Tip of the red giant branch distances. I. Optimization of a maximum likelihood algorithm

Accurate distances to galaxies can be determined from the luminosities of stars at the tip of the red giant branch (TRGB). We use a maximum likelihood algorithm to locate the TRGB in galaxy color-magnitude diagrams. The algorithm is optimized by introducing reliable photometric errors and a completeness characterization determined with artificial star experiments. The program is extensively tested using Monte Carlo simulations, artificial galaxies, and a sample of nearby dwarf galaxies observed with the Hubble Space Telescope WFPC2 and ACS. Our procedure is shown to be reliable, to have good accuracy, and to not introduce any systematic errors. The methodology is especially useful in cases in which the TRGB approaches the photometric limit and/or the RGB is poorly populated.