Impact of Simultaneous Stellar Modeling Uncertainties on the Tip of the Red Giant Branch for Axion-Election Coupling

We present a novel method for incorporating the effects of stellar modeling uncertainties into constraints on the axion-electron coupling constant found using the observed calibration of the tip of the red giant branch (TRGB) I band magnitude $M_I$.~We simulate grids of models with varying initial stellar mass, helium abundance, metallicity, and axion-electron coupling ${\alpha }_{26}={10}^{26}{g}_{ae}^2\mathrm{/}4\pi$ but different (fixed) mixing lengths and mass loss efficiencies.~We then train separate machine learning emulators to predict $M_I$ as a function of the varying parameters for each grid.~Our emulators enable the use of Markov Chain Monte Carlo simulations where ${\alpha }_{26}$ is varied simultaneously with the stellar parameters.~One of our grids yields a bound ${\alpha }_{26}\le 0.75$ at the 95% confidence limit, a factor of $\sim 3.7$ weaker than previous bounds;~while the other grid yields ${\alpha }_{26}\le 1.58$ at the 95% confidence limit, a factor $\sim 7.8$ weaker than previous bounds.~We demonstrate that the different values we find are due to covariances between stellar and axion physics that are not accounted for by single parameter variations.~Our results suggest that the bound on ${\alpha }_{26}$ derived using empirical calibrations of the TRGB I band magnitude need to be reevaluated using simultaneous parameter variation.~Alternative methods that use the bolometric luminosity instead of $M_I$ are more robust because they are not reliant upon theoretical predictions of the effective temperature.