Why is the Star Formation Rate Proportional to Dense Gas Mass?

Abstract One of the most profound empirical laws of star formation is the Gao–Solomon relation, a linear correlation between the star formation rate (SFR) and the dense molecular gas mass. It is puzzling how the complicated physics in star formation results in this surprisingly simple proportionality. Using archival Herschel and Atacama Large Millimeter/submillimeter Array observations, we derived the masses of the most massive cores ( M core max ) and masses of the gravitationally bound gas ( M gas bound ) in the parent molecular clouds for a sample of low-mass and high-mass star-forming regions. We discovered a significant correlation of log ( M core max / M ⊙ ) = 0.506 log ( M gas bound / M ⊙ ) − 0.32 . Our discovered M core max – M gas bound correlation can be approximately converted to the Gao–Solomon relation if there is (1) a constant 30% efficiency of converting M core max to the mass of the most massive star ( m star max ), and (2) if the SFR and m star max are tightly related through log ( SFR / ( M ⊙ yr −