We address a simple model where the Kennicutt-Schmidt ( KS ) relation between the macroscopic densities of star-formation rate ( SFR , \rho _ { sfr } ) and gas ( n ) in galactic discs emerges from self-regulation of the SFR via supernova feedback .
It arises from the physics of supernova bubbles , insensitive to the microscopic SFR recipe and not explicitly dependent on gravity .
The key is that the filling factor of SFR-suppressed supernova bubbles self-regulates to a constant , f \sim 0.5 .
Expressing the bubble fading radius and time in terms of n , the filling factor is f \propto S n ^ { - s } with s \simeq 1.5 , where S is the supernova rate density .
A constant f thus refers to \rho _ { sfr } \propto n ^ { 1.5 } , with a density-independent SFR efficiency per free-fall time \sim 0.01 .
The self-regulation to f \sim 0.5 and the convergence to a KS relation independent of the local SFR recipe are demonstrated in cosmological and isolated-galaxy simulations using different codes and recipes .
In parallel , the spherical analysis of bubble evolution is generalized to clustered supernovae , analytically and via simulations , yielding s \simeq 1.5 \pm 0.5 .
An analysis of photo-ionized bubbles about pre-supernova stars yields a range of KS slopes but the KS relation is dominated by the supernova bubbles .
Superbubble blowouts may lead to an alternative self-regulation by outflows and recycling .
While the model is over-simplified , its simplicity and validity in the simulations may argue that it captures the origin of the KS relation .