Origins of Scatter in the Relationship Between HCN 1-0 and Dense Gas
  Mass in the Galactic Center
  We investigate the correlation of HCN 1-0 with dense gas mass in the Galactic
center. We find that in general (on the ~10 pc size scale of individual
molecular cloud cores) HCN 1-0 is well correlated with the dense molecular gas
mass using a standard log-log relationship. However individual clouds in this
environment show systematic deviations from this relationship that contribute
to around 0.75 dex of scatter. Most notably, Sgr B2, the most massive cloud in
the Galactic center, has an integrated HCN 1-0 intensity of cloud less than
half its mass, and several other clouds including GCM-0.02-0.07 show an
enhancement of HCN 1-0 by a factor of 2-3 relative to clouds of comparable
mass. We also find that HCN 1-0 is more intense for a given mass in the
large-scale diffuse emission in the central 300 parsecs compared to the compact
emission from individual cloud cores. We identify the two primary sources of
scatter in the relationship between HCN 1-0 and dense gas mass to be
self-absorption (which reduces the observed HCN 1-0 intensity of Sgr B2) and
variations in HCN abundance, which appear to increase the brightness of HCN 1-0
in GCM-0.02-0.07 and other clouds. We find that these sources of scatter would
only contribute to an ~10% error in the dense gas mass inferred from the HCN
1-0 intensity in the Galactic center. However, the implied order of magnitude
HCN abundance variations between Galactic center clouds, and the systematic
nature of these variations warn of potential biases in the use of HCN as dense
gas mass tracer in more extreme environments, such as AGN and shock-dominated
regions. Finally, we also investigate other tracers having transitions near 3
mm, finding that HNCO, HNC and HCO+ largely behave like HCN, while HC3N, and
CH3CN are higher fidelity tracers of the amount of gas in clouds like Sgr B2
that suffer from strong self-absorption of the HCN 1-0 line. [abridged]
