Introduction

These stars vary in luminosity caused by occultation of one of a close pair of stars passes in front of the other, thus eclipsing it and reduce the total luminosity of the binary system.

Class EA is the most widespread of the groups (Algol being the typical star) and consists of a binary in which the two stars revolving around each other are at a large distance apart. Eclipses occur with a deep principle minimum, a shallow secondary minimum, and relative stability in brightness outside the eclipses.

Class EB (Beta Lyrae the typical star) has two stars that are generally giants or supergiants of low density and unequal size that are not very far from each other. Because of their mutual attraction they take on an ovoid shape, and their light curve is therefore very rounded, very often with an appreciable secondary minimum.

Class EW (W Uma the typical star) is similar to the previous group except that here the two stars are dwarfs, almost equal in size and brightness. There are very close to each other, even in contact. The two components are highly deformed by their attraction and the light curve secondary minima has almost the same amplitude as the principle minimum.

EA: Algol

The EA or Algol variables occur in large numbers; there are about 3500 known. They are from spectral types O to M and include not only giants and supergiants but also dwarfs. The most frequently appearing spectra are those of type A, followed by B and F.

There are several main types of light curve. First there is the Algol type in which the secondary minimum is very small because of the great difference in the luminosity of the components. In some of these stars the secondary component is so faint that the secondary minimum is practically undetectable (AW Peg, for example).

The second light curve is from pairs formed by stars that are of roughly equal size and brightness. The secondary minimum is then almost as large as the principle minimum, for example Y Cyg.

The third type of light curve is from binaries formed of one bright star of average size and a fainter star of great size. The principle minimum is then wide since the occultation of the principle star by the secondary lasts a long time. The secondary minimum is not very deep. This is also the case with very long-period binaries.

Algol variables have extremely variable periods, ranging from less than 0.1 day to 10,000 days or more. Very short and very long periods are quite rare. The bulk of stars of this type have periods from 0.5 day and 10 days, with a modal value between 2.5 and 3 days.

EB: Beta Lyrae

The rounded light curve of the EB stars is due to the elliptical shape of the components. Since they are frequently of the same spectral type and thus of comparable brightness, the secondary minimum is often pronounced. These stars are generally giants or supergiants with not very late spectra, mainly O or B but also A and F. The masses are often large as these are stars with high luminosity. There are 600 EB variables known with period from 0.4 day to nearly 200 days. They are fairly concentrated at four days, with a marked modal value of between 0.8 and 1 day. Long periods are rare, only three are known that exceed 100 days and these are large sized supergiants: v Sgr (137.94 days), BM Ca (197.28) and W Cru (198.53 days).

EW: W Uma

The EW group (W Uma the typical star) consists mainly of dwarfs, belonging to spectral types dF and dG. The two components are often comparable in size and brightness, with the secondary minimum almost as deep as the first. About 500 are known. There periods are always short. There is a very marked modal value between 0.3 and 0.4 day. The is a correlation between the spectral type and the period, with a transition between K spectra for the shortest periods and A spectra for the longest.

The EW stars are old stars belonging to Population II. However the presence of EP, EQ, ER, and ES Cep in a galactic cluster (NGC 188) of medium age means that while there are certainly Population II stsrs of EW type some probably fall into an intermediate population.

Double (star) Talk

Ellipsoidal Variables

The General Catalog has created a separate class for a dozen stars called ellipsoidal variables. These are binaries whose components have an ovoid shape but whose plane of revolution makes a large angel with the direction of the line of sight. There are therefore no eclipses, but merely a variation in the apparent stellar area. This produces slight variations in brightness (a few hundredths of a magnitude) detectable in bright stars. These are all stars with B or A spectra concentrated in the galactic arms (Orion and Perseus), and they occur in OB associations or young galactic clusters. They therefore form a typical Population I.

Two Notable Binary Star Effects

There are two effects observed in a large number of binaries. The first is limb darkening. This effect is clearly seen on our own Sun. At the center of the star where the atmosphere of the star is traversed through the least thickness, we receive radiation from deeper and thus hotter layers than that from the edges where the thickness of the atmosphere crossed is much greater. On stars like the Sun the edges are slightly less bright than the central region. The darkening varies with the wavelength; it is very small in the infrared, still not very pronounced in the visible, but becomes more so in the ultraviolet. In eclipsing binaries, the effect appears as a rounding of the light curve, with the angles being smoothed.

The second effect is less obvious; when the components are very close, as in classes EB and EW, they assume a slightly ovoid shape and are then presented to us as an ellipsoid of varying area. However small it is, the change produces a slight variation in the apparent magnitude; the curve instead of being a straight line outside the eclipses, is slightly rounded. This is a very common effect.

