Binary Stars

two stars that are close to one another in space and that constitute a physical system whose components are bound by forces of mutual gravitational attraction. The components revolve in elliptical orbits around a common center of mass and move together in our galaxy. Binary stars are a special case of multiple stars, which sometimes consist of several components (as many as eight). They are classified according to the method of detection as visual binaries (their components can be seen visually with the aid of a telescope or on a photographic plate), spectroscopic binaries (their binary nature is evident from the periodic shifts or doubling of their spectral lines), eclipsing binaries (their components periodically block one another from the observer), astromet-ric binaries, or dark companions (very precise measurements of positions make it possible to detect periodic shifts of a star under the influence of the dark companion revolving around it), and photometric binaries (because of a difference in the surface temperatures of the components, precise elec-trophotometry at different colors reveals their difference from single stars). Sometimes it is possible to determine the binary nature of a star by its composite (combined) spectrum or by the identical apparent proper motion of two stars that are not too close to one another (widely separated pairs).

Multiple systems can include various types of binary star. For example, a component of a visual binary can itself be a binary of one of the aforementioned types. The types of binaries described constitute physical systems and are called physical binaries. Pairs of stars whose components are great distances apart in the line of sight and only by chance (and temporarily) seem very close together in the sky also have the appearance of binary stars. In the course of time, they will drift apart and cease to be considered as binary stars. Such systems are called optical binaries. In compiling catalogs, only those objects are listed as binary stars whose distance between components does not exceed a certain limit, which depends on the brightness (apparent stellar magnitude) of the primary star and its companion. Thus, for example, two stars of the second stellar magnitude can be considered components of a binary system if the distance between them is less than 40”, and two stars of the ninth stellar magnitude can be so considered if the distance does not exceed 3”. Exhaustive study of binary stars is very important since it provides a reliable means of determining the masses of stars and, in a number of cases, of determining the dimensions of the components and their shape and density, the law of the change in density with increasing distance from the center of the star, and the structure of stellar atmospheres. All other means of determining the masses of stars are based on determining the masses of binary stars.

The study of binary stars began in the middle of the 17th century when Galileo discovered several binary stars and proposed a method for determining the relative parallax of the bright primary star of an optical binary star in relation to the fainter and therefore probably more distant star. A total of about 20 binary stars were discovered by the middle of the 18th century; at that time, the first measurements were also made of the position angle of the companion θ and the distance between the components p (Figure 1). In the 1780’s, after 25 years of observation, the British astronomer W. Herschel detected a distinct orbital (since it was curvilinear) motion of the companion relative to the primary star in several stars and estimated the periods of revolution of several stars. Physical binaries were discovered in this manner. The Russian astronomer V. la. Struve laid a firm foundation for the study of binary stars with his many years of research. He discovered many new binary stars (his catalog of 3,110 binaries was published in 1827), measured the position of the companions of 2,640 binaries (published in 1837), and determined the exact positions of binaries on the meridian circle over a period of 20 years (published in 1852). The British astronomer J. Herschel extended the study of binary stars to the southern sky. The Russian astronomer O. V. Struve studied the problem of systematic errors in measuring binaries. About 60,000 visual binaries were known by the middle of the 20th century. Various types of filar micrometers have been used since the time of W. Herschel to measure various types of visual binaries, and stellar interferometers

Flgure 1

have been used for the smallest angular distances. It is possible to measure distances as small as 0.1”—0.2” with large telescopes. The use of photography to measure binary stars produces excellent results for distances greater than 1”-2”.

The apparent relative motion of the companion around the primary star follows an ellipse (including the circle and straight line as special cases of this curve). The primary star is always inside the ellipse but usually not at the focus of the apparent orbit. The radius vector (joining the primary star with its companion) describes areas proportional to time, that is. Kepler’s second law is valid for binary stars. The apparent orbit of a binary star (Figure 2.a) is a projection of the true orbit (Figure 2, b) onto the plane of the paper (perpendicular to the line of sight). Many methods have been developed for determining the elements of orbits of binary stars: the semimajor axis, the inclination of the orbit, the eccentricity, the position angle of the line of the nodes at which the plane of the orbit intersects the plane of the sky. the longitude of the periastron (the angle between the line of the nodes and the line joining the periastron and the apastron in the plane of the true orbit), the period of revolution, and the moment (dates) when the companion passes the periastron. Only about 2,000 of several tens of thousands of visual binaries display an orbital motion, and orbits have been calculated for only about 300. The star BD-8°4352 has the shortest period (1.72 years), and of the long periods only those that do not exceed 500 years are more or less reliable. For pairs with equally large proper motions, periods are formally on the order of hundreds of thousands of years.

