Radiation Pressure Limits on the Star Formation Efficiency and Surface Density of Compact Stellar Systems

TL;DR

This paper investigates how radiation pressure from dust-enshrouded star-forming regions limits the efficiency and surface density of compact stellar systems, suggesting a universal upper limit influenced by metallicity.

Contribution

It derives the maximum star formation efficiency and surface density constrained by radiation pressure, highlighting a metallicity-dependent upper limit for compact stellar systems.

Findings

Maximum star cluster formation efficiency is about 0.9.

Gas clouds above a certain surface density expand due to radiation pressure.

Observed stellar surface densities are consistent with the predicted upper limit.

Abstract

The large columns of dusty gas enshrouding and fuelling star-formation in young, massive stellar clusters may render such systems optically thick to radiation well into the infrared. This raises the prospect that both "direct" radiation pressure produced by absorption of photons leaving stellar surfaces and "indirect" radiation pressure from photons absorbed and then re-emitted by dust grains may be important sources of feedback in such systems. Here we evaluate this possibility by deriving the conditions under which a spheroidal, self-gravitating, mixed gas-star cloud can avoid catastrophic disruption by the combined effects of direct and indirect radiation pressure. We show that radiation pressure sets a maximum star cluster formation efficiency of $\epsilon_{\rm max} \sim 0.9$ at a (very large) gas surface density of $\sim 10^5 M_\odot$ pc$^{-2} (Z_\odot/Z) \simeq 20$ g cm$^{-2} (Z_\odot/Z)$, but that gas clouds above this limit undergo significant radiation-driven expansion during star formation, leading to a maximum stellar surface density very near this value for all star clusters. Data on the central surface mass density of compact stellar systems, while sparse and partly confused by dynamical effects, are broadly consistent with the existence of a metallicity-dependent upper-limit comparable to this value. Our results imply that this limit may preclude the formation of the progenitors of intermediate-mass black holes for systems with $Z \gtrsim 0.2 Z_\odot$.