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We present the first observations of H$^{13}$CN$(1-0)$, H$^{13}$CO$^+(1-0)$ and SiO$(2-1)$ in NGC,6240, obtained with the IRAM PdBI. Combining a Markov Chain Monte Carlo (MCMC) code with Large Velocity Gradient (LVG) modelling, and with additional da ta from the literature, we simultaneously fit three gas phases and six molecular species to constrain the physical condition of the molecular gas, including mass$-$luminosity conversion factors. We find $sim10^{10}M_odot$ of dense molecular gas in cold, dense clouds ($T_{rm k}sim10$,K, $n_{{rm H}_2}sim10^6$,cm$^{-3}$) with a volume filling factor $<0.002$, embedded in a shock heated molecular medium ($T_{rm k}sim2000$,K, $n_{{rm H}_2}sim10^{3.6}$,cm$^{-3}$), both surrounded by an extended diffuse phase ($T_{rm k}sim200$,K, $n_{{rm H}_2}sim10^{2.5}$,cm$^{-3}$). We derive a global $alpha_{rm CO}=1.5^{7.1}_{1.1}$ with gas masses $log_{10}left(M / [M_odot]right)=10.1_{10.0}^{10.8}$, dominated by the dense gas. We also find $alpha_{rm HCN} = 32^{89}_{13}$, which traces the cold, dense gas. The [$^{12}$C]/[$^{13}$C] ratio is only slightly elevated ($98^{230}_{65}$), contrary to the very high [CO]/[$^{13}$CO] ratio (300-500) reported in the literature. However, we find very high [HCN]/[H$^{13}$CN] and [HCO$^+$]/[H$^{13}$CO$^+$] abundance ratios $(300^{500}_{200})$ which we attribute to isotope fractionation in the cold, dense clouds.
We present the results of interferometric spectral line observations of Arp 220 at 3.5mm and 1.2mm from the Plateau de Bure Interferometer (PdBI), imaging the two nuclear disks in H$^{13}$CN$(1 - 0)$ and $(3 - 2)$, H$^{13}$CO$^+(1 - 0)$ and $(3 - 2)$ , and HN$^{13}$C$(3 - 2)$ as well as SiO$(2 - 1)$ and $(6 - 5)$, HC$^{15}$N$(3 - 2)$, and SO$(6_6 - 5_5)$. The gas traced by SiO$(6 - 5)$ has a complex and extended kinematic signature including a prominent P Cygni profile, almost identical to previous observations of HCO$^+(3 - 2)$. Spatial offsets $0.1$ north and south of the continuum centre in the emission and absorption of the SiO$(6 - 5)$ P Cygni profile in the western nucleus (WN) imply a bipolar outflow, delineating the northern and southern edges of its disk and suggesting a disk radius of $sim40$ pc, consistent with that found by ALMA observations of Arp 220. We address the blending of SiO$(6 - 5)$ and H$^{13}$CO$^+(3 - 2)$ by considering two limiting cases with regards to the H$^{13}$CO$^+$ emission throughout our analysis. Large velocity gradient (LVG) modelling is used to constrain the physical conditions of the gas and to infer abundance ratios in the two nuclei. Our most conservative lower limit on the [H$^{13}$CN]/[H$^{13}$CO$^+$] abundance ratio is 11 in the WN, cf. 0.10 in the eastern nucleus (EN). Comparing these ratios to the literature we argue on chemical grounds for an energetically significant AGN in the WN driving either X-ray or shock chemistry, and a dominant starburst in the EN.
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