Starspots and Magnetism: Testing the Activity Paradigm in the Pleiades and M67

We measure starspot filling fractions for 240 stars in the Pleiades and M67 open star clusters using APOGEE high-resolution H-band spectra. For this work we developed a modified spectroscopic pipeline which solves for starspot filling fraction and starspot temperature contrast. We exclude binary stars, finding that the large majority of binaries in these clusters (80%) can be identified from Gaia DR3 and APOGEE criteria -- important for field star applications. Our data agree well with independent activity proxies, indicating that this technique recovers real starspot signals. In the Pleiades, filling fractions saturate at a mean level of 0.248$\pm$0.005 for active stars with a decline at slower rotation; we present fitting functions as a function of Rossby number. In M67, we recover low mean filling fractions of 0.030$\pm$0.008 and 0.003$\pm$0.002 for main sequence GK stars and evolved red giants respectively, confirming that the technique does not produce spurious spot signals in inactive stars. Starspots also modify the derived spectroscopic effective temperatures and convective overturn timescales. Effective temperatures for active stars are offset from inactive ones by -109$\pm$11 K, in agreement with the Pecaut & Mamajek empirical scale. Starspot filling fractions at the level measured in active stars changes their inferred overturn timescale, which biases the derived threshold for saturation. Finally, we identify a population of stars statistically discrepant from mean activity-Rossby relations and present evidence that these are genuine departures from a Rossby scaling. Our technique is applicable to the full APOGEE catalog, with broad applications to stellar, galactic, and exoplanetary astrophysics.