Eclipsing Binaries and Other Variable Stars

Onov acovg nokka ccepaaia, Paaxa ¡i-ncpo icakati

(Don't get overwhelmed, and be cautious)

Variable stars are stars that vary in apparent brightness with time. In fact, all stars are variable at some level of precision, over some timescale. In astronomy there are three basic timescales:

• dynamic (the time it would take for a star to collapse under gravity if radiation and particle pressure were removed), typically tens of minutes;

• thermal (the time to exhaust its stored thermal energy), typically millions of years (as the energy is depleted by the luminosity); and

• nuclear (the time to exhaust its nuclear energy), typically, billions of years.

The relevant timescales for variable stars are between the dynamic and the thermal, but certainly much closer to the dynamic.

In fact the term "variable star" is usually reserved for stars that vary in brightness by some detectable amount over the interval of the observations. We have no prehistoric record of such events, but we certainly have ancient records. See, for example, Kelley & Milone (2005, esp., Chap. 5) for an extensive summary. In the recent past (50 years or so), the observational precision has been of order 0.01 magnitude or

J. Kallrath, E.F. Milone, Eclipsing Binary Stars: Modeling and Analysis, Astronomy 3

and Astrophysics Library, DOI 10.1007/978-1-4419-0699-1.1, © Springer Science+Business Media, LLC 2009

more. At present, photometry has, in principle if not usually in practice, improved by an order of magnitude, and at the level of millimagnitudes, most stars will appear variable. For example, Howell et al. (2005) found in a survey of the galactic cluster NGC 2301 that 56% of 4000 stars were variable at an amplitude of 0.002 magnitude or greater, the precision limit of the survey for the brightest 5 magnitudes of the survey. To keep our present exposition within reasonable bounds, for present purposes, for the most part we will stick to the more classical limit to define a "variable star," namely a star with brightness variation of > 1% or so and over timescales of millennia or less (down to seconds or less). More specifically, in the wider literature variable stars have been held to be variable if they vary in optical wavelengths (~ 0.35 to < 1.0 ^m) over intervals of decades or less; cf. Hoffmeister etal. (1985).

There are many fine monographs on the subject of variables, both generally and specifically. We will mention the latter under the appropriate group. The most recent general summary of which we are aware is by Sterken (1997). Other general works which are somewhat more dated but still offer interesting insights include Hoffmeister et al. (1984/1985); Petit (1985); Strohmeier (1972); and Glasby (1969).

Like the animal, vegetable, and mineral categories in the "Twenty Questions" parlor game of some decades back, variable stars are classically assigned to one of three main categories:

• "geometric" variables;

• "pulsating" variables; and

• "eruptive" variables.

In another classification scheme, a broader distinction was made between "extrinsic" and "intrinsic" variables, with "geometric" variables considered "extrinsic," and the other two "intrinsic." We shall discuss geometric, pulsating, and eruptive variables in sequence.

A "geometric" variable varies not due to its own physical behavior but because of changing aspect,1 i.e., the viewable part of a star changes with time. This category includes the EBs and also examples where the eclipse is due to a disk or a planet. It can also include pulsars, which vary mainly because of rotation, and spotted stars in the sense that the spots cause light modulation over a rotation period; spots usually do not last for decades, but there are exceptions [e.g., RW Com, cf. Milone et al. (1980)]. Finally, a cataclysmic variable (see below) may have a large "hump" (due to a hot spot) in its light curve which may be asymmetric due to eclipse by the companion star. Thus the degree to which geometric effects cause the observed variation will differ with the type of system.

1 Aspect means the appearance of an object as viewed from a given direction.

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