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# 14.3 Binary Star Systems

Some of the stars that are close together in the sky are at different distances and only seem to be aligned as seen from Earth. John Michelle showed that there were too many pairs for all of them to be accounted for by accidental alignments. However, his argument only applies in a general, or statistical, sense; it cannot be used to conclude that any particular system is a true binary star. We define a binary system as a pair of stars that we can prove to be bound by gravity by following their orbits. The first evidence for a physical association came nearly forty years after Michell’s work. In 1804, William Herschel noticed that Castor (the brightest star in the constellation Gemini) has a faint companion near it. By taking a series of photographs over several months, he demonstrated the two stars moved around each other in a binary orbit. Herschel’s discovery was the first observation of gravitational orbits beyond the Solar System — an important confirmation that the law of gravity is universal.

In a binary system, the brighter star is usually designated A and the fainter star B (for instance, Castor A and Castor B). The more massive star is usually called the primary. The less massive one is called the secondary. Normally, the primary is also star A, the brighter star. Astronomers usually classify binaries according to how they are detected. There are four main types of detection.

Two supermassive stars orbiting one another in the open cluster Pismis 24. Click here for original source URL.

visual binary is a physical binary in which the orbiting pair can be resolved (seen separately) with a telescope. This is the type that it is easiest to identify and it is the type first discovered by Herschel. Over 100,000 have been cataloged. Images taken over a period of months or years can show clearly that two stars orbit each other. The motion of the pair on the plane of the sky is combined with the Doppler motion along the line of sight to give the stars’ true three-dimensional orbit. However, in many other cases only one of the two binary stars is visible, For these binaries, detection of the second star is indirect. Imagine a giant and a dwarf star in orbit — these two stars may be so different in brightness that only one can be detected with a telescope. Or the two stars may appear so close together on the sky that a telescope cannot tell them apart. The separation of most visual binaries is 10 to 20 A.U. At a separation of 20 A.U., we can use the small angle equation to calculate the distance at which the binary would subtend an angle of 1 arc second, D = (206,265 × 20) / 1 = 4 × 106 A.U. = 4 × 106 / 2 × 105 = 20 parsecs. In other words, beyond about 20 parsecs the typical binary would have too small a separation to be resolved eaily with a small ground-based telescope. Large telescopes using adaptive optics could push the resolution limit down to 0.05 arc seconds, so the distance limit to about 400 parsecs or 1300 light years, which is still the "local" Milky Way. Indirect methods of binary detection need to be used for the rest of the galaxy and beyond.

In a spectroscopic binary, the individual stars are too close together in the sky to be resolved. Periodic Doppler shifts of the spectral lines reveal the orbital motion. In some cases only the spectrum of one star can be detected. Spectra taken on two dates will show absorption lines that mark the spectrum shift from red to blue and back again, indicating a periodic Doppler shift due to the orbit. We get more information when two sets of spectral lines are seen. In a spectrum with a double set of absorption lines, astronomers can track one star receding and one star approaching. As the orbit progresses and the stars are moving perpendicular to the line of sight, the spectral lines merge. Several thousand pairs have had their spectra measured in this way.

Eclipsing binary star animation. Click here for original source URL.

An eclipsing binary is a binary pair (generally unresolved) whose orbit is seen nearly edgewise. Because our line of sight lies in, or nearly in, the orbital plane, the stars alternately eclipse each other. Eclipses are detected by plotting light curves, or plots of brightness versus time. Depending on the relative brightness and size of the stars, the eclipse of the primary may produce a marked, short-term decrease in brightness. This may be followed by a decrease in brightness due to the eclipse of the secondary. The star then returns to its normal brightness and the cycle repeats. Astronomers can use the shape and timing of the eclipses to learn about the sizes of the two stars. Of course they have to be lucky enough to see a system whose orbital plane is nearly parallel to the line of sight. Binary orbits occur at random angles in space and the orientation is only favorable for eclipses in a small percentage of the cases. NASA's Kepler satellite has found more than 2000 eclipsing binaries by staring at 160,000 stars for several years.

An astrometric binary likewise occurs when a bright star is moving around an unseen companion. Extremely careful measurements of its position, relative to background stars, can reveal its motion, in turn revealing that it is a binary and has an unseen companion. We learn information about the unseen companion, as well as the visible star. This method is also important in detection of smaller mass companions, like brown dwarfs and planets. Because the method only works for nearby stars out to about 10 parsecs, few astrometric binaries are known.

One interesting facet of binary stars is that very different types of stars can be paired: massive and not so massive, giant and dwarf, red and blue. They can be born together and so share an evolutionary history, or they can have captured each other at very different stages in their lives. The variety offers challenges for both measurement and the imagination.

What can we learn from binary stars? The most important application of binary star studies is in determining star masses. We can determine the masses of the two stars from an analysis of the orbit. By contrast, the mass of an isolated single star can only be determined in terms of a model of stellar structure. Most eclipsing binaries also show Doppler shifts, which allows very detailed analysis of the motions, masses, and sizes of the stars. To take a simple example, suppose the Doppler shifts reveal that one star moves in a circular orbit at 100 kilometers per second, and timing of the eclipse shows that it takes 10,000 seconds (about 3 hours) to pass in front of the other star. Then the diameter of the primary star must be about 1 million kilometers (distance = speed × time = 100 × 10,000 = 106). Since mass is the main driver of stellar evolution, this type of observation is one of the most accurate checks on theories of stars.