Let us consider a molecular cloud that gravitationally collapses to form stars. The amount of mass available to form stars scales linearly with the mass density of the cloud . The rate of collapse is given by the Jeans timescale where is the constant of gravity, so the star formation rate per unit volume scales with the mass density as
In practice, mass density (and star formation density) per unit volume are difficult to measure, so this rule is typically written in terms of density per unit area
This power law is not to different from the value inferred from observations .