Determining the forsterite abundance of the dust around asymptotic giant branch stars

Aims. We present a diagnostic tool to determine the abundance of the crystalline silicate forsterite in AGB stars surrounded by a thick shell of silicate dust. Using six infrared spectra of high mass-loss oxygen rich AGB stars we obtain the forsterite abundance of their dust shells. Methods. We use a monte carlo radiative transfer code to calculate infrared spectra of dust enshrouded AGB stars. We vary the dust composition, mass-loss rate and outer radius. We focus on the strength of the 11.3 and the 33.6 μm forsterite bands, that probe the most recent (11.3 μm) and older (33.6 μm) mass-loss history of the star. Simple diagnostic diagrams are derived, allowing direct comparison to observed band strengths. Results. Our analysis shows that the 11.3 μm forsterite band is a robust indicator for the forsterite abundance of the current mass-loss period for AGB stars with an optically thick dust shell. The 33.6 μm band of forsterite is sensitive to changes in the density and the geometry of the emitting dust shell, and so a less robust indicator. Applying our method to six high mass-loss rate AGB stars shows that AGB stars can have forsterite abundances of 12% by mass and higher, which is more than the previously found maximum abundance of 5%.