Atmospheric Sputtering+

Isotope Fractionation

Application to Mars

Also: comments on Titan Nitrogen

Mars Atmosphere and Ionosphereexobase altitude dashed line

Mars exobase altitude is depends on the solar activity: 180km is an average. Note: there are molecules and molecular ions at the exobase, unlike at earth. Corona, region above exobase, is eventually dominated by O and O+.

Hot O in ‘corona’ (exosphere)

exobase

Hot Atom Production

Suprathermal particles with kinetic energies E >~10 Tx are produced in various nonthermal processes:

Because there are molecules and molecular ions at the exobase:

Dissociative recombination of molecular ions

Photon and electron impact dissociation

€

AB+ + e → Ahot* + Bhot

*

AB + hν (e) → Ahot* + Bhot

* + (e)

Produce kinetic energies up to a few eV:at Mars O2

+ and CO2.

‘Sputtering of Atmosphere’Johnson,Space Science Revs. 69, 215, 1994

On non-magnetized bodies

energetic ions, A+, can penetrate the exobase and collide with

atmospheric molecules, BCharge exchange and momentum transfer

collisions

by solar wind (H+,He+2) ions or

by pick-up ions formed in the corona

(O+ at Mars)

; )'()'()(

)()(

transfermomentum

exchange charge ;

EEEE

EE

BABA

BABA

+→++→+

−++

++

Momentum transfer: the suprathermal atoms with kinetic energies up to 100’s of eV

Charge exchange: high-energy ion is converted

to an neutral with approx. the same energy.

Exobase

AtmosphericCorona

BallisticTrajectories

col >> H(Kn >> 1)Particle Tracking

col ~ H(Kn ~ 1)

Thermosphere Fluid-like col << H (Kn << 1)

€

Kn is Knudsen number ≈ λ col

H(for a atmosphere)

Exobase = Transition Region: Goes from collisional to collisionless

Can describe using Boltzmann Transport Equations

or Monte Carlo Simulations

Boltzmann Transport Equations

Evolution of suprathermal atoms in the atmosphere is often calculated via Boltzmann-type kinetic equations with sources, sinks and collisions

One such equation for the density and speed distribution for each species.

This is the distribution we used for Jeans escapeNonequilibrium:

Typically too difficult so simulations are used

Direct Simulation Monte Carlo Model:

Approximate the atmospheric gas by a finite number of modeling particles each with a very large weight

A) Calculate the motion of the model particles subject to gravity in a time step, dt

B) Calculate the probability of a collision for every particle in dt

C) If collisions occur in dt: calculate new speeds of colliding particles and return to A for a new dt

Deflection of Solar Wind Non-Magnetized Planet

Solar fields try to move through ionized region Induces currents

Currents deflect the fields (Lenz’s law)

Ionopause : Solar Wind Pressure = Pressure from IonosphereFluid Picture But Ions can have large gyroradii + penetrate ionopause

and exobase

Planet

Photons produce ionosphere

Solar Wind

H+, He+, etc plusMagnetic + Electric Fields

Interaction of solar wind plasmawith the Martian atmosphere

Hot O in the corona can become ionized, O+.

The O+ are picked up and accelerated by the solar fields (~keV) and can beswept away or impact the atmosphere

Impacting ions produceatmospheric sputtering

A+ can be an ion with large gyro radius that reaches exobase or a neutralized ion that then ignores the fields and penetrates the exobaseand collides with atmospheric molecules B

Sputtering Yield, Y Number of molecules with energy greater than Ees that cross the exobaseEscape Flux = Y x Incident Ion Flux Therefore, need to calculate: Number of recoils molecules, B, set in     motion with energy, E, greater than Ees

B

A

B

A

A+

ExobaseMolecules B

B

might escape

Atmospheric Sputtering (cont.)

