coupled ion and neutral rotating model of titan’s upper atmosphere v. de la haye et. al. (2008)

Coupled Ion and Coupled Ion and Neutral Rotating Neutral Rotating Model of Titan’s Model of Titan’s

Upper Upper AtmosphereAtmosphere

V. De La Haye et. al. (2008)V. De La Haye et. al. (2008)

Joseph WestlakeUniversity of Texas at San Antonio

Southwest Research [email protected]

Joseph Westlake ([email protected])

Coupled ion and neutral rotating Coupled ion and neutral rotating model of Titan’s upper atmospheremodel 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


Model HeritageModel Heritage


Ion Neutral Temp. Model: Ion Neutral Temp. Model: couplingcoupling


Ion Neutral Temp. Model:Ion Neutral Temp. Model: solar Flux at the top of the atmospheresolar 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)

0

50

100

150

200

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300

1980 1985 1990 1995 2000 2005

Years

F AV 10.

7 cm

Rad

io S

olar

Flu

x (s

.f.u

.)

-30

-20

-10

0

10

20

30

Subs

olar

Lat

itud

e (D

egre

es)

Voyager Cassini Flybys


Ion Neutral Temp. Model:Ion Neutral Temp. Model: solar flux through Titan’s upper solar flux through Titan’s upper

atmosphereatmosphere

• 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:Ion Neutral Temp. Model: electron fluxelectron 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:Ion Neutral Temp. Model: modeling the atmospheric neutralsmodeling 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:Ion Neutral Temp. Model: boundary conditions for the neutrals: 600 km / boundary conditions for the neutrals: 600 km /

exobaseexobase

• 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:Ion Neutral Temp. Model: modeling the exospheremodeling the exosphere

• Liouville TheoremDensity expressed as a function of the energy distribution of the particles at the exobase:


Ion Neutral Temp. Model:Ion Neutral Temp. Model: modeling the ionsmodeling the ions

• Photochemical equilibrium is assumed for the ions:

Production = Loss

- Newton-Raphson Technique


Ion Neutral Temp. Model:Ion Neutral Temp. Model: thermal structurethermal 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:Ion Neutral Temp. Model: the rotating model – time constants the rotating model – time constants

considerationsconsiderations

• 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:Ion Neutral Temp. Model: the rotating model – implementationthe 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 Composition: The neutral and ion species of the modelThe 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 ionsAdapted from Keller et al. (1998)


The Composition:The Composition: photo- and electron impact ionization and photo- and electron impact ionization and

dissociationsdissociations

• Nitrogen

• Methane

• Acetylene

• Ethylene

• Ethane

• H, H2, N, HCN, HC3N, C2N2


The Composition:The Composition: the main ion-neutral schemethe 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 Composition: the main ion-neutral scheme – production the main ion-neutral scheme – production

ratesrates

Local time dependent production rates for C2H4

Local time dependent production rates for H2CN+


The Composition:The Composition: subsequent production of key subsequent production of key

hydrocarbonshydrocarbons

Local time dependent production rates for C2H6

Note the influence of C2H5+ and

C3H7+


The Composition:The Composition: production of heavy hydrocarbons and key production of heavy hydrocarbons and key

ionsions

Local time dependent

production rates for c-C6H6


The Composition:The Composition: fixed temperature mode – first neutral density fixed temperature mode – first neutral density

resultsresults

• 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 Average Composition ComparisonComparison

• 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 In Progress and Future WorkWork

• Future Work:– Produce self

consistent thermal coupling.

– Receive and work with dynamical inputs from T-GITM.

– Constrain the exospheric inputs

Thank YouThank You

Joseph WestlakeUniversity of Texas at San Antonio

Southwest Research [email protected]


Ion Neutral Temp. Model:Ion Neutral Temp. Model: modeling the atmospheric neutrals - modeling the atmospheric neutrals -

implementationimplementation

• The Chemistry Equation:

• Crank Nicholson Scheme:

• 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)

• Triadiagonal Matrix:


Ion Neutral Temp. Model:Ion Neutral Temp. Model: modeling the ions - implementationmodeling 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


• HCN rotational cooling (Jared Bell)– Property of the HCN molecule

– Equations:

Shape of the rotational lines: voigt profile

Ion Neutral Temp. Model:Ion Neutral Temp. Model:thermal structure (2)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:

• Boundary conditions– Lower boundary: fixed

temperature– Upper boundary: zero gradient

coupled ion and neutral rotating model of titan’s upper atmosphere v. de la haye et. al. (2008)

Documents

neutral productionalso

t5 model

discretizationjoseph

heritagejoseph westlake

neutral species47 ions

d composition model

euvac model of richards

major species