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.