New calibrated models for the TRGB luminosity and a thorough analysis of theoretical uncertainties

The luminosity of the Tip of the Red Giant Branch (TRGB) is instrumental for the construction of the distance ladder, and its accurate modelling is key for determining the local Hubble parameter. In this work, we present an extensive quantitative analysis of the TRGB luminosity, accounting for virtually all input physics that affect it: chemical composition, opacity, diffusion, nuclear reaction rates, electron screening, neutrinos, convection efficiency, boundary conditions and mass loss, amongst others. Our analysis is based on a newly produced grid of $\sim 3\times 10^6$ TRGB models, evolved from pre-main sequence up to the helium ignition at the TRGB, and covering a wide range of metallicity (Z = 0.0001-0.02) and initial mass (M = 0.8-1.4 $M_{\odot}$). Through a Monte-Carlo analysis, we study the systematic variation of the TRGB luminosity due to the combined effect of all above input physics, and show that a maximum theoretical uncertainty of about $1.6 \%$ is still present on the current generation of models, dominated by systematics of radiative opacity. Results are also provided in several photometric bands. As a by-product of our analysis, we demonstrate robust evidence for the linear response of the Tip luminosity to individual changes of input physics, which can significantly simplify future analyses. A comparison of our results with other stellar evolution codes shows excellent agreement, while our grid of models is available upon reasonable requests.