Simulating the circumstellar H₂CO and CH₃OH chemistry of young stellar objects using a spherical physical-chemical model

Context. Young stellar objects (YSOs) and their environments are generally geometrically and dynamically challenging to model, and the corresponding chemistry is often dominated by regions in non-thermal equilibrium. In addition, modern astrochemical models have to consider not only gas-phase reactions, but also solid-state reactions on icy dust grains. Solving the geometrical, physical, and chemical boundary conditions simultaneously requires a high computational effort and still runs the risk of false predictions due to the intrinsically non-linear effects that can occur. As a first step, solving problems of reduced complexity is helpful to guide more sophisticated approaches. Aims. The objective of this work is to test a model that uses shell-like structures (i.e., assuming a power-law number density and temperature gradient of the environment surrounding the YSO) to approximate the geometry and physical structure of YSOs, that in turn utilizes an advanced chemical model that includes gas-phase and solid-state reactions to model the chemical abundances of key species. A special focus is set on formaldehyde (H2CO) and methanol (CH3OH) as these molecules can be traced in the gas phase but are produced on icy dust grains. Furthermore, this kind of molecule is believed to be key to understanding the abundance of more complex species. We compare the influence of the geometry of the object on the molecular abundances with the effect induced by its chemistry. Methods. We set up a model that combines a grain-gas phase chemical model with a physical model of YSOs. The model ignores jets, shocks, and external radiation fields and concentrates on the physical conditions of spherically symmetric YSOs with a density and temperature gradient derived from available spectral energy distribution observations in the infrared. In addition, new observational data are presented using the APEX 12 m and the IRAM 30 m telescopes. Formaldehyde and methanol transitions have been searched for in three YSOs (R CrA-IRS 5A, C1333-IRAS 2A, and L1551-IRS 5) that can be categorized as Class 0 and Class 1 objects, and in the pre-stellar core L1544. The observed abundances of H2CO and CH3OH are compared with those calculated by the spherical physical-chemical model. Results. Compared to a standard “ρ and T constant” model, i.e., a homogeneous (flat) density and temperature distribution, using number density and temperature gradients results in reduced abundances for the CO hydrogenation products formaldehyde and methanol. However, this geometric effect is generally not large, and depends on the source and on the molecular species under investigation. Although the current model uses simplified geometric assumptions the observed abundances of H2CO and CH3OH are well reproduced for the quiescent Class 1 object R CrA-IRS 5A. Our model tends to overestimate formaldehyde and methanol abundances for sources in early evolutionary stages, like the pre-stellar core L1544 or NGC 1333-IRS 2A (Class 0). Observational results on hydrogen peroxide and water that have also been predicted by our model are discussed elsewhere