hydrogen and methane in titan's atmosphere:...

Hydrogen and Methane in Titan's Atmosphere: Chemistry, Diffusion, Escape, and

the Hunten Limiting Flux Principleby

Darrell F. Strobel

Johns Hopkins University

&

Jun Cui

Nanjing University

Refs: Strobel, D. F, Canadian J. Phys., Don Hunten Memorial Issue, in press, 2012; Strobel, D. F., and J. Cui, Titan’s Upper Atmosphere/Exosphere, Escape Processes and and Rates, to appear in Titan: Surface, Atmosphere and Magnetosphere , eds: I. Mueller-Wodarg, C. Griffith, E. Lellouch, T. Cravens, Cambridge University Press / Cambridge Planetary Science Series, 2012.

http://www.telegraph.co.uk/�

For a multi component low Mach # fluid (N₂, CH₄, H₂, Ar) the individual conservation of momentum equations are

The effects of eddy diffusion are incorporated in thecontinuity equation

w/ Pre Cassini escape rates: CH4 ,7.6×1024, H2 3.2×1027 s⁻¹

ExobaseTwo problems for CH4:1. 3525 km density too high2. Scale height too large

Kn = 1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 km

Titan Low: blue; Titan Limiting: red; INMS data: black dashed

Limiting escape rates: CH4 ,1.5×10²⁷, H2 9.4×10²⁷ s⁻¹Low escape rates: CH4 ,7.6×1024, H2 3.2×1027 s⁻¹

Magenta: H2 limiting; CH4 LowNote CH4 mole fraction is too

large at all altitudes

Kn =1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 km

Note the lower boundary for these calculations was the surface!

Upper Atmosphere: CH4 from INMS measurements

The N2 and CH4 number densities at altitudes below 2000 km acquired during the inbound T25 flyby of Cassini with Titan. Several model profiles are also indicated, revealing unambiguously a temperature decrement of 20 K near the exobase in both the N2 and CH4 components, as well as a significant CH4 loss rate of 2 x 1027 s-1 on Titan. Among Titan INMS flybys, 9 show similar features of temperature decrement as approaching the exobase.

Strobel, D. F., and J. Cui, in Titan: Surface, Atmosphere and Magnetosphere, CUP, in press, 2012

Upper Atmosphere: CH4 from INMS measurements

Similar to previous figure but for the inbound T57 flyby, revealing a temperature increase of25 K near the exobase in both the N2 and CH4 components, as well as a significant CH4 loss rate of 4 x 1027 s-1. Such a feature is seen in 6 out of 21 Titan flybys analyzed in this work.


Flyby n(N2) cm-3

n(CH4) cm-3

n(H2) cm-3

Tn K

Φs(CH4) cm-2s-1

Φs(H2) cm-2s-1

Plasma e-

Plasma Ions

Energetic protons

T5 2.1×107 4.6×106 7.5×105 160 5.4×109 1.1×1010 PS PS Medium T18 3.8×106 1.8×106 1.5×106 128 negl. 1.1×1010 Lobe Lobe High T21 2.6×107 5.5×106 8.6×105 162 3.2×109 1.3×1010 Mixed Mixed High T23 2.3×107 4.2×106 9.6×105 148 2.0×109 1.1×1010 PS PS Medium T25 4.1×107 4.5×106 6.5×105 178 3.1×109 1.1×1010 U U Low T26 2.0×107 3.5×106 1.1×106 149 2.1×109 9.0×109 BM HR Medium T28 6.5×106 1.1×106 1.0×106 144 negl. 1.0×1010 Mixed Mixed High T29 1.2×107 1.9×106 9.4×105 162 4.1×109 1.2×1010 PS PS Medium T30 7.5×106 1.4×106 8.3×105 157 3.2×109 1.2×1010 Mixed Mixed Medium T32 2.5×106 7.2×105 1.8×106 131 negl. 1.2×1010 MS MS High T36 1.4×107 1.5×106 7.5×105 188 3.9×109 1.3×1010 PS PS High T39 1.5×106 4.6×105 1.2×106 120 negl. 9.0×109 PS PS High T40 4.6×106 8.4×105 1.3×106 137 negl. 1.0×1010 BM HR Medium T42 7.5×106 1.7×106 1.0×106 161 2.6×109 1.3×1010 MS MS High T43 6.6×105 2.7×105 1.4×106 113 negl. 8.0×109 Lobe Mixed High/Medium T48 4.3×106 1.4×106 1.6×106 151 3.3×109 1.2×1010 U U High/Medium T50 2.1×106 9.0×105 2.0×106 135 negl. 1.1×1010 Mixed Mixed High T56 9.0×105 3.6×105 1.2×106 132 negl. 1.1×1010 Mixed - High T57 4.0×106 1.0×106 1.0×106 150 3.6×109 1.4×1010 Mixed - High/Medium T58 3.0×106 6.7×105 9.9×105 143 7.0×109 1.1×1010 PS - Medium T59 2.4×106 1.1×106 1.5×106 140 negl. 1.0×1010 Mixed - Medium T61 7.0×105 3.4×105 1.5×106 115 6.2×109 1.0×1010 Lobe - High/Medium

