Characteristic scale of star formation. I. Clump formation efficiency on local scales

We have used the ratio of column densities (CDR) derived independently from the 850-$\mu$m continuum JCMT Plane Survey (JPS) and the $^{13}$CO/C$^{18}$O $(J=3-2)$ Heterodyne Inner Milky Way Plane Survey (CHIMPS) to produce maps of the dense-gas mass fraction (DGMF) in two slices of the Galactic Plane centred at $\ell$=30$^{\circ}$ and $\ell$=40$^{\circ}$. The observed DGMF is a metric for the instantaneous clump-formation efficiency (CFE) in the molecular gas. We split the two fields into velocity components corresponding to the spiral arms that cross them, and a two-dimensional power-spectrum analysis of the spiral arm DGMF maps reveals a break in slope at the approximate size scale of molecular clouds. We interpret this as the characteristic scale of the amplitude of variations in the CFE and a constraint on the dominant mechanism regulating the CFE and, hence, the star-formation efficiency in CO-traced clouds.