Atmospheric Structures and Convection

The photospheric thermal structures of the AMES-Cond models with
T
ranging from 3000 to 100K are displayed in
Figure 5. The convection zones are labeled with
cross-symbols. As
decreases, the photosphere becomes
progressively more isothermal. While the convection zone retreats to
deeper layers down to
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
.
For
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
K,
,
solar composition
model. It appears that their opacity contribution accounts for 100
and 300K of heating in the photospheric (
)
and internal
(
)
layers respectively. The models become unstable to
convection further out when atomic lines are included (
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. H_{2}O 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
K and
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
-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
,
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
.
This has
for effect that the outer structures level off between
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
-range. Below
1800K, the greenhouse effect saturates and the outer thermal structure
resumes its decrease in temperature with decreasing
.
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 .

.