Quantifying Uncertainties on the Tip of the Red Giant Branch Method

We present an extensive grid of numerical simulations quantifying the uncertainties in measurements Tip Red Giant Branch (TRGB). These incorporate a luminosity function composed 2 magnitudes red giant branch (RGB) stars leading up to tip, with asymptotic (AGB) contributing exclusively for at least magnitude above RGB tip. quantify sensitivity TRGB detection and measurement three important error sources: (1) sample size near (2) photometric (3) degree self-crowding population. The creates population supra-TRGB due blending one or more just below This last is ultimately difficult, though still possible, disentangle from true AGB stars. In analysis given here, precepts general methodology as used Chicago-Carnegie Hubble Program (CCHP) has been followed. However, Appendix, we introduce test set new tip kernels which internally self-consistent smoothing. are generalizations two-step model by CCHP (smoothing followed Sobel-filter detection), where based on successive binomial-coefficient approximations Derivative-of-a-Gaussian (DoG) edge detector, commonly modern digital image processing.