Formaldehyde Densitometry of Starburst Galaxies: Density-Independent
  Global Star Formation
  Accurate techniques which allow for the derivation of the spatial density in
star formation regions are rare. A technique which has found application for
the derivation of spatial densities in Galactic star formation regions utilizes
the density-sensitive properties of the K-doublet transitions of formaldehyde
(H2CO). In this paper, we present an extension of our survey of the
formaldehyde 1(10)-1(11) (lambda = 6.2 cm) and 2(11)-2(12) (lambda = 2.1 cm)
K-doublet transitions of H2CO in a sample of 56 starburst systems (Mangum etal.
2008). We have extended the number of galaxies in which both transitions have
been detected from 5 to 13. We have improved our spatial density measurements
by incorporating kinetic temperatures based upon NH3 measurements of 11 of the
galaxies with a total of 14 velocity components in our sample (Mangum etal.
2013). Our spatial density measurements lie in a relatively narrow range of
from 10^(4.5) to 10^(5.5) cm^(-3). This implies that the Schmidt-Kennicutt
relation between L_(IR) and M_(dense): (1) Is an indication of the dense gas
mass reservoir available to form stars, and (2) Is not directly dependent upon
a higher average density driving the star formation process in the most
luminous starburst galaxies. We have also used our H2CO measurements to derive
two separate measures of the dense gas mass which are generally smaller, in
many cases by a factor of 10^2-10^3, than those derived using HCN. This
disparity suggests that H2CO traces a denser, more compact, component of the
giant molecular clouds in our starburst galaxy sample.
  We also report measurements of the rotationally-excited lambda = 6.3 cm
2P_(1/2) J=1/2 state of OH and the H111alpha radio recombination line taken
concurrently with our H2CO 1(10)-1(11) measurements.
