrum to appear as the B9 star is gradually occluded and its radiation illuminates the atmosphere of the supergiant. Recent research has noted that the chromosphere of the K5 supergiant, as illuminated by the tiny B9 star, can change from eclipse to eclipse.
Returning to Algol, Hermann Carl Vogel in 1889 provided additional evidence to support Goodricke's binary eclipse theory by studying the star's Doppler shift. When two stars in a binary pair are orbiting each other, we see a Doppler shift in the spectra as one star is moving towards Earth and the other moves away. When this happens, the chemical absorption lines in one star are Doppler-shifted towards the blue end of the spectrum, and the other star's lines are Doppler-shifted towards the red end. We can thus examine the chemical composition of each star in the binary pair separately by noting the Doppler changes at precise times in the variable star's period. Some binary stars do not eclipse each other as viewed from the Earth and can only be identified by observing this Doppler shift.
Later research has shown additional factors that contribute to variability in eclipsing binary stars: the "reflection" and "limb darkening" effects. The reflection effect - a technical misnomer because it also includes radiative brightening - occurs when the half of a dim star that is facing Earth is illuminated by reflection and radiation from a brighter companion. As we saw when examining ζ Aurigae, the reflection combines with the emission spectrum from atoms excited by the brighter star's radiation, and the result is a gradual increase in brightness in between the two minima. Limb darkening, a factor discovered through careful observation of the sun, is caused by differences in brightness over the sphere of a star. When seen from the Earth, the edges of a star tend to be darker than the center. Sensitive instruments can observe limb darkening as momentary spikes in brightness during eclipses of a binary system.
When considering all these effects, it is possible to study in detail an eclipsing binary star system. Using advanced mathematical simulations, an astronomer can propose a model for the star system that specifies the size, orbital period, orbital inclination, and spectral types of each star in the binary. This hypothesis can be tested by observing the binary star and interpolating a light curve. The light curve can then be compared against the model using an O-C diagram - a type of graphical analysis that compares the variable star's observed brightness against its calculated brightness according to the proposed model. The O-C diagram makes errors in a model easily visible by showing the distribution of errors in predicted patterns. Since many variable stars undergo slight and unpredictable changes in orbital periods (sometimes happening due to mass exchanges between the pair of stars), this diagram can help to isolate the model from random sampling errors.
Eclipsing binary stars can therefore provide us with a wealth of information. With so many tools available to investigate an eclipsing binary star system, it is possible for even amateur astronomers to provide helpful observations, which contribute to the body of star knowledge that Argelander began in 1863.
References
1. Variable Stars, J.S. Glasby, 1969, Harvard University Press
2. The Study of Variable Stars using Small Telescopes, John Percy, 1986, Cambridge University Press
3. Variable Stars, M. Petit, 1982, Masson
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