Optical properties of non-stoichiometric amorphous silicates with application to circumstellar dust extinction

Optical constants of non-stoichiometric amorphous magnesium-iron silicates are determined. It is demonstrated that these can well reproduce the observed mid-infrared emission spectra of evolved stars. Stoichiometric and non-stoichiometric amorphous magnesium-iron silicate films are fabricated by pulsed laser deposition. Transmittance and ellipsometry measurements are performed in the wavelength range between 2 and 200 $\mu$m and 1.7 and 33 $\mu$m, respectively. Optical constants are derived from transmittance and ellipsometric $\Psi$ and $\Delta$ spectra by means of oscillator models. The optical constants are applied in radiative transfer models for examining reproducibility of the observed spectral features of circumstellar dust shells around supergiants. The spectra of four selected supergiants are dominated by amorphous silicate dust emission in the wavelength range of 9 and 25 $\mu$m. To obtain a good fit to the observed spectra, we take into account amorphous corundum and metallic iron particles as additional dust components to account for dust emission at $\lambda<8 \mu$m and in between the two silicate features. For each of the objects, a set of model parameters (dust mass, condensation temperature) is derived by an automated optimization procedure which well reproduces the observation. Consequently, our model spectra using the new optical data find that the silicate bands at $\approx 10$ and $\approx 18 \mu$m depend on the magnesium and iron ratio in the silicate system, and that a good fit requires a significant iron content of the amorphous silicate dust component to reproduce the observed peak positions and shape of the silicate bands.