Day-night cold traps for TiO in hot Jupiter atmospheres

Temperature inversion leading to a hot stratosphere have been observed in some hot-Jupiter. Theoretical models predict that such a temperature inversion can be caused by the presence of a strong absorber in the visible in the high atmosphere. Titanium oxide have been proposed to be a good candidate for being this extra-absorber. Although the temperature in the day side of these planets can be high enough to maintain titanium oxide in a gaseous phase, it is not the case in the night side. In this work we discuss how the day/night temperature contrast can lead to the depletion of titanium oxide in the high atmosphere of hot-Jupiter. Using 1D and 3D models we found some constraints on the vertical diffusion coefficient needed to maintain enough titanium oxide in the upper atmosphere to create a temperature inversion. These constraints are similar to the ones given by Spiegel et al. (2009) for the vertical cold trap but hold for all the planets, even the ones that are too hot to be affected by the vertical cold trap