Eclipsing Variables

Eclipsing variables are periodic (that is, the cycle of variation repeats relatively reliably). This broad grouping was historically divided into three phenomenological classes according to the appearance of the light curves: Algols, p Lyrae systems, and W Ursae Majoris systems. The characteristics of these light curve types are discussed in the following subsections. Algols

The prototype is p Persei, also known as Algol. In visible passbands, the striking characteristics are approximately constant light outside eclipse and minima that fall and rise abruptly and occupy only a small fraction of the full light curve, typically less than ~ 15% for each minimum. Typically, the longer the period, the shorter the fraction of light curve taken up by eclipse. The periods range from days to weeks or more in length. Usually such light curves suggest little interaction between components. This is often but not generally true because the shapes of light curves in optical bands can be misleading. For example, where the depths of the two minima are very different, the temperatures of the component stars are different,2 and the hotter, bluer star may dominate the light from the system. The light curve may rise near secondary minimum, indicating a "reflection effect," actually a reprocessing of the hotter stars' radiation as it impinges on the atmosphere of its companion, increasing the cooler star's luminosity in the irradiated area - best seen around the secondary minimum. If it were not for the secondary minimum, which may be shallow or even absent in optical passbands, the reflection effect would peak at the phase of mid-secondary minimum. The effect is especially noticeable if the cooler star is significantly larger. If looked at in infrared passbands, the cooler star will contribute relatively more to the combined light and may resemble a p Lyrae-type light curve (see below). In extreme cases, the redder component is so highly evolved that it may be filling its Roche lobe and sending a stream of material toward its companion. This is, in fact, the case with Algol itself (cf. Chen & Reuning (1966)). Not all systems with Algol-like light curves will be in this state, however; the components are often two similar stars and not so close to each other that they are distorting each other's shapes. When the stars are far apart, their shapes may be approximated by spheres. It suffices to note that the spherical approximation would not be adequate for all cases. We discuss further this class of eclipsing variable under the EB designation "EA" in the section below. As outlined in Sect. 3.1.6 binary systems in which components are well within their Roche lobes are called "detached" systems and those in which one component fills its Roche lobe are called "semi-detached."

2 As we will learn later, this conclusion is valid only for circular orbits (actually, true Algols are interacting and are likely to have only circular orbits) and stars of similar size.

The prototype gives its name to the class. The light curve continuously varies across the cycle of variation, and the minima occupy a fairly large proportion of the cycle. The periods are typically days, but when giants or supergiants are involved, the period may be much longer. The important thing is not the cycle length or the scale of the system, but the relative size of the stars to the size of the orbit. The continuous variation of light is partially due to the changing aspects of the stars as they rotate, classically known as the "ellipsoidal variation."

The relative depths of the minima indicate the temperature difference between components; redder passbands tend to show less different depths. The light curves give the (correct) impression that the stars are interacting gravitationally. In fact, the stars are undergoing tidal distortions and their shapes reflect this distortion. Roche geometry is generally used to accurately model these systems' properties. This class of eclipsing variable is further discussed under the EB type "EB" in Sect. 1.2.2. W Ursae Majoris or W UMa

The prototype is an eclipsing binary with period less than a day, characteristic of the class. Like j3 Lyrae stars, the light curve varies continuously, but the depths of the minima are usually similar, but rarely exactly identical. Systems that exhibit these light curves are thought to arise from binaries in physical contact, not through a stream, but through an actual neck of material that bridges the small distance between the inward pointing edges of the components. Such systems are known as "over-contact" or if just barely touching, as "contact" systems. Although some astronomers use the term contact to refer to both contact and over-contact systems, here we will use the term exclusively in its narrower meaning. Roche geometry is used generally for the accurate modeling of the components of these systems. There are two subclasses of WUMa systems, about which capable astronomers argue endlessly: A-type and W-type systems. In A-type systems the more massive star is larger and hotter; in W-type systems, the more massive star is larger but cooler than its companion. Although both types of systems may exhibit asymmetries in light curves, the W-type tends to exhibit more of this sort of behavior. There may be a difference in depth of up to 0.1 magnitude. As well, there may be a difference in brightness between the maxima (a phenomenon sometimes referred to as the "O'Connell effect," which is quantitatively defined as

where m refers to the magnitude and the subscripts I and II refer to the maxima following the primary and secondary minimum, respectively. This means that AmI is positive if maximum I is brighter (has a smaller magnitude) than maximum II. The O'Connell effect may be found in many close binary systems of several types, but quite often in W-type UMa systems; cf. Davidge & Milone (1984) for a discussion of contributive causes. This class of eclipsing variables is further discussed under EB type "EW" in Sect. 1.2.2.

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