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We present 29 likely members of the young $\rho$ Oph or Upper Sco regions ofrecent star formation that exhibit "accretion burst" type light curves in $K2$time series photometry. The bursters were identified by visual examination oftheir ~80 day light curves, though all satisfy the $M < -0.25$ flux asymmetrycriterion for burst behavior defined by Cody et al. (2014). The burst sourcesrepresent $\approx$9% of cluster members with strong infrared excess indicativeof circumstellar material. Higher amplitude burster behavior is correlated withlarger inner disk infrared excesses, as inferred from $WISE$ $W1-W2$ color. Theburst sources are also outliers in their large H$\alpha$ emission equivalentwidths. No distinction between bursters and non-bursters is seen in stellarproperties such as multiplicity or spectral type. The frequency of bursters issimilar between the younger, more compact $\rho$ Oph region, and the older,more dispersed Upper Sco region. The bursts exhibit a range of shapes,amplitudes (~10-700%), durations (~1-10 days), repeat time scales (~3-80 days),and duty cycles (~10-100%). Our results provide important input to models ofmagnetospheric accretion, in particular by elucidating the properties ofaccretion-related variability in the low state between major longer durationevents such as EX Lup and FU Ori type accretion outbursts. We demonstrate thebroad continuum of accretion burst behavior in young stars -- extending thephenomenon to lower amplitudes and shorter timescales than traditionallyconsidered in the theory of pre-main sequence accretion history.

A continuum of accretion burst behavior in young stars observed by K2