Observations of Eclipsing Binary Stars Binary stars are quite common. In fact, most stars are in binary or multiple star systems. If the orbital plane of a binary star is seen by us nearly edge-on, the stars will alternately eclipse each other. These binary stars are so far away from us that they look like single stars in photographs, but their brightness varies in a particular way due to the eclipses - these are known as eclipsing binary stars. About 6,000 stars of this type are known in our Galaxy and other nearby galaxies. Eclipsing binary stars are a rich source of information about the physical properties (mass, size, luminosities, internal structure, etc.) of stars and their evolution through time. In fact, the American astronomer Henry Norris Russell called the study of eclipsing binaries the "Royal Road to the stars." The accuracy with which the fundamental physical properties can be determined is impressive. Often the masses and sizes of the stars are known to better than 1% accuracy. The investigation of an eclipsing binary star usually proceeds through a number of stages. First is the discovery stage. Most eclipsing binaries have been discovered in surveys covering large sections of the sky looking specifically for stars whose brightness varies (variable stars). Images of a certain section of the sky are obtained repeatedly over a period of months or years, and then searched for variable stars. The earliest surveys used photographic plates as detectors. Photographic plates are not an ideal type of detector for many purposes, but they have one outstanding virtue - they are incredibly cheap. Also, during the late 19th and early 20th century, photographic plates were the only game in town for large area work. The exercises "Mac Chart" and "Mac.Period" are meant to show what can be done with observations of this sort. One of the most valuable early surveys was organized by Harvard Observatory and covered a large part of the whole sky, both Northern and Southern hemispheres, with photographic techniques during the years from about 1888 to 1962. Since they were trying to cover a lot of sky, the interval between plates of a given area of the sky could be weeks or months, and the date of observation also depended on the weather. In addition, when a section of the sky was too close to the Sun, which it is for some fraction of the year, it could not be observed. Thus, the times of observation were somewhat randomly spaced. More recently, CCD detectors have been employed for these purposes. These detectors are nearly ideal, with high quantum efficiency and linear response over a wide dynamic range. The MACHO project surveyed the Large Magellanic Cloud in this way looking for gravitational micro-lensing events over a period of years. As a byproduct, they found a large number (611) of eclipsing binary stars (Alcock et al. 1997, Astron. J., 114, 326). The figure below shows a light curve of one of these eclipsing binaries in the LMC. In a light curve like this, primary eclipse falls at phase 0.0 and, if the stars have circular orbits, secondary eclipse falls at phase 0.5. It doesn't do that in this case, so the orbits must be eccentric. The observations obtained during the discovery phase are often not all that accurate, so this phase is usually followed by a refinement phase with different measurement techniques for stars of particular interest. One of these techniques is to observe the brightness with improved precision near predicted times of eclipse to determine accurate dates of minima in order to improve the predictions of eclipses. The exercise "Dates of Minima" is meant to simulate the results of this type of study. New techniques, such as spectroscopy, are used in this phase to measure the radial velocities of each star over the orbit. This data is necessary to determine the absolute masses and sizes of the stars. Finally, the photometry and radial velocity data can be combined to produce a complete picture of the binary star. The exercise "Binary Stars" simulates this process. The end result of these activities, which are often done by several astronomers widely separated from each other by both space and time, are masses, sizes, and luminosities of a pair of stars, both of which have the same age. Theoretical models that predict how a star changes as it ages must be able to match the observations of this type, or the model must be rejected. Thus the study of eclipsing binary stars severely limits the models that describe our understanding of stars.