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Towards detecting methanol emission in low-mass protoplanetary discs with ALMA: The role of non-LTE excitation

The understanding of organic content of protoplanetary discs is one of the main goals of the planet formation studies. As an attempt to guide the observational searches for weak lines of complex species in discs, we modelled the (sub-)millimetre spectrum of gaseous methanol (CH$_3$OH), one of the simplest organic molecules, in the representative T Tauri system. We used 1+1D disc physical model coupled to the gas-grain ALCHEMIC chemical model with and without 2D-turbulent mixing. The computed CH$_3$OH abundances along with the CH$_3$OH scheme of energy levels of ground and excited torsional states were used to produce model spectra obtained with the non-local thermodynamic equilibrium (non-LTE) 3D line radiative transfer code LIME. We found that the modelled non-LTE intensities of the CH$_3$OH lines can be lower by factor of $>10$--$100$ than those calculated under assumption of LTE. Though population inversion occurs in the model calculations for many (sub-)millimetre transitions, it does not lead to the strong maser amplification and noticeably high line intensities. We identify the strongest CH$_3$OH (sub-)millimetre lines that could be searched for with the Atacama Large Millimeter Array (ALMA) in nearby discs. The two best candidates are the CH$_{3}$OH $5_0-4_0~A^+$ (241.791 GHz) and $5_{-1}-4_{-1}~E$ (241.767 GHz) lines, which could possibly be detected with the $\sim5σ$ signal-to-noise ratio after $\sim3$ hours of integration with the full ALMA array.