The puzzle of the cluster-forming core mass-radius relation and why it
  matters
  We highlight how the mass-radius relation of cluster-forming cores combined
with an external tidal field can influence infant weight-loss and disruption
likelihood of clusters after gas expulsion. Specifically, we study how the
relation between the bound fraction of stars staying in clusters at the end of
violent relaxation and the cluster-forming core mass is affected by the slope
and normalization of the core mass-radius relation. Assuming mass-independent
star formation efficiency and gas-expulsion time-scale
$\tau_{GExp}/\tau_{cross}$ and a given external tidal field, it is found that
constant surface density cores and constant radius cores have the potential to
lead to the preferential removal of high- and low-mass clusters, respectively.
In contrast, constant volume density cores result in mass-independent cluster
infant weight-loss, as suggested by observations. Our modelling includes
predictions about the evolution of high-mass cluster-forming cores, a regime
not yet covered by the observations. An overview of various issues directly
affected by the nature of the core mass-radius relation is presented (e.g.
cluster mass function, galaxy star formation histories, globular cluster
self-enrichment). Finally, we emphasize that observational mass-radius
data-sets of dense gas regions must be handled with caution as they may be the
imprint of the molecular tracer used to map them, rather than reflecting
cluster formation conditions. [Abridged]
