Synthetic Spectra

In Figure 8 we display the spectral sequence of brown dwarfs to extrasolar giant planets (hereafter EGP) model atmospheres from ${\rm T}_{\rm eff}= 3000$ to 200K in the total gravitational settling (AMES-Cond) approximation. All dust opacity is neglected, but also all optical molecular opacity sources disappear due to the condensation of species involving Ti, V, Ca and Fe (TiO, VO, CaH, FeH, etc.), making these models transparent to the emergent radiation bluewards of 1.0 $\mu$m. Because of the absence of dust opacity, the photospheric layers are very cool compared to non-depleted atmospheres. The formation of optical atomic resonance lines and infrared molecular bands is then favored. We observe that water vapor bands (0.93, 0.95, 1.2, 1.4, 1.8, 2.5, and 5-10 $\mu$m in the window shown by this plot) increase rapidly in strength. Another striking consequence of the cool photospheric temperatures is the formation of CH₄ bands (3.5 and 6-10 $\mu$m, with weaker bands at 1.6 and 2.2 $\mu$m appearing in cooler models) already at 2000K. Methane gradually replaces water vapor bands while H₂O condenses out to ice below 300K.

One major feature of the AMES-Cond model spectra is the extraordinary growth of atomic resonance absorption lines at short wavelengths. have explored grainless models of methane dwarfs and found that van der Waals broadening of K I and Na I resonance optical lines can extend to several thousands of Angstroms on each side of the line cores. Our models behave similarly. Figure shows how the van der Waals wings of the Na I D and K I resonance lines at $\lambda$5891,5897Å and $\lambda$7687,7701Å completely depress the optical flux of cool brown dwarfs. In this case ( ${\rm T}_{\rm eff}= 1000$K, $\log g= 5.0$), the wings extend largely over 7000Å on each side of the line center. This is as large as hydrogen Balmer line wings in cool white dwarfs! However, to our knowledge, it is the first case of such behavior in metal lines encountered in stellar astronomy. While the van der Waals collisional C6 damping constant may be sufficiently accurate for the treatment of alkali element lines in the hydrogenic approximation in low mass stars and red dwarfs where these lines rarely exceed a width of 50Å, this treatment becomes questionable under these unprecedent conditions as also concluded by . Here, we observe for example that the red wings of these transitions prevents even a fraction of the flux from escaping in the J-band window around 1.25 $\mu$m, while observed spectral distributions of methane dwarfs tend to carry more flux in this window. The reason for such large line broadening is not the decreasing ${\rm T}_{\rm eff}$ of the photospheric gas pressure. It is rather, as also observed by for metal-depleted atmospheres, the result of the increasing transparency of the atmosphere which allows us to see deeper into the structure to inner high pressure depths. The line wing flux integrates therefore over an increasingly large column density of the atmosphere as optical molecular opacities vanish via condensation.

Figures and 11 display the change of the optical to red spectra as a function of temperature, where the gradual disappearance of TiO, VO, FeH, and CaH bands (by condensation of related species) and gradual strengthening of optical Na I D and K I lines becomes obvious. The TiO band systems ($\lambda$0.545, 0.616, 0.639, 0.665, 0.757, 0.774, 0.886 $\mu$m) become undetectable below 2000K, while the MgH ($\lambda$0.513 $\mu$m), CaH ($\lambda$0.694 and 0.706 $\mu$m), VO ($\lambda$0.829, 0.848 and 0.961 $\mu$m), FeH ($\lambda$0.990 $\mu$m) bands persist down to 1500K. The CrH bands at $\lambda$0.861 $\mu$m, already visible at 2500K in these AMES-Cond models, grow in strength as ${\rm T}_{\rm eff}$ decreases until it disappears by condensation of Cr₂O₃ below 900K. However, we must point out that red dwarfs are heavily reddened by dust opacities at least down to ${\rm T}_{\rm eff}= 2000$K, so that the Cond models overpredict the strength of CrH bands over that temperature range. Still, clearly the CrH bands become one of the strongest molecular system to be observed in the red spectra of cooler brown dwarfs.