Table 1: Titan flybys with useful, continuous INMS measurements of neutral composition of the thermosphere and exosphere. Neutral densities at a common exobase (1500 km), inferred neutral temperature at exobase, and derived fluxes. Characterization of magnetospheric plasma environment: e- (Rymer et al., 2009), ions (Nemeth et al., 2011) and energetic protons (Garnier et al., 2010). Notation PS = plasma sheet, BM = bimodal, MS = magnetosheath, U = unclassified, negl = negligible (i.e. the INMS density is well described by a diffusive equilibrium model).

2.4x109 1.1x 010

Flux variance:H2:13%CH4: 82%mean


<T> varies from 110 to 190 KFigure 4. Shown are the singleflyby effective ThermosphericTemperatures plotted versus time since TA. The red circles represent the plasma sheet flybys, the blue circles show the lobe flybys, and the gray circles give all other classifications. The flybygroupings T25/T26 andT55/T56/T57, which are separated by 1 Titan day (16 Earth days), show that Titan's thermosphere responds to varying plasma environmentson timescales less than 1 Titan day.

Westlake et al., Titan's thermospheric response to various plasma environments,JGR, 116, A03318, 12 PP., 2011 doi:10.1029/2010JA016251. Plasma classification from Rymer, A. M., H. T. Smith, A. Wellbrock, A. J. Coates, and D. T. Young, 2009. Discrete classification and electron energy spectra of Titan's varied magnetospheric environment, GRL, 36, L15109, doi:10.1029/2009GL039427.

ThermosphereTemperatures

Volkov, et al. 2011. Thermally-driven atmospheric escape: Transition from hydrodynamic to Jeansescape, Astrophys. J. Lett., 729 L24 doi: 10.1088/2041-8205/729/2/L24.

HS = hard sphereVHS = variable HS

Slide 9For 1 component atmosphere

Review of Escape Regime• Hydrodynamic escape:

Atoms: λ < 2.1; Diatomic Molecules: λ < 2.4

Transition region for Atoms: 2.1 < λ < 2.8; and for Diatomic Molecules: 2.4 < λ < 3.6; note it is sharp.

• Thermal Jeans Escape/”collisionless” exospheric escape: Atoms: λ > 2.8; Molecules: λ > 3.6

• H: λexo ~ 2.45, 1.93, 1.42 for T = 110, 140, 190 K

• H2: λ exo ~ 4.9, 3.86, 2.84 for T = 110, 140, 190 K

• CH4: λ exo ~ 39, 31, 23 for T = 110, 140, 190 K

• N2: λ exo ~ 69, 54, 40 for T = 110, 140, 190 KVolkov, et al. 2011. Thermally-driven atmospheric escape: Transition from hydrodynamic to Jeansescape, Astrophys. J. Lett., 729 L24 doi: 10.1088/2041-8205/729/2/L24.

Calculation illustrating the H₂ mole fraction profile, μ(H₂), (dashed line INMS data),the H₂ fluxnormalized by (r/r₀)² to its surface value and compared with the normalized Hunten limiting flux,φl(H₂). Strobel, Canadian J. Phys., in press, 2012 Hunten Memorial Issue.

