Examining Lyman-alpha Emitters through MillenniumTNG in anticipation of DESI-II

The goal of this study is to conduct a timely analysis of the high-redshift star-forming galaxy populations, which will be informative in designing next-generation experiments and their extragalactic targets. We use the hydrodynamical simulation MillenniumTNG (MTNG) to model Lyman-alpha Emitting (LAE) galaxies to extract key properties such as their clustering and occupation statistics. We define LAEs through an empirical relation between star formation rate (SFR) and Lyman-alpha flux. We also explore two other definitions, finding that imposing an additional cut on the maximum stellar mass of the galaxy sample, which approximates the effect of a low escape fraction at high halo mass, leads to a 5-10\% decrease of the linear bias of the population. As expected, we find that the HOD mass parameters rapidly decrease with increasing number density. Additionally, the HOD parameter $\sigma$ also decreases with number density, implying that the SFR-halo mass relationship becomes tighter for low-luminosity objects. Surprisingly, the non-linear clustering, estimated by the parameter $r_0$, is fixed at fixed number density, whereas the linear bias parameter varies with redshift as $b(z) \propto (1 + z)$, suggesting that our LAE samples are relatively stable and long-lived. Finally, we study the amount of galaxy assembly bias present at $z = 2, \ 3$ and find that while at $z = 2$ it is roughly $\lesssim$10\%, at $z = 3$ it decreases significantly to $\lesssim$5\%. This suggests that assembly bias effects become less important at high $z$ likely due to the lower number of cumulative two-halo interactions (mergers, splashback, stripping, etc.). While our study is based on a single full-physics simulation, we expect our results to reflect the properties of LAEs in the Universe. We demonstrate that our findings are in good agreement with previous results using both observations and simulations.