Close Binary Eclipsing Systems

We adopt a triple system of classifying eclipsing binary systems: according to the shape of the combined light curve, as well as to physical and evolutionary characteristics of their components. The classification based on light curves is simple, traditional, and suits the observers; the second and third classification methods take into account positions of the binary-system components in the (Mv, B-V) diagram and the degree of inner Roche lobe filling. Estimates are made by applying the simple criteria proposed by Svechnikov and Istomin (1979).


Within the GCVS you will find over 6000 eclipsing binary variable stars. The Algol-type eclipsing binary stars are the most numerous; however, over one thousand eclipsing stars have not been well studied and as a result have not been categorized within the three major groups (i.e. EA, EB, or EW). One thousand ill-defined eclipsing binaries, classified as "E:", can certainly be described as a target-rich environment for any observer!

Of course, upon close examination most of these stars are considered to be faint, even at maximûm brightness, or they display a small amplitude and as a result will require instrumentation to properly observe them throughout their entire cycle. If you're a serious visual observer, this does not present a hopeless challenge. A casual examination of the variables classified as "E:" readily expose a handful of stars that you can easily study by using visual methods. For example, consider the following two stars: HO CMa, maxima - 7™55, minima - 8™62 with a period that seems to be undetermined; and V536 Mon, maxima -9™ 10, minima - 10T10 with a period of 31^035. Both of these stars can be studied using visual means and without a doubt many others with similar characteristics can be found.

If you question that visual observers are able to adequately observe stars with similar, apparently limiting characteristics such as a small amplitude or faintness, read carefully within this chapter the results obtained by Kari Tikkanen, an observer from Finland who uses binoculars to observe variable stars. His results are encouraging.

While eruptive, pulsating, cataclysmic and rotating stars are said to be intrinsic variables because their variability is caused by different internal physical mechanisms, eclipsing binaries are called extrinsic variables and their study requires complex physical models in addition to the requisite stellar physics to describe their variable characteristics. Constructing these physical models requires the use of both astrophysics and geometry; good reasons that the study of eclipsing binary stars is considered a complex labor. Let's examine some of the physical properties that have some bearing on the study of these stars.

Usually, astronomers classify physical binary stars according to the manner of detection. To understand what we can learn from binary stars, it helps to understand the different methods used to observe them.

Visual binaries are physical pairs in which both members can be resolved with your eye, a telescope or a camera. Over 65,000 visual binary stars have been studied by astronomers. Should you ever become tired of variable stars, visual binary stars provide a great area of study for amateur astronomers!

With spectroscopic binaries, the individual stars cannot be resolved. The orbital motions are revealed by periodic Doppler shifts in the star's spectral lines. There are two subtypes of spectroscopic binary stars: those in which one spectrum can be detected; and those in which two sets of spectral lines are seen. The latter, displaying lines of both stars, yield more information to the observer.

An eclipsing binary is a pair of stars with a mutual orbit that is seen nearly edgewise and therefore, is producing eclipses. Because our line of sight lies in, or nearly in, the orbital plane, the stars alternately pass in front of each other. The light curves that you prepare after observing these stars will reveal much about the pair. Eclipsing binary stars is the topic of this chapter.

An eclipsing-spectroscopic binary shows both Dop-pler shifts and detectable eclipses. This is the most informative type of binary, permitting very detailed analysis of motions, masses, and sizes of stars.

An astrometric binary is one revealed not by Doppler shifts or eclipses, but by motions measured with respect to background stars.

Conducting eclipsing binary studies often involves the combination of photometric and spectroscopic data. Photometric data is principally light curves while spectroscopic data is primarily radial velocity curves produced by measuring the Doppler shift in spectral lines. In principle, interrogation of the light curve surrenders the orbital inclination and eccentricity, relative stellar sizes and shapes, perhaps the mass ratio in a few cases, the ratio of surface brightnesses, and brightness distributions of the stars among other quantities. If radial velocities are available, the masses and semimajor axis may also be determined. Radial velocity can be retrieved from journal articles so you can use it to carry out very thorough studies of these stars. Many other parameters describing the system and the individual stars may be determined, in principle, if the light curve data displays high precision and the stars do not differ greatly from your assumed model. A great computer program that will help you study eclipsing binary stars is Binary Maker 2.0, provided by David H. Bradstreet, Contact Software, Norristown, PA 19401-5505.

In some cases it's possible to determine the position of each star within the binary system, especially during the eclipse. The greatest loss of brightness is when the fainter star passes in front of the brighter star, causing the total brightness of the system to drop. When the fainter star is positioned off to one side of the brighter star, relative to the direct line of sight, the system is brightest. As the fainter star passes behind the brighter star, the system again loses light but not as much as when a portion of the brighter star's light is blocked. As we will see, there are many configurations involving two stars (Figure 7.1).

Shown next are prototypical light curves corresponding to the classical categories of Algol, f) Lyrae, and W Uma stars, known as EA, EB and EW variables respectively.

