The many-faceted light curves of young disk-bearing stars in Upper Sco and $\rho$ Oph observed by $K2$ Campaign 2

The $K2$ Mission has photometrically monitored thousands of stars at high precision and cadence in a series of $\sim$80-day campaigns focused on sections of the ecliptic plane. During its second campaign, $K2$ targeted over 1000 young stellar objects (YSOs) in the $\sim$1-3 Myr $\rho$ Ophiuchus and 5-10 Myr Upper Scorpius regions. From this set, we have carefully vetted photometry from {\em WISE} and {\em Spitzer} to identify those YSOs with infrared excess indicative of primordial circumstellar disks. We present here the resulting comprehensive sample of 288 young disk-bearing stars from B through M spectral types and analysis of their associated $K2$ light curves. Using statistics of periodicity and symmetry, we categorize each light curves into eight different variability classes, notably including "dippers" (fading events), "bursters" (brightening events), stochastic, and quasi-periodic types. Nearly all (96\%) of disk-bearing YSOs are identified as variable at 30-minute cadence with the sub-1\% precision of {\em K2}. Combining our variability classifications with (circum)stellar properties, we find that the bursters, stochastic sources, and the largest amplitude quasi-periodic stars have larger infrared colors, and hence stronger circumstellar disks. They also tend to have larger H$\alpha$ equivalent widths, indicative of higher accretion rates. The dippers, on the other hand, cluster toward moderate infrared colors and low H$\alpha$. Using resolved disk observations, we further find that the latter favor high inclinations, apart from a few notable exceptions with close to face-on disks. These observations support the idea that YSO time domain properties are dependent on several factors including accretion rate and view angle.