2025ApJ...980..218S

The tip of the red giant branch (TRGB) stars have attracted intensive attention in recent years because their I-band absolute magnitudes, M_I, are often used for distance calibration in the Hubble constant measurements because of its almost independence on metallicity ([Fe/H]). However, a discrepancy exists between various studies, and the theoretical stellar model predicts the dependence of their luminosity on [Fe/H]. Here, we present a careful study of the dependence of absolute magnitudes and color indexes on metallicity in optical and near-infrared bands. With the TRGB stars identified in 33 Galactic globular clusters by the reddest color in the G_BP - G_RP versus G_RP diagram, it is confirmed that M_I is almost constant of -4.017 ± 0.036 ± 0.027 mag when [Fe/H] < -1.2, which would give H₀ = 70.86 ± 1.2 ± 0.9 km s^–1 Mpc^–1 with this updated luminosity calibration for Type Ia supernovae. However, for [Fe/H] > -1.2, M_I is found to become fainter with lower metallicity, which would lead to a larger Hubble constant. In the optical G_BP, G_RP, and V bands, the absolute magnitude of TRGB stars tends to increase with metallicity, while in the infrared J, H, and K_s bands, the variation with metallicity shows an inverse tendency. In addition, the analytical relations of the color indexes with metallicity are presented, which have smaller dispersion than those derived for the corresponding absolute magnitudes.