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We aim to (1) set up simple and general analytical expressions to estimatemass-loss rates of evolved stars, and (2) from those calculate estimates forthe mass-loss rates of asymptotic giant branch (AGB), red supergiant (RSG), andyellow hypergiant stars in our galactic sample. Rotationally excited lines ofCO are a very robust diagnostic in the study of circumstellar envelopes (CSEs).When sampling different layers of the CSE, observations of these molecularlines lead to detailed profiles of kinetic temperature, expansion velocity, anddensity. A state-of-the-art, nonlocal thermal equilibrium, and co-moving frameradiative transfer code that predicts CO line intensities in the CSEs oflate-type stars is used in deriving relations between stellar andmolecular-line parameters, on the one hand, and mass-loss rate, on the other.We present analytical expressions for estimating the mass-loss rates of evolvedstellar objects for 8 rotational transitions of the CO molecule, apply them toour extensive CO data set covering 47 stars, and compare our results to thoseof previous studies. Our expressions account for line saturation and resolvingof the envelope, thereby allowing accurate determination of very high mass-lossrates. We argue that, for estimates based on a single rotational line, theCO(2-1) transition provides the most reliable mass-loss rate. The mass-lossrates calculated for the AGB stars range from 4x10^-8 Msun/yr up to 8x10^-5Msun/yr. For RSGs they reach values between 2x10^-7 Msun/yr and 3x10^-4Msun/yr. The estimates for the set of CO transitions allow time variability tobe identified in the mass-loss rate. Possible mass-loss-rate variability istraced for 7 of the sample stars. We find a clear relation between thepulsation periods of the AGB stars and their derived mass-loss rates, with alevelling off at approx. 3x10^-5 Msun/yr for periods exceeding 850 days.

astronomy and astrophysics

Probing the mass-loss history of AGB and red supergiant stars from CO  rotational line profiles - II. CO line survey of evolved stars: derivation of  mass-loss rate formulae