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Complex periodic variables (CPVs) are stars that exhibit highly structuredand periodic optical light curves. Previous studies have indicated that thesestars are typically disk-free pre-main-sequence M dwarfs with rotation periodsranging from 0.2 to 2 days. To advance our understanding of these enigmaticobjects, we conducted a blind search using TESS 2-minute data of 65,760 K and Mdwarfs with $T$<16 mag and $d$<150 pc. We found 50 high-quality CPVs, andsubsequently determined that most are members of stellar associations. Amongthe new discoveries are the brightest ($T$$\approx$9.5 mag), closest($d$$\approx$20 pc), and oldest ($\approx$200 Myr) CPVs known. One exceptionalobject, LP 12-502, exhibited up to eight flux dips per cycle. Some of thesedips coexisted with slightly different periods, and the shortest-duration dipsprecisely matched the expected timescale for transiting small bodies at thecorotation radius. Broadly, our search confirms that CPVs are mostly young($\lesssim$150 Myr) and low-mass ($\lesssim$0.4 $M_\odot$). The flux dipscharacteristic of the class have lifetimes of $\approx$100 cycles, althoughstellar flares seem to induce sudden dip collapse once every few months. Themost plausible explanation for these phenomena remains corotatingconcentrations of gas or dust. The gas or dust is probably entrained by thestar's magnetic field, and the sharp features could result from a multipolarfield topology, a hypothesis supported by correspondences between the lightcurves of CPVs and of rapidly rotating B stars known to have multipolarmagnetic fields.

Transient Corotating Clumps Around Adolescent Low-Mass Stars From Four Years of TESS