Figure 2

The first spectroscopic binary was discovered in 1889. A periodic doubling of spectral lines occurs in its spectrum, which indicates the orbital motion of both components about a common center of mass. A periodic shift of single lines is observed in other binary stars of this type: the lines of the fainter components are not noticeable in the spectrum. The following elements of the orbit can be found by analyzing the curve of variations in the radial velocities (velocity curve) of a spectroscopic binary—the period, eccentricity, moment (date) of crossing the periastron, and the longitude of the periastron—as well as the product a sin i (a is the semimajor axis and i is the inclination of the orbit) and the radial velocity y of the center of mass. Figure 3 gives some idea of the nature of radial velocities in relation to the shape and disposition of the orbit. Orbits have been calculated for 500 of the approximately 2,000 spectroscopic binaries that have been discovered. Their periods range from 4.7 hours to 60 years.

If the inclination of the orbit is close to 90°, it is possible to observe periodic mutual eclipses of the components. Depending on the relative sizes and luminosities of the components, the total brightness of the eclipsing binary will experience more or less long and deep minimums (primary minimums). It is possible to judge the elements of such a star’s orbit from the, shape of the light curve, that is, the curve of the star’s brightness (Figure 4). The shortest known period is 4.7 hours and the longest. 57 years. The Russian astronomer S. N. Blazhko developed the first general method for calculating the orbits of eclipsing binaries in 1911.

Figure 3. Dependence of radial velocities on shape and disposition of orbit of spectroscopic binaries: e is orbital eccentricity, and ω is longitude of periastron

Analysis of the light curves makes it possible to determine not only the elements of an eclipsing binary’s orbit but also the relative dimensions of the stars in comparison with the dimensions of the orbit, the shape of the stars, and their surface luminosities. Together with the results of other observations of binary stars, such analysis makes it possible to determine many stellar characteristics. Thus, if one also has a graph of radial velocities, then it is possible to determine the dimensions of the orbit, the diameters of the stars themselves in km, and the luminosities of the stars. In some cases (admittedly rare) it is also possible to study the structure and composition of the stellar atmospheres, the presence of expanding and rotating envelopes, the law of the loss of mass by the more massive star, and the evolution of the system.

Figure 4. Light curve of eclipsing binary star and its corresponding system of two stars

The application of Kepler’s third law to binary stars whose distance is known makes it possible to calculate the sum of the masses of the components, expressed in units of solar mass: M₁ + M₂ = a³/π³P², where π is the parallax of the star, a is the semimajor axis of the orbit in seconds of arc and P is the period of revolution. If it is also possible to determine the relationship of the masses of the components from observations, then it is possible to compute the mass of each component separately. For spectroscopic binaries it is possible to determine only the magnitude (M₁ + M₂)sin³i.

If the lines of both components are visible in the spectrum, it is also possible to determine the ratio of the masses. The totality of all determinations of masses of components of binary stars has made it possible to disclose the important relationship between the masses and luminosities of stars; this has theoretically been confirmed and is now widely used to determine the masses of single stars on the basis of their luminosities.

Special (very laborious and refined) studies of the proper motions of certain stars have shown the presence of one or several planetlike bodies around them with masses on the order of the mass of the planet Jupiter. This has provided the first reliable indications of the existence of planetary systems other than our solar system.

Duality (and, in general, multiplicity) is a very widespread phenomenon among stars of our galaxy. It is very probable that there are more multiple systems than single stars. At least, in the galactic regions of the sun (where, it can be assumed, we know almost all the stars) out of 30 stars 17 are single, and 13 are multiple (29 components). Binary stars do not differ in physical characteristics and kinematics from single stars and evidently have the same origin as single stars. Several different hypotheses have been proposed on the origin of binary stars: the division of single stars when their stability was lost due to rapid axial rotation; the capture of one star by another; simultaneous formation within a single nebula. It is very probable that multiple stars form in stellar associations. The theory of the origin of binary stars should also explain a number of observed regular statistical laws and relationships between various physical characteristics of binary stars and elements of their orbits. Binary systems that include variable stars as a component are of special interest. Both binary stars and star clusters are suitable for verifying modern notions about the evolution of the stars.