Can TiO Explain Thermal Inversions in the Upper Atmospheres of Irradiated Giant Planets?

Spitzer Space Telescope infrared observations indicate that several transiting extrasolar giant planets have thermal inversions in their upper atmospheres. Above a relative minimum, the temperature appears to increase with altitude. Such an inversion probably requires a species at high altitude that absorbs a significant amount of incident optical/UV radiation. Some authors have suggested that the strong optical absorbers titanium oxide (TiO) and vanadium oxide (VO) could provide the needed additional opacity. However, if regions of the atmosphere are cold enough for Ti and V to be sequestered into solids they might rain out and be severely depleted. With a model of the vertical distribution of a refractory species in gaseous and condensed form, we address the question of whether enough TiO (or VO) could survive aloft in an irradiated planet's atmosphere to produce a thermal inversion. We find that, without significant macroscopic mixing, a heavy species such as TiO -- especially one that can condense in a cold-trap region -- cannot persist in a planet's upper atmosphere. In our model, the amount of macroscopic mixing that would be required to loft TiO to millibar pressures ranges from ~10^7 to ~10^{11} cm^2/s on HD 209458b, HD 149026b, TrES-4, OGLE-TR-56b, and WASP-12b, depending on the planet and on assumed condensate sizes. Such large values may be problematic for the TiO hypothesis. [Abridged]