A Complete Survey of the Satellites in the NGC 4437 Group and Implications of a Magnitude Gap for Galaxy Group Assembly History

Both observations and cosmological simulations have recently shown that there is a large scatter in the number of satellites of Milky Way (MW)-like galaxies. In this study, we investigate the relation between the satellite number and galaxy group assembly history, using the r-band magnitude gap (Δm₁₂) between the first and the second brightest galaxy as an indicator. From 20 deg² of Hyper Suprime-Cam Subaru Strategic Program Wide layer, we identify 17 dwarf satellite candidates around NGC 4437, a spiral galaxy with about one-fourth of the MW stellar mass. We estimate their distances using the surface brightness fluctuation (SBF) method. Then we confirm five candidates as members of the NGC 4437 group, resulting in a total of seven group members. Combining the NGC 4437 group (with Δm₁₂=2.5 mag) with other groups in the literature, we find a stratification of the satellite number by Δm₁₂ for a given host stellar mass. The satellite number for given host stellar mass decreases as Δm₁₂ increases. The same trend is found in simulated galaxy groups in the TNG50 simulations. We also find that the host galaxies in groups with a smaller Δm₁₂ (like NGC 4437) have assembled their halo mass more recently than those in larger gap groups, and that their stellar-to-halo mass ratios (SHMRs) increase as Δm₁₂ increases. These results show that the large scatter in the satellite number is consistent with a large range of Δm₁₂, indicating diverse group assembly histories. In addition, the correlations increase as the radius limit for group definition increases, showing that satellite galaxies should be searched in a wide area to use Δm₁₂ as an indicator for galaxy assembly.