Simplified models of circumstellar morphologies for interpreting high-resolution data. Analytical approach to the equatorial density enhancement

Abstract: 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. 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. \emph{ALMA} data) using 3D models. We develop a simplified analytical parametrised description of a 3D EDE, with a 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 {\tt 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 \emph{ALMA} observations...