Coupled Ion and Neutral Rotating Model of Titan’s Upper Atmosphere V. De La Haye et. al. (2008)

1. Coupled Ion and Neutral Rotating Model of Titan’s Upper AtmosphereV. De La Haye et. al. (2008) Joseph Westlake University of Texas at San Antonio Southwest Research Institute joseph.westlake@swri.edu

2. Coupled ion and neutral rotating model of Titan’s upper atmosphere • Included processes • Photodissociation • Neutral chemistry • Ion-neutral chemistry • Electron recombination to neutral production • Also has a simplified chemical scheme (19 species) • TA and T5 model runs published in De La Haye et al. (2008) • 1-D composition model. • 36 neutral species • 47 ions • Both solar and magnetospheric energy inputs included • Rotation to account for diurnal variations • Constant latitude

3. Model Heritage

4. Ion Neutral Temp. Model: coupling

5. Ion Neutral Temp. Model:solar Flux at the top of the atmosphere • Solar flux at the top of the atmosphere: • Method developed by Bougher et al. based on Torr and Torr (1985) and on the EUVAC model of Richards et al (1994) • Inputs: F10.7 cm and FAv10.7cm • Output wavelength bins: • 14 FUV (1050-1750 Å) • Lyman alpha (1215.7 Å) • 37 EUV bins (50-1050 Å) • 3 soft X-ray bins (16-50 Å)

6. Ion Neutral Temp. Model:solar flux through Titan’s upper atmosphere • Soft X-ray and EUV absorbed by major species: • N2 (16 -1450Å) • CH4 (1000 -1450Å) • Less energetic photons penetrate deeper and are absorbed by minor species: • C2H2, C2H4, C2H6, HC3N, …

7. Ion Neutral Temp. Model:electron flux • Electrons • Saturn’s magnetospheric electrons • (traveling along magnetic field lines) • Photoelectrons & secondary electrons • Model of Gan et al. (1992) • Electron energy code •  thermal electrons (Maxwellian) • Two stream transport code •  suprathermal electrons Gan et al. (1992)

8. Ion Neutral Temp. Model:modeling the atmospheric neutrals • Vertical transport • Equation for major and minor species • Molecular diffusion (Ds) for a multi-component gas • Eddy diffusion (K) fixed (INMS Data) / • Chemistry • Crank-Nicholson Scheme for Discretization

9. Ion Neutral Temp. Model:boundary conditions for the neutrals: 600 km / exobase • Upper boundary • 1- Varying exobase altitude • Note: • Cases separated for H2 and H, • compared to N2 and other species • 2- Thermal escape • Important for H and H2 • Negligible for all other species • Lower boundary • Total density: • hydrostatic equilibrium starting • from a data point using the • temperature and mean molecular • mass of the last iteration • Non reactive species: • Fixed mixing ratio • Reactive species • (short lifetime < TTitan/100) •  Photochemical equilibrium

10. Ion Neutral Temp. Model:modeling the exosphere • Liouville Theorem • Density expressed as a function of the energy distribution of the particles at the exobase:

11. Ion Neutral Temp. Model:modeling the ions • Photochemical equilibrium • is assumed for the ions: • Production = Loss - Newton-Raphson Technique

12. Ion Neutral Temp. Model:thermal structure • The thermal structure of Titan’s upper atmosphere is still in question: • UVIS data  presence of a mesopause • UVIS and CIRS data + hydrostatic equilibrium  cannot match INMS data • CIRS and INMS data  no mesopause • Most runs use a fixed temperature profile • Self consistent thermal structure is in progress. • The thermal • structure model: • Heat transfer equation • Two sources of energy: • Solar photons • Magnetospheric electrons • One cooling mechanism: • Radiation in the • HCN rotational lines

