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 starspots, accreting dust disks, corotating 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 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 feature's longevity using over one year of combined data, and (3) we probe the expected color dependency with multicolor photometry. In this process, we also revisit the stellar parameters accounting for activity effects, study stellar flares as activity indicators over year-long timescales, and develop toy models to simulate typical morphologies. We rule out most hypotheses, and only (i) corotating material clouds and (ii) spots and misaligned disks remain feasible-with caveats. For (i), corotating dust might not be stable enough, while corotating 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 corotating gas clouds. While the complex rotators' mystery remains, these new observations add valuable pieces to the puzzle going forward.