Variability in the Massive Open Cluster NGC 1817 from K2: A Rich Population of Asteroseismic Red Clump, Eclipsing Binary, and Main Sequence Pulsating Stars

We present a survey of variable stars detected in K2 Campaign 13 within the massive intermediate age ($\sim1$ Gyr) open cluster NGC 1817. We identify a complete sample of 44 red clump stars in the cluster, and have measured asteroseismic quantities ($\nu_{\rm max}$ and/or $\Delta \nu$) for 29 of them. Five stars showed suppressed dipole modes, and the occurrence rates indicate that mode suppression is unaffected by evolution through core helium burning. A subset of the giants in NGC 1817 (and in the similarly aged cluster NGC 6811) have $\nu_{\rm max}$ and $\Delta \nu$ values at or near the maximum observed for core helium burning stars, indicating they have core masses near the minimum for fully non-degenerate helium ignition. Further asteroseismic study of these stars can constrain the minimum helium core mass in red clump stars and the physics that determines this limit. Two giant stars show photometric variations on timescales similar to previously measured spectroscopic orbits. Thirteen systems in the field show eclipses, but only five are probable cluster members. We identify 32 $\delta$ Sct pulsators, 27 $\gamma$ Dor candidates, and 7 hybrids that are probable cluster members, with most new detections. We used the ensemble properties of the $\delta$ Sct stars to identify stars with possible radial pulsation modes. Among the oddities we have uncovered are: an eccentric orbit for a short-period binary containing a $\delta$ Sct pulsating star; a rare subgiant within the Hertzsprung gap showing $\delta$ Sct pulsations; and two hot $\gamma$ Dor pulsating star candidates.