€

Y ∝ [ Probability of an Energy Transfer Collision

near the Exobase] × [No. of recoils with T > Ees ]

x [Fraction crossing exobase]

Probability of A + colliding with B near the exobase

~ σA+B

Nx

σA+B

= 'energy transfer' cross section

Nx = column density at exobase

~ 1/σ BB; collision cross section for B

Number with T > Ees ≈ [T / Ees ]

T is the average energy transfer by A+

Fraction crossing exobase ≈ 1/4 (like Jeans escape)

Therefore,

Y ~ (1/4) T

E es

σA+B

σ BB

Y is seen to be proportional to the ratio of two cross sections

The cross section for A+ producing a recoil

The cross section for B colliding

with another atmospheric molecule B

A Simplified Transport Equation collisions between identical particles: Benergy distribution only(ignore spatial dis.)

G(T,E)dE is number of recoils set in motion with energy between E and E+dE by a particle of

energy T produced by an incident ion, A+.

G(T,E)dE = [Probability that a particle of energy T creates a recoil of energy E] plus [Probability that an earlier recoil produced

attains energy E or produces another recoil with energy E

€

Elastic Collision : B + B ; σ BB → σ (drop B's)

G(T,E)dE = 1

σ (T)

dσ

dE

⎛

⎝ ⎜

⎞

⎠ ⎟dE

+ 1

σ (T)∫ dσ

dE'dE' G(T - E',E) + G(E',E)[ ]

G(T,E) = 0 ; T < E (i.e. recoils have lower energy)

For hard sphere (billiard ball) collisions: exact solution

1

σ

dσ

dEdE =

dE

T for such collisions

Find G(T, E) = T E2 , T > E

For a realistic potential

G(T,E) ≈ βT

E 2,

β weakly depends on B; for atoms ~ 6/π 2

Atmospheric Sputtering (cont.) Use the Recoil Distribution

Isotropic Cascade (like Jeans escape)

€

Use the distribution for the number of recoils set in motion between E and E + dE

G ≈ βT

E 2; T > E

Escape : E > E es (E' = E - E es )

also assume T >> E es

Energy distribution for those that escape (the sputter ejecta)

f(E') ≈ E es

(E' + E es )2

; normalized

Angular Distribution (like Jeans escape) ~ 1

4Yield ∝ Probability of a cascade occurring near exobase

Y ≈ 1

4 G(T,E) Nx

dσA+B

dTdT

⎡

⎣ ⎢

⎤

⎦ ⎥Ees

∞

∫

Y ≈ β

4

(Sn )A+B

E es σ BB

⎧ ⎨ ⎩

⎫ ⎬ ⎭

Here

(Sn )A+B

= T ∫dσ

A+B

dTdT

= averaged energy transfer cross section, often called stopping cross section

i.e. dE

dx

⎛

⎝ ⎜

⎞

⎠ ⎟A+

= nB(Sn )A+B

energy loss per unit path of A+ in B

Atmospheric Sputtering (Cont.)

€

At Mars (dominated by O near exobase)

Solar Wind : YH+ ~ 0.014 (96%)

YHe++ ~ 0.27 (4%)

Solar Wind Erosion rate = 0.12 x[2 x108 /cm2/s]

~ 2 x107 O/cm2/s

Not so different from Jeans rate for H

However; Pick - up O+ : YO+ ~ 8.7 !

Also : Dissociative recombination can produce

mini - cascade of collisions

O2+ + e → O + O + ΔE

produces 2O with T ~ ΔE

2; if T > E es

then O can escape directly or knock others out

if T < E es they populate the hot atoms in corona

Titan : pick - up N+ and N2+

very efficient sputterers

Also N 2+ + e → N + N

Hot oxygen at Mars

• Dissociative recombination ionosphere is O2

+

Escape energy for O: 2.1eVprocesses 1 and 2 might lead to escape 3 and 4 only produce hot O in corona

Dissociative recombination primarily populates corona

Sputtering by O+ picked-up in corona ( ~keV) primarily causes escape

Simulated an O corona: low and high solar activity, and then a multispecies corona•energy spectra from Luhmann and Koyzra 1991

⎪⎪⎩

⎪⎪⎨

⎧

++++++++

→++

eVSODO

eVDODO

eVDOPO

eVPOPO

eO

84.0)()(

06.3)()(

02.5)()(

99.6)()(

11

11

13

33

2

Hot Oxygen at Mars LOW SOLAR ACTIVITY

Energy Distribution Function

Calculated – solidThermal – dashe

Left vertical line –suprathermal region

Right vertical line –escape energy.

