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