1. 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

2. Ti ~ 10 -7 O ~ 10 -3 H ~ 1 Background : Abundance of Ti the solar nebula. Si ~ 10 - 4.5

3. Background : Abundance of TiO2 in Aspen.

4. 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. 2010 DENIS J0006579−643654

5. 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. 2008 Optical depth - τ

6. 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 ?

7. Temperature field of HD209458b 10 -5 10 -3 10 -1 10 -180 -9090 P in bar 180 0 Latitude (°) 90 -90 45 -45 Longitude (°) 0 T (K) P~3days M~0.69Mj R~1.29Rj Stratosphere

8. Solid TiO Gaseous TiO Solid TiO Gaseous TiO T (K) 10 -5 10 -3 10 -1 10 P in bar 0 Latitude (°) 90 -90 45 -45 -180 -9090 180 Longitude (°) 0 Temperature field of HD209458b P~3days M~0.69Mj R~1.29Rj Stratosphere

9. 5000 4000 3000 2000 1000 0 -1000 10 -5 10 -3 10 -1 10 -9090 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

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

11. 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 ?

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

13. 1D- Numerical model Night side : Settling and diffusion Day side : Diffusion only

14. 1D- Numerical model Night side : Settling and diffusion Day side : Diffusion only 2 parameters : Kp and Vp

15. 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

16. Cungingham velocity V m/s Settling : final velocity of droplets in the atmosphere P in bar Particle size in micrometer 1101000.1 100 1 10 -2 10 -4 10 -6 10 4 100 1 10 -2 10 -4 10m/s 1m/s 0.1m/s

17. Results : abundance profiles P in bar 10 -6 10 -4 10 -2 1 100 0 0.2 0.4 0.6 0.8 1 a=1μm Kz=10 8 cm 2 /s f TiO < 0.5 f 0 at 1mBar

18. Results : abundance profiles P in bar 10 -6 10 -4 10 -2 1 100 0 0.2 0.4 0.6 0.8 1 a=1μm Kz=10 9 cm 2 /s f TiO ~ 0.5 f 0 at 1mBar

19. Results : abundance profiles P in bar 10 -6 10 -4 10 -2 1 100 0 0.2 0.4 0.6 0.8 1 a=1μm Kz=10 10 cm 2 /s 0 0.2 0.4 0.6 0.8 f TiO > 0.5 f 0 at 1mBar

20. Kz in cm 2 /s 10 12 10 11 10 10 9 10 8 10 7 0.1110100 1 0.6 0.8 0.4 0.2 0 Results: constrain on Kz 10 13 Abundance at 1mBar Particle size (μm) Χ/Χ 0

21. Kz in cm 2 /s 10 12 10 11 10 10 9 10 8 10 7 0.11 10 100 1 0.6 0.8 0.4 0.2 0 Results: comparison with the vertical cold trap 10 13 Abundance at 1mBar Particle size (μm) Χ/Χ 0 Spiegel et al. 2009

22. Kz in cm 2 /s 10 12 10 11 10 10 9 10 8 10 7 0.11 10 100 1 0.6 0.8 0.4 0.2 0 10 13 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

23. Settling : Sinking timescale of droplets in the atmosphere

24. 100μm case 3 days 9 days 10 days 7 days

25. 2.5μm case Vertical slice at the equator Dayside zonal average ~10 days period variability ! Equatorial band more depleted than the poles

26. 1μm 0.5μm 2.5μm 10μm Results : Abundance for Different sizes

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

28. 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.

29. Results : Abundances in HD209458b at 1mbar

30. Kz in cm 2 /s 10 12 10 11 10 10 9 10 8 10 7 0.1110100 1 0.6 0.8 0.4 0.2 0 Results of the 1D model : constrain on Kz 10 13 Abundance at 1mBar Particle size (μm) Χ/Χ 0

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

32. 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 !