Discussion and Conclusions

We have investigated the two limiting cases of dust in low mass stars and brown dwarfs atmospheres by comparing two sets of models: 1) AMES-Cond with models ranging from ${\rm T}_{\rm eff}= 3000$ to 100K in 100K step, and with gravities ranging from $\log g= 2.5$ to 6.0 in steps of 0.5 dex at solar metallicity, and 2) AMES-Dusty with models from ${\rm T}_{\rm eff}= 3000$ to 1400K in steps of 100K, with gravity ranging from $\log g= 3.5$ to 6.0 in steps of 0.5 dex. The AMES-Cond grid corresponds to the case where all dust has disappeared from the atmosphere by gravitational settling while the AMES-Dusty grid describes the case of negligible settling throughout the atmosphere. The two sets of models rely on the assumption that dust forms in equilibrium with the gas phase. See also for the corresponding evolution models of late type stars and brown dwarfs and a more detailed description of their photometric properties.

From the comparison of the two limits described here, and their comparisons to observations (see Section ), we find that dwarfs with ${\rm T}_{\rm eff}\ge 1800$K are successfully described by the full-dusty limit and conclude that dust must be in close equilibrium with the gas phase with little sedimentation, or compensated sedimentation effects. This would be the case if, for example, convective mixing was efficient in returning material to the line forming regions. We are exploring these issue by modeling, hydrodynamically, the convection in 3D models (Ludwig et al 2000, in preparation).

Observations of T dwarfs such as Gliese 229B indicate that brown dwarfs with ${\rm T}_{\rm eff}\le 1300$K are, on the other hand, more closely following the full-settling limiting case as has been shown also by and . However there has been a history of failure to explain the optical spectra of these cool brown dwarfs since the discovery of Gl229B. For example, claimed a veiling due to photo-dissociation by the parent starlight in the upper brown dwarf atmosphere. But this suggestion did not pass the acid test, and free-floating T dwarfs were discovered . Finally, and have stressed the importance of the $\lambda$5891,5897Å Na I D and $\lambda$7687,7701Å K I resonance doublets. Our analysis recover the latter results in predicting the red wings of these lines to heat up the photospheric thermal structure by as much as 100K, and to define the pseudo-continuum out to at least 1.1 $\mu$m in T dwarfs. This indicates that red flux out to 1.1 $\mu$m must be sensitive to gravity. We also find that the traditional Lorentz profile does not describe adequately their red wings, beyond 5000Å from the line center: it overestimate the wing opacity contribution. While this overestimation has negligible effects on the thermal structure as long as the lines are included in the calculation, it is important to realize that an adequate handling of the collisional broadening of alkali lines by H₂ and He must be developed in order to model successfully the optical to 1.1 $\mu$m flux and VRI colors of T dwarfs . Nevertheless we believe that our AMES-Cond models, limited in the coveraged of the atomic line wings contributions, can provide the full-settling limit that they were intended to define.

Based on the Cond models, we also find that currently known T dwarfs with effective temperatures around 1000K are in a special regime where several of their important spectral features start to reverse their behavior with decreasing ${\rm T}_{\rm eff}$: Cs I lines weaken as Cs begins to lock into CsCl, and CO and NH3 bands begin to grow in strength as a result of decreasing background opacities. While , , and all fail to reproduce these features in Gl229B with solar composition models in thermodynamic equilibrium, it is perhaps due to the fact that each of these spectral synthesis analysis were based upon thermal structures exempt of atomic line opacities? Indeed, in the fit to the overall spectrum, a sub-solar composition could compensate (via an increased pressure) for the neglect of atomic line opacities in the thermal structure calculations. To clarify the issue of the metallicity of Gl229B, we need to explore the composition of the parent star Gl229A. This work is in progress and will be published shortly. However, we feel that it is unlikely, though not impossible, that the first known T dwarfs be metal-deficient, while more massive brown dwarfs are only found in metal-rich environments.

There remains a regime between 1300 and 1800K where brown dwarfs should behave between these limits. We hope that our two sets of models can help bracket brown dwarf's properties and identify objects. They can also be used to evaluate the effects of intrinsic variability as weathering effects that cause clouds to form and vanish. The full-dusty models give the aspect of a cloudy atmosphere while the Cond models resemble a cloud-free sky.

In the atmospheres of brown dwarfs and late-type M dwarfs, the dust likely forms in clouds distributed more or less evenly across the dwarf's surface as we observe on planets. These cloud layers should be well-confined close to the deepest/hottest level where the grain-type can condense . But the physical process that defines this confinement of the cloud layers are not known. It could either be: i)an inefficient condensation of the dust in the upper atmosphere, or ii) an efficient gravitational settling (sedimentation) of the dust in those upper layers. Time-dependent grain growth analysis must be done to determine the first. This work is under progress at the Berlin University. But our CE calculations indicate that the local [T,P] conditions favor dust formation. The second can be understood by opposing sedimentation and convective mixing, one pushing the grains down, the other bringing upwards material to condense. Since the convection zone retreats progressively from the photosphere with decreasing ${\rm T}_{\rm eff}$, it seems to be a natural explanation of the fact that dust also retreats from the photosphere as ${\rm T}_{\rm eff}$ decreases. This is why we mention the potential importance of gravitational settling throughout this paper.

