The spectra of UCDs are dictated by their atmospheric physics and properties, and a proper understanding thereof should thus allow accurate predictions of UCD properties and ultimately their evolutionary behaviour. Several models have been produced that try to explain the changes in the spectral and photometric characteristics that are observed for L and T dwarfs and to explain what happens at the transition between the two subclasses. These models can have very different effects on the resulting spectra and colours, depending on how they treat dust in the atmosphere (e.g. the amount of dust, grain size and composition). Traditionally stellar modelling relied on gray models that lacked any inclusion of dust, but clearly this is not the case for UCDs, where dust plays a significant role in the underlying physics, shaping their appearance.
Lyon (Phoenix) group models
The NextGen models (Baraffe et al. 1998) were some of the first models produced to try and physically describe the appearance of UCDs, they do not include dust grains, but take into account opacities, however they tend only to be useful for Teff>1700K. The latest
results from the Lyon group present two model scenarios, one to explain the hotter, redder L dwarfs, known as the DUSTY models (Chabrier et al. 2000a; Baraffe et al. 2002) and the COND (condensate) models (Allard et al. 2001; Baraffe et al. 2003) that try to explain the cooler, bluer T dwarfs (both models are for solar metallicity scenarios). The models use mixtures of several hundred gas and liquid species and opacities of more than 30 types of sub-micron sized dust grains, including Aluminium, Magnesium and Calcium silicates. For this they assume that dust forms in equilibrium with the gas phase. The DUSTY models are applied to temperatures ∼3000-1400K and log g=3.5-6.0 and take into account both the formation and opacity caused by dust grains. They describe reasonably well the NIR colours and spectra of early-mid L dwarfs, where Teff>1800K but the predicted optical
colours show discrepancies from observations on the order of 0.2-0.3 mags. The COND models take into account the formation of dust but no effects of atmopheric opacity, representing the dust-free appearance and general bluer colours of T dwarfs. This model is presented for Teff from 3000-700K and log g=2.5-6.0. The properties of UCDs with
Teff≤1300K are better described by the COND models than the DUSTY models. These
models both struggle to reproduce observations seen at the transition between late L to early T dwarfs, suggesting that at this stage dust seen in the photosphere of L dwarfs primarily forms lower in the atmosphere of T dwarfs, and gravitationally settles below the photosphere, with the observed atmosphere being relatively dust-free. They state that these models used together represent extremes that might be expected in the properties of UCDs.
AMES models
The AMES group (Marley et al. 2002; Saumon et al. 2003) produced models using a self-consistent treatment of cloud formation. They suggest that i − z colour is extremely sensitive to chemical equilibrium assumptions, having an affect of up to ∼2 mags on colour. They consider not only the sedimentation of condensates but also the efficiency of the process to help explain both L and T dwarfs and the L/T transition with the same model, for solar metallicity. As such they attempt to represent an intermediate
between the DUSTY and COND extremes. In this case the cloud decks are confined to a fraction of the pressure scale height and the models assume that it is sedimentation that controls vertical mixing in the clouds, causing the observed turnover in J − K colour with decreasing Teff. They also take into account grain sizes between 10-100µm and assume
that if the grain size is less than the observed wavelength of light, Rayleigh scattering dominates and has little affect on opacity. The problems with this model are that while it predicts the overall trend seen by observations, the finer details are not matched, e.g. the peak of the model value in J − K is not as red as that observed, and the models predict a move to bluer colours that is much slower than is actually observed.
Tsuji models
The models of Tsuji, Nakajima & Yanagisawa (2004) use an empirical unified cloud model for cases of log g=4.5-5.5, where they assume the dust column density is relative to that of the gas column density in the photosphere for this range of log g. Their initial models assumed that dust forms everywhere, as long as the thermodynamic conditions are right for condensation (Tsuji, Ohnaka & Aoki 1996). However this was only good for predicting the colours of late M and early L dwarfs. Their latest models include the segregation of dust from gaseous mixing at a corresponding critical temperature (TCR; related to the
temperature of condensation). Dust then remains in the photosphere of warm dwarfs where Teff>TCRis optically thick. In cooler dwarfs where Teff<TCR, producing an optically
thin region and the dust is segregated and precipitated. This model represents the L/T transition reasonably well on a colour-magnitude diagram and from spectra, however the detailed behaviour does not match observations (e.g. see the J − K, MJ diagram in Tsuji
& Nakajima 2003). Tuscon models
Burrows, Sudarsky & Hubeny (2006) use a model of refractory clouds, coupled with the latest gas-phase molecular opacities for dust molecules, similar to those used by the Lyon group. They also look at the effects of gravity and metallicity and vary grain size, cloud scale height and cloud distribution, applicable over a Teff=2200-700K range. They show
generally good agreement with the observed spectra of NIR colours for early-mid L and mid-late T dwarfs and by varying gravity parameters get a closer fit to the L/T transition than other models. However they do not reproduce the apparent brightening seen in the
J- band at the transition, nor the dimming at very late T. They suggest that the L/T transition is likely related to gravity and possibly metallicity but needs better explanation. As yet no self-consistent model has been presented that can reproduce the observed characteristics of L and T dwarfs and how they evolve from one type to the other consis- tently in both optical and NIR colours and spectra. It seems evident that the treatment of dust plays a vital part in fully understanding the underlying physical processes at work. Also the affects of gravity and metallicity are largely ignored by the models, with the exception of the latest Burrows models and may also play a significant role.