13. Ion Neutral Temp. Model:the rotating model – time constants considerations • Comparison of the time constants: • Time constants for neutral chemistry, diffusion and thermal structure are comparable to a Titan rotation •  zenith angle variation with day and night should be taken into account. • The ion lifetimes are extremely short •  assumed to be • instantaneous • Chemistry can be • neglected for N2 and CH4 • at altitudes >900 km • compared to diffusion • Expressions • used for the • time constants: / /

14. Ion Neutral Temp. Model:the rotating model – implementation • Division into local time sectors: • Constant latitude / varying zenith angle • Constant magnetospheric inputs • Wind component taken into account Muller-Wodarg et al. 2000

15. The Composition:The neutral and ion species of the model • 35 neutrals • inspired from Lebonnois et al. (2001) and Wilson & Atreya (2004) • Excited states of atomic nitrogen: N(2D), N(2P) • Excited state of methylene: 1CH2 • Excited state of cyanoacetylene: HC3N* • Excited state of acetylene: C2H2** • 47 ions • Adapted from Keller et al. (1998)

16. The Composition:photo- and electron impact ionization and dissociations • Nitrogen • Acetylene • Ethylene • Ethane • Methane • H, H2, N, HCN, HC3N, C2N2

17. The Composition:the main ion-neutral scheme • The chemical scheme starts from the photo- and electron impact dissociation and ionization of Nitrogen and Methane • Note: • This scheme is self- • sufficient and shows • the major production • mechanisms for each • of the species present • except CH3.

18. The Composition:the main ion-neutral scheme – production rates • Local time dependent production rates • for C2H4 Local time dependent  production rates for H2CN+

19. The Composition:subsequent production of key hydrocarbons Local time dependent  production rates for C2H6 Note the influence of C2H5+ and C3H7+

20. The Composition:production of heavy hydrocarbons and key ions Local time dependent  production rates for c-C6H6

21. The Composition:fixed temperature mode – first neutral density results • Run of the ion-neutral coupled model • Fixed temperature mode • Rotating mode • Lower boundary mixing ratios: • From Lebonnois (2001) • Adjusted to fit the INMS data • Diurnal average density profiles of the main components for the TA and T5 conditions

22. Average Composition Comparison • From Magee et al. (submitted). • Compares INMS measurements between 1000 and 1100 km to the De La Haye et al. (2008) TA and T5 model runs. • Good correspondence with the major neutrals. • HCN and other light, short-lived neutrals are affected heavily by dynamics (see Bell et al.).

23. Work In Progress and Future Work • Future Work: • Produce self consistent thermal coupling. • Receive and work with dynamical inputs from T-GITM. • Constrain the exospheric inputs

24. Thank You Joseph Westlake University of Texas at San Antonio Southwest Research Institute joseph.westlake@swri.edu

25. Ion Neutral Temp. Model:modeling the atmospheric neutrals - implementation • The Chemistry Equation: • Crank Nicholson Scheme: • Triadiagonal Matrix: • Solved for all species simultaneously using the Thomas algorithm • Transform the tridiagonal matrix into an upper-triangular matrix then compute the unknown densities by taking into account the upper and lower boundary conditions and using back substitution (Tannehill et al., 1997)

26. Ion Neutral Temp. Model:modeling the ions - implementation • Newton-Raphson Technique • To find the root of a function F(x) = 0, first expand in a Taylor series about the estimated root xn: • To improve the estimated root at each iteration (xn+1, xn+2,…) • Perform this technique for this function: • The Jacobian matrix is given by: Where Which finally gives

27. Ion Neutral Temp. Model:thermal structure (2) • Heat transfer equation: • Conductivity for a gas mixture • Solar Absorption: • Absorption of the energy of the magnetospheric e-: • ~ 40 eV per ion-electron pair • Global heating efficiencies: • HCN rotational cooling (Jared Bell) • Property of the HCN molecule • Equations: • Shape of the rotational lines: voigt profile • Boundary conditions • Lower boundary: fixed temperature • Upper boundary: zero gradient