1. A Time-Evolving, Transonic Numerical Atmospheric Model: Description, Validation, and Application to Hydrodynamic Loss Chris Parkinson Institut d’Astrophysique de Paris Seminar June 14, 2005

2. Introduction  Hydrodynamic Escape from Planetary Atmospheres  What is hydrodynamic escape (HDE)?  Why develop a new model for planetary atmospheres: what questions are we trying to answer?  How is this new model being developed?  Recent results and current/future work  Hydrodynamic Escape from Planetary Atmospheres  What is hydrodynamic escape (HDE)?  Why develop a new model for planetary atmospheres: what questions are we trying to answer?  How is this new model being developed?  Recent results and current/future work

3.  In Jean’s escape, particles at the exobase can escape from the planet, typically the vertical flow from the atmosphere is small  HDE arises when the flow speed becomes large  In Jean’s escape, particles at the exobase can escape from the planet, typically the vertical flow from the atmosphere is small  HDE arises when the flow speed becomes large Hydrodynamic Escape from Planetary Atmospheres

4.  For HDE, a substantial fraction of the thermospheric energy budget powers escape of gas from the atmosphere; it is possible that heavier species can be “dragged” along during HDE  In this case atmospheric expansion due to HDE will be the dominant loss process  For HDE, a substantial fraction of the thermospheric energy budget powers escape of gas from the atmosphere; it is possible that heavier species can be “dragged” along during HDE  In this case atmospheric expansion due to HDE will be the dominant loss process

5.  HDE is an important process in atmospheric evolution of the terrestrial planets and CEGPs (Close-in Extrasolar Giant Planets)  can change the composition from primordial values irreversibly  hydrogen escape important as it can affect the oxidation state of the atmosphere and because it results in the loss of water vapour on terrestrial planets  HDE is an important process in atmospheric evolution of the terrestrial planets and CEGPs (Close-in Extrasolar Giant Planets)  can change the composition from primordial values irreversibly  hydrogen escape important as it can affect the oxidation state of the atmosphere and because it results in the loss of water vapour on terrestrial planets

6. Why do we need a new HDE for planetary atmospheres? To understand this, you first need to understand: What questions do we want to answer?

7. For Instance…(outstanding problems)  Did early Venus initially have an ocean? (Kasting and Pollack, 1983)  Isotopic ratios (i.e. fractionation: D/H, N, and noble gases) are very different on terrestrial planets even though they are believed to be formed from similar material (Hunten et al., 1987; Pepin, 1991)  Did early Venus initially have an ocean? (Kasting and Pollack, 1983)  Isotopic ratios (i.e. fractionation: D/H, N, and noble gases) are very different on terrestrial planets even though they are believed to be formed from similar material (Hunten et al., 1987; Pepin, 1991)

8. and…  Greenhouse warming by methane in the atmosphere of the early Earth? CH 4 density on early Earth dependent on HDE, strongly influencing its atmospheric climate and composition, i.e. (Pavlov et al., 2000; 2001)  “blow-off” on HD209458b (Osiris) (Vidal-Madjar et al., 2003; 2004)  Greenhouse warming by methane in the atmosphere of the early Earth? CH 4 density on early Earth dependent on HDE, strongly influencing its atmospheric climate and composition, i.e. (Pavlov et al., 2000; 2001)  “blow-off” on HD209458b (Osiris) (Vidal-Madjar et al., 2003; 2004)

9. EarthMarsTitan CO 2 atmosphere P surf ~ 610 Pa T surf ~ 210 K Very eccentric orbit Major topography Dust storms N 2 atmosphere P surf ~ 1.5x10 5 Pa T surf ~ 93 K Thick haze layers Methane ‘hydrology’ Slowly rotating N 2 atmosphere P surf ~ 1x10 5 Pa T surf ~ 288 K Water cycle Oceans & land surfaces

10. By Vidal-Madjar, A. Hydrodynamic Escape

11. HD Escape Equations

12. What is an hydrodynamic escape model (HDE)? Core solver Problem specific code WENO (weighted essentially non-oscillatory) finite difference scheme with AMR (adaptive mesh refinement); Lax-Friedrichs scheme, Godonov scheme, etc. Generally is conceptually (and practically) split into two components: Everything else regarding the physics of our particular problem: geometric considerations, tidal forces, viscosity, heating, gravity etc.

