Upper galaxy mass from gas cooling ($M_{\mathrm{cool}}\text{ of order a galactic mass}$)

In simple hierarchical models, increasing system mass raises the virial temperature and can carry primordial gas beyond its efficient atomic line-cooling interval. At assembly densities, the cooling-time constraint then distinguishes galaxy-sized condensations from larger hot groups or clusters. The resulting characteristic mass is approximate, depends on composition and structure, and does not prohibit subsequent mergers of already formed stellar systems.