Eclipsing and Pulsating Stars

Eclipsing variables are binary star systems whose orbital plane just happens to lie perpendicular to the plane of the sky. The stars alternately eclipse each other, thereby cutting off each other's light. The amount of light lost at each eclipse depends on the surface brightnesses of the two stars; the eclipse of the star with the greater surface brightness35 undergoes the deeper eclipse so that the system light is lowest at this phase. In European literature, the first report that the star b Persei or Algol varied in brightness was made by G. Montanari in 1669, but this bright star must have had multiple prior discoveries. That its popular name comes from the Arabic, al ghul, the demon, would seem to support this idea. The first known explanation for its variation in terms of a geometric effect—either a rotating spot on a star or an eclipse of one star by a companion—was given by J. Goodricke, in 1783, when he was about 18 years old. In 1784, he discovered the variation of b Lyrae and of the pulsating star 8 Cephei. It is astronomy's loss that Goodricke

35 Formally defined as the radiance, or the amount of energy radiated each second by a square meter of surface area into a unit solid angle at the source. See §3.1.2.1 for a discussion of the terms used to describe stellar brightness.

died only two years after these discoveries. One fainter eclipsing binary is included in Table 5.9: 44(i) Bootis, the brightest of the W Ursae Majoris system of binaries, more commonly called "contact systems." because their atmospheres are literally in contact. It is included because of its very short period (~6 hours). Eclipsing binary systems represent only a fraction of all binary star systems; many binaries are detected only because of traces of a second star in the spectrum or because changes in the Doppler shift of one or both stars' spectral lines can be seen, showing that the system is a single-lined or double-lined spectroscopic binary.

The earliest report of the periodic variability of a star is that of D. Fabricius in 1596, but essentially this was forgotten until in 1639 P. Holwarda rediscovered the variability of o Ceti, or Mira (or stella mira—star of wonder). Subclasses of pulsating stars include the Cepheids, the Mira or long-period variables (LPVs), the semiregular variables (whose periodicities are cyclic but not strictly periodic), and the RV Tauri variables that are pulsating stars with more complicated waveforms (many have alternating high and low maxima, for example). Pulsating stars with maximum brighter than 5th magnitude are included in Table 5.9. Pulsating variables are intrinsically variable. They undergo changes both in surface temperature and in size so that both surface brightness and surface area vary with time. A change in either causes a change in brightness. In the case of Mira, the temperature change leads to a change in the wavelength at which the star radiates the peak of its spectral radiation. As it expands and the outer layers cool, it radiates a greater percentage of its energy in the infrared, causing it to look much fainter than it actually is (the bolometric magnitude variation is much smaller than is the optical or visual light variation). In visual light, it is invisible to the naked eye long before it reaches the minimum of its light curve. It is difficult to believe that a star that varies so greatly in magnitude was not observed repeatedly by the careful watchers of the skies in ancient Babylon, China, India, and elsewhere.

Some pulsating stars are multiperiodic so that the light curve is a complicated combination of several superimposed waves, making periodicities more difficult to detect. The class of pulsating stars also includes stars that are referred to as "semiregular" (SR) and those whose light curves are merely cyclic rather than strictly periodic, so that the level of brightness may not be precisely predicted from cycle to cycle. The SR stars and at least some RV Tauri stars are among the latter. There are also periodic stars that vary in light because of their distorted shapes, for example, the ellipsoidal variables, which are thought to be tidally distorted close binary systems but that are not eclipsing systems (Morris 1985); others may vary because of the presence of variable dark or bright areas on their disks due to strong magnetic field effects modulated by rotation or, in binary systems, by the orbital period. The Sun could be considered a variable star on this basis, because it undergoes changes in brightness due to the effects of varying dark sunspots, as well as bright gaseous areas called plages and faculae. Earlier, we discussed the solar cycle briefly, but much longer term variation is possible too.

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