Binary Stars

One major stellar property remains for us to discover. We could learn the masses of the stars if we can observe the effect that that mass has on nearby stars. We need a binary star system.

The study of binary stars can be dated to the 1780's. Until then people thought that all stars were single like our Sun and that the stars were randomly distributed around the sky. Chance alignments as viewed from Earth might make stars appear to be double stars, but we wish to study the true binary stars, stars that are close together and orbit one another under their mutual gravitational fields.

William Hershel embarked on a project to measure stellar parallax, that long-sought shifting in the positions of the nearby stars as a result of the motion of the Earth. He took up a suggestion of Galileo that by finding double stars, the motion of the brighter (and presumably closer) member would be easier to spot because the fainter member would give a reference point. Statistically, stars close enough together to be useful should occur once for every 300,000 stars. In the first year, however, Hershel found 484 such pairs. He had discovered binary stars.

Binary stars fall into various categories by the method in which they are discovered. The first group is the visual binary stars. We see both companion stars and can follow the orbit over time. About 10% of all stars are in this category. Orbital periods are measured in decades or centuries. Using Kepler's 3^rd Law (P² µ a³), we can deduce that the two stars must be rather far apart from each other. Occasionally, stars are found whose proper motion across the sky is not a straight line as it must be if the star if single and unperturbed. This subset is called astrometric binaries. At times the mass of the unseen companion is announced to be too small for the object to be a star. None of these reports have been confirmed to date.

A second type of binary star is the spectroscopic binary since its duality is detected in the spectrum. If we are recording the simultaneous spectra of two stars, we may see a periodic shifting back and forth of the spectral lines. This is simply the Doppler Effect caused by the orbital motion. When a star moves towards us, the lines are slightly blue-shifted. As the orbital motion carries the star away from us, the lines are red-shifted. Of course, the orientation of the orbital plane must be nearly perpendicular to the plane of the sky in order for us to see the effect. The stars show orbital periods of days to weeks, suggesting that they are close together. Indeed, if they were not close to one another, their orbital velocities would be too small to measure using the Doppler Effect.

Another way of detecting the binary nature of stars is through the measurement of brightness change. If the orbital plane is aligned nearly perpendicular to the plane of the sky, the stars have a chance to eclipse one another. By monitoring the brightness, we can see the eclipses. The primary, or deeper, eclipse always occurs when the brighter of the two stars is being eclipsed. Eclipsing binary stars also permit us to measure radius. The restrictions on the eclipsing systems are similar to those for the spectroscopic binaries and many stars have been detected in both ways. The details of how the light varies during the orbit helps us measure properties of the orbit, the size and shape of the component stars, and how light is distributed across the surface of each star.

When the fundamental data are combined, we can plot the brightness of the stars versus the mass. The graph is called the Mass-Luminosity relationship. We learn that the bright stars are also the massive stars. Faint stars are the low mass objects. We can also (for eclipsing binary systems) plot the radii for the stars along the Main Sequence on the H-R diagram. We find that the bright O and B stars are also quite large compared to the K and M stars. They are all called dwarfs because they fall along the Main Sequence, but not all dwarfs are created equal.