The Maximum Stellar Surface Density Due to the Failure of Stellar Feedback

TL;DR

This paper proposes a new model explaining the universal maximum stellar surface density by the failure of stellar feedback at high densities, aligning with observations across diverse stellar systems.

Contribution

The authors introduce an alternative model where feedback becomes ineffective above a critical surface density, naturally predicting the observed maximum stellar surface density.

Findings

The model predicts $ m \Sigma_{max} \\sim 100 \\Sigma_{crit}$, matching observations.

Predicted maximum surface density is robust across scales and metallicities.

The observed $\\Sigma_{max}$ indicates where stellar feedback fails.

Abstract

A maximum stellar surface density $\Sigma_{max} \sim 3 \times 10^5\,{\rm M_\odot\,pc^{-2}}$ is observed across all classes of dense stellar systems (e.g. star clusters, galactic nuclei, etc.), spanning $\sim 8$ orders of magnitude in mass. It has been proposed that this characteristic scale is set by some dynamical feedback mechanism preventing collapse beyond a certain surface density. However, simple analytic models and detailed simulations of star formation moderated by feedback from massive stars argue that feedback becomes {\it less} efficient at higher surface densities (with the star formation efficiency increasing as $\sim \Sigma/\Sigma_{crit}$). We therefore propose an alternative model wherein stellar feedback becomes ineffective at moderating star formation above some $\Sigma_{crit}$, so the supply of star-forming gas is rapidly converted to stars before the system can contract to higher surface density. We show that such a model -- with $\Sigma_{crit}$ taken directly from the theory -- naturally predicts the observed $\Sigma_{max}$. $\Sigma_{max}\sim 100\Sigma_{crit}$ because the gas consumption time is longer than the global freefall time even when feedback is ineffective. Moreover the predicted $\Sigma_{max}$ is robust to spatial scale and metallicity, and is preserved even if multiple episodes of star formation/gas inflow occur. In this context, the observed $\Sigma_{max}$ directly tells us where feedback fails.