# The Rest-frame $H$-band Luminosity Function of Red Sequence Galaxies in Clusters at $1.0 < z < 1.3$

## TL;DR

This study investigates the luminosity distribution of red sequence galaxies in high-redshift clusters, revealing a deficit of faint galaxies and evidence for gradual build-up of the faint red sequence over cosmic time.

## Contribution

First measurement of the rest-frame H-band luminosity function of red sequence galaxies at z~1, showing evolution and environmental effects on faint galaxy buildup.

## Key findings

- Faint end slope of the luminosity function is shallow at high redshift.
- Faint red sequence galaxies increase in luminosity over 2.6 Gyr.
- Faint-to-luminous ratio decreases with redshift, indicating gradual build-up.

## Abstract

We present results on the rest-frame $H$-band luminosity functions (LF) of red sequence galaxies in seven clusters at 1.0 < z < 1.3 from the Gemini Observations of Galaxies in Rich Early Environments Survey (GOGREEN). Using deep GMOS-z' and IRAC $3.6 \mu$m imaging, we identify red sequence galaxies and measure their LFs down to $M_{H} \sim M_{H}^{*} + (2.0 - 3.0)$. By stacking the entire sample, we derive a shallow faint end slope of $ \alpha \sim -0.35^{+0.15}_{-0.15} $ and $ M_{H}^{*} \sim -23.52^{+0.15}_{-0.17} $, suggesting that there is a deficit of faint red sequence galaxies in clusters at high redshift. By comparing the stacked red sequence LF of our sample with a sample of clusters at z~0.6, we find an evolution in the faint end of the red sequence over the ~2.6 Gyr between the two samples, with the mean faint end red sequence luminosity growing by more than a factor of two. The faint-to-luminous ratio of our sample ($0.78^{+0.19}_{-0.15}$) is consistent with the trend of decreasing ratio with increasing redshift as proposed in previous studies. A comparison with the field shows that the faint-to-luminous ratios in clusters are consistent with the field at z~1.15 and exhibit a stronger redshift dependence. Our results support the picture that the build up of the faint red sequence galaxies occurs gradually over time and suggest that faint cluster galaxies, similar to bright cluster galaxies, experience the quenching effect induced by environment already at z~1.15.