How would one estimate the rotation period of a star from its spectrum?
It takes a spot &quot;bump&quot; half the rotation period to traverse from the blue side of the line profile to the red.
You can see that the bump has maybe moved across 20% of the profile in one night, so the rotation period would be estimated as $\sim 10$ days.
Looking up the period of Sigma Gem - it is 19.6 days. So my method is not very accurate by eye, but you would need to simulate the star plus spot spectrum more accurately to take account of limb darkening and the spectral resolution of the spectrograph.