Gas opacity

The opacity of the very inner part of the protoplanetary accretion disc is dominated by various gaseous species. Here, the temperature is too high for dust to be present.

Compared to the calculation of dust opacities, the calculation of accurate Rosseland and Planck mean gas opacities is more challenging due to the large variation in frequency, temperature, and density of the absorption coefficient of numerous molecules, atoms, and ions. In addition, the body of data to be handled easily amounts to several millions of absorption lines per molecule.

Missing data for absorption lines are critical for the calculation of Rosseland mean gas opacity since it is dominated by transparent spectral regions due to the harmonic nature of the averaging process. Therefore, each Rosseland mean is only a lower limit of the correct value. The opposite is true for the case of the Planck mean opacity - missing data for weak lines or bands cause an overestimation of the strong lines. Therefore, a Planck mean is always an upper limit of the case of ideally complete data.

The dust opacity model for protoplanetary accretion discs outlined in the previous sections is supplied by a new table of gas opacities assembled on the basis of Helling ([1999]) and Schnabel ([2001]). The chemical equilibrium routine and data have been updated. The gas opacity model is outlined in Helling et al. ([2000]) and only a short summary is given here. The Rosseland and the Planck mean opacities are calculated from opacity sampled lines lists. The data for the line absorption coefficients used in Helling et al. ([2000]) (CO - Goorvitch & Chackerian  [1994]; TiO - Jørgensen [1994]; SiO - Langhoff & Bauschilder [1993]; H$_2$O - Jørgensen & Jensen [1993]; CH - Jørgensen et al. [1996]; CN, C$_2$ - Jørgensen & Larsson [1990]; C$_3$ - Jørgensen [1989]; HCN, C$_2$H$_2$ - Jørgensen [1990]) were supplemented by data from the HITRAN96 database (CH$_4$, NH$_3$, HNO$_3$, H$_2$CO, CO$_2$, N$_2$O, O$_3$, SO$_2$, NO$_2$, HO$_2$, H$_2$, O$_2$, NO, OH, N$_2$). The opacity sampling of the latter was carried out by Schnabel ([2001]). The set of continuum opacities and scattering includes continuum absorption from H (Karzas & Latter [1961]), H$^-$ (John [1988]), H$+$H (Doyle [1968]), H$_2^-$ (Somerville [1964]), H$_2^+$ (Mihalas [1965]), He$^-$ (Carbon et al. [1969]), He, C, Mg, Al, Si (all from Peach [1970]) as well as Thompson scattering on free electrons and Rayleigh scattering for H and He (Dalgarno [1962]) and are the same like in Helling et al. ([2000]).

Using this approach, the Rosseland and Planck mean gas opacities were computed for temperature ranges between $500$ K and $10\,000$ K and for gas densities between $\sim 10^{-18}$ gcm$^{-3}$ and $\sim 10^{-7}$ gcm$^{-3}$. In contrast to the dust opacity, no simplified analytical expression can be found for the gas mean opacities because of there sensitive dependence on temperature and density. Thus, we apply a second-order interpolation in order to calculate the gas opacities for any given temperature and density value from tabulated values.