  The high-energy emission from low-mass stars is mediated by the magnetic
dynamo. Although the mechanisms by which fully convective stars generate
large-scale magnetic fields are not well understood, it is clear that, as for
solar-type stars, stellar rotation plays a pivotal role. We present 270 new
optical spectra of low-mass stars in the Solar Neighborhood. Combining our
observations with those from the literature, our sample comprises 2202
measurements or non-detections of H$\alpha$ emission in nearby M dwarfs. This
includes 466 with photometric rotation periods. Stars with masses between 0.1
and 0.6 solar masses are well-represented in our sample, with fast and slow
rotators of all masses. We observe a threshold in the mass-period plane that
separates active and inactive M dwarfs. The threshold coincides with the
fast-period edge of the slowly rotating population, at approximately the
rotation period at which an era of rapid rotational evolution appears to cease.
The well- defined active/inactive boundary indicates that H$\alpha$ activity is
a useful diagnostic for stellar rotation period, e.g. for target selection for
exoplanet surveys, and we present a mass-period relation for inactive M dwarfs.
We also find a significant, moderate correlation between
$L_{\mathrm{H}\alpha}/L_{\mathrm{bol}}$ and variability amplitude: more active
stars display higher levels of photometric variability. Consistent with
previous work, our data show that rapid rotators maintain a saturated value of
$L_{\mathrm{H}\alpha}/L_{\mathrm{bol}}$. Our data also show a clear power-law
decay in $L_{\mathrm{H}\alpha}/L_{\mathrm{bol}}$ with Rossby number for slow
rotators, with an index of $-1.7 \pm 0.1$.
