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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 email@example.com
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
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)
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, …
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)
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
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
Ion Neutral Temp. Model:modeling the exosphere • Liouville Theorem • Density expressed as a function of the energy distribution of the particles at the exobase:
Ion Neutral Temp. Model:modeling the ions • Photochemical equilibrium • is assumed for the ions: • Production = Loss - Newton-Raphson Technique
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
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: / /
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
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)
The Composition:photo- and electron impact ionization and dissociations • Nitrogen • Acetylene • Ethylene • Ethane • Methane • H, H2, N, HCN, HC3N, C2N2
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.
The Composition:the main ion-neutral scheme – production rates • Local time dependent production rates • for C2H4 Local time dependent production rates for H2CN+
The Composition:subsequent production of key hydrocarbons Local time dependent production rates for C2H6 Note the influence of C2H5+ and C3H7+
The Composition:production of heavy hydrocarbons and key ions Local time dependent production rates for c-C6H6
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
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.).
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
Thank You Joseph Westlake University of Texas at San Antonio Southwest Research Institute firstname.lastname@example.org
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)
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
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