A binary star is defined as a star system formed by two stars orbiting around their common center of mass; the brighter star is called primary, while the other is called companion or secondary.
The observations made since the nineteenth century suggest that there are many stars that are part of binary systems or multiple systems, composed of more than two stars. The term double star is sometimes used as a synonym of binary star, but sometimes indicates both binary stars physically linked to each other and optical binaries, i.e. pairs of stars that appear close when observed from Earth, but that have no gravitational link between them. It can be verified if a double star is optical when the two components have sufficiently distinct values of proper motion or radial velocity, or when parallax measurements reveal that they have different distances from Earth. However, there are many double stars for which it has not yet been possible to determine whether they are physically bound binaries or only apparent doubles.
Often the two components that form a binary star are visible to the naked eye or through the use of observational instruments; such a binary is called a visual binary. Many visual binaries have long orbital periods, on the order of hundreds or thousands of years, and therefore their orbits are known only with uncertainty. Other binaries instead have such a narrow orbit that they are not resolvable even with optical instrumentation, but are recognizable as such only by indirect techniques such as spectroscopy (spectroscopic binaries) or astrometry (astrometric binaries). If a binary has an orbital plane parallel to the Earth’s line of sight, its components will eclipse each other; these binaries are called eclipse binaries or, when they are recognizable by the changes in brightness produced by eclipses, photometric binaries.
If the components of a binary system are close enough together (tight binaries), they may distort each other’s atmospheres and, in some cases, may even exchange material so as to alter their normal evolution. A variety of close binaries are the so-called contact binaries, which are so close to each other that they share a considerable percentage of matter. Binaries can also give rise to planetary nebulae and are the origin of cataclysmic variables, particularly novae and Type Ia supernovae. Binary stars also play an important role in astrophysics, since the calculation of their orbits allows to estimate the masses of the two components and, indirectly, other parameters such as radius and density.
Since the distance separating the two components of a binary star is always much less than the distance of the pair from Earth, there are very few binary stars that can be observed with the naked eye: they, on the contrary, appear as a single star because they are too close to be separated by the human eye. A notable exception is the pair Mizar-Alcor, belonging to the constellation Ursa Major, which appears separated by 11.8 arcminutes and can be distinguished with the naked eye if you have good eyesight. The two stars are physically about a quarter of a light year apart and are about 80 light years from us.
However, in most cases to separate the two components of a binary star is necessary to use an instrumentation: in fact, the smaller the distance between the two components and the greater the distance of the pair from Earth, the greater must be the angular resolving power of the instrument needed to separate them. The brightness of the stars is another important factor: bright stars, because of their glare, are in fact more difficult to separate than fainter ones. Some binary stars have a sufficiently small separation and are sufficiently distant from Earth that they cannot be resolved even by the most powerful telescopes; however, the construction of increasingly large and powerful telescopes allows the direct observation of an increasing number of binary stars.
One of the most striking aspects of the observation of binaries is the contrast of colors between their components that some of them show; one of the most spectacular binaries in this sense is Albireo, a star of third magnitude belonging to the constellation of Swan. It is one of the easiest visual binaries to observe because of the wide separation between the two components and their difference in color: the brighter star of the pair is blue, while its companion is orange; the brighter component is actually itself a close binary.
However, the colors that observers report are often very discordant with each other; these discrepancies may be due to a variety of factors, such as the type of telescope used, atmospheric conditions, the difference in brightness between the components of the pair, the effects of contrasting colors and the perception of colors by the observer. In the amateur field, smaller telescopes have an advantage over larger ones because small instruments provide an optimal level of light to distinguish the colors of brighter binaries: too much illumination (as well as too little) makes color perception difficult and uncertain.
When observing a double star, one first tries to ascertain whether it is a true binary or just an optical pair; one of the easiest ways to do this is to observe the orbital motion of the two stars around their common center of mass. This method can be used if the orbital period is not too long, so that the relative motion of the two stars can be observed over time. We proceed in this case by measuring the position angle of the less bright star relative to the brighter one and their angular distance, and these measurements are repeated over time. After a sufficient number of observations, they are collected in a polar coordinate system, where the brightest star occupies the origin and where is drawn the most probable ellipse passing through the points where the less bright star has been observed; actually this ellipse does not coincide with the real orbit of the secondary, but with its projection on the plane of the sky. From this apparent ellipse it is still possible to calculate the parameters of the orbit, where the semi-major axis is expressed in angular units, unless the parallax, and therefore the distance, of the system is not known.
The calculation of orbital parameters is of fundamental importance in astronomy, since it is the only direct method for evaluating the mass of stars. When the orbital period is too long to appreciate changes in the position of the two stars, the distances, radial velocities and proper motion of the stars in the pair are measured: if these measurements give equal or similar values, then the pair is probably gravitationally bound. In fact, if two stars are physically bound, then they will be more or less at the same distance from us and will share the same proper motion in the sky.