Zhicheng He, Enci Wang, Luis C. Ho, Yingjie Peng, Huiyuan Wang, Yong Shi, Tao Wang, Yongquan Xue, Tinggui Wang

How galaxies stop forming stars is a complex and central problem in astrophysics. Numerous physical mechanisms have been proposed, yet a simple, unified framework connecting these mechanisms remains lacking. Here, we derive a step-function quenching response from the fundamental principle of gas mass conservation, governed by the competition between gas-supply and gas-depletion timescales. This response also enables the gas-supply timescale to be inferred from the observed quenched fraction. Applying this method to approximately 350,000 galaxies, we find a characteristic gas-supply timescale of ~1 Gyr, reveal distinct inside-out and outside-in quenching signatures associated with supermassive black holes and dark matter halos, respectively, and identify galaxies with intermediate stellar surface mass densities as occupying a critical state for quenching and rejuvenation. Our work establishes a unified physical framework in which a simple step-function response captures how diverse physical processes regulate galaxy quenching and the resumption of star formation through their effects on the competition between gas-supply and gas-depletion timescales.