Galactic H2CO Densitometry I: Pilot survey of Ultracompact HII regions and methodology

We present a pilot survey of 21 lines of sight towards UCHII regions in the H2CO 1-1 (6cm) and 2-2 (2cm) transitions, using the H2CO centimeter lines as a molecular gas densitometer. Using Arecibo and Green Bank beam-matched observations, we measure the density of 51 detected H2CO line pairs and present upper limits on density for an additional 24 detected 1-1 lines. We analyze the systematic uncertainties in the H2CO densitometer, achieving H2 density measurements with accuracies ~ 0.1-0.3 dex. The densities measured are not correlated with distance, implying that it is possible to make accurate density measurements throughout the galaxy without a distance bias. We confirm that ultracompact HII regions are associated with gas at densities n(H2)~10^5cm^-3. The densities measured in line-of-sight molecular clouds suggest that they consist of low volume filling factor (f~10^-2) gas at high (n(H2)>10^4cm^-3) density, which is inconsistent with purely supersonic turbulence and requires high-density clumping greater than typically observed in gravoturbulent simulations. We observe complex line morphologies that indicate density variations with velocity around UCHII regions, and we classify a subset of the UCHII molecular envelopes as collapsing or expanding. We compare these measurements to Bolocam Galactic Plane Survey 1.1mm observations, and note that most UCHII regions have 1.1mm emission consisting of significant (5-70%) free-free emission and are therefore not necessarily dominated by optically thin dust emission. A comparison of our data with the Mangum et al. starburst sample shows that the area filling factor of dense (n(H2)~10^5cm^-3) molecular gas in typical starburst galaxies is <~0.01, but in extreme starburst galaxies like Arp 220, is ~0.1, suggesting that Arp 220 is physically similar to an oversized UCHII region.