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Abstract

The treatment of convection is one of the largest remaining uncertainties in models of low mass stars. The Mixing Length Theory (MLT) for super-adiabatic convection has come under particular scrutiny. Evidence is mounting that a single value of the mixing length parameter ($α_\mathrm{MLT}$) should not be applied universally across stellar model grids, although simulations and asteroseismic calibrations disagree on how it should vary with stellar parameters. A variable $α_\mathrm{MLT}$ causes critical systematic changes to the ages of low mass stars, the key age tracers for galactic and exoplanetary studies. In this work we use classical (non-seismic) geometric radii and specialized MIST isochrones with a variable $α_\mathrm{MLT}$ to measure mixing length in detached eclipsing binaries (DEBs) and interferometrically resolved stars, finding plenty of evidence for non-solar $α_\mathrm{MLT}$. In particular we find that standard evolutionary models overpredict the radii of metal-poor interferometric stars and that a sub-solar $α_\mathrm{MLT}$/$α_{\mathrm{MLT},\odot}\sim0.50-0.75$ can neatly explain this discrepancy, consistent with other empirical calibrations and in stark contrast to simulations. We infer low convective efficiency in cool, rapidly rotating lower main-sequence stars, consistent with the known phenomenon of magnetically-induced radius inflation. We also identify several slowly rotating DEBs whose measurements cannot be reproduced by standard isochrones, and we propose these systems as useful case studies of non-solar mixing length in stars outside of the Sun. However, we find no definitive population level correlations between $α_\mathrm{MLT}$ and stellar parameters among the DEBs, calling into question the existence of a ubiquitous mixing length calibration in low mass stars.

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