On the potassium-rotation connection in late-type Alpha Persei stars

We present measurements of the \ion{K}{i} $\lambda 7699$ line from spectra of 19 late-type members of the $\alpha$Persei cluster obtained with the Intermediate Dispersion Spectrograph at the Isaac Newton Telescope. These stars span a narrow range of $T_{\mathrm{e}\mathrm{f}\mathrm{f}}$, from 5091 K to 4771 K, and a wide range of $v\sin i$ values (9 ${\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$–170 ${\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$). We find empirically that larger rotational broadening increases the equivalent width of \ion{K}{i} $\lambda 7699$ linearly for $v\sin i$ values from 15 ${\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$ to 75 ${\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$. This correlation breaks down for $v\sin i>$ 75 ${\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$. After correction for this effect, we show that the potassium line equivalent widths do not correlate with $v \sin i$.}