The Interplay between the IMF and Star Formation Efficiency through Radiative Feedback at High Stellar Surface Densities

The observed rest-UV luminosity function at cosmic dawn ($z \sim 8-14$) measured by JWST revealed an excess of UV-luminous galaxies relative to many pre-launch theoretical predictions. A high star-formation efficiency (SFE) and a top-heavy initial mass function (IMF) are among the mechanisms proposed for explaining this excess. Although a top-heavy IMF has been proposed for its ability to increase the light-to-mass ratio ($\Psi_{\mathrm{UV}}$), the resulting enhanced radiative pressure from young stars could decrease the star formation efficiency (SFE), potentially driving galaxy luminosities back down. In this Letter, we use idealized radiation hydrodynamic simulations of star cluster formation to explore the effects of a top-heavy IMF on the SFE of clouds typical of the high pressure conditions found at these redshifts. We find that the SFE in star clusters with solar neighbourhood-like dust abundance decreases with increasingly top-heavy IMF's -- by $\sim 20 \%$ for an increase of factor 4 in $\Psi_{\mathrm{UV}}$, and by $50 \%$ for a factor $\sim 10$ in $\Psi_{\mathrm{UV}}$. However, we find that an expected decrease in the dust-to-gas ratio ($\sim 0.01 \times \mathrm{Solar}$) at these redshifts can completely compensate for the enhanced light output. This leads to a (cloud-scale; $\sim 10 \, \mathrm{pc}$) SFE that is $\gtrsim 70\%$ even for a factor 10 increase in $\Psi_{\mathrm{UV}}$, implying that highly efficient star formation is unavoidable for high surface density and low metallicity conditions. Our results suggest that a top-heavy IMF, if present, likely coexists with efficient star formation in these galaxies.