Algol type (EA) light curves are typically almost flat-topped, suggesting that any photometric effects due to

Figure 7.1. Light illustrating the min and maximum brightness for an eclipsing binary the proximity of the stars are small. A large difference between the depths of the two minima is evident and in some cases the smaller of the two is difficult to detect. You may even find, at some wavelengths (for example, when using science filters), that the secondary minimum may be undetectable and there may even be an increase in light near the expected phase of secondary minimum due to the reflection effect. Within a binary system, the presence of a second star leads to an increased brightness on the side that faces toward the companion star. The increased brightness is caused by heating from the radiant energy of the companion star. Obviously, this results in an increase of temperature. As you probably understand, since thermal energy is the physical cause for this phenomenon it is somewhat misleading to use the expression reflection effect (Figure 7.2).

One effect of reflection on binary star light curves is to increase the light around the secondary eclipse relative to that near the primary eclipse. Another effect is to produce a concave, or upward curvature, of the light curve between eclipses. When the two stars within a binary system have similar temperatures and are close but not actually over-contact, it may be necessary to consider multiple refection effects. The eclipsing binary BF Aurigae is an example for such a binary. The first star heats the second star, and the second star, now warmer, then heats the first star more than otherwise expected because of its own raised temperature. This

Figure 7.1. Light illustrating the min and maximum brightness for an eclipsing binary

Figure 7.2. Artist's conception of the reflection effect. Notice the brightness of the facing sides of each star. Copyright: Gerry A. Good.

Figure 7.2. Artist's conception of the reflection effect. Notice the brightness of the facing sides of each star. Copyright: Gerry A. Good.

process is iterative, meaning that it compounds itself, and leads to higher temperatures on the facing hemispheres of the two stars.

Beta Lyrae (EB) light curves, on the other hand, show continuous variability, characteristic of tidally distorted stars with a large difference in depths of minima. This type of light curve usually indicates stars with different surface brightnesses. The prototype variable (f) Lyrae) for this group of eclipsing stars was discovered to be a variable star by John Goodricke in 1784. The changes are most easily noticed by comparing fi to its neighbor y Lyrae, which has a magnitude of 3T2. At maximum light, ¡i and y are nearly equal in brightness; however, at its minimum, P is only half the brightness of y. Beta Lyrae is an excellent variable to observe using binoculars. It's bright and so are the comparison stars.

The W UMa (EW) light curve is also continuously variable, similar to the fi Lyrae light curve, 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 detached or semidetached binaries, while the EW systems are over-contact.

The expressions detached, semidetached, and over-contact arise from morphological classification of binaries. Detached systems contain widely separated stars. Semidetached systems are still separated but one star fills its Roche lobe. Contact systems exist when both stars precisely fill their Roche lobes. In over-contact systems, both stars overfill their Roche lobes and establish a common envelope. Such systems can only exist for astronomically significant times if the orbits are circular and the components rotate synchronously.

As an aid to studying the light curves of eclipsing binaries, the deeper minimum in the light curve is called the primary minimum when the difference in depths of the two minima is clearly discerned. The designation may be arbitrary in cases when there is no difference. Astronomers usually compute the decimal fraction of a photometric cycle, called the phase, from the primary minimum. As I'm sure you remember, the phase for other variable stars begins at the brightest part of their cycle.

When it's time to designate the primary star, an astronomer's background usually determines how it is done. The definition varies among photometrists, spectroscopists, and theoreticians, and so the designation is not always consistent. Within the context of photometry, the star being eclipsed at primary minimum is usually called the primary star. As you probably understand, this classification is not necessarily one of size or mass but rather related to temperature. For circular orbit binaries, it is the star possessing the greatest brightness per unit area that is eclipsed at primary minimum. In many cases, this star is usually the more massive of the two.

During spectroscopic study, the usage is occasionally confusing. When studying spectral features, the star with the stronger spectral lines, usually the one with the apparently greater luminosity, is most often classified as the primary star. In radial velocity investigations, the primary star is the one with the smaller radial velocity amplitude, which obviously is the more massive star. While the more massive star is usually the more luminous and, as a result the hotter star, there are cases when this is not true. When theoretical studies are considered, this classification situation becomes even more confusing. Within considering the stellar evolution of a binary star system, the designation "primary"

sometimes refers to the originally more massive star which can become the lower-mass star because of mass transfer. Confusing? It's best to check, very carefully, when reviewing a journal article or book, to be sure which star is which.

The Jagiellonian University Observatory, also known as the Cracow Observatory in Poland (http://www.oa.uj. maintains a card catalog containing the times of minima and other information on approximately 2000 eclipsing binary stars. The data has been collected at the observatory since the early 1920s. You'll also find the International Supplement (SAC -Supplemento ad Annuario Cracoviense) containing ephemerides for one year that include 880 stars recognized as eclipsing binaries (of Algol, fi Lyrae, or W Ursae Maioris type).

Dan Burton maintains a nice Web site, Eclipsing Binary Stars, where you can finding information regarding these stars including some photometry on fi Lyrae and 68 Herculis, software and a model for computing light curves. The address for the Web site is (

Besides the three well-known eclipsing star systems, a new class of eclipsing system was introduced in 2000 (IBVS 5135). Known as the planetary eclipsing transit, this configuration requires a planet rather than a companion star to cause the eclipse. If you want to detect extra-solar planets, this is the type of binary system they you'll want to observe.

Along with the eclipsing systems themselves, the GCVS includes additional classifications based upon the physical characteristics of stars found within binary systems. Additional classifications are also based upon Roche lobes. Table 7.1 lists the GCVS classifications.

Observation Key

A Mixed stars

Mixed amplitudes Xi Mixed periods <3> Visual, CCD/PEP

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