How would one estimate the rotation period of a star from its spectrum

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The discussion centers on estimating a star's rotation period using its spectral data, specifically observing shifts in flux due to starspots. The "bumps" in the flux profile indicate the movement of a starspot across the star's surface as it rotates. The challenge lies in correlating the observed wavelength shifts to a time scale for accurate rotational period estimation. Reference material, including a figure from Gray's work, is suggested for further understanding. The conversation emphasizes the need for a time-based analysis to derive the rotation period effectively.
SJay16
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Homework Statement
Using the profiles in Figure 18.29, make an estimate for the rotation period of σ Gem.
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Screenshot (156).png

The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a single time-stable position-stable spot.

The "bumps" slightly shifts, as indicated by the arrows in the top line profile compared to the bottom profile, as the spot "moves across" the surface as the star as it rotates; I'm just not sure how to get an estimate of the rotational period from this given just the wavelength for the abscissa, it would make sense if the abscissa was on a timescale.

Figure reference : Gray, D. (2005). The Observation and Analysis of Stellar Photospheres (3rd ed.), page 498. Cambridge: Cambridge University Press. doi:10.1017/CBO9781316036570
 
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