13.  Watson et al. (1981): shooting method to solve steady state HDE equation for early Earth and Venus  Kasting and Pollack (1983) solve the steady state HDE problem for Venus  Chassefiere (1996) solves steady state HDE problem with application to water- rich early Cytherian atmosphere  Watson et al. (1981): shooting method to solve steady state HDE equation for early Earth and Venus  Kasting and Pollack (1983) solve the steady state HDE problem for Venus  Chassefiere (1996) solves steady state HDE problem with application to water- rich early Cytherian atmosphere Some Previous Models (Time Independent)

14. Previous models (Time Dependent)  Gombosi et al. (1985) uses Godonov technique to resolve 3-D time-dependent dusty gas dynamical flow near cometary nuclei  Tian et al. (2005) uses Lax-Friedrichs method previously used by Toro (1999), LeVeque (1999) and de Sterck (2001) to discuss transonic hydrodynamic escape flow from extrasolar planetary atmospheres; 1-D model, solving very simple,non-extreme cases…not extensible to higher dimensional calculations  Gombosi et al. (1985) uses Godonov technique to resolve 3-D time-dependent dusty gas dynamical flow near cometary nuclei  Tian et al. (2005) uses Lax-Friedrichs method previously used by Toro (1999), LeVeque (1999) and de Sterck (2001) to discuss transonic hydrodynamic escape flow from extrasolar planetary atmospheres; 1-D model, solving very simple,non-extreme cases…not extensible to higher dimensional calculations

15.  A new technique has been developed for the treatment of hydrodynamic loss processes from planetary atmospheres  A WENO (weighted essentially non- oscillatory) finite difference scheme with AMR (adaptive mesh refinement) is employed.  overcomes the instabilities inherent in modelling transonic conditions by solving the coupled, time dependent mass, momentum, and energy equations, instead of integrating time independent equations.  A new technique has been developed for the treatment of hydrodynamic loss processes from planetary atmospheres  A WENO (weighted essentially non- oscillatory) finite difference scheme with AMR (adaptive mesh refinement) is employed.  overcomes the instabilities inherent in modelling transonic conditions by solving the coupled, time dependent mass, momentum, and energy equations, instead of integrating time independent equations.

16. Results to date  Core solver has been validated in three dimensions including simple chemistry etc in a computational study of turbulent mixing at the Caltech ASC Centre (D. Hill, 2003) for a WENO-centred, finite difference method suitable for large-eddy simulation of strong shocks (i.e. Richtmeyer-Meshkov (RM) instability) in a rectangular tube with end-wall shock reflection and reshock of the evolving mixing layer.  I have developed/validated a 1-D model of HDE against existing cases in the literature for a simple heating function in a hydrostatic atmosphere for Titan and the Earth using this core solver.  Results: time evolving gnuplot graphs and RM instability video  Core solver has been validated in three dimensions including simple chemistry etc in a computational study of turbulent mixing at the Caltech ASC Centre (D. Hill, 2003) for a WENO-centred, finite difference method suitable for large-eddy simulation of strong shocks (i.e. Richtmeyer-Meshkov (RM) instability) in a rectangular tube with end-wall shock reflection and reshock of the evolving mixing layer.  I have developed/validated a 1-D model of HDE against existing cases in the literature for a simple heating function in a hydrostatic atmosphere for Titan and the Earth using this core solver.  Results: time evolving gnuplot graphs and RM instability video

17. Final Remarks and Future Directions:  Validate model against simple cases of Tian et al. (2000) and address deficiencies in paper  Add tidal force terms and more complicated heating terms (code done, just interface)  The technique is extensible to two and three dimensions and for cases of physical interest involving light hydrogen gas moving through a heavier gas such as N 2 lower in the atmosphere or quantifying the observed blow-off on the extrasolar planet Osiris.  To solve the problem properly, we need to go to higher dimension calculations!  Add chemistry appropriate to planetary atm.