Atacama Large Millimetre/sub-millimetre Array (ALMA) observations of the CO(1-0) and CO(2-1) emissions from the circumstellar envelope of the Asymptotic Giant Branch (AGB) star EP Aqr have been made with four times better spatial resolution than previously available. They are analysed with emphasis on the de-projection in space of the effective emissivity and flux of matter using as input a prescribed configuration of the velocity field, assumed to be radial. The data are found to display an intrinsic axi-symmetry with respect to an axis making a small angle with the line of sight. A broad range of wind configurations, from prolate (bipolar) to oblate (equatorial) has been studied and found to be accompanied by significant equatorial emission. Qualitatively, the effective emissivity is enhanced near the equator to produce the central narrow component observed in the Doppler velocity spectra and its dependence on star latitude generally follows that of the wind velocity with the exception of an omni-present depression near the poles. In particular, large equatorial expansion velocities produce a flared disc or a ring of effective emissivity and mass loss. The effect on the determination of the orientation of the star axis of radial velocity gradients and possibly competing rotation and expansion in the equatorial disc is discussed. In general, the flux of matter is found to reach a broad maximum at distances of the order of 500 au from the star. Arguments are given that may be used to prefer one wind velocity distribution to another. As a result of the improved quality of the data, a deeper understanding of the constraints imposed on morphology and kinematics has been obtained.
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