Modelling the radio emission of the gas envelope of evolved axially symmetric stars

Pham Ngoc Diep, P.T. Nhung, P.T. Anh, P. Darriulat, H.T. Dat, D.T. Hoai, N.T. Phuong & N.T. Thao

Vietnam National Satellite Center

The unprecedented quality of the observations available from the Atacama Large Millimetre/sub-millimetre Array (ALMA) calls for analysis methods making the best of them. We address this issue in the context of the study of the radio emission of the gaseous circumstellar envelopes of evolved stars. Such stars, being in a transition phase between spherically symmetric stars and Planetary Nebulae of irregular shapes, often display an approximately axially symmetric configuration of the wind velocity. The issue of reconstructing in space their morphology and kinematics is addressed in the approximation of rotational invariance about a well-defined star axis. In a first part, a systematic use of simulated observations allows for identifying the main problems and for constructing quantities aimed at solving them. In particular the evaluation of the orientation of the star axis in space and the differentiation between expansion along the star axis and rotation about it are given special attention. The use of polar rather than Cartesian sky coordinates is shown to better match the morphology and kinematics of actual stars, which are functions of the star latitude and of the radial distance. The radial dependence of the gas density and temperature and the possible presence of velocity gradients are briefly considered. In a second part, the results obtained in the first part are applied to a few real stars taken as examples with the aim of evaluating their usefulness when applied to concrete cases. A third part takes stock of what precedes and attempts at formulating some guidelines for modelling the radio emission of evolved stars, limited however to the mathematics and geometry of the problem, physics considerations being ignored. The aim is to help developing analysis methods allowing for more reliable and more quantitative conclusions than previously possible, in particular for a better understanding of the uniqueness and limitations of the proposed models.

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