3D mixing in hot jupiters atmospheres: I. application to the day/night cold trap in hd 209458b

Context. Hot Jupiters exhibit atmospheric temperatures ranging from hundreds to thousands of Kelvin. Because of their large day-night temperature differences, condensable species that are stable in the gas phase on the dayside-such as TiO and silicates-may condense and gravitationally settle on the nightside. Atmospheric circulation may counterbalance this tendency to gravitationally settle. This three-dimensional (3D) mixing of condensable species has not previously been studied for hot Jupiters, yet it is crucial to assess the existence and distribution of TiO and silicates in the atmospheres of these planets. Aims. We investigate the strength of the nightside cold trap in hot Jupiters atmospheres by investigating the mechanisms and strength of the vertical mixing in these stably stratified atmospheres. We apply our model to the particular case of TiO to address the question of whether TiO can exist at low pressure in sufficient abundances to produce stratospheric thermal inversions despite the nightside cold trap. Methods. We modeled the 3D circulation of HD 209458b including passive (i.e. radiatively inactive) tracers that advect with the 3D flow, with a source and sink term on the nightside to represent their condensation into haze particles and their gravitational settling. Results. We show that global advection patterns produce strong vertical mixing that can keep condensable species aloft as long as they are trapped in particles of sizes of a few microns or less on the nightside. We show that vertical mixing results not from small-scale convection but from the large-scale circulation driven by the day-night heating contrast. Although this vertical mixing is not diffusive in any rigorous sense, a comparison of our results with idealized diffusion models allows a rough estimate of the effective vertical eddy diffusivities in these atmospheres. The parametrization K _zz=5 × 10⁴/P_bar m²s ^-1Kzz=5 × 104Pbarm2s-1, valid from ~1 bar to a few μbar, can be used in 1D models of HD 209458b. Moreover, our models exhibit strong spatial and temporal variability in the tracer concentration that could result in observable variations during either transit or secondary eclipse measurements. Finally, we apply our model to the case of TiO in HD 209458b and show that the day-night cold trap would deplete TiO if it condenses into particles bigger than a few microns on the planet's nightside, keeping it from creating the observed stratosphere of the planet.