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Binary stars are crucial to our studies of stars because they allow us to precisely measure a star's mass.
There are four types of binary stars:
The types of binary stars are distinguished by how we detect them.
A visual binary is one where we can see both stars in the two-body system. Obviously, the stars must be fairly close to us in order to resolve the two stars using a telescope. If they are very far from us or are very close to each other, then they will appear as one star and we must use a different technique to distinguish the two stars.
Thus, we find visual binary stars when they are relatively close to us and when they are relatively far apart from each other. However, if they are far apart from each other, then they will have a large orbital period, perhaps even hundreds of years.
The image below shows the double star Castor A and Castor B. (Interestingly, it turns out that both Castor A and Castor B are themselves binary stars.) Castor B is a white dwarf with a much smaller mass than Castor A. They are so far apart that they haven't even completed one orbit yet.
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In the image, Castor A appears to be stationary. Why? Answer
Note that masses of stars can be computed from visual binaries; however, it's very difficult because of the large periods of the orbits.
For a binary system made up of a hotter star and cooler star, the stellar spectrum will be a combination of the two spectra. If the light from one of the stars is much less bright than the other, then the brighter star's spectrum will dominate.
The radial velocity (the part of the velocity of the star that comes toward us or away from us) can be measured by looking at the Doppler shift of the absorption lines in the star's spectrum. As a star moves toward us, the absorption lines are blueshifted (i.e. move to higher frequencies), and as a star moves away from us, absorption lines are redshifted (i.e. move to lower frequencies).
The applet below will help you understand this. It demonstrates the shifting of absorption lines for binary stars as the stars orbit one another. You can adjust the masses of the stars, the semi-major axis lengths, the eccentricity, and the tilt of the orbit (with respect to us). You should adjust the parameters and view how they affect the Doppler shift of the absorption lines and thus how they affect the graphs of radial velocity of the stars.
For bright binary stars that are relatively close and have small companions, we may be able to visually see it move relative to the background stars even though we can't see its companion.
A good example is Sirius A. It has a small, white dwarf companion that could not be viewed until the Hubble Telescope took the picture shown below. However, even before the companion was viewed, Sirius was known to be binary star because of the companion's gravitational pull on Sirius and the deviation of Sirius' orbit with respect to background stars.
The picture below shows Sirius A's motion relative to background stars. It is a combination of its proper motion and its orbital motion. The orbit of Sirius B is deduced from the orbit of Sirius A.
The picture below is of the orbits of Sirius A and Sirius B deduced from the previous picture.
The applet below will help you understand eclipsing binary stars. The graph of a star's brightness as a function of time is referred to as the star's light curve. In this case, the graph shows brightness of the star as a function of theta, the angle from 0 to 360 degrees, of the green star in its orbit. You should adjust the angle of inclination of the orbit, the separation, and the stellar classification of the stars to see how it affects the light curve.
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