From 2000K, we also see the H₂O band system at $\lambda$0.927 $\mu$m becoming increasingly stronger. The Na I D resonance doublet remains visible down to 400K, and K I already begins to get locked into dust below about 900K, a temperature typical of currently known methane dwarfs such as Gl229B. Other features growing in strength as ${\rm T}_{\rm eff}$ decreases are the lines of alkali elements such as Li I at $\lambda$6708Å, Rb I at $\lambda$7802 and 7949Å, Cs I at $\lambda$8523 and 8946Å, and Na I at $\lambda$8185Å. We also note the presence of diagnostic lines further in the near-infrared such as the K I doublet at $\lambda$11693,11776 and $\lambda$12436,12525Å,and a Na I line at $\lambda$11409Å.

The $\lambda$6708Å Li line, normally used to determine the substellar nature of brown dwarfs , remains detectable down to 700K. The Na I. Rb I and Cs I lines keep increasing in strength, but this is likely an artifact of the inevitable incompleteness of thermochemical databases in the construction of the chemical composition at these temperatures.

Thanks to R. Freedman (NASA-Ames), we were able to replace the band model approximation by a detailed line list for VO besides also being able to include CrH lines for which we had no previous counterparts. The result is that the present models show weaker VO bands, relative to TiO, strength than in previous models. A detailed comparison to high resolution observations of M and brown dwarfs is being published separately . However, note that the VO line list does not include C-X system at 0.75 $\mu$m. Our current models, therefore, overestimate the flux in the 0.75 $\mu$m region.

In Figure , we explore the behavior of the 4.55 $\mu$m CH₃D band system between ${\rm T}_{\rm eff}= 2000$ and 400K. At those wavelengths, H₂O provides the pseudo-continuum absorption. In the limit of the Cond models, CH₃D is practically undetectable until it begins to grow from 1000K to lower effective temperatures. The ammonia band at around 11 $\mu$m behaves similarly as can be seen from Figure 13. This is a result of the growing transparency of the atmosphere while water begins to condense in the uppermost layers of these Cond models. Note that although CO bands at 4.67 $\mu$m are not visible in Cond models with ${\rm T}_{\rm eff}\ge 1800$K, these bands do appear in corresponding brown dwarfs and stars. This is because the Cond limit does not apply for those dusty dwarfs.

In Figure 14, we present the full dusty (AMES-Dusty) limiting case from 2500 to 1500K. Here the strong heating effects of dust opacities prevent the formation of methane bands, and H₂O is dissociated while producing a hotter water vapor opacity profile, much weaker and more transparent to radiation. From 1700K, the grain opacity profiles rapidly dominate the UV to red spectral region, smoothing out the emergent flux into a continuum. Only the cores of the strongest atomic resonance lines (Na I D and K I) can be seen. The result is a spectral distribution guetting closer to the equivalent blackbody distribution of same effective temperature (see also Figure 20). Note however, that Dusty models can never be approximated by blackbodies because of the important optical-to-red dust veiling, and the strong near-IR water vapor bands. We have explored the effects of grain sizes on these models and found that for grains with sizes in the submicron to micron range, the increased cross-sections are compensated by the corresponding reduction in the number density of these grains given the conservation of the elemental abundance. For grains with sizes beyond 10 $\mu$m, an increased global opacity is found which produces even redder models. But grains are likely to be distributed in a spectrum of sizes where the balance between coagulation, sedimentation and condensation decides the upper limit of the masses reached. Preliminary calculations (T. Guillot, private communication) which will be published separately show that, when accounting for all the relevant processes, the grain sizes remain in the submicron range. We are therefore confident that the current models with grain sizes in the submicron range do constitute an adequate full dusty limit for these dwarfs.