Machine Learning the Tip of the Red Giant Branch

A method for investigating the sensitivity of the tip of the red giant branch (TRGB) I band magnitude $M_I$ to stellar input physics is presented.~We compute a grid of $\sim$125,000 theoretical stellar models with varying mass, initial helium abundance, and initial metallicity, and train a machine learning emulator to predict $M_I$ as a function of these parameters.~First, our emulator can be used to theoretically predict $M_I$ in a given galaxy using Monte Carlo sampling.~As an example, we predict $M_I=-3.87_{-0.08}^{+0.11}$ in the Large Magellanic Cloud (F20).~Second, our emulator enables a direct comparison of theoretical predictions for $M_I$ with empirical calibrations to constrain stellar modeling parameters using Bayesian Markov Chain Monte Carlo methods.~We demonstrate this by using empirical TRGB calibrations to obtain new independent measurements of the metallicity in three galaxies.~We find ${\log }_{10}(Z)=-2.167_{-0.492}^{+0.404}$ and ${\log }_{10}(Z)=-2.098_{-0.528}^{+0.388}$ in the Large Magellanic Cloud (F20 and Y19 respectively), ${\log }_{10}(Z)=-2.146_{-0.505}^{+0.400}$ in NGC 4258, and ${\log }_{10}(Z)=-2.143_{-0.508}^{+0.401}$ in $\omega$-Centauri.~The LMC and NGC 4258 measurements are consistent with other measurements within $<1\sigma$ errors, and the $\omega$-Centauri measurement are within $<2\sigma$ errors.