The tip of the red giant branch as a distance indicator for resolved galaxies. 2: Computer simulations

Based on both empirical data for the nearby galaxies, and on computer simulations, we show that measuring the position of the tip of the first-ascent red-giant branch provides a means of obtaining the distances to nearby galaxies with a precision and accuracy comparable to using Cepheids and/or RR Lyrae variables. We present an analysis of synthetic I vs (V-I) color magnitude diagrams of Population 2 systems to investigate the use of the observed discontinuity in the I-band luminosity function as a primary distance indicator. In the simulations we quantify the effects (1) signal to noise, (2) crowding, (3) population size, and (4) non-giant-branch-star contamination, on the method adopted for detecting the discontinuity,, measuring its luminosity, and estimating its uncertainity. We discuss sources of systematic error in the context of observable parameters, such as the signal-to-noise ratio and/or surface brightness. The simulations are then scaled to observed color-magnitude diagrams. It is concluded, that from the ground the tip of the red-giant-branch method can be sucessfully used to determine distances accurate to +/- 10% for galaxies out to 3 Mpc (mu approximately 27.5 mag); and from space a factor of four further in distance (mu approximately 30.6 mag) can be reached using HST. This method can be applied whereever a metal-poor population (-2.0 less than Z less than -0.7) of red-giant stars is detected (whose age is in the range 7-17 Gyr), whether that population resides in the halo of a spiral galaxy, the extended outer disk of a dwarf irregular, or in the outer periphery of an elliptical galaxy.