Fundamental spectroscopic determination of projected rotation rates of slowly rotating stars is challenging because the rotational broadening of the spectral lines is often comparable to, or smaller than, the broadening from other sources, most notably macroturbulence. Fourier techniques have the advantage over direct profile matching when the observed profiles are complete, but when the profiles are severely blended, the Fourier analysis is compromised. A process of modeling partial profiles for determining the rotation rate for stars having blended spectral lines is investigated and applied to the evolved star α Hya (K3 II-III). Projected rotation higher than 5 km s~(-1) can be definitively ruled out for this star. Not all lines are equally good, depending on the amount of blending and also depending on the strength of the line, as the balance between the thermal and non-thermal components changes. A modest ambiguity arises between macroturbulence and rotational broadening, but a careful look at the differences between the observations and the models allows one to measure the rotation with acceptable precision. The result for α Hya is v sin i = 2.6 ± 0.3 km s~(-1).
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