Cosmo-tomography toward PKS 1830-211: Variability of the quasar and of its foreground molecular absorption monitored with ALMA

Context. Time variability of astronomical sources provides crude information on their typical size and on the implied physical mechanisms. PKS 1830-211 is a remarkable radio-bright lensed quasar with a foreground molecular absorber in the lens galaxy at z = 0.89. Small-scale morphological changes in the core-jet structure of the quasar - which is magnified by the lensing - result in a varying illumination of the absorber screen, which in turn causes variations in the absorption profile. Aims. We aim to study the time variations of the system (the two main lensed images of the quasar and the two corresponding sightlines in the absorber) in order to obtain constraints on both the quasar activity and small-scale structures in the interstellar medium of the absorber. Methods. We used ALMA to monitor the submillimeter continuum emission of PKS 1830-211, together with the absorption spectra of the H2O and CH molecules, with 17 visits spread over six months in 2016. Complementing this, we used available ALMA data to investigate changes in the system in the period 2012-2022. Results. From the continuum data, we followed the evolution of the flux density, flux-density ratio, spectral index, and differential polarization between the two lensed images of the quasar; all quantities show significant variations related to the intrinsic activity of the quasar. We propose a simple parametric model of a core plus a ballistic plasmon to account for the continuum evolution, from which we constrain a time delay of 25 +/- 3 days between main lensed images. The spectral lines reveal significant variations in the foreground absorption profile. A principal component analysis highlights apparent wavy time variations, possibly linked to the helical jet precession period of the quasar. From the deep averaged spectra towards the southwest image, we detect the absorption of the rare isotopolog (CH)-C-13 and estimate an abundance ratio of (CH)-C-12/(CH)-C-13 similar to 150. We also measure the oxygen isotopic ratios, O-16/O-18 = 65.3 +/- 0.7 and O-18/O-17 = 11.5 +/- 0.5 in the z = 0.89 absorber. Finally, we find a remarkable continuous shallow trough in the water absorption spanning a velocity interval of nearly 500 km s(-1). This broad absorption could be the signature of an extra-planar molecular component. Conclusions. All together, the system formed by the quasar PKS 1830-211 and its foreground lens-absorber acts as a powerful gravitational microscope, providing us with the possibility to dissect small-scale structures in both the ISM of the foreground absorber and the jet of the background quasar.