Spectroscopic determination of stellar masses: Mene, Mene, Tekel, Arcturus

The determination of stellar masses (i.e. surface gravities) from spectroscopic data requires, in principle, a complete understanding of stellar atmospheric structure, including the effects of turbulence and convection, departures from LTE and plane parallel structure, and variations in abundances of individual elements. Where very accurate data are available, as for Arcturus, it becomes clear that the uncertainties in derived effective temperatures, surface gravities, and abundances are both rather larger and somewhat more interdependent than is usually supposed. As a result, it takes surprisingly large error bars, e.g. M = 0.7 +- 0.5 solar mass, to bracket all modern determinations of the mass of Arcturus. Here it is discussed why this is so and what, if anything, can be done about it. (author)