The term given to a pair of stars that can be determined to be orbiting each other only by measuring their periodic Doppler shifts is a spectroscopic binary.

Here's why:

* Spectroscopic binaries are binary star systems where the stars are too close together to be visually resolved (separated) by telescopes.

* Doppler shifts are changes in the frequency of light emitted from an object due to its motion towards or away from us. In the case of stars, these shifts can be detected in their spectral lines.

* By measuring the periodic Doppler shifts of the stars' spectral lines, astronomers can determine that the stars are orbiting each other, and even calculate their orbital period and masses.

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