Vacuum Surface Environments and Processes  II

Sources, Sinks, and the Behavior of Volatiles

Spring 2003

Surface-bounded exospheres (review)

Molecules are gravitationally trapped, but collisionless:
Mean free path > scale height

• In a collisional atmosphere, the scale height, H, is the e-folding length of pressure, density, etc.
• It is the "characteristic height" of atmospheric molecules determined by a balance between their thermal energy and gravitational potential energy (below is per mol):

  RT = µgH --> H = RT/µg

  where
  • µ = molar mass (kg/mol)
    
  • R = universal gas constant (8.314 J/K/mol)
    
  • T = temperature
    
  • g = gravitational constant (9.8 J/m/kg)
    

Molecules travel on ballistic trajectories

• In a collisionless atmosphere, energy is still partitioned between thermal (kinetic) energy and gravitational (potential) energy
• Now H is simply the height of a typical bounce of a single molecule:

  kT = mgH --> H = kT/mg

  where
  • m = mass of a molecule (kg)
  • T = temperature
  • k = Boltzmann constant (1.381 x 10^-23 J/K)
  • g = gravitational constant (9.8 J/m/kg)

  Now multiply both sides by N (Avogadro's Number) and use the relationship

  R = kN

  to get:

  H = RT/µg

  (same as above!)

"Atmosphere" in contact with surface and space, not with itself

Constituents are not shielded from solar wind, UV, X-rays, or cosmic rays

Sources of Volatiles

O, Na, He, K, H in Mercury's atmosphere come from surface

• O, Na, K result from vaporization of meteorites, sputtering of surface minerals, diffusion from subsurface (on Mercury, dayside)
• H₂, He delivered by solar wind as ions, converted to neutrals at surface (ion recombination)
• spatial/temporal variations in abundance are clues

Ar on the Moon results from radioactive decay of K in crust

H₂O from IDP's, meteorites, and asteroids

• about 5-10% water
• water must be retained during initial impact (below ~10 km/sec all is retained; above ~30 km/sec all is lost for comets)

H₂O, CO₂ from comets

• huge volume per impact, large volatile content (~50%)
• water retention favors short-period comets. Jupiter family comets (Jupiter-crossing orbits and derived from the Kuiper Belt) are better candidates than Halley-type comets (large range of orbital parameters and derived from the Oort Cloud)
• hyperbolic or parabolic comets much too fast (70 km/sec).
• extinct comet nuclei may also be a large source
• perhaps on the order of 1 or 10 have impacted the Moon or Mercury

H₂O, CO₂ from outgassing (volcanism); hard to quantify

Table below indicates the amount delivered to the surface over the age of the Solar System, before any loss processes take place (from Moses et al., 1999)

What could the polar volatiles on Mercury and the Moon be, if not water ice?

• Suggestions: elemental sulfur, CO₂, hydrogen, etc.
• Water is the most likely because of its cosmic abundance, its known radar properties, and its low vapor pressure. Any other proposed substance must have these same qualities, to the same degree. For example, if the deposits are elemental sulfur, the vapor pressure is so low they might be expected to form actual polar caps, not discrete features.

Sinks for Volatiles

Vapