Interpreting the sub-linear Kennicutt-Schmidt relationship: The case for
  diffuse molecular gas
  Recent statistical analysis of two extragalactic observational surveys
strongly indicate a sublinear Kennicutt-Schmidt (KS) relationship between the
star formation rate (Sigsfr) and molecular gas surface density (Sigmol). Here,
we consider the consequences of these results in the context of common
assumptions, as well as observational support for a linear relationship between
Sigsfr and the surface density of dense gas. If the CO traced gas depletion
time (tau_mol) is constant, and if CO only traces star forming giant molecular
clouds (GMCs), then the physical properties of each GMC must vary, such as the
volume densities or star formation rates. Another possibility is that the
conversion between CO luminosity and Sigmol, the XCO factor, differs from
cloud-to-cloud. A more straightforward explanation is that CO permeates the
hierarchical ISM, including the filaments and lower density regions within
which GMCs are embedded. A number of independent observational results support
this description, with the diffuse gas comprising at least 30% of the total
molecular content. The CO bright diffuse gas can explain the sublinear KS
relationship, and consequently leads to an increasing tau_mol with Sigmol. If
Sigsfr linearly correlates with the dense gas surface density, a sublinear KS
relationship indicates that the fraction of diffuse gas fdiff grows with
Sigmol. In galaxies where Sigmol falls towards the outer disk, this description
suggests that fdiff also decreases radially.
