Classical Cases of Non-solar Mixing Length in Low Mass Stars

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.