Phenomenological Classification of Eclipsing Binary Light Curves

Examples of prototypical light curves are shown in Fig. 1.1. They correspond to the classical categories, discussed above, of "Algol," "ft Lyrae," and "W UMa" light curves, also known as EA, EB, and EW light curves, respectively.

Fig. 1.1 (continued) Classes of light curves. (a) Shows a synthetic "Algol"-type light curve (V band). It has been produced using the parameter file algolv.bmd from the Binary Maker 2.0 examples collection (Bradstreet, 1993). (b) Shows a synthetic "ft Lyrae"-type light curve (V band) and has also been produced with Binary Maker 2.0 (Bradstreet, 1993) using the parameters for RU Ursae Minoris given in the Pictorial Atlas (Terrell et al. 1992,(p. 107). (c) Shows a synthetic "W UMa"-type light curve (V band). It has been produced using the parameter file abandb.bmd from the Binary Maker 2.0 examples collection (Bradstreet, 1993)

10 Note that e Aurigae is enormously large. It contains an F0 supergiant with an estimated radius, depending on the distance, between about 100 and 227 R0.

(a) Synthetic "Algol" type light cure (V band).

(a) Synthetic "Algol" type light cure (V band).

Light Curve Algol

Phase

(b)Synthetic "ß Lyrae" type light cure (V band).

Light Curve Uma
Phase

(c) Synthetic "W UMa" type light cure (V band).

Phase

Fig. 1.1 (continued)

The EA light curves are typically almost flat-topped, suggesting that effects due to the proximity of the components are small, with a large difference between the depths of the two minima. Indeed, in some wavelengths the secondary minimum may be undetectable, and there may be an increase in light near the expected phase of secondary minimum due to the "reflection effect."

The EB light curves, on the other hand, are continuously variable (the "ellipsoidal variation"11), characteristic of tidally distorted components, and with a large difference in depths of minima indicating components of quite different surface brightness.

Finally, the EW (or W UMa) light curve is also continuously variable, but with only a small difference in the depths of the minima. The variation outside the eclipse in the latter two types is indeed due to proximity effects (mainly the tidally distorted shapes of the stars), but the EB light curves arise from detached12 or semi-detached binaries, whereas EW systems are over-contact.13 The expression "EA light curve," on the other hand, is somewhat misleading. Judged by the light curve, the system may look undistorted, but only in light from the visible (or, as infrared astronomers refer to it, the "optical") part of the spectrum. In the infrared, for example, Algol itself presents a continuously variable light curve and a fairly deep secondary minimum (Fig. 1.2). This reveals quite clearly that the bluer, hotter component in the system is relatively small and undistorted, and its radiation enhances the bright inner face of its companion.

These considerations show the value of treating all aspects of the light of the system in light curve analysis, and not only their geometric characteristics. Unfortunately, in many cases the system geometry has been the only goal of light curve investigations.

As studies of Algol itself show, EB analysis is a formidable astrophysical task (see Sect. 1.3.5 for further examples). The field includes radiation physics and sometimes hydrodynamics. It borrows methods from celestial mechanics, thermodynamics, and other branches of physics. Physical models are required for radiation transport in the components' atmospheres and for the dynamic forces controlling the stellar mass distributions.

11 The expression ellipsoidal variation, or less correct oblateness effect, is more generally used in the context of the Russell-Merrill model (see Sect. 6.2.1), where the shape of the light curve is modeled as due to ellipsoidal stars. The term oblateness should be reserved for rotational but not for tidal distortion.

12 The expressions "detached," "semi-detached," and "over-contact" arise from morphological classification of binaries (Sects. 1.2.3 and 3.1.6). Detached systems have separated stars. Semidetached systems are still separated but one component fills its critical lobe.

13 Sometimes, these systems are called contact system; in this book we reserve this term only for the case in which both components fill their critical lobes exactly. This special mathematical case seems not to occur in real binaries. More generally, in the over-contact systems both stars overfill their inner Lagrangian surfaces and establish a common envelope. Such systems can exist for astronomically significant times only if the orbits are circular and the components rotate synchronously.

Fig. 1.2 U, V, and infrared light curves of Algol. The plot has been produced with Binary Maker 2.0. The parameters are taken from the Pictorial Atlas (Terrell et al. 1992, p. 239) and from Kim (1989)
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