Atmospheric Structures and Convection

The photospheric thermal structures of the AMES-Cond models with T $_{\rm eff}$ ranging from 3000 to 100K are displayed in Figure 5. The convection zones are labeled with cross-symbols. As ${\rm T}_{\rm eff}$ decreases, the photosphere becomes progressively more isothermal. While the convection zone retreats to deeper layers down to ${\rm T}_{\rm eff}= 1000$K, an outer convection zone begins to form in the clouds until this zone detaches itself from the inner convection regime in models cooler than 500K. Meanwhile, the inner convection continue to retreat inwards. This appears to confirm qualitatively earlier work by and . Yet even in our coolest models, the inner convection zone always reaches at least up to an optical depth of $\tau_{1.2 {\mu}m} = 10$. For ${\rm T}_{\rm eff}= 1000$K for example, the convection zone seems to be quite deeper in Burrows et al (1997) models (roughly P_gas > 100 bar as seen from their Figure 5) than in our models. Note that we treat the convection according to the Mixing Length Theory from the onset of the Schwarzchild criterion while Burrows et al (1997) assumed a pure adiabatic mixing throughout the convective unstable zones. But this appears to be a valid approximation since our calculations indicate that the true temperature gradient as predicted by the MLT remains within 0.05% of the adiabatic gradient value at each layer. So the difference appears to lie in the opacities included in the construction of the respective models: their models would be more transparent to radiation than ours.

The optical resonance lines of K I and Na I D also contribute significantly to the optical opacity and the heating of the atmospheric layers. We have explored their impact on the thermal structure of a ${\rm T}_{\rm eff}= 1000$K, $\log g= 5.0$, solar composition model. It appears that their opacity contribution accounts for 100 and 300K of heating in the photospheric ( $\log P = 5.5$) and internal ( $\log P = 8.5$) layers respectively. The models become unstable to convection further out when atomic lines are included ( $\log P = 7.76$versus 8.1). And uncertainties in the applicability of Lorentz profiles (estimated from models computed with restricted coverage of the line wing opacity contributions) produce a corresponding uncertainty of less than 40K in the photosphere and 150K in the internal layers. These uncertainties are therefore of little importance for the synthetic spectra and evolution models, compared to those tied to the treatment of the dust (Cond vs Dusty), and incomplete molecular opacities (e.g. H₂O opacity profile. See Allard, Hauschildt & Schwenke, 2000). However, neglecting the K I and Na I D doublet opacities altogether in the construction of the thermal structures has a greater impact and fully explains the difference between our models and those of Burrows et al (1997). Indeed, while our model at ${\rm T}_{\rm eff}= 500$K and $\log g= 5.0$do not present detached convection zones, we reproduce exactly the several detached convection zone found by these authors when neglecting atomic line opacity in the model construction. We must conclude from this that these opacities were neglected in their work. The reality of the occurrence of detached convection zone is therefore likely closer to our predictions.

The thermal structures of the fully dusty AMES-Dusty models over the T $_{\rm eff}$-range where dust begins to form (2500 to 1500K) are displayed in Figure 6 at constant gravity. The convection zone, marked by dotted lines, extends out to T _gas = 2500K is all these models. This corresponds to optically thin layers in models hotter than 1600K. Even down to 500K, these dusty atmospheres never become fully radiative. But the interesting part is what happens to photospheric regions as grain opacities begin to heat up the outer layers. Within the photosphere (marked by with full circles and triangles), the temperature normally decrease smoothly with decreasing ${\rm T}_{\rm eff}$, and the thermal structures parallel for grainless models. Here, the greenhouse effect of the dust tends to raise the temperature of the outer layers increasingly with decreasing ${\rm T}_{\rm eff}$. This has for effect that the outer structures level off between ${\rm T}_{\rm eff}= 2600$and 1800K to a T_gas-value in a narrow range between 1280 and 1350K. The slope of the thermal structure in the line forming region becomes therefore increasingly flatter in that ${\rm T}_{\rm eff}$-range. Below 1800K, the greenhouse effect saturates and the outer thermal structure resumes its decrease in temperature with decreasing ${\rm T}_{\rm eff}$. It is interesting to note that 1800K is also the break-up temperature where full-dusty atmospheres become unrealistic in modeling brown dwarfs. This can be seen from Figure 6 of and from Section below. We believe that grains sedimentation has certainly started at these temperatures as also concluded by , and .

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