Carbonates and ices in the $z=0.89$ galaxy-absorber towards PKS 1830-211 and within star-forming regions of the Milky Way

A pair of 6.0 and 6.9 $\mu$m absorption features are frequently observed in Milky-Way (MW) molecular-clouds and YSOs; they also occur in the $z=0.886$ rest-frame of a molecule-rich spiral galaxy obscuring blazar PKS 1830-211. I calibrate $\chi^2$-fitting methods which match observations with two or three laboratory spectra. The 6.0-$\mu$m component is dominated by H$_2$O ice, as expected. Included MW sources were selected using opacity criteria which limit the range of explored H$_2$O-ice column densities to 1.6--$2.4 \times 10^{18}$ molecules cm$^{-2}$, while the H$_2$O-ice density in the galaxy absorber is $(2.7\pm 0.5)\times 10^{18}$ molecules cm$^{-2}$. CH$_3$OH ice and / or small (< 0.1-$\mu$m-sized) Ca- and Mg-bearing carbonates contribute at 6.9 $\mu$m. The 41 % CH$_3$OH : H$_2$O molecular ratio in the PKS 1830-211 absorber is significantly higher than in the molecular cloud towards Taurus-Elias 16 (<7.5 %) and similar to the highest value in MW YSOs (35 % in AFGL 989). Fitted carbonate (-CO$_3$) : H$_2$O ratios in the galaxy absorber of 0.091 % are low in comparison to most of the ratios detected in the MW sample (0.2 - 0.4 %; $\sim 0$ % in AFGL 989). Inorganic carbonates could explain the increased oxygen depletion at the diffuse-medium-to-molecular-cloud transition which Jones \& Ysard associated with unobserved organic carbonates or materials with a C:O ratio of 1:3.