The Model Atmosphere

We use the model atmosphere code PHOENIX (version 10.8). The original versions of PHOENIX were developed for the modeling of novae and supernovae ejecta described by , and is dotted of a detailed radiative transfer that allows for spherical symmetry. Its more recent application to cool dwarfs is described in detail by , and has served to generate grids of stellar model atmospheres which successfully described low mass stars in globular clusters and the galactic disk main sequence . These former model grids are known to the stellar community as the 1995 Extended and the 1996-1999 NextGen models, and allowed a preliminary incursion into the regime of evolved brown dwarfs down to T $_{\rm eff} = 1600\,$K (Extended models) and to 900K . These models successfully predicted the general spectroscopic properties of evolved brown dwarfs prior to the discovery of Gliese 229B, which then helped confirm its very cool brown dwarf nature . Yet the lack, in these essentially stellar models, of dust condensation in the chemical equilibrium made them inadequate to model in detail such cool objects.

The addition to PHOENIX of the treatment of condensation in the chemical equilibrium, and of dust clouds, as described in Sections and 3, was completed in 1996 , and served to compute M dwarfs and brown dwarfs model atmospheres, synthetic spectra and broadband colors for specific analysis and interior models . In this paper we present the final version of these models in two limiting cases: (1) ``AMES-Dusty'' which include both the dust formation in the chemical equilibrium and opacities, and; (2) ``AMES-Cond'' which include the effects of condensation in the chemical equilibrium but ignores the effects of dust opacities altogether. This latter case is computed to explore the case where dust grains have formed, but have disappeared completely (eg by sedimentation i.e. settling below the photosphere). These two model sets also distinguish themselves from the standard NextGen models by the use of the NASA AMES H₂O and TiO line lists while the NextGen models were computed using the line list. This choice is motivated by the incompleteness of the 1994 lists to high gas temperatures (T _gas > 2000K) as discussed in .

For the purpose of this analysis, we use the radiative transfer in plane-parallel mode. The convective mixing is treated according to the Mixing Length Technique (MLT). We consider pressure-dependent line-by-line opacity sampling treatment for both atomic and molecular lines in all models. We do not pre-tabulate or re-manipulate the opacities in any way: PHOENIX includes typically $\approx\ 15\times 10^{6}$ molecular and atomic transitions which are re-selected at each model iteration and each atmospheric depth point from our data base described above. The lines are selected from three representative layers of the atmosphere at each model iteration to ensure consistency of the calculation. Van der Waals pressure broadening of the atomic and molecular lines is applied as described by . We neglect the effects of convective motion on line formation since the velocities of the convection cells are too small to be detected in low-resolution spectra and will have a negligible influence on the transfer of line radiation.

A trial atmospheric profile is applied, the equations of hydrostatic and radiative transfer are solved, and the solution is tested until convergence is reached. The model is considered converged when the energy is conserved within a tenth of a percent from layer to layer. At each of the model iterations, a spectrum with typically over 30,000 points is generated which samples the bolometric flux from 0.001 to 500 $\mu$m with a step of 2Å in the region where most of the flux is emitted (i.e. 0.1 to 10 $\mu$m). The final spectrum must generally be degraded to the instrumental resolution before being compared to low-resolution observations of stars and brown dwarfs. The model atmospheres are characterized by the following parameters: (i) the surface gravity, $\log(g)$, (ii) the effective temperature, ${\rm T}_{\rm eff}$, (iii) the mixing length to scale height ratio, $\alpha$, here taken to be unity, (iv) the micro-turbulent velocity $\xi$, here set to $2\hbox{$\,$ km$\,$ s$^{-1}$ }$, and (v) the element abundances taken from .

For this paper we have calculated a uniform grid of AMES-Cond models ranging from ${\rm T}_{\rm eff}= 3000$ to 100K in 100K steps, and with gravities ranging from $\log g= 2.5$ to 6.0 in steps of 0.5 dex at solar metallicity. The AMES-Dusty grid was calculated 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. All models were fully converged.

Although PHOENIX can treat the effects of external radiation fields on the model atmosphere and the synthetic spectrum , we assume here a negligible external radiation field for simplicity. It is clear, however, that UV radiation impinging on the brown dwarf, from a hotter companion, will change the structure of the atmosphere and the corresponding spectra. We are investigating these effects in a separate publication .

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