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The mechanism behind that contradiction is simple enough to state in one line, and the paper’s authors compute it carefully because the commonly quoted version understates it by an order of magnitude. Surface rotation Doppler-broadens any spectral line by a fraction of its energy equal to the star’s equatorial velocity over the speed of light, $\Delta$ E/E $\approx$ $v_{eq}$/c = 2$\pi$$\nu$ R/c $\approx$ 1.3$\times$10^{-1}($\nu$/500\,$\text{Hz}$)(R/12\,$\text{km}$) , where $\nu$ is the star’s spin frequency and R its radius.

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