From Haloes to Galaxies. II. The Fundamental Relations in Star Formation and Quenching

Star formation and quenching are two of the most important processes in galaxy evolution. We explore local Universe interrelationships among key integrated properties, including stellar mass $M_*$, star rate (SFR), specific SFR (sSFR), molecular gas $M_{\rm H_2}$, efficiency (SFE) to ratio $\mu$. aim identify fundamental scaling relations these properties their interrelationships. show H_2}$-SFR, SFR-$M_*$ H_2}$-$M_*$ relation can be simply transformed from $\mu$-sSFR, SFE-$\mu$ SFE-sSFR relation, respectively. The transformation, principle, increase or decrease scatter each relation. Interestingly, we find latter three all have significantly smaller than former corresponding relations. probability achieve observed small by accident is extremely close zero. This suggests that scatters driven a more physical connection quantities. then large due systematic dependence on other process. propose sSFR-$\mu$-SFE as Fundamental Formation Relation (FFR), which governs process, provides simple framework study Other relations, Kennicutt-Schmidt law, star-forming main sequence sequence, derived FFR.