Chapter 14: The Milky Way

Wilhelm Herschel, German-British astronomer.

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 Michell 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.

Two supermassive stars orbiting one another in the open cluster Pismis 24

A visual binary is a physical binary in which the orbiting pair can be resolved (seen separately) with a telescope. This is the type that 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 easily 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.

Eclipsing binary star animation

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.

Two stars of different size orbiting the center of mass. The spectrum can be seen to split depending on the position and velocity of the stars. The shift of Star A is greater than that of Star B because the tangential velocity is higher. The line width of Star B is greater than that of Star A because the Star B is larger and more luminous.

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 analyses 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 the 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.