Curves of constant radial velocity C contributing to the rotational Doppler broadening of spectral lines. a) C-curves for a Maunder-like surface angular velocity law with ∂Ω(θ) /∂θ > 0; b) C-curves for a law given by Eq. (3) with γ > 0, so that ∂Ω(θ) /∂θ > 0; c) C-curves for a law given by Eq. (3) with γ < 0, so that ∂Ω(θ) /∂θ < 0. In cases a) and b) the largest Doppler displacement is produced in the limb at the equator, while in case c) is produced in the center of the upper closed curves. Case b) identifies the lines producing the same Doppler displacement, Cr = Cd, where Cr (red dotted line) indicates rigid surface rotation, and Cd (red dashed line) a differential surface rotation. In all cases the parent Doppler displacement from rigid rotation is determined by the straight line touching the corresponding Cd curve at the equator.
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