Editing Binary star (section)

====Spectroscopic binaries====<!-- This section is linked from [[Redshift]] -->
{{more citations needed section|date=July 2012}}
[[File:Algol AB movie imaged with the CHARA interferometer - labeled.gif|thumb|right|[[Algol|Algol B]] orbits [[Algol|Algol A]]. This animation was assembled from 55 images of the [[CHARA array|CHARA interferometer]] in the [[H band (infrared)|near-infrared H-band]], sorted according to orbital phase.]]
Sometimes, the only evidence of a binary star comes from the [[Doppler effect]] on its emitted light. In these cases, the binary consists of a pair of stars where the [[spectral line]]s in the light emitted from each star shifts first towards the blue, then towards the red, as each moves first towards us, and then away from us, during its motion about their common [[center of mass]], with the period of their common orbit.

In these systems, the separation between the stars is usually very small, and the orbital velocity very high. Unless the plane of the orbit happens to be [[perpendicular]] to the line of sight, the orbital velocities have components in the line of sight, and the observed [[radial velocity]] of the system varies periodically. Since radial velocity can be measured with a [[spectrometer]] by observing the [[Doppler effect|Doppler shift]] of the stars' [[spectral line]]s, the binaries detected in this manner are known as ''spectroscopic binaries''. Most of these cannot be resolved as a visual binary, even with [[telescope]]s of the highest existing [[Angular resolution|resolving power]].

In some spectroscopic binaries, spectral lines from both stars are visible, and the lines are alternately double and single. Such a system is known as a double-lined spectroscopic binary (often denoted "SB2"). In other systems, the spectrum of only one of the stars is seen, and the lines in the spectrum shift periodically towards the blue, then towards red and back again. Such stars are known as single-lined spectroscopic binaries ("SB1").

The orbit of a spectroscopic binary is determined by making a long series of observations of the radial velocity of one or both components of the system. The observations are plotted against time, and from the resulting curve a period is determined. If the orbit is [[circle|circular]], then the curve is a [[Trigonometric function|sine]] curve. If the orbit is [[ellipse|elliptical]], the shape of the curve depends on the [[orbital eccentricity|eccentricity]] of the ellipse and the orientation of the major axis with reference to the line of sight.

It is impossible to determine individually the [[semi-major axis]] ''a'' and the inclination of the orbit plane ''i''. However, the product of the semi-major axis and the sine of the inclination (i.e. {{nobr|''a''&thinsp;sin&thinsp;''i''}}) may be determined directly in linear units (e.g. kilometres). If either ''a'' or ''i'' can be determined by other means, as in the case of eclipsing binaries, a complete solution for the orbit can be found.<ref>{{cite web |url=http://www.astro.cornell.edu/academics/courses/astro101/lectures/lec16.htm |title=Stellar Masses |first=T. |last=Herter |publisher=Cornell University |url-status=dead |archive-url=https://web.archive.org/web/20120617150857/http://www.astro.cornell.edu/academics/courses/astro101/lectures/lec16.htm |archive-date=June 17, 2012 |df=dmy-all}}</ref>

Binary stars that are both visual and spectroscopic binaries are rare and are a valuable source of information when found. About 40 are known. Visual binary stars often have large true separations, with periods measured in decades to centuries; consequently, they usually have orbital speeds too small to be measured spectroscopically. Conversely, spectroscopic binary stars move fast in their orbits because they are close together, usually too close to be detected as visual binaries. Binaries that are found to be both visual and spectroscopic thus must be relatively close to Earth.