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Why are visual binaries and eclipsing binaries relatively rare compared to spectroscopic binaries?
Visual Binaries are rare compared to spectroscopic binaries because visual binaries have widely separated members bright enough to be observed and monitored separately.
The orbital plane of the pair of stars in Eclipsing Binariesare almost edge-on to our line of sight. In this case we observe a periodic decrease of starlight intensity as one member of the binary passes in front of the other.
Spectroscopic Binaries are too distant from us to be resolved into separate stars, but they can be indirectly perceived by monitoring the back-and-forth Doppler shifts of their spectral lines as the stars orbit one another and their line-of-sight velocities vary periodically.
To summarize, Visual Binaries and Eclipsing Binariesare harder to identify and observe compared to the Spectroscopic Binaries, therefore Visual Binaries and Eclipsing Binaries are much more rare.
McMillan, Chaisson , et. al. Astronomy: A Beginner's Guide to the Universe Fourth Edition. Upper Saddle River, NJ : Pearson Education, Inc., 1995.
Visual binaries involve stars close enough to be seen as separate in a telescope, which is less common. Eclipsing binaries require a specific alignment where one star passes in front of the other, which is less likely. Spectroscopic binaries are more common because they can be detected by shifts in spectral lines even if the stars are not visually separated.
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