Dependence of Multi-band Absolute Magnitudes and Color Indexes of the Tip of Red Giant Branch Stars on Metallicity in the Galactic Globular Clusters

TL;DR

This study investigates how the brightness and color of red giant stars at the tip of their branch depend on metallicity, refining their use as standard candles for measuring cosmic distances.

Contribution

It provides a detailed analysis of the metallicity dependence of TRGB stars' magnitudes across multiple bands, updating calibration methods for distance measurements.

Findings

$M_I$ is nearly constant for [Fe/H] < -1.2, supporting its use as a standard candle.

$M_I$ becomes fainter with higher metallicity above -1.2, affecting Hubble constant estimates.

Optical magnitudes increase with metallicity, while infrared magnitudes decrease, showing opposite trends.

Abstract

The tip of red giant branch (TRGB) stars have attracted intensive attention in recent years because their $I$-band absolute magnitudes, $M_\rm I$, 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 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 $G_{\rm BP}-G_{\rm RP}$ vs. $G_{\rm RP}$ diagram, it is confirmed that $M_\rm I$ is almost constant of $-4.017 \pm 0.036 \pm 0.027$ mag when $[\rm Fe/H]<-1.2$, which would give $H_0=70.86\pm 1.2\pm0.9$ $\rm kms^{-1} Mp c^{-1}$ with this updated luminosity calibration for type Ia supernovae. However, for $[\rm Fe/H]>-1.2$, $M_\rm I$ is found to become fainter with lower metallicity, which would lead to a larger Hubble constant. In the optical $G_{\rm BP}, G_{\rm RP}$ and $V$ bands, the absolute magnitude of TRGB stars tends to increase with metallicity, while in the infrared $J, H$, and $K_{\rm S}$ 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.