Space reconstruction of the morphology and kinematics of axisymmetric radio sources

Abstract

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. Reconstructing in space the morphology and kinematics of radio sources is an underdetermined problem that requires imposing additional constraints for its solution. The hypothesis of rotational invariance, which is a good approximation to, or at least a good reference for the description of the gas envelopes of many evolved stars and protostars, is particularly efficient in this role. In the first part of the article, 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 to display the results of the analysis is shown to often better match the morphology and kinematics of actual stars. The radial dependence of the gas density and temperature and the possible presence of velocity gradients are briefly considered. In the second part, these results are applied to a few 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 formulates some guidelines for modelling the radio emission of axisymmetric radio sources, limited however to the mathematics and geometry of the problem, physics considerations being generally ignored.

The nascent wind of AGB star R doradus: evidence for a recent episode of enhanced mass loss

“…The main sources of anisotropy are rotation, expansion and local excesses or depletions that may be caused, for example, by turbulence, shocks or the presence of a stellar or planetary companion. Rotation about an axis projecting at position angle θ on the plane of the sky (Diep et al 2016;Nhung et al 2018) produces a sine wave modulation of the xVz asymmetry that cancels for θ = ±90 • and has amplitude proportional to sin i, where i is the angle of the rotation axis with the line of sight (the z axis). Radial expansion does not produce any anisotropy if it is spherical but does if it is axisymmetric about the axis of rotation and enhanced near the poles or near the equator.…”

“…When enhanced near the poles, it also produces a sine wave modulation of the xVz asymmetry, that is instead maximal for θ = ±90 • . The combination of bipolar expansion and rotation about a same axis produces a sine wave with a phase-shift θ0 that depends on the relative importance of expansion with respect to rotation (Diep et al 2016;Nhung et al 2018).…”

High-resolution ALMA observation of the 12CO(3–2) and 350 GHz continuum emissions of the debris disc of 49 Ceti

“…The point is simply that the emission observed at large values of |x|, namely at large disc radii, contributes more than what is observed along lines of sight pointing to x = 0. We define (Diep et al 2016) the effective emissivity ρ(x, y, z) as…”

Astrophysics research at DAP

“…A number of evolved stars at different stages of evolution and different orientations in space have been studied at DAP using observations of the high resolution continuum and line emissions from dust grains and gas molecules [8][9][10][11][12][13][14][15]. Methods to study and reconstruct in space axisymmetric radio sources (a common feature of young and old stars) have been developed to this effect [16,17]. A review of studies made by the team in this field, dealing with the presence of high Doppler velocity wings in the spectra of O-rich AGB stars, is presented elsewhere in these Proceedings [18].…”