We have already seen that even if both stars cannot be seen in a binary system we may be able to infer the presence of an unseen companion by its gravitational influence on the motion of the primary star. There is a second important method that allows us to infer that a system is binary, even if we cannot see that visually, provided we can collect enough light from the system to observe its spectrum.

Doppler Shifts for Binary Stars

Consider the following image of an idealized binary star system where the two stars have equal masses and are in circular orbits. We further idealize the situation by assuming that each star has a single spectral line at the same frequency when the stars are at rest.

A Double-Line Spectroscopic Binary

Because of the motion of the two stars around their common center of mass, each star is alternatively moving toward the observer and then away. But because of the Doppler effect, this means that the spectral lines will periodically be shifted up and down in wavelength, and that for the two stars this shift will be in the opposite direction: when star A is moving toward us, star B is moving away from us, and vice versa.

Spectroscopic Binaries

Thus, if we consider an idealized situation where each star has a single spectral line at the same frequency when the stars are at rest, we get the situation in the adjacent animation. The spectral lines shift up and down periodically, and out of phase. This is a clear sign that there are two stars present in the system. If we cannot see them, but conclude that there are two stars because of these effects in the spectrum, we say that this is a spectroscopic binary. Actually, most stars that are classified as binaries are not visual binaries, but instead it has been deduced that they are binaries from the spectrum. Thus, they are spectroscopic binaries.

Here is a java applet that allows you to explore spectroscopic binary systems (Source)

Double-Line Spectroscopic Binaries

The following figure illustrates a portion of an actual spectrum for a spectroscopic binary. The curves represent light intensity, so the dips correspond to dark regions of the spectrum or absorption lines.

Spectral lines in a spectroscopic binary

In this segment of the spectrum we see that the spectral line periodically doubles and then merges into a single line, indicating the presence of two stars giving opposite Doppler shifts.

In the more realistic case there will be a whole set of spectral lines in each star, and they will shift up an down out of phase. The situation illustrated here, where lines from both stars are seen in the spectrum, is called a double-line spectroscopic binary.

Single-Line Spectroscopic Binaries

In many cases the spectral lines from one of the stars in a spectroscopic binary are much stronger than those from the other star. In the most extreme case, the spectral lines from only one of the stars may be visible. Even in that case, it may be possible to infer that the system is a spectroscopic binary because the single set of lines will still shift up and down periodically in frequency (imagine deleting the line associated with star B in the above animation and note the motion of the remaining line associated with star A). A spectroscopic binary in which only the lines from one of the stars can be seen is called a single-line spectroscopic binary

Velocity Curves for Spectroscopic Binaries

In the adjacent image the velocity curve for a spectroscopic binary is illustrated. The corresponding positions on the orbits for two components are labeled with numbers correlated with diagrams shown below the graph, assuming the observer to be to the right.

Motion toward the observer gives a blue shift (negative velocity) while motion away from the observer gives a red shift (positive velocity). For example, at position 1 the red star has maximal velocity away from the observer and the blue star has maximal velocity toward the observer, while at position 2 the radial velocity of each star relative to the observer is zero.

A Catalog of Spectroscopic Binary Systems

Here is a catalog of information on spectroscopic binary systems, and here are instructions for using it.

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