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Analysis and Interpretation of Astronomical Spectra 87

19 Spectroscopic Binary Stars

19.1 Terms and Definitions

> 50% of the stars in our galaxy are gravitationally connected components of double or
multiple systems. They concentrate primarily within the spectral classes A, F and G [170].
For the astrophysics these objects are also of special interest because they allow a deter-
mination of stellar masses independently of the spectral class. Soon after the invention of
the telescope, visual double stars were also observed by amateur astronomers. Today the
spectroscopy has opened for us also the field of spectroscopic binary stars.

An in-depth study of binary star orbits is demanding and requires eg celestial mechanics
skills. Here should only be indicated, what can be achieved by spectroscopic means. Scien-
tifically relevant results are usually only possible associated with long term astrometric and
photometric measurements. Spectroscopic binary stars are orbiting in such close distances
around a common gravity center, that they can’t be resolved even with the largest tele-
scopes in the world. They betray their binary nature just by the periodic change in spectral
characteristics. For such close orbits Kepler's laws require short orbital periods and high-
track velocities, significantly facilitating the spectroscopic observation of these objects.

In contrast to the complex behaviour of multiple systems, the motion of binary stars follows
the three simple Kepler’s laws. Its components rotate at variable velocities in elliptical

orbits around a common Barycenter B (center of gravity). The following sketch shows a fic-

tional binary star system with stars of the unequal sizes and . For simplicity their ellip-

tical orbits are running here exactly in the plane of the drawing as well as the sight line to
Earth which in addition runs parallel to the minor semi-axes. For this perspective special
case the orbital velocity at the Apastron (farthest orbital point) and Periastron (closest

orbital point) corresponds also to the observed radial velocity . The recorded maximum

values (amplitudes) are referred in the literature with . The following layout corresponds

to an orbit- inclination of (sect. 19.3).

VrM1 P= K1 VrM2 A

Apastron Periastron B Periastron Apastron

M1 M2 M1 Minor semi axis b Major semi axis a M2

VrM1 A VrM2 P= K2

Sight line to VrM1 A = Radial velocity M1 at Apastron
Earth VrM1 P = Radial velocity M1 at Periastron
VrM2 A = Radial velocity M2 at Apastron
VrM2 P = Radial velocity M2 at Periastron