Why Binary Stars Are Important

Binary stars are important, first, because they are numerous. Latham et al. (1992, p. 140) conclude that the frequency of spectroscopic binaries detected in the galactic halo is not significantly different from that in the disk, despite differences in kinematic properties and chemical composition. The observed frequency is approximately 20%; the actual frequency is higher because many binaries remain undetected. In the solar neighborhood, where we have the benefit of proximity so that proper motion variations can be detected, the frequency is more than 50% - and several stars are in fact multiple systems.

The second reason why binaries are important is that they are the primary source of our knowledge of the fundamental properties of stars. For example, the direct determination of the mass of any astronomical object requires measurable gravitational interaction between at least two objects (galaxy-galaxy, star-star, star-planet, planet-satellite). In galaxy-galaxy interactions, the distances and separations are so large that no detectable motion on the plane of the sky is possible. In star-planet interactions the objects contrast so greatly in brightness that outside the solar system only the highest possible - and until recently rarely attained - precision can resolve the objects. Typically in the latter case, only the star's motions are detectable, and the properties of that star must be assumed, mainly on the basis of binary star studies, in order to deduce the properties of the planet. In star-star interactions, the variations in position and velocity caused by orbital motion are detectable for a wide range of stellar separations and up to at least a factor of 5 in brightness. It is often the case that both stars may be studied in any of several ways, depending on their distances, brightnesses, and motions. Other basic properties of stars and of the systems they constitute can be determined through analysis of observational data, depending on the observational technique by which the interaction is studied. The four main types of binaries described by the observational technique are visual, astrometric, spectroscopic, and EB systems. We discuss each type in turn.

1.2.1.1 Visual Double Stars

For visual double stars, true binary star systems (as opposed to purely optical doubles) in which both components are visible and resolvable in a telescopic eyepiece, it is possible to determine the component masses M1 and M2. They are derived from Kepler's third law (3.1.62) and the moment equation a1 M1 = a2M2, where a1 and a2 are the semi-major axes of the absolute orbits of the components about a common center of mass.3 The derivable orbital elements include the size or semi-major axis a and shape of the relative orbit and the inclination i of the plane of the orbit against the plane of the sky. Because, however, in most cases4 only the angular semi-major axes can be determined in this way, parallax measurements are needed to establish linear values. Due to the limited accuracy of parallax measurements, this method has been restricted to the near-solar neighborhood, within about 30 parsecs; however, high spatial resolution surveys have improved the situation. The Hipparcos space astrometry mission (1989-1993) acquired median astrometric accuracies of ~ 0.001 arc-sec, and the resulting catalogue contains 12,195 detected double or multiple star systems. Such a nearby sample of stars may suffer from selectivity effects. Most of the stars of this sample have spectral types later than F5, for example. Nevertheless, it is a valuable sample because it enables us to calibrate stellar luminosities, which is the basis for all standard candles of all the types of stars thus studied.

If only one component is visible, because the other is too faint and/or is too close to its brighter companion to be separated through telescopic resolution alone, gravitational effects may help us to prove that the system is a binary. Such a system, in which an orbital motion is detected by astrometric methods, is called an astro-metric binary. The faint companion may be nominally resolvable but hidden in the glare of the bright component. Sirius B is such a star: The much smaller and fainter component of the "Dog Star", the "Pup" was first observed visually by Alvan G. Clark in 1862, but Sirius had been recognized by 1844 to be a binary on the basis of its proper motion variability discovered by Friedrich Wilhelm Bessel (1845). For a fine discussion of the extraction of data from astrometric binaries in general and of the Sirius system in particular, we recommend Aitken (1964) and Lindenblad (1970).

Another interesting type of astrometric binary is presented by cases where the components are so close that they are, or have been until recently, unresolvable.

3 Unfortunately, only in a few cases is it possible to measure the semi-major axes a1 and a2 of the absolute orbits separately. In most cases, only the relative orbit and its semi-major axis a = a1 + a2 can be determined.

4 There are a few cases of spectral-visual binaries which also give the absolute value of a.

Resolving power, or the ability to resolve fine detail, can be described mathematically by where A is the minimum angular separation in radians, D is the aperture of the telescope, and X is the wavelength in the same units. This quantity is, in fact, the central radius of the diffraction disk or Airy disk, the central portion of the diffraction image or Airy figure. See Couteau (1981, p. 32) for a lucid discussion. Adaptive optics5 makes use of a "reference star" to achieve sub-arc-second seeing within a small region of the field of view known as the isoplanatic patch, within which atmospheric fluctuations are correlated to ~ 1 rad. The actual isoplanatic patch is a few arc-seconds, typically. This technique permits ground-based telescopes to achieve an order of magnitude improvement in resolution. If other contributions to the "seeing budget" can be minimized as well, the resolution can approach the theoretical (angular) resolving power of the telescope. Adaptive optics are necessary to overcome the effect of atmospheric seeing; in space, instrumental resolution is the limiting condition. The repaired Hubble Space Telescope (HST), for example, has an effective resolution of about 0.05 arc-sec, permitting direct viewing of both the separation and the rough surface details of the Pluto-Charon system. Direct angular measurements of some of the largest of the sky's bright stars are now possible.

A number of less direct but more effective techniques also permit high angular resolution:

• Lunar occultations: The edge of the Moon occasionally occults a star or stellar system within the maximum range of its declination: about ±28°. Analysis of the resulting diffraction pattern intensities can determine binary star separations and even the diameters of stars down to about 0.001 arc-sec.

• Phase interferometry: Around 1920, Michelson (1920); Michelson & Pease (1921); and Pease (1925) determined the sizes of bright red giant stars with the help of a phase interferometer mounted on the 100-in. telescope at Mt. Wilson. The practical limit to angular resolution with this method was about 0.01 arc-sec and was set by two factors: mechanical flexure of the interferometer arm and atmospheric seeing. The arm bore two mirrors which were the equivalents of Young slits, and whereas a length of 25 ft was successful, an attempt at 50 ft was not. More recent work in this area has been done by groups in France (beginning with A. Labeyrie in 1974), a group at the US Naval Observatory (Flagstaff, Arizona), and at JPL (beginning with Shao and Staelin in 1979), among others.

• Aperture synthesis: Several modern groups have succeeded in using arrays of telescopes separated by up to 100 m and improved equipment to produce higher quality in resolution and stability and to extend the interferometry to two dimensions. The availability of new autocorrelation methods to combine fringes from separate telescopes permits the determination of binary separations

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