Hunten Limiting Flux Validity for H2 in Titan’s Atmosphere

Hunten LimitingFlux valid inhomopause Region

Escape rates: CH4 ,2.8×1027,H2, 9.7×1027 s⁻¹

Surface flow rates: CH4 ,1.2×1028,H2, -0.0 s⁻¹

Surface H2 molefraction = 0.0028

Kzz X 2

Comparison of GCMS and INMS Results Yelle et al., Icarus, 2006

Best fit to the data has anUpward flux of 9.8´109 cm-2s-1 ~ 2.5 timesthe Jeans escape flux.

Jeans EscapeFlux

H2: λ exo ~3.9

Globally averaged INMS density profile of H₂ and the calculated Jeans escape rate as a function of radial distance assuming escape probability of unity with T=141 K (solid lines)and Strobel (2012) standard model with T=148.6 K, the Jeans escape rate and Knudsen number are shown by dashed lines. The calculated escape rate is 9.2×1027 H₂ s⁻¹, derived from diffusion modeling of the data (Cui et al.,2011; Hunten limiting rate and numerical solutions to the fluid equations, Strobel, 2012).

1.5Actual FluxJeans Flux

»

H2: λ exo ~3.9

Volkov, et al. 2011. Thermally-driven atmospheric escape: Transition from hydrodynamic to Jeansescape, Astrophys. J. Lett., 729 L24 doi: 10.1088/2041-8205/729/2/L24.

HS = hard sphereVHS = variable HS

H2: λ exo ~3.9

For 1 component atmosphere

Slide – The Methane Density Profile in the Upper Atmosphere

In Titan’s upper atmosphere the CH4 density profile can be interpreted in two limiting ways:1) Diffusively controlled:

a. Vigorous vertical mixing with negligible upward CH4 flux, but 40Ar density profile excludes this interpretation and also compounds the H2

problem. Slide 17b. Large upward CH4 flux equivalent to escape rate of (1-2) x 1027 s-1, but no evidence of CH4 products in Saturn’s magnetosphere at Titan’s orbit. Slide 18

2) Chemically controlled: This requires that ~2 x 1027 CH4 s-1 be removed in the altitude region where INMS measurements are made (compare Slides 20/21). A loss rate due to magnetospheric dissociation by ionization and ion-neutral reactions must exceed the solar ionization rate by more than an order of magnitude. No evidence that the magnetosphere deposits this much power. Slides 22-26

Refs: Yelle, et al., Icarus 182, 567-576, 2006; JGR, 113, doi:10.1029/2007JE003031,E10003, 2008; Strobel, Canadian J. Phys., in press, 2012 Hunten Memorial Issue.

Calculated density profiles (solid lines), INMS density profiles (dashed lines


Surface flow rates: CH4 ,1.5×1028,H2, -1.4×1028 s⁻¹

Kzz X 8,high Ar homopause = 3625 kmcompared to 3500 km

Note calculated Arand H2 do not fitINMS data

Slide 17




HASI N2

Kn =1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 kmKn = 0.0018 @ 3600 km

CH4 diffusivelycontrolled with Kzz

constrained by 40Ar

Slide 18

• Vigorous eddy mixing/high homopause “may” solve the CH4 problem, but it makes explaining the high H2 mole fraction in the thermosphere worse and there is a limit on how high the homopause can be, if the 40Ar mole fraction profile is a constraint.

• To reduce the CH₄ escape rate, loss mechanisms must be operative in the same region as INMS measurements are acquired and be of sufficient magnitude (equal to the inferred escape rate of ~ 1027 CH4 s-1) that the CH₄ density profile is controlled by chemistry/loss rather than diffusion. But according to Fig. 3 in Bell et al. 2010 the total integrated aerosol trapping rate above the minimum altitude of INMS measurements is only ∼10²⁰ CH₄ s⁻¹, seven orders of magnitude below what is required to remove upward flowing CH₄. If the loss process is dominant below the lowest INMS altitude, then a large upward CH4 flux and/or vigorous vertical mixing are required to explain the profile as diffusively controlled. Clearly as formulated, aerosol trapping fails.

