Revealing the Physical Conditions around Sgr A* using Bayesian Inference
  -- I. Observations and Radiative Transfer
  We report sub-arcsecond ALMA observations between 272 - 375 GHz towards Sgr
A*'s Circumnuclear disk (CND). Our data comprises 8 individual pointings, with
significant SiO (8(7) - 7(6)) and SO (7 - 6) emission detected towards 98
positions within these pointings. Additionally, we identify H2CS (9(1,9) -
8(1,8)), OCS (25 - 24) and CH3OH (2(1,1) - 2(0,2)) towards a smaller subset of
positions. By using the observed peak line flux density together with a
Bayesian Inference technique informed by radiative transfer models, we
systematically recover the physical gas conditions towards each of these
positions. We estimate that the bulk of the surveyed gas has temperature T <
500 K and density n $\lessapprox 10^{6}$ cm$^{-3}$, consistent with previous
studies of similar positions as traced by HCN clumps. However, we identify an
uncharacteristically hot (T $\approx 600$ K) and dense (n $\approx 10^{6}$
cm$^{-3}$) source in the Northeastern Arm. This position is found to be
approximately consistent with a gravitationally bound region dominated by
turbulence. We also identify a nearby cold (T $\approx 60$ K) and extremely
dense (n $\approx 10^{7}$ cm$^{-3}$) position that is again potentially bound
and dominated by turbulence. We also determine that the total gas mass
contained within the CND is M $\approx 4 \times 10^{4}$ $M_{\odot}$.
Furthermore, we qualitatively note that the observed chemical enrichment across
large scales within the CND is consistent with bulk grain processing, though
multiple desorption mechanisms are plausibly responsible. Further chemical
modelling is required to identify the physical origin of the grain-processing,
as well as the localised H2CS and OCS emission.
