Dust in the Photospheric Environment: Unified Cloudy Models of M, L, and T Dwarfs

Abstract

We report an attempt to construct unified cloudy models of M, L, and T dwarfs. For this purpose, we first discuss opacities as well as thermochemical properties of the cool and dense matter. Below about 2000 K, refractory material condenses, and dust will play a major role as a source of opacity. Then a major problem in modeling the photospheres of very cool dwarfs is how to treat dust and, especially, how dust could be sustained in the static photosphere for a long time. Under the high density of the photospheres of cool dwarfs, dust forms easily at the condensation temperature, T cond , but the dust will soon grow larger than its critical radius r cr (at which the Gibbs free energy of condensation attains the maximum) at the critical temperature T cr . Such large dust grains with r gr ≳ r cr will soon segregate from the gas and precipitate below the photosphere. For this reason, dust exists effectively only in the limited region of T cr ≲ T ≲ T cond in the photosphere, and this means that a dust cloud is formed deep in the photosphere rather than in the cooler surface region. With this simple model of the dust cloud, we show that the nongray model photosphere in radiative-convective equilibrium can be extended to T eff values as low as 800 K. Since T cond ≈ 2000 K for the first condensates such as corundum and iron, the dust cloud is rather warm and necessarily located deeper in the photosphere (τ > 1) for the cooler objects (note that T ≈ T eff at τ ≈ 1). This explains why dust apparently shows little observable effect in T dwarfs. For warmer objects, the dust cloud, which is always formed at the same temperature range of T cr ≲ T ≲ T cond , can be located nearer the surface (τ < 1), and, for this reason, L dwarfs appear to be dusty. We show that the recently proposed spectral classification of L and T dwarfs can consistently be interpreted by a single grid of our unified cloudy models with the thin dust cloud deep in the photosphere.