A Low-mass, Pre-main-sequence Eclipsing Binary in the 40 Myr Columba Association -- Fundamental Stellar Parameters and Modeling the Effect of Star Spots

Young eclipsing binaries (EBs) are powerful probes of early stellar evolution. Current models are unable to simultaneously reproduce the measured and derived properties that are accessible for EB systems (e.g., mass, radius, temperature, luminosity). In this study we add a benchmark EB to the pre-main-sequence population with our characterization of TOI 450 (TIC 77951245). Using Gaia astrometry to identify its comoving, coeval companions, we confirm TOI 450 is a member of the $\sim$40 Myr Columba association. This eccentric ($e=0.2969$), equal-mass ($q=1.000$) system provides only one grazing eclipse. Despite this, our analysis achieves the precision of a double-eclipsing system by leveraging information in our high-resolution spectra to place priors on the surface-brightness and radius ratios. We also introduce a framework to include the effect of star spots on the observed eclipse depths. Multicolor eclipse light curves play a critical role in breaking degeneracies between the effects of star spots and limb-darkening. Including star spots reduces the derived radii by $\sim$2\% from an unspotted model ($>2\sigma$) and inflates the formal uncertainty in accordance with our lack of knowledge regarding the star spot orientation. We derive masses of 0.1768($\pm$0.0004) and 0.1767($\pm$0.0003) $M_\odot$, and radii of 0.345($\pm$0.006) and 0.346($\pm$0.006) $R_\odot$ for the primary and secondary, respectively. We compare these measurements to multiple stellar evolution isochones, finding good agreement with the association age. The MESA MIST and SPOTS ($f_{\rm s}=0.17$) isochrones perform the best across our comparisons, but detailed agreement depends heavily on the quantities being compared.