| Abstract
| - Context. Equatorial density enhancements (EDEs) are a very common astronomical phenomenon. Studies of the circumstellar environments (CSE) of young stellar objects and of evolved stars have shown that these objects often possess these features. These are believed to originate from different mechanisms, ranging from binary interactions to the gravitational collapse of interstellar material. Quantifying the effect of the presence of this type of EDE on the observables is essential for a correct interpretation of high-resolution data. Aims. We seek to investigate the manifestation in the observables of a circumstellar EDE, to assess which properties can be constrained, and to provide an intuitive bedrock on which to compare and interpret upcoming high-resolution data (e.g. ALMA data) using 3D models. Methods. We develop a simplified analytical parametrised description of a 3D EDE, with possible substructure such as warps, gaps, and spiral instabilities. In addition, different velocity fields (Keplerian, radial, super-Keplerian, sub-Keplerian and rigid rotation) are considered. The effect of a bipolar outflow is also investigated. The geometrical models are fed into the 3D radiative transfer code LIME, that produces 3D intensity maps throughout velocity space. We investigate the spectral signature of the J = 3−2 up to J = 7−6 rotational transitions of CO in the models, as well as the spatial aspect of this emission by means of channel maps, wide-slit position-velocity (PV) diagrams, stereograms, and spectral lines. Additionally, we discuss methods of constraining the geometry of the EDE, the inclination, the mass-contrast between the EDE and the bipolar outflow, and the global velocity field. Finally, we simulated ALMA observations to explore the effects of interferometric noise and artefacts on the emission signatures. Results. The effects of the different velocity fields are most evident in the PV diagrams. These diagrams also enable us to constrain the EDE height and inclination. A level of degeneracy may occur in the shapes of individual PV diagrams for different global velocity fields. The orthogonal PV diagrams may completely eliminate this ambiguity. Information on the EDE substructure is evident in the channel maps, but cannot be recovered from the PV diagrams, nor from the spectral lines. However, stereograms enable the detection of warping. For most inclinations the spectral lines are relatively broad, making it difficult to distinguish from an eventual superposed bipolar outflow component. Only under low inclination angles can one distinguish between these structures. Simulations of synthetic ALMA observations show how emission is affected when the largest angular scale of an antenna configuration is exceeded. For a rotating EDE, the emission around zero velocity will first fade because of destructive interference.
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