Determination of Orbital Elements

Like all double stars, the eclipsing binaries provide valuable information for astrophysics, particularly about their stellar masses that are so important in the study of stellar evolution. Because so much work has been devoted to the determination of orbital elements of these systems, it is not possible to describe it all here.

Omitting the detailed and sophisticated mathematics it is still possible to give a taste of the methodology used. The first step is to construct a corrected light curve; one from which secondary distortions has been removed (limb darkening, ellipticity of components, etc.). The depth of the two types if minimum first enables the relative luminosity of the two components to be established. If we denote the radius of the orbit M (or the semi-major axis) by a, the relative values R(1) and R(2) of the radii can be calculated. These are R(1)/a and R(2)/a. A photometric study also enables the inclination i, of the system to be calculated.

To pass to absolute values, an additional parameter is required; the distance to the Sun. Since the parallax is unknown (except in a few cases), the spectroscopic parallax is used together with the curve of the radial velocities of the two components. With these data, the absolute value a sin i is calculated, and as i (and hence sin i) are known, the value of a can be determined. Since the relative radii are known, the absolute values of R(1) and R(2) can be obtained. Knowing the orbital radius and the distance, the masses M(1) and M(2) can be determined, together with the densities since the stellar radii are known. Significant progress has been made in our knowledge of absolute values of orbital elements.

Variations of Periods

For a long time it was thought that the periods of eclipsing binaries were constant; it is now known none of them are. The observed variations are small, but they are nonetheless significant in their cumulative effect, as in the case of the Cepheids. The period of Algol, for example, seemed constant at 2.86731 days for a century. In 1882, there was an abrupt change and since then a continuous increase. Its period in 1988 was about 2.86729 days.

For some stars, the change is continuous, as in the case of SW Lac, whose period increased from 0.3207214 day in 1813 to 0.3207281 day in 1988. While a change of 6.7 millionths of a day is minuscule, but over 40 years it represents a difference of 0.3 day, almost equal to the period.

In some cases the variation is abrupt. So, the period of U Cep has occasionally suffered large changes.

These variations are found in all types of eclipsing binary, although the EW class appears to be the most susceptible to them. Two possible causes are: a third star in some of the systems perturbing the orbit; Algol, for instance, is in reality a triple star system; and in close binaries, another effect occurs – the transfer of mass from one component to the other; this transfer alters the mass ratio and thus modifies the orbit.

Eccentric Orbits

Some binaries have highly elliptical orbits, a feature that is revealed in their light curves. Because of the ellipticicty, the distance between components A and B varies a great deal and hence the orbital velocity of B varies from one point to another. It is a maximum at the periapsis and a minimum at the apoapsis.

This variation produces a displacement of what is called the line of apsides, that is, the line joining the periapsis and the apoapsis. The major axis in fact turns on itself and this shows up in the asymmetry in the light curve since the secondary minimum does not occur at the midpoint of the cycle between two principle minima.

This effect has been detected since 1937 in several stars, such as RZ Cas, TW Dra, RT Per and RV Mon. It is now known to occurring a large number of eclipsing binaries. IT is a periodic effect, but the period is often difficult to determine since it is very long: 248 years for V523 Sgr, 284 years for RV Mon and 300 years for YY Sgr. One exception is GL Car, which has an apsidal period of 25 yrears.

Mass Transfer

Consider a binary system A and B. The Lagrangian point L is the point at which attractive forces of the two components are equal and opposite. If one of the stars occupies a volume sufficient to reach the Lagrangian point, the surface of the volume occupied is called the Roche surface and the volume itself is called the Roche lobe.

Consider the case in which A is a star in the latter stages of development, a red giant say, with a large volume for the relatively small mass. If it completely fills it Roche lob, the material further from the center than the point L will be attracted by B and will fall on to the latter’s surface: there is mass transfer from A to B.

With close binaries, three cases have to be considered. In the first, neither component reaches its Roche lobe. Nothing therefor happens, except a certain amount of deformation of the stars due to their mutual attraction, which causes them to become pear-shaped. Such a system, composed of young stars in the early stages of evolution, is called a “detached binary.” In the second case, component A reaches or exceeds its Roche lobe, while B remains well inside it. There is mass transfer from A to B; such a system, where the more massive component evolves more rapidly than the other, is called a “semi-detached binary.” Finally, there is the case where both components have reached their Roche lobes, when there is a reciprocal mass transfer from A to B and from B to A, the formation of a common atmospheric envelope. This is said to be a “contact binary”.

The mass transfers produce complex physical phenomena that would be too lengthy to discuss here. One point to make, however, is that the transfer changes the mass of both components and thus the mass ratio. This produces changes in the orbit and the period. The period increases if it is the more massive star that loses mass, and decreases if it is the less massive star that loses mass. Mass transfer also explains the fact that, in many cases, the principle star is a dwarf (class V) whereas the secondary star is a giant or sub-giant. This apparent anomaly is due to mass transfer; initially, the sub-giant is more massive, but loses an appreciable proportion of its mass to the other smaller star.

