AB Aur is a Herbig Ae star that hosts a prototypical transition disk. The disk shows a plethora of features connected with planet formation mechanisms. Understanding the physical and chemical characteristics of these features is crucial to advancing our knowledge of planet formation. We aim to characterize the gaseous disk around the Herbig Ae star AB Aur. A complete spectroscopic study was performed using NOEMA to determine the physical and chemical conditions. We present new observations of the continuum and 12CO, 13CO, C18O, H2CO, and SO lines. We used the integrated intensity maps and stacked spectra to derive estimates of the disk temperature. By combining our 13CO and C18O observations, we computed the gas-to-dust ratio along the disk. We also derived column density maps for the different species and used them to compute abundance maps. The results of our observations were compared with Nautilus astrochemical models. We detected continuum emission in a ring that extends from 0.6 to 2.0 arcsec, peaking at 0.97 and with a strong azimuthal asymmetry. The molecules observed show different spatial distributions, and the peaks of the distributions are not correlated with the binding energy. Using H2CO and SO lines, we derived a mean disk temperature of 39 K. We derived a gas-to-dust ratio that ranges from 10 to 40. The comparison with Nautilus models favors a disk with a low gas-to-dust ratio (40) and prominent sulfur depletion. From a very complete spectroscopic study of the prototypical disk around AB Aur, we derived, for the first time, the gas temperature and the gas-to-dust ratio along the disk, providing information that is essential to constraining hydrodynamical simulations.Moreover, we explored the gas chemistry and, in particular, the sulfur depletion. The derived sulfur depletion is dependent on the assumed C/O ratio. Our data are better explained with C/O ~ 0.7 and S/H=8e-8.
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