ALMA $\mathrm{^{13}CO}$(J=1-0) Observations of NGC 604 in M33: Physical Properties of Molecular Clouds.

We present Atacama Large Millimeter/submillimeter Array (ALMA) observations of $\mathrm{^{13}CO(J=1-0)}$ line and 104 GHz continuum emission from NGC 604, a giant HII region (GHR) in the nearby spiral galaxy M33. Our high spatial resolution images ( 3.2"$\times$ 2.4", corresponding to $13 \times 10$ pc physical scale) allow us to detect fifteen molecular clouds. We find spatial offsets between the $^{13}CO$ and 104 GHz continuum emission and also detect continuum emission near the centre of the GHR. The identified molecular clouds have sizes ranging from 5-21 pc, linewidths of 0.3-3.0 $\mathrm{kms^{-1}}$ and luminosity-derived masses of (0.4-80.5) $\times 10^3$ M$_{\bigodot}$. These molecular clouds are in near virial equilibrium, with a spearman correlation coefficient of 0.98. The linewidth-size relationship for these clouds is offset from the corresponding relations for the Milky Way and for NGC 300, although this may be an artefact of the dendrogram process.