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Binary Stars

Stars are often born in groups.  Early in the history of the universe, many stars were born in compact clusters of hundreds of thousands or millions of stars called globular clusters.  More recent star formation within the Galactic disk gives rise to open clusters of hundreds or thousands of stars.  But stars are also born in smaller groupings of two or three.

Many of the bright, nearby stars are members of binary or triplet star systems. For instance, the brightest star in the sky, Sirius, is a member of a triple-star system.  The second-closest star to Earth, Rigil Kentaurus (α Centauri) has a slightly-dimmer companion star.  Another bright, nearby star, Procyon (α Canis Minoris), has a 13th magnitude companion star.  These systems are not unusual.  In fact, multiple star systems of main-sequence stars are far more common than single main-sequence stars in the Galactic disk.  The binary main-sequence star systems slightly outnumber single main-sequence stars.  The ratios of binary systems to triplet and quadruplet systems is 46:9:2.[1]  This means that only 34% of the main sequence stars in the Galactic disk have no companion stars.

Generally a binary star looks like a single star to the eye.  At a distance of 5 parsecs, a pair of stars separated by 200 AU would have a separation on the sky of only 40 arc seconds, which is about the angle spanned by Saturn's rings.  This separation is easily resolved with a telescope.  Binary stars that can be resolved with a telescope are angularly-resolved binaries.  But most binary systems are too distant to resolve with a telescope.  These systems betray their binary nature through their spectra.  As the stars in a binary system orbit one-another, their spectra are Doppler shifted, so that one sees the spectral lines of one star shifted in frequency relative to the spectral lines of the other star.  Binary systems that reveal themselves in this way are called spectroscopic binaries.

Binary stars, when they are widely separated, are described as the action of Newtonian gravity on two point-masses.  Each star moves in an elliptical orbit, and the motion of one star relative to the other also traces an ellipse.  The relationship between the period and the semimajor axis (the average of the maximum and minimum separation of the stars) of a binary system is given by Kepler's laws: the square of the period is proportional to the cube of the semimajor axis.  The physics of binary star motion is therefore very simple when the stars are far enough apart that their tidal influence on each-other is negligible.  This simple physics makes the binary star the best tool for weighing stars.

The size of a binary star system is more like the size of the Solar System than the separation between stars in the stellar neighborhood.  The orbital periods of the majority of binary stars are between 1/3 and 300,000 years, with the median at 14 years.[2]  Only a tiny fraction of binary stars have periods shorter than 1 day or longer than 1 million years.  For a binary system with a total mass of 1 solar mass, the median orbital period of 14 years corresponds to a semimajor axis of only 6 AU, which is slightly more than Jupiter's distance from the Sun.  For a 1/3 year period, the semimajor axis is 0.5 AU, and for a 300,000 year period, it is 4,500 AU.  These separations increase with an increase in the total mass of the system as the total mass to the one-third power, so the semimajor axis of a 10-solar-mass binary system is only 2.2 times greater than that of a 1-solar-mass system with the same period.  With Solar-System like values, the semimajor axis of a binary system is tiny compared to the average separation of more than a parsec (206,000 AU) between the stars of the Galactic disk.

The eccentricities of binary star orbits fall into two classes.  For binary stars with periods longer than 3 years, the orbits are generally very elliptical, with most having eccentricities e ranging between 0.3 and 0.9 (a circular orbit has e = 0, and a parabolic orbit has e = 1.  Mercury, the Solar System planet with the most eccentric orbit, has e =  0.2).  For periods of less than 3 years, the orbits are much more circular, with a large majority of the orbits having eccentricities between 0.15 and 0.45.  This effect is attributed to the tidal dissipation of orbital energy in these tightly-bound systems, which causes the orbits to become circular.  In binary systems with periods of less than 1 day, the tidal dissipation of energy is so efficient that the orbits have eccentricities of 0.

Besides having circular orbits, the stars in the most tightly-bound systems are close enough to tidally distort and heat each-other.  If the stars in such a binary system are so close that each star fills its Roche lobe and the photospheres touch, the system is a contact binary star; if the stars are so close that one fills its Roche lobe, but the other does not, then the system is a semi-detached binary star; if neither star fills its Roche lobe, the system is a detached binary star.  The evolution of these binary stars is complex, with some evolving into the brilliant compact binary systems that contain compact objects, such as degenerate dwarfs, neutron stars, and black holes.

One final, striking aspect of binary stars is the relative masses of the stars in a system.  For binary systems with orbital periods longer than 100 years, the secondary (less massive) star tends to be of very low mass, just as the stars in the Galactic disk tend to be of very low-mass, but for systems with orbital periods less than 100 years, the secondary star's mass tends to be close to the mass of the primary star.  This difference in the secondary's mass with orbital period suggests that the long-period binaries are either created by a different process than the short-period binaries, or the process that creates binary stars behaves much differently when creating a larger system than when creating a small system.

The commonness and small size of the binary stars in our Galaxy have implications for the theories of star formation.  The majority of stars are members of binary systems, so binary systems form very easily within the Galactic disk.  The size of a binary system is generally about the size of our Solar System; this has lead astrophysicists to associate the separation between stars with the size of the cloud that gave birth to the stars in the binary system.  The idea that a binary system is born when its stars are born is supported by more recent observations of binary systems that contain a T Tauri star.  These stars are very young variable stars of between 0.1 and 3 solar masses that have not yet settled down onto the main sequence.  They are from one million to several tens of millions of years old.  T Tauri stars are found to have companion stars with the same frequency as the main-sequence star, and the distribution of their periods is similar to the binary stars containing main-sequence stars.  A T Tauri star and its companion are of the same age.[3]  These properties support the idea that stars are born with their companions, as it is unlikely that they could acquire companions so rapidly after birth.  Binary stars therefore tell us something about how stars are born.

[1]Abt, Helmut A., and Levy, Saul G.  “Multiplicity Among Solar-Type Stars.”  The Astrophysical Journal Supplement Series 30 (March 1976): 273–306.

[2]Duquennoy, A., and Mayor, M.  “Multiplicity Among Solar-Type Stars in the Solar Neighborhood: II. Distribution of the Orbital Elements in an Unbiased Sample.”  Astronomy and Astrophysics 248 (1991): 485–524.

[3]White, R.J., and Ghez, A.M.  “Observational Constraints on the Formation and Evolution of Binary Stars.”  The Astrophysical Journal 556 (20 July 2001): 265–295.

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