Young massive clusters (YMCs) have central stellar mass surface densities exceeding $10^{4} M_{odot} pc^{-2}$. It is currently unknown whether the stars formed at such high (proto)stellar densities. We compile a sample of gas clouds in the Galaxy which have sufficient gas mass within a radius of a few parsecs to form a YMC, and compare their radial gas mass distributions to the stellar mass distribution of Galactic YMCs. We find that the gas in the progenitor clouds is distributed differently than the stars in YMCs. The mass surface density profiles of the gas clouds are generally shallower than the stellar mass surface density profiles of the YMCs, which are characterised by prominent dense core regions with radii ~ 0.1 pc, followed by a power-law tail. On the scale of YMC core radii, we find that there are no known clouds with significantly more mass in their central regions when compared to Galactic YMCs. Additionally, we find that models in which stars form from very dense initial conditions require surface densities that are generally higher than those seen in the known candidate YMC progenitor clouds. Our results show that the quiescent, less evolved clouds contain less mass in their central regions than in the highly star-forming clouds. This suggests an evolutionary trend in which clouds continue to accumulate mass towards their centres after the onset of star formation. We conclude that a conveyor-belt scenario for YMC formation is consistent with the current sample of Galactic YMCs and their progenitor clouds.
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