Variations in Star Formation History and the Red Giant Branch Tip
  We examine the reliability of the tip of the red giant branch (TRGB) as a distance indicator for stellar populations with different star formation histories (SFHs) when photometric errors and completeness corrections at the TRGB are small. In general, the TRGB-distance method is insensitive to the shape of the SFH except when it produces a stellar population with a significant component undergoing the red giant branch phase transition. The I-band absolute magnitude of the TRGB for the middle and late stages of this transition (~1.3-1.7 Gyr) is several tenths of a magnitude fainter than the canonical value of M_I ~ -4.0. If more than 30% of all stars formed over the lifetime of the Universe are formed at these ages, then the distance could be overestimated by 10-25%. Similarly, the TRGB-distance method is insensitive to the metallicity distribution of stars formed except when the average metallicity is greater than <[Fe/H]> = -0.3. If more than ~70% of all stars formed have [Fe/H] > -0.3, the distance could be overestimated by ~10-45%. We find that two observable quantities, the height of the discontinuity in the luminosity function at the TRGB and the median (V-I)_0 at M_I = -3.5 can be used to test if the aforementioned age and metallicity conditions are met. 
Michael K. Barker (1), Ata Sarajedini (1) and Jason Harris (2) ((1)   University of Florida, (2) Steward Observatory)