How Robust Is the Cosmic Distance with the Tip of Red Giant Branch against Stellar Population Variations?

Abstract

The tip of the red giant branch (TRGB) provides a key standard candle for extragalactic distance measurements and for refining the Hubble constant. We test its robustness by quantifying how metallicity, alpha-element enhancement, age, and initial helium abundance modulate the TRGB luminosity, using synthetic composite color-magnitude diagrams in the I and F814W bands. We find that metallicity and alpha-element enhancement are the primary drivers of TRGB variation, while age introduces only a modest effect and helium abundance is negligible. At fixed age and helium content, increasing the mean metallicity by 0.5 dex or the alpha-element enhancement by 0.3 dex produces the well-known systematic dimming of 0.046 and 0.050 mag, respectively, in MITRGB , and of 0.093 and 0.044 mag, respectively, in MF814WTRGB . By comparison, changes in the age of 3 Gyr and in the initial helium abundance of 0.10 yield minor luminosity shifts, with average changes of 0.031 and 0.009 mag, respectively, in MITRGB , and of 0.035 and 0.027 mag, respectively, in MF814WTRGB , substantially smaller than those caused by variations in metallicity or alpha-element enhancement. For mixed stellar populations under typical stellar-halo metallicity conditions, the net variation in MITRGB arising from each combination of the alpha-element enhancement, age, and initial helium abundance remains below 0.028 mag, well within reported systematic uncertainties. Together, these results reaffirm the TRGB as a highly robust distance indicator and support its continued use as an independent anchor for precision cosmology in the era of the Hubble-tension debate.