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We present an empirical determination of the mass-loss rate as a function ofstellar luminosity and effective temperature, for oxygen-rich dust-enshroudedAsymptotic Giant Branch stars and red supergiants. To this aim we obtainedoptical spectra of a sample of dust-enshrouded red giants in the LargeMagellanic Cloud, which we complemented with spectroscopic and infraredphotometric data from the literature. Two of these turned out to be hotemission-line stars, of which one is a definite B[e] star. The mass-loss rateswere measured through modelling of the spectral energy distributions. We thusobtain the mass-loss rate formula log Mdot = -5.65 + 1.05 log(L / 10,000 Lsun)-6.3 log(Teff / 3500 K), valid for dust-enshrouded red supergiants andoxygen-rich AGB stars. Despite the low metallicity of the LMC, both AGB starsand red supergiants are found at late spectral types. A comparison withgalactic AGB stars and red supergiants shows excellent agreement between themass-loss rate as predicted by our formula and that derived from the 60 micronflux density for dust-enshrouded objects, but not for optically bright objects.We discuss the possible implications of this for the mass-loss mechanism.

An empirical formula for the mass-loss rates of dust-enshrouded red supergiants and oxygen-rich Asymptotic Giant Branch stars