Day/night cold trap of TiO in hot Jupiters atmospheres Vivien Parmentier 1, Adam Showman 2, Tristan Guillot 1 1 Observatoire de la Côte d'Azur, Nice, France 2 Lunar and Planetary Lab, University of Arizona HD209458b Longitude Latitude 2000 K 800 K 1000 K 1200 K 1400 K 1600 K 1800 K

Ti ~ O ~ H ~ 1 Background : Abundance of Ti the solar nebula. Si ~

Background : Abundance of TiO2 in Aspen.

Background : presence of TiO/VO in brown dwarf TiO : Titanium oxyde Condensation temperature ~ 1800K at 1mbar ~ 2000K at 1bar The presence of the TiO absorption band define the separation between M dwarf and L dwarf. Martin et al DENIS J −643654

TiO / VO Hydrogene An additional absorber in the upper atmosphere can explain the presence of a temperature inversion Two classes of planets ? pL planets : close to their star, TiO is gaseous and there is a temperature inversion. pM planets, further away, colder, without temperature inversion. Titanium oxide, already observed in brown dwarf, is a good candidate for being this absorber. An extra-absorber explains the inversions ? Fortney et al Optical depth - τ

But might be depleted by the vertical cold trap if Kzz < 10 7 cm 2 /s. A certain amount of TiO at 1mbar f TiO = 0.5 f solar is needed in order to create the temperature inversion. Spiegel 2009 An extra-absorber explains the inversions ?

Temperature field of HD209458b P in bar Latitude (°) Longitude (°) 0 T (K) P~3days M~0.69Mj R~1.29Rj Stratosphere

Solid TiO Gaseous TiO Solid TiO Gaseous TiO T (K) P in bar 0 Latitude (°) Longitude (°) 0 Temperature field of HD209458b P~3days M~0.69Mj R~1.29Rj Stratosphere

P in bar Latitude (°) 0 Mean eastward velocities HD209458b U m/s Superotation on hot Jupiter See Adam Showman talk yesterday Showman & Polvani 2011 – Showman 2009 – Rauscher & Menou 2010 Dobbs-dixon 2008 – Heng 2010

The day/night cold trap Night side : Settling and diffusion Day side : Diffusion only

Questions Is the day/night cold trap strong enough to deplete the TiO for the dayside atmosphere ? Is it's reparation homogeneous over the planet ? What is the value of Kzz in the atmosphere of hot Jupiters ?

Diffusion : equations 3D – model big simulations 1D – highly idealized toy model A lot of approximations and simplifications...

1D- Numerical model Night side : Settling and diffusion Day side : Diffusion only

1D- Numerical model Night side : Settling and diffusion Day side : Diffusion only 2 parameters : Kp and Vp

Settling : final velocity of a droplet in the atmosphere Sphere of radius a falling in the fluid have a final velocity of : a V When the mean free path of the molecules becomes bigger than the size of the particle : Cunningham 1910

Cungingham velocity V m/s Settling : final velocity of droplets in the atmosphere P in bar Particle size in micrometer m/s 1m/s 0.1m/s

Results : abundance profiles P in bar a=1μm Kz=10 8 cm 2 /s f TiO < 0.5 f 0 at 1mBar

Results : abundance profiles P in bar a=1μm Kz=10 9 cm 2 /s f TiO ~ 0.5 f 0 at 1mBar

Results : abundance profiles P in bar a=1μm Kz=10 10 cm 2 /s f TiO > 0.5 f 0 at 1mBar

Kz in cm 2 /s Results: constrain on Kz Abundance at 1mBar Particle size (μm) Χ/Χ 0

Kz in cm 2 /s Results: comparison with the vertical cold trap Abundance at 1mBar Particle size (μm) Χ/Χ 0 Spiegel et al. 2009

Kz in cm 2 /s Abundance at 1mBar Particle size (μm) Χ/Χ 0 Results: comparison with the vertical cold trap Day/night cold trap for TiO should be as important as vertical cold trap. This gives greater constraints on Kz for very hot Jupiter Spiegel et al. 2009

Settling : Sinking timescale of droplets in the atmosphere

100μm case 3 days 9 days 10 days 7 days

2.5μm case Vertical slice at the equator Dayside zonal average ~10 days period variability ! Equatorial band more depleted than the poles

1μm 0.5μm 2.5μm 10μm Results : Abundance for Different sizes

Results : Abundances in HD209458b at 1mbar For condensates greater than a few micrometer, the atmosphere should be depleted in TiO

Nucleation is very fast for Tio (<1s) and will form particles of 0.01 to 0.1 micrometer (Helling 2001) Can particles grow that big ? All the TiO nucleates very fast and no more TiO is present to grow the particles. TiO2 grains might be used as a condensation site for other species, SiO2 for example Approximate growth time- scale of SiO2 grains.

Results : Abundances in HD209458b at 1mbar

Kz in cm 2 /s Results of the 1D model : constrain on Kz Abundance at 1mBar Particle size (μm) Χ/Χ 0

Results : Kzz in HD209458b at 1mbar Kzz ~ 1.5∙10 9 cm2/s

Conclusion → Day-Night cold trap should be as important as vertical cold trap for hot-Jupiters. It holds for all the hot- Jupiter → TiO should rain out if it condenses in particles are bigger than a few micrometer in the night side, else it should stay in the upper atmosphere and be able to create a temperature inversion → TiO condensates alone can't grow that big in hot-Jupiter atmosphere, it would need another species to condense, like SiO2 → Some variability of ~10 days period appear in the model. If confirmed, this could have interesting observational consequences. → We measure Kzz in HD209458b model atmosphere to be Kzz ~ 1.5∙10 9 cm2/s above 1bar I'm in Santa-Cruz until next June !