# The Absolute Magnitudes of Red Horizontal Branch Stars in the ugriz System

## TL;DR

This study calibrates the absolute magnitudes of red horizontal branch stars in the SDSS ugriz system, revealing how metallicity and age influence their brightness and identifying the i filter as optimal for distance measurements.

## Contribution

It provides new calibration formulas for RHB star magnitudes as functions of metallicity and age in the ugriz system, with the i filter identified as most effective for distance estimation.

## Key findings

- The i filter has the smallest scatter in magnitude calibration.
- Metallicity coefficients decrease from u to z filters.
- Age coefficients increase from u to z filters.

## Abstract

Based on photometric data of the central parts of eight globular clusters and one open cluster presented by An and his collaborators, we select red horizontal branch (RHB) stars in the (g-r)0-g0 diagram and make a statistical study of the distributions of their colors and absolute magnitudes in the SDSS ugriz system. Meanwhile, absolute magnitudes in the Johnson VRI system are calculated through the translation formulae between gri and VRI in the literature. The calibrations of absolute magnitude as functions of metallicity and age are established by linear regressions of the data. It is found that metallicity coefficients in these calibrations decrease, while age coefficients increase, from the blue $u$ filter to the red $z$ filter. The calibration of Mi= 0.06[Fe/H]+0.040t+0.03 has the smallest scatter of 0.04 mag, and thus i is the best filter in the $ugriz$ system when RHB stars are used for distance indicators. The comparison of the MI calibration from our data with that from red clump stars indicates that the previous suggestion that the $I$ filter is better than the V filter in distance determination may not be true because of its significant dependence on age.