On the Red Giant Branch: Ambiguity in the Surface Boundary Condition Leads to ≈100 K Uncertainty in Model Effective Temperatures

The effective temperature (T _eff) distribution of stellar evolution models along the red giant branch (RGB) is sensitive to a number of parameters including the overall metallicity, elemental abundance patterns, the efficiency of convection, and the treatment of the surface boundary condition (BC). Recently there has been interest in using observational estimates of the RGB T _eff to place constraints on the mixing length parameter, α _MLT, and possible variation with metallicity. Here we use 1D Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution models to explore the sensitivity of the RGB T _eff to the treatment of the surface BC. We find that different surface BCs can lead to ±100 K metallicity-dependent offsets on the RGB relative to one another in spite of the fact that all models can reproduce the properties of the Sun. Moreover, for a given atmosphere T-τ relation, we find that the RGB T _eff is also sensitive to the optical depth at which the surface BC is applied in the stellar model. Nearly all models adopt the photosphere as the location of the surface BC, but this choice is somewhat arbitrary. We compare our models to stellar parameters derived from the APOGEE-Kepler sample of first ascent red giants and find that systematic uncertainties in the models due to treatment of the surface BC place a limit of ≈100 K below which it is not possible to make firm conclusions regarding the fidelity of the current generation of stellar models.