Suprathermal tail includes escaping flux;

Atoms between vertical lines populate corona.

Hot oxygen corona at Mars

Thermal fraction:exospheric temperatureT=180 K (solar min.)

Nonthermal fraction: O2

+ dissociativerecombination + atmospheric sputtering.

Compared to:•Nagy & Cravens 1988;•Lammer & Bauer 1991.

LOW SOLAR ACTIVITY

Different height scales!

Hot oxygen at Mars atmospheric loss

Nonthermal process- O2

+ DR

Escape flux(cm-2s-1)

Loss rate (х1024 О/s)

McElroy (1972) 6 х107 50.0

Lammer, Bauer (1991)

6 х106 5.0

Luhmann (1991)

7 х106 6.0

Kim et al. (1998)

3.3х106 2.7

Hodges (2000) 3.6х107 28.0

This work, M1,M2

(4.1-5.6)х107 (33.0-45.0)

Extrapolated back in time using             changes in EUV fluxNet Loss rate ~4.5х1025 O/sEquivalent to 1 earth’s atmosphere

Solar minimum activity

Solar maximum activity

Soleil

Soleil

rotation

n~100cm-3

n~1000cm-3

n~10cm-3

The Martian CoronaUse of a 3D Monte Carlo model for the non-thermal component + a thermal component.

Examples of exospheric density in the equatorial plane

-5 0 5

7

4

0

-2

7

4

0

-2

f(r,

v) (

cm-6 s

3 )

Results of a 1D Multi-Species

Net escape to space~10 m of water

~0.15 bar of CO2

large uncertaintiesEnough to lose

greenhouse effect?

Escape rate (s-1)

Low solar activity

High solar activity

Dissociative

Recombination

O 2.11025 51025

CO 51022 5.81022

Sputtering

O 3.71023 2.51025

CO22.51022 1.51024

CO 2.91022 1.61024

O 7.41022 3.51024

Early Mars?: atmosphere-planet surface interaction

Atmospheric Loss at Mars

From Chassefiere and Leblanc (2004)

When magnetic fields collapseddid atmospheric sputtering remove enough

gas to cause loss of Greenhouse effectAnd, therefore, cause the freezing out of

the remaining atmosphere?

Calibrated using the fact that epoch 2EUV before presenthas, roughly, the same average solar wind and EUV flux as we have at present at solar maximum.Therefore, model can be tested by Mars Express measurements.

PHOBOS (solar max)

MEX(solar min))

Loss to space after dynamo extinctionLoss ofMagnetic fields

Atmospheric Sputtering at Mars

Extended hot oxygen corona at Mars is populated mainly by the suprathermal oxygen atoms formed in the O2

+ dissociative recombination in both low and high levels of solar activity.

Atmospheric sputtering results in the additional population of the extended hot corona and in a large increase of the oxygen loss rate, especially at high solar activity

However, it is a complicated feedback process(Johnson and Luhmann, J.Geophys. Res. 103, 3649, 1998)

But by testing simulations against accurate space craft measurements (Mars Express) of the corona and the solar wind and solar fields we can hope to simulate earlier epochs and learn whether there were sufficient green house gases for and early wet Mars: will need to include sulfur species

Nitrogen Isotopes Titan Atmosphere: 96% N2

Parts per 1000

Requires 40 Earth’s atmospheres to be lost!!

Outgassing is likely NH3

Eventually converted by photodissociation to N2

Whereas the N2 does not escape efficiently large amounts of NH3 (Ees =0.41eV) can

escape by non-thermal processes(primarily atmospheric sputtering)

Nitrogen at TitanRemember For non-thermal, nearly mass independent, escape processes, diffusive separation determines population at exobase and, therefore, the isotopic fractionation

Present day enhancement of light species at exobase --> large loss required??

