You are observing a binary star system and obtain a series of spectra of the light from the two stars. In this spectrum, most of the absorption lines shift back and forth as expected from the Doppler Effect. A few lines, however, do not shift at all, but remain at the same wavelength. How can we explain the behavior of the non-shifting lines?

The behavior of the non-shifting lines is due to the spinning and rotation of stars toward and away from us as the earth rotates and spines

Explanation:

Assuming we obtain a spectrum from a distant star that is rotating in the same plane as us then the light gathered is a combination of light from across the disc of the star. As part of the star appears to rotate towards us, its light will be blueshifted.

Also the light from the part of the star rotating away from us will be redshifted.

The middle section of the disc that is moving tangentially to us will not exhibit Doppler-shift. That is, do not shift at all, but remain at the same wavelength

The effect is that the star's spectral lines will appear smeared out. This broadening of lines can be distinguished from the effects of pressure broadening due to stellar pressure.

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