Dust Clouds Construction and Opacities

In this paper, we account for the dust opacity only in the limiting case of the AMES-Dusty models where gravitational settling is neglected and which are relevant for the analysis of hot red dwarfs. In these models, cloud layers build up automatically following the condensation equilibrium which determines the atmospheric layers occupied by the grains. The study of the jovian planets suggests that cloud layers are not generally distributed homogeneously over the atmospheric surface. But if the nucleation process of dust grains is favored by a combination of high gas densities and low gas temperatures, hotter red dwarfs could be expected to retain more easily smaller grains in their photosphere, and have them more uniformly distributed over the stellar surface. In this work, we account for the average effect of the presence of clouds on the model structures and emitted spectra. We therefore assume a plane-parallel symmetry, i.e. an homogeneous distribution of clouds across the surface of the brown dwarfs. The spectral distribution of a brown dwarf with a more complex ring pattern of clouds familiar to jovian planets could, in the end, be reconstructed from a mosaic of the present models until a full three dimensional calculation becomes possible.

Early attempts to compute the opacities of grains were made by and . More detailed calculations, including the effects of chemical equilibrium calculations and grain size distributions were reported by and . have described the computation of the opacity of grains with the inclusion of equilibrium condensation abundances, the effects of the distribution of grain sizes, and the effect of grain shape through the Continuous Distribution of Ellipsoid (CDE) model of . These calculations included the absorption and scattering due to magnesium silicates, iron, carbon, and silicon carbide grains for a wide range of chemical compositions down to 700 K. We have explored the CDE method employed by Alexander & Ferguson, but have retained a purely spherical shape of the grains in the present study for simplicity. Another difference with Alexander & Ferguson is that, instead of approximating the number density of grains indirectly, these quantities are now provided by our chemical equilibrium as described in Section . 26 new condensates have been added to the original list of Fe, C, SiC and magnesium silicates, for a total of 30 among which are MgSiO₃, Mg₂SiO₄, Al₂O₃ and MgAl₂O₇, using polarizability constants from laboratory studies by , , , and . Figure  and 2 suggest that the calcium silicates can also play an important role in the opacity of brown dwarf atmospheres. In fact, complex calcium silicates (here Ca₂Al₂SiO₇, Ca₂MgSi₂O₇, and CaMgSi₂O₆) are amoung the most abundant species in the layers where these grains are present. Since, for the latter two species, no data were available to construct their opacity profiles, we have simulated their opacity using the profile of Ca₂Al₂SiO₇. We includes in general, more accurate number densities, and better and more complete cross-sections of dust grains than included in . Updated Rosseland and Planck opacities computed with these updated opacities will be published in more details separately .

The opacity profiles of these grains are shown in Figure . Most spectral distributions seen in this plot are pure absorption profiles. Scattering contributes only at UV to optical wavelengths for the grain sizes adopted. Corundum, enstatite, forsterite, hematite, magnetite, and Ca₂Al₂SiO₇ have absorption cross-sections exceeding those of water vapor. In a brown dwarf atmosphere, however, water is at least two orders of magnitudes more abundant then most of these grain species, so that water vapor remains the leading opacity source between 1 and 8 $\mu$, and beyond 20 $\mu$m. In other words, grains do not contribute significantly to the opacities in the near-infrared where water bands still dominate the brown dwarf spectra from J to K (1.0 to 3 $\mu$m). We have demonstrated in Section 2 that grain species have concentrations similar to those of TiO, VO and most other optical absorbers. The impact of the grain opacities is, therefore, to enhance and gradually replace the optical opacities as these gas phase species disappear via condensation.

The extinction caused by grains in a stellar atmosphere also depends on the rate of grain formation and the resulting size distribution. For all grains included we have assumed, as in Alexander & Ferguson, an interstellar size distribution of the grains with diameters ranging from 0.00625 to 0.24 $\mu$m. For comparison, and assumed grains with a fixed diameter of 0.1 $\mu$m in their model atmosphere calculations. Although those choices are purely arbitrary, the consequences are minimal since the grain diameter cancels out in the opacity calculations as long as: (1) abundance conservation is assumed i.e. larger grains must lock more particles, reducing the number of grains per gram of stellar plasma, and, (2) that the cross-sections behave in the Rayleigh limit, i.e. the wavelength is larger than the size of the grains. Our tests, shown in Figure , confirm that this is the case for 1 to 10 $\mu$m-size grains, but they also indicate that the scattering increases rapidly for sizes larger than 10 $\mu$m, i.e. when the Rayleigh limit beaks down over the wavelengths carrying flux in these objects. But even is the opacities are sensitive to the grain sizes beyond the Rayleigh regime, the enormous scattering effects seen for 100 $\mu$m grains in Figure 4 seems to exclude the presence of such grains in brown dwarfs. We therefore believe that such large grains tend rapidly to become larger by coagulation to be eliminated by sedimentation in these high-gravity atmospheres. An accurate answer to this question can only come from time-dependent grain growth calculations incorporating the effects of sedimentation, diffusion, coagulation and coalescence for the conditions prevailing in brown dwarfs atmospheres. See for a detailed description of the dust opacities used in the present models.

for a detailed description of the dust opacities used in the present models.