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

We present an empirical determination of the mass-loss rate as a function of stellar luminosity and effective temperature, for oxygen-rich dust-enshrouded Asymptotic Giant Branch stars and red supergiants. To this aim we obtained optical spectra of a sample of dust-enshrouded red giants in the Large Magellanic Cloud, which we complemented with spectroscopic and infrared photometric data from the literature. Two of these turned out to be hot emission-line stars, of which one is a definite B[e] star. The mass-loss rates were measured through modelling of the spectral energy distributions. We thus obtain the massloss rate formula log. M = - 5.65 + 1.05 log(L/10 000 L-circle dot) - 6.3 log(T-eff/3500 K), valid for dust-enshrouded red supergiants and oxygen-rich AGB stars. Despite the low metallicity of the LMC, both AGB stars and red supergiants are found at late spectral types. A comparison with galactic AGB stars and red supergiants shows excellent agreement between the mass-loss rate as predicted by our formula and that derived from the 60 mu m flux density for dust-enshrouded objects, but not for optically bright objects. We discuss the possible implications of this for the mass-loss mechanism.