2013ApJ...766..108M

Accurate techniques that allow for the derivation of the spatial density in star formation regions are rare. A technique that 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 1₁₀-1₁₁(λ = 6.2 cm) and 2₁₁-2₁₂(λ = 2.1 cm) K-doublet transitions of H₂ CO in a sample of 56 starburst systems. 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. Our spatial density measurements lie in a relatively narrow range from 10^4.5 to 10^5.5/cm3. 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 H₂ CO measurements to derive two separate measures of the dense gas mass which are generally smaller, in many cases by a factor of 10²-10³, than those derived using HCN. This disparity suggests that H₂ CO traces a denser, more compact component of the giant molecular clouds in our starburst galaxy sample. We also report measurements of the rotationally excited λ = 6.3 cm ²Π_1/2 J = 1/2 state of OH and the H111α radio recombination line taken concurrently with our H₂ CO 1₁₀-1₁₁measurements.