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Binary and Variable Stars Overview For a casual observer, binary star systems can often be confused with variable stars, and vice versa. The reason for this is that they both seem to vary their output of light. However, these two phenomenon are not related*, for binary stars are two stars that are locked in each others' gravitational pull and are destined to go through the universe spinning around each other. A variable star, on the other hand, is a star that, for one reason of another, changes its luminosity in either a predictable pattern or at random. *There are always exceptions to the rule, and in this case the exception is cataclysmic variable stars - stars in a binary system where one steels matter from the other and the extra mass periodically erupts in a thermonuclear explosion on the star's surface. Binary Star Systems Estimates are that at least 60% of stars are members of a binary (or more) system. These common systems can form in two main ways. Most frequently, they are born the
same way all other stars are - in a nebula.
The only difference is where they form: In the parent nebula, the two constituent
stars of the future binary system form closely to one another. After they are "born" (initiation
of hydrogen fusion), their solar winds blow
away all of the surrounding nebular material, and because of their proximity,
the two stars cannot escape each other's gravitational pull. Therefore, they
are locked together. (Note that this is also applicable
to more than two stars; our closest neighbor, Proxima Centauri, is part of a
triple star system, examples of four star systems abound, as are five, six, and
more.) The other way for a binary system to form is if a free star happens to fall into another star's gravitational pull, and become locked in orbit because it does not have enough energy to escape. (This is the same way some planets get their moons: An asteroid is captured by a planet's gravitational pull.) Historical Note: An older theory of binary formation proposed that the two stars were once one star, and they later split into two. A binary star system works very simply. In the diagram (right), the system consists of a high-mass neutron star and a blue supergiant (not to scale). Because the neutron star has a higher mass than its companion, the center of gravity of the system will lie closer to it than the blue supergiant. Its orbit around the center of gravity will also be smaller than the other star's. The time of orbit can last anywhere from less than half an hour (the record is five minutes in a white dwarf binary system) to millions of years, depending on how close the stars get. The reason that binary systems are sometimes mistaken for variable stars is because some eclipse periodically, as seen from Earth. This means that at certain points in their orbits, one of the stars will pass in front of the other one, and thus block out part of its light. Sometimes, if one of the stars is a neutron star or black hole, it can pull material from its companion star. In the case of a neutron star, the material will build up on the surface, and then it will periodically erupt in a massive explosion. This is called a cataclysmic variable (see below). Binary stars are important in stellar science because it is
only when a star is in a binary system that we have the possibility of deriving
its true mass. However, there is another complication -- only the minimum masses can be calculated because the system could be inclined relative to Earth. However, knowing the minimum masses of the stars can still help to develop, verify, or disprove theories of stellar evolution. There is the rare case when the system is turned so that we see it directly edge-on. This is called an eclipsing binary system. In the case of an eclipsing binary, we see each star pass directly in front of the other one. In these cases, the masses can be directly determined for the stars. Variable Stars A variable star gets its name because it can change in size, which we on Earth observe as a change in brightness. When the star is as its smallest, it is brightest, and when it is at its largest, it is at its dimmest. The reason for this is somewhat counter-intuitive. Throughout the cycle, the star produces the same amount of energy. When it is large, that energy has to fill a greater volume; therefore the energy is more spread out within the star and on its surface, so it is dimmer. The converse is then also true. Variable stars are not variable for their entire lifetimes. Mira variables, for example, become so only when they are old and unstable. Cepheid variables are only variable for a short time when they are along the Horizontal Giant Branch. A specific example is Polaris, the North Star; its fluctuations seem to have been dying off recently, indicating that it is coming out of its unstable phase. Mira Variables Variables are named after the most famous Mira variable, Mira, in the constellation the Cetus, the Whale. They are old, red giant stars. At this late stage in their evolution, they have grown unstable and pulsate. Their pulsation cycle can last for anywhere between a few hundred days to several years, and can vary between eight different magnitudes - a measure of brightness. Since they are so unstable, their cycles are not necessarily constant from one to the next. Cepheid Variables The Cepheid Variables are named after the first one to be discovered: Delta Cepheid Cepheids have cycles that last a few days, and they vary by as much as two magnitudes. Unlike Mira variables, the Cepheid variable stars have extremely regular pulsation rates, and their cycles are directly linked to their absolute magnitude - the true measure of a star's brightness.
RR Lyrae Stars RR Lyrae stars are a sub-classification of Cepheid variables. They have a much shorter oscillation period - usually less than a day - and are all about 90 times brighter than the sun.
Cataclysmic variables always have a binary companion, and do not pulsate via the same mechanism as the other variable stars so-far discussed. They draw matter from their companion star, as shown in the diagram** above. In this diagram, a very massive neutron star is drawing material from its binary companion, a blue supergiant. After it draws a sufficient amount of material, it erupts in an explosion that can raise its luminosity by as much as 10 magnitudes. However, the stars are not destroyed, and can repeat their cycles again and again, each cycle lasting up to hundreds of thousands of years. **Diagram is not to scale. 
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This
derivation comes from 
This
makes Cepheid variables one of the most important types of stars, for they can
act as a "cosmic yardstick." By measuring the star's pulsation period,
astronomers are able to judge its absolute magnitude. Then, by measuring its 
Cataclysmic
Variables