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 

	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.