Complex modulation of rapidly rotating young M dwarfs: adding pieces to the puzzle

New sets of young M dwarfs with complex, sharp-peaked, and strictly periodic photometric modulations have recently been discovered with Kepler/K2 (scallop shells) and TESS (complex rotators). All are part of star-forming associations, are distinct from other variable stars, and likely belong to a unified class. Suggested hypotheses include star spots, accreting dust disks, co-rotating clouds of material, magnetically constrained material, spots and misaligned disks, and pulsations. Here, we provide a comprehensive overview and add new observational constraints with TESS and SPECULOOS Southern Observatory (SSO) photometry. We scrutinize all hypotheses from three new angles: (1) we investigate each scenario's occurrence rates via young star catalogs; (2) we study the features' longevity using over one year of combined data; and (3) we probe the expected color dependency with multi-color photometry. In this process, we also revisit the stellar parameters accounting for activity effects, study stellar flares as activity indicators over year-long time scales, and develop toy models to simulate typical morphologies. We rule out most hypotheses, and only (i) co-rotating material clouds and (ii) spots and misaligned disks remain feasible - with caveats. For (i), co-rotating dust might not be stable enough, while co-rotating gas alone likely cannot cause percentage-scale features; and (ii) would require misaligned disks around most young M dwarfs. We thus suggest a unified hypothesis, a superposition of large-amplitude spot modulations and sharp transits of co-rotating gas clouds. While the complex rotators' mystery remains, these new observations add valuable pieces to the puzzle going forward.