Probing Environmental Dependence of High-Redshift Galaxy Properties with the Marked Correlation Function

In hierarchical structure formation, correlations between galaxy properties and their environments reveal important clues about galaxy evolution, emphasizing the importance of measuring these relationships. We probe the environmental dependence of Lyman-break galaxy (LBG) properties in the redshift range of $3$ to $5$ using marked correlation function statistics with galaxy samples from the Hyper Suprime-Cam Subaru Strategic Program and the Canada--France--Hawaii Telescope U-band surveys. We find that the UV magnitude and color of magnitude-selected LBG samples are strongly correlated with their environment, making these properties effective tracers of it. In contrast, the star formation rate and stellar mass of LBGs exhibit a weak environmental dependence. For UV magnitudes and color, the correlation is stronger in brighter galaxy samples across all redshifts and extends to scales far beyond the size of typical dark matter halos. This suggests that within a given sample, LBGs with high UV magnitudes or colors are more likely to form pairs at these scales than predicted by the two-point angular correlation function. Moreover, the amplitude of the marked correlation function is generally higher for LBG samples compared to that of $z \sim 0$ galaxies from previous studies.We also find that for LBG samples selected by the same absolute threshold magnitude or average halo mass, the correlation between UV magnitudes and the environment generally becomes more pronounced as the redshift decreases. On the other hand, for samples with the same effective large-scale bias at $z\sim 4$ and $5$, the marked correlation functions are similar on large scales.