Feedback in Forming Star Clusters: The Mass-Radius Relation and Mass
  Function of Molecular Clumps in the Large Magellanic Cloud
  We derive the mass-radius relation and mass function of molecular clumps in
the Large Magellanic Cloud (LMC) and interpret them in terms of the simple
feedback model proposed by Fall, Krumholz, and Matzner (FKM). Our work utilizes
the dendrogram-based catalog of clumps compiled by Wong et al. from $^{12}$CO
and $^{13}$CO maps of six giant molecular clouds in the LMC observed with the
Atacama Large Millimeter Array (ALMA). The Magellanic Clouds are the only
external galaxies for which this type of analysis is possible at the necessary
spatial resolution ($\sim1$ pc). We find that the mass-radius relation and mass
function of LMC clumps have power-law forms, $R \propto M^{\alpha}$ and $dN/dM
\propto M^{\beta}$, with indices $\alpha = 0.36 \pm 0.03$ and $\beta= -1.8 \pm
0.1 $ over the mass ranges $10^2 M_\odot \lesssim M \lesssim 10^5 M_\odot$ and
$10^2 M_\odot \lesssim M \lesssim 10^4 M_\odot$, respectively. With these
values of $\alpha$ and $\beta$ for the clumps (i.e., protoclusters), the
predicted index for the mass function of young LMC clusters from the FKM model
is $\beta \approx 1.7$, in good agreement with the observed index. The
situation portrayed here for clumps and clusters in the LMC replicates that in
the Milky Way.