€

fA = [ rAB ]q ; q-1 = RABexo −1

Homopause : ~ 800 km

Exobase : ~ 1500 km ; Δzx ~ 700km

H ~ 40 km (lower altitudes)

~ 80 km ( high altitudes)

Exobase Enhaneement of 14 : R14N/15Nexo ~ exp

700

80

⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢

⎤

⎦ ⎥

1/14

~ 1.87 (actual ~ 1.45)

Therefore - -guess what - -they assume there must be Eddy Mixing

Using data - -

r14N/18N = Solar

Titan

⎛

⎝ ⎜

⎞

⎠ ⎟

15 /14

≈ 0.002

0.011

and using R14N/15Nexo ~ 1.45

fA ≈ 0.026 or ~ 1/40th remains

Titan's atmosphere is believed to be similar to Earth's early atmosphere. Toby Owens said: "What we've got is a very primitive atmosphere that has been preserved for 4.6 billion years. Titan gives us the chance for cosmic time travel . . . going back to the very earliest days of Earth when it had a similar atmosphere.”

The proportion of heavy nitrogen-15 in the atmosphere of Titan is much greater than that around other planets. Scientists believe that the lighter nitrogen-14 was lost over geologic times scales for reasons that remain unknown. Requires that most of the atmosphere evaporated into space, a process in which the nitrogen-14 would have escaped more easily than nitrogen-15. But it would mean that Titan once had an atmosphere 40 times as thick as Earth's - making it a dwarf version of a gas planet. 'This bizarre world may be far more complex that we have begun to imagine,' says Soderblom.

The nitrogen isotopes are telling us something about the way planetary atmospheres are formed rather than how they evolve. Why do we insist that a star's "children" all be born at the same time? Hannes Alfv 始wrote in Evolution of the Solar System, "..the Laplacian concept of a homogeneous gas disc provides the general background for most current speculations. The advent of magneto-hydrodynamics about 25 years ago and experimental and theoretical progress in solar and magnetospheric physics have made this concept obsolete but this seems not yet to be fully understood.”

The electrical model of planet birth proposes that planets are born by electrical expulsion of some of the matter of a star or gas giant in a tremendous "flare.” http://www.thunderbolts.info/

Summary• Titan should be simple: large 15N/14N

ratio.

Now mostly N2, likely derived from NH3which is lighter; atmospheric sputtering is likely the principal loss process (e.g., this can remove all atmosphere from large Jovian moons) (Johnson ApJ572, 1077, 2002)

But it is not simple--loss appears too large and C is not fractionated

Affected by atmospheric structure in earlier epochs and recycling in the surface: CH4 --> hydrocarbons

• Mars is complex But--if you start the clock when the

intrinsic field froze, there is hope Still all species are not similarly

fractionated: reservoirs?

Volatile Reservoirsand Exchange

Mars Isotopes• Some elements in the martian atmosphere display

large isotopic fractionations suggesting loss of a major portion of the atmosphere

• D/H ratio (measured by earth-based spectra and in martian meteorite water) five times Earth’s

• 15N/14N ratio: 60% enriched over Earth's (measured by Viking and in martian meteorites)

• 38Ar/36Ar ratio: 30% enriched over Earth's

• 136Xe/130Xe ratio that is 16-25% enriched over solar Xe and in carbonaceous meteorites (Ar and Xe measurements are from shock-implanted gases in EETA79001)

• Kr isotopes in EETA79001 closely resemble solar as do Xe isotopes in Chassigny. Minor component of N in EETA79001 + Zagami has 15N/14N similar to Earth's.

• Findings indicate that at least two reservoirs of these gases exist on Mars, one a mass-fractionated atmospheric component and one likely an unfractionated mantle-derived component.

• How can such different reservoirs be used to define in detail the volatile evolution of Mars?

Summary

Things to Know:

Hot Atom Processes

Atmospheric Sputtering

Modeling Non-equilibrium Regions

Recoil Energy Distribution

Atmospheric Sputtering Yields

Model of Mars Corona

Atmospheric Loss Estimates

Isotope Fractionation at Mars

Nitrogen Fractionation at Titan