The Compactness of Galaxy Groups in the Sloan Digital Sky Survey

We use an updated version of the halo-based galaxy group catalog of Yang et al., and take the surface brightness of the galaxy group ($\mu_{\rm lim}$) based on projected positions and luminosities of galaxy members as a compactness proxy to divide groups into sub-systems with different compactness. By comparing various properties, including galaxy conditional luminosity function, stellar population, active galactic nuclei (AGN) activity, and X-ray luminosity of the intra-cluster medium of carefully controlled high (HC) and low compactness (LC) group samples, we find that the group compactness plays an essential role in characterizing the detailed physical properties of the group themselves and their group members, especially for low mass groups with $M_h \lesssim 10^{13.5}h^{-1}M_{\odot}$. We find that the low-mass HC groups have a systematically lower magnitude gap $\Delta m_{12}$ and X-ray luminosity than their LC counterparts, indicating that the HC groups are probably in the early stage of group merging. On the other hand, a higher fraction of passive galaxies is found in the HC group, which however is a result of systematically smaller halo-centric distance distribution of their satellite population. After controlling of both $M_h$ and halo-centric distance, we do not find any differences for both the quenching faction and AGN activity of the member galaxies between the HC and LC groups. Therefore, we conclude that the halo quenching effect, which result in the halo-centric dependence of galaxy population, is a faster process compared to the dynamical relaxed time-scale of galaxy groups.