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
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.
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
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.
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
for using it.