Northern Galactic Molecular Cloud Clumps in Hi-GAL: Clump and Star
  Formation within Clouds
  We investigate how the properties of Galactic giant molecular clouds (GMCs)
and their denser substructures (clumps) correlate with the local star formation
rate. We trace clouds using the $^{12}$CO(3-2) transition, as observed by the
CO High Resolution Survey (COHRS). We identify their constituent clumps using
thermal dust emission, as observed by the Herschel infrared GALactic plane
survey (Hi-GAL). We estimate star formation rates in these clouds using 70
$\mu$m emission. In total, we match 3,674 clumps to 473 clouds in
position-position-velocity space spanning the Galactic longitude range
$10^\circ<\ell<56^\circ$. We find that more massive clouds produce more clumps
and more massive clumps. These clumps have average number densities an order of
magnitude greater than their host clouds. We find a mean clump mass fraction of
$0.20^{+0.13}_{-0.10}$. This mass fraction weakly varies with mass and mass
surface density of clouds, and shows no clear dependence on the virial
parameter and line width of the clouds. The average clump mass fraction is only
weakly dependent upon Galactocentric radius. Although the scatter in our
measured properties is significant, the star formation rate for clouds is
independent of clump mass fraction. However, there is a positive correlation
between the depletion times for clouds and clump mass fraction. We find a star
formation efficiency per free fall time of $\epsilon_{\mathrm{ff}}=0.15\%$ for
GMCs but $\epsilon_{\mathrm{ff}}=0.37\%$ for clumps.