The transfer may be rapid. Taking a binary consisting initially of two large stars A and B with masses of 20 and 8 solar masses. Calculations show that the time between the beginning of mass transfer and its end is only 20,000 years, which is very short on an astronomical scale. At the end of that time, mass transfer had reduced A to 5.4 solar masses, while B had reached a massive 22.6 solar masses. Mass transfer also produces other effects, the major one being the following. If one of the components is a very dense star (white dwarf or pulsar), material falling on it at a high velocity raises the temperature considerably, which causes it to emit x-rays.

Binaries with Intrinsic Variations

Some eclipsing binaries have one, if not two, variable components. The variations are of all types. The ex-nova, such as VV Pup or UX UMa, which are characterized by flickering or the dwarf nova also with flickering, apart from the explosions of the U Geminorium or Z Camopardalis types. These sometimes make the observations of the eclipse difficult to observe.

AN UMa shows another type of variation. It is an ex-nova similar to V Sge and is also an eclipsing binary with a very short period of 0.0797 day, but it also shows variations that are long and irregular with an amplitude of 2 magnitudes and lasting several hundred days. These are interpreted as being due to the existence of a gaseous cloud of varying opacity that surrounds the binary. The cloud occults the system and its varying opacity produces changes in the observed brightness.

YY Gem and CM Dra are red dwarfs with emission spectra which have small variations of the BY Draconis type and sometimes flares like UV Ceti. Flares have been observed in class EW binaries, such as I Boo and U Peg.

A very different but very interesting case is that of AS Cas, an Algol variable with a period of 1.3669 days. The spectral types of the components are A3 + K. The A3 component is a delta Scuti type star with a period of 0.058 day and an amplitude of 0.05 magnitude.

Red giants and super-giants often show intrinsic variations. This is so with VV Cep, a very long period binary; the M component is a semi-regular variable. Its period has not been accurately determined but seems to be about 200 days for a maximum amplitude of 0.5 magnitude. Several stars similar to VV Cep are known, particularly AZ Cas and KQ Pup.

Eta Aur is another long-period binary with irregular variations of small magnitude. RX Cas, a class EB binary, is different; it has a period of 32.230 days and the spectral types of unknown type, with a long period (513 days) and an amplitude of 0.4 magnitude.

RS Canum Venaticorum Binaries

In 1931, a distortion was noticed in the maximum of the light curve of RS CVn which was of such a form that it could not be attributed to any known phenomenon such as limb darkening or ellipticity of the components. In 1946, the same effect was found in AR Lac and this was confirmed the following year by photoelectric observations. It then began to be realized that a new type of variation was being seen, but it has only been since the 1970’s that observations made at all wavelengths allowed the mechanism to be understood. From that time on, RS CVn and similar stars were considered to form a special group of binaries.

RS CVn is an Algol variable with a period of 4.798 days. It consists of a sub-giant of spectral type K0 IV and an F$ V dwarf, which shows intense emission lines of ionized calcium outside of eclipses. Photoelectic observations clearly reveal the oscillation during the maximum. Its amplitude varies between 0.05 and 0.2 magnitude and it does not always occur at the same point in the curve. Its displacement in phase is periodic, the period being 10 years. Its amplitude varies periodically.

Observations made with radio telescopes have revealed the existence of very intense radio flares; in addition, satellite observations have shown that RV CVn is a fairly intense X-ray source, also with abrupt flares.

At least 40 of these stars are now known. One pint that they have in common is that one or both of the components are of spectral type F or G (dwarfs or sub-giants) with emission lines of ionized calcium and even sometimes of hydrogen that are often strong. A binary of interest because of its proximity (18 parsecs), is UX Ari. This is a spectroscopic binary with a period of 6.438 days and spectral type G5 V + K0 IV. It does not show eclipses, but does have the RV Cvn type oscillations and is also a powerful X-ray source.

A number of these stars (RT Lac, AR Lac, SZ Psc, TT Pyx) have very strong radio emissions. There flares release an amount of radio-wave energy that is a million times greater than that of solar eruptions; in February 1978, the binary V711 Tau even had an enormous radio flare that was 100 million times more intense that the chromospheric eruptions of our own Sun! These stars are also X-ray sources, and their X-ray flares are sometimes 10,000 times stringer that those of the Sun.

The origin of these effects seems to be the same as those that are called the “active regions” of the Sun, that is, the coronal prominences. These are ejections of hot gases that are undergoing violent motion but cannot escape since they are trapped by magnetic fields. Considerable heating occurs, which causes the generation of X-rays. This is the undoubtedly the same phenomenon as that in the RS Canum Vanaticorum stars, but the intensity there is much greater. A gigantic luminous spot is formed and its apparent brightness with the orbital motion of the binary.