The Cond models represent a limiting case where these cloud layers are all sitting below the photosphere, independently of the cause for the cloud confinement. The Dusty models on the other hand represent a case where confinement does not occur. So it is clear that nature is likely between the Cond and Dusty limits, with partial gravitational settling occurring with a fraction that varies with depth in the atmosphere, the detailed modeling of this process relies on characteristic diffusion time scales for several processes such as condensation, sedimentation, coagulation and convective mixing to name a few which are not known accurately for the type of grains important under the conditions prevailing in brown dwarf atmospheres. Models incorporating these effects can therefore only be exploratory. The two limits described here will remain useful until the physics of these processes become solidly mastered.

All the models discussed in this paper are available upon request. We will also provide, as we have in the past, colors computed from these spectra on any requested color system. Please send requests to France Allard and consult the CRAL anonymous ftp site.

We wish to thank specially Richard Freedman (NASA-Ames) for joining us in the analysis of the VO and CrH line formation in M dwarfs and brown dwarfs, Hans G. Ludwig (Lund) for a lot of very instructive discussions and for his interest in dust formation in brown dwarfs, and Tristan Guillot (Obsv. de Nice) for his support and interesting collaborations to come. We thank also Gilles Chabrier, Isabelle Baraffe and Travis Barman for proofreading and providing some orientation to the draft. This research is supported by CNRS as well as NASA LTSA NAG5-3435 and a NASA EPSCoR grant to Wichita State University. Peter Hauschildt and Andreas Schweitzer acknowledge support in part from NASA ATP grant NAG 5-3018, NAG 5-8425 and LTSA grant NAG 5-3619 to the University of Georgia. Some of the calculations presented in this paper were performed on the IBM SP2 of the CINES, and the UGA UCNS at the San Diego Supercomputer Center (SDSC) and the Cornell Theory Center (CTC), with support from the National Science Foundation. We thank all these institutions for a generous allocation of computer time.

. But the physical process that defines this confinement of the cloud layers are not known. It could either be: i)an inefficient condensation of the dust in the upper atmosphere, or ii) an efficient gravitational settling (sedimentation) of the dust in those upper layers. Time-dependent grain growth analysis must be done to determine the first. This work is under progress at the Berlin University. But our CE calculations indicate that the local [T,P] conditions favor dust formation. The second can be understood by opposing sedimentation and convective mixing, one pushing the grains down, the other bringing upwards material to condense. Since the convection zone retreats progressively from the photosphere with decreasing ${\rm T}_{\rm eff}$, it seems to be a natural explanation of the fact that dust also retreats from the photosphere as ${\rm T}_{\rm eff}$ decreases. This is why we mention the potential importance of gravitational settling throughout this paper.

The Cond models represent a limiting case where these cloud layers are all sitting below the photosphere, independently of the cause for the cloud confinement. The Dusty models on the other hand represent a case where confinement does not occur. So it is clear that nature is likely between the Cond and Dusty limits, with partial gravitational settling occurring with a fraction that varies with depth in the atmosphere, the detailed modeling of this process relies on characteristic diffusion time scales for several processes such as condensation, sedimentation, coagulation and convective mixing to name a few which are not known accurately for the type of grains important under the conditions prevailing in brown dwarf atmospheres. Models incorporating these effects can therefore only be exploratory. The two limits described here will remain useful until the physics of these processes become solidly mastered.

All the models discussed in this paper are available upon request. We will also provide, as we have in the past, colors computed from these spectra on any requested color system. Please send requests to France Allard and consult the CRAL anonymous ftp site.

We wish to thank specially Richard Freedman (NASA-Ames) for joining us in the analysis of the VO and CrH line formation in M dwarfs and brown dwarfs, Hans G. Ludwig (Lund) for a lot of very instructive discussions and for his interest in dust formation in brown dwarfs, and Tristan Guillot (Obsv. de Nice) for his support and interesting collaborations to come. We thank also Gilles Chabrier, Isabelle Baraffe and Travis Barman for proofreading and providing some orientation to the draft. This research is supported by CNRS as well as NASA LTSA NAG5-3435 and a NASA EPSCoR grant to Wichita State University. Peter Hauschildt and Andreas Schweitzer acknowledge support in part from NASA ATP grant NAG 5-3018, NAG 5-8425 and LTSA grant NAG 5-3619 to the University of Georgia. Some of the calculations presented in this paper were performed on the IBM SP2 of the CINES, and the UGA UCNS at the San Diego Supercomputer Center (SDSC) and the Cornell Theory Center (CTC), with support from the National Science Foundation. We thank all these institutions for a generous allocation of computer time.