Figure 3. Simulated aerosol trapping rates for model 6 (see section 3.1), depicting the typical variation in aerosol trapping rates with altitude inT-GITM. Bell - 2010JE003638

( )aero aero aeroL N C n n e=

Bell, J. M., et al., 2010. Simulating the one-dimensional structure of Titan's upper atmosphere: 2. Alternative scenarios for methane escape, JGR, 115, E12018, doi:10.1029/2010JE003638.

http://www.agu.org/journals/je/je1012/2010JE003638/body.shtml�




Aerosol removal or lossof CH4 below INMS

altitudes

Slide 20


Escape rates: CH4 , 9.1×1024,H2, 9.4×1027 s⁻¹


Aerosol removal or lossof CH4 at INMS altitudes

Slide 21



HASI N2

Enhanced magnetosphericIonization and loss of

CH4 at INMS altitudes

Slide 22

Kn =1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 kmKn = 0.0018 @ 3600 km

Calculated density profiles (solid lines), INMS revised density profiles (dashed lines)



CRAVENS ET AL.: GRL, 2008Processes Required CH4

(cm-2s-1)

Ionosphericchemical CH4 loss

1.3 x 109

Stevens: 4.5 x108

Lavvas: 3.5 x 108

Ly α CH4dissociation

5.8 x 109

Yung: 2.9 x 109

Shah et al. ApJ,703:1947–1954, 2009

Ionization rate (cm–3 s–1) obtained using the O+

energy spectrum only between 10 and 100 keV and a cosine distribution starting altitude 2000 km above surface; maximum (dashed) and median (solid).

( )2 8 2 12

0

1 4.5 10ir p r dr cm sr

- -´ò :

Slide 23

8

8

42 10 10.54 10

´=

´

In thermosphere energy depositionof 6.3 e9 eV cm-2 s-1 produces2.6 e8 ion pairs cm-2 s-1

Titan Energy Source MagnitudesEnergy source Reference r at peak energy flux Global input

(km) (erg/cm^2/s) (GW)Solar Lyman-alpha LASP- solar min 3400 0.017 2.4Solar Lyman-alpha LASP-solar med 3400 0.022 3.2Solar Lyman-alpha LASP- solar max 3400 0.027 4Solar EUV SEE-solar min 3700 0.008 1.5Solar EUV SEE-solar med 3700 0.018 3.1Solar EUV SEE-solar max 3700 0.022 4Mag e- PS Rymer (2009) 4000 0.0026 0.5Mag e- Lobe Rymer (2009) 4000 0.0002 0.04Mag e- MS Rymer (2009) 4000 0.004 0.8Mag e- Bimodal Rymer (2009) 4000 0.0016 0.3Mag i+ PSMag i+ LobeMag i+ MSMag i+ BimodalENAs Brandt (2011) 3400 0.008 1.1O+ ions Shah (2009) 3500 0.01 1.4

Solar!

(1.7-2.7) e-2(0.8-2.2) e-2

(2.4-4) e9(1.5-4) e9

Conclusions cont• But why is there no UV signature of this deposition

in the UVIS data: “Magnetospheric particle excitation may be weak or sporadic, since the nightside EUV spectrum on this orbit shows no observable nitrogen emission features and only H Ly-β.” (Ajello, J.M. et al. (2007), Titan airglow spectra from Cassini Ultraviolet Imaging Spectrograph 597 (UVIS): EUV analysis, Geophys. Res. Lett., 34, L24204, doi:10.1029/2007GL031555.)

• “These Titan UV airglow observations are therefore comprised of emissions arising only from solar processes on N2 with no detectable magnetospheric contribution.” (Stevens, M H. et al., 2011. The production of Titan's ultraviolet nitrogen airglow, J. Geophys. Res., 116, A05304, doi:10.1029/2010JA016284.)

Density profiles of N₂, CH₄, H₂ normalized by their values at r=3933 km, (where Kn=0.15, the upper limit of the validity of fluid equations). Radial distance in units of 3933 km, thus 0.05~200km. The globally averaged INMS data are the dash dot lines. The numerical solutions to the fluid equations of Strobel 2012 are the solid lines, and calculated collisionless theory exospheric densities are the dotted lines.

