# The Global Star-Formation Law by Supernova Feedback

## TL;DR

This paper presents a supernova feedback-based model explaining the origin of the Kennicutt-Schmidt relation in galactic discs, supported by simulations showing self-regulation of star formation through supernova bubbles.

## Contribution

It introduces a simple, physics-based model linking supernova bubble dynamics to the star-formation law, independent of microscopic star formation recipes.

## Key findings

- The KS relation emerges from supernova bubble self-regulation.
- Simulations confirm the constant filling factor of SFR-suppressed bubbles.
- Analytical and simulation results yield a KS slope around 1.5.

## Abstract

We address a simple model where the Kennicutt-Schmidt (KS) relation between the macroscopic densities of star-formation rate (SFR, $\rho_{\rm sfr}$) 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 $s\sim 1.5$, where $S$ is the supernova rate density. A constant $f$ thus refers to $\rho_{\rm sfr} \propto n^{1.5}$, 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.