Simplified models of stellar wind anatomy for interpreting high-resolution data Analytical approach to embedded spiral geometries

Context. Recent high-resolution observations have shown that stellar winds harbour complexities that strongly deviate from spherical symmetry, which generally is assumed as standard wind model. One such morphology is the Archimedean spiral, which is generally believed to be formed by binary interactions, as has been directly observed in multiple sources. Aims. We seek to investigate the manifestation in the observables of spiral structures embedded in the spherical outflows of cool stars. We aim to provide an intuitive bedrock with which upcoming ALMA data can be compared and interpreted. Methods. By means of an extended parameter study, we modelled rotational CO emission from the stellar outflow of asymptotic giant branch stars. To this end, we developed a simplified analytical parametrised description of a 3D spiral structure. This model is embedded into a spherical wind and fed into the 3D radiative transfer code LIME, which produces 3D intensity maps throughout velocity space. Subsequently, we investigated the spectral signature of rotational transitions of CO in the models, as well as the spatial aspect of this emission by means of wide-slit position-velocity (PV) diagrams. Additionally, we quantified the potential for misinterpreting the 3D data in a 1D context. Finally, we simulated ALMA observations to explore the effect of interferometric noise and artefacts on the emission signatures. Results. The spectral signatures of the CO rotational transition v = 0 J = 3-2 are very efficient at concealing the dual nature of the outflow. Only a select few parameter combinations allow for the spectral lines to disclose the presence of the spiral structure. If the spiral cannot be distinguished from the spherical signal, this might result in an incorrect interpretation in a 1D context. Consequently, erroneous mass-loss rates would be calculated. The magnitude of these errors is mainly confined to a factor of a few, but in extreme cases can exceed an order of magnitude. CO transitions of different rotationally excited levels show a characteristical evolution in their line shape that can be brought about by an embedded spiral structure. However, if spatial information on the source is also available, the use of wide-slit PV diagrams systematically expose the embedded spiral. The PV diagrams also readily provide most of the geometrical and physical properties of the spiral-harbouring wind. Simulations of ALMA observations prove that the choice of antenna configuration is strongly dependent on the geometrical properties of the spiral. We conclude that exploratory endeavours should observe the object of interest with a range of different maximum-baseline configurations.