We present an analysis of gas densities in the central R?=?300 pc of the Milky Way, focusing on three clouds: GCM –0.02–0.07 (the 50 km s?1 cloud), GCM –0.13–0.08 (the 20 km s?1 cloud), and GCM 0.25+0.01 (the "Brick"). Densities are determined using observations of the J?=?(3–2), (4–3), (5–4), (10–9), (18–17), (19–18), (21–20), and (24–23) transitions of the molecule HC3N. We find evidence of at least two excitation regimes for HC3N and constrain the low-excitation component to have a density less than 104 cm?3 and the high-excitation component to have a density between 105 and 106 cm?3. This is much less than densities of 107 cm?3 that are found in Sgr B2, the most actively star-forming cloud in the Galactic center. This is consistent with the requirement of a higher-density threshold for star formation in the Galactic center than is typical in the Galactic disk. We are also able to constrain the column density of each component in order to determine the mass fraction of "dense" (n > 105 cm?3) gas for these clouds. We find that this is ~15% for all three clouds. Applying the results of our models to ratios of the (10–9) and (3–2) line across the entire central R?=?300 pc, we find that the fraction of dense (n > 104 cm?3) gas increases inward of a radius of ~140 pc, consistent with the predictions of recent models for the gas dynamics in this region. Our observations show that HC3N is an excellent molecule for probing the density structure of clouds in the Galactic center.
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