Requirements for H2• Additional production of H2 (factor of 2) beyond

conventional chemistry is needed to account for the H2 mole fraction profile in Titan’s atmosphere and the implied downward H2 flux at the surface, which is comparable to the escape flux at the top of the atmosphere.

• The additional production must be in the upper atmosphere and associated with magnetospheric energetic particle deposition. Next Slides

Escape rates: CH4 ,2.2×1027,H2, 6.3×1027 s⁻¹ Standard chemistry


Slide 28


Kn =1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 kmKn = 0.0018 @ 3600 km

Escape rates: CH4 , 2.2×1027,H2, 6.9×1027 s⁻¹ Enhanced Catalytic chemistry


Slide 29


Kn =1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 kmKn = 0.0018 @3600 km



HASI N2



Slide 30

Kn =1 @ 4120Kn = 0.7 @ 4080Kn = 0.15 @ 3930 kmKn = 0.0018 @ 3600 km




•The CH4 escape problem is seemingly intractable, if its escape rate must be limited to typical non-thermal rates . Neither vigorousvertical mixing, which is inconsistent with the 40Ar mole fraction profile and makes it even more difficult to account for the elevated H2 mole fractions measured by INMS, nor the aerosol trapping mechanism which was formulated to be most effective below altitudes probed by INMS are solutions. An extremely largechemical loss of due to magnetospheric particle ionization wouldreduce the escape rate to desired rates, but Cassini magneto-spheric measurements rule out the required particle fluxes by an order of magnitude. There has been no reported detection of carbon bearing ions in the outer magnetosphere of Saturn commensurate with the large inferred CH4 escape rates.• In Johnson [2009] review: "But in the absence of new exothermic processes, the present estimates for recoil production are not sufficient to drive the largest escape rates suggested ~1027 CH4 s-1

"

Summary

Summary cont.• CH4 density profile: high homopause, but ruled out by 40Ar, OR

magnetospheric particle precipitation induced loss, but no extra UV N2 emission beyond solar and required power deposition far in excess of Shah et al. ApJ, 2009, OR large CH4 escape rate/upward flux, but no mechanism for ~ 1027 CH4 s-1

• H2 mole fraction profile: need at least factor of 2 additional source beyond conventional chemistry, e. g. magnetospheric induced CH4

loss, but no extra UV N2 emission, unless due to very energetic ions or a reduction in the INMS H2 mole fraction profile

• 40Ar mole fraction profile based on two separate MS measurements and depends on accurate “calibration /interpretation of mass 40”

• Quantitatively, the measured and derived magnetospheric power inputs to the upper atmosphere are smaller than solar EUV and UV power input on a globally averaged, orbitally averaged basis. Only on very rare occasions does magnetospheric power input equal solar input.

Global, Orbit Averaged Escape Rate Summary• Hydrogen atoms: Hedelt et al. QH = 1.7 x 1027 s-1 at the exobase.

In terms of total H atoms, at most about 10% are in atomic form. Hunten limiting rate ~ 1 ×1027 s⁻¹

• Hydrogen molecules: ~ 1.0×1028 s⁻¹ ; from Hunten limiting flux/rate at homopause; in transition region with enhanced Jeans escape ~ 1.0×1028 s⁻¹

• Methane: ?? Non-thermal ~ 6 × 1025 CH4 s−1 ; to inferred from thermospheric density profile ~ (1-2) ×1027 s⁻¹; DSMC calculations (Tucker & Johnson, PSS, 57, 1889-1894, 2009doi:10.1016/j.pss.2009.06.003) give basically Jeans escape rate

• Nitrogen: Non-thermal ~ 2 × 1025 N s−1 ; no evidence from thermospheric N2 density profile for N escape

• Various isotopes: If one cannot accurately infer the CH4upward flux from its density/mole fraction profile, it is a bit of stretch to deduce escape rates for isotopes which have lower S/N than CH4 INMS data.

http://dx.doi.org/10.1016/j.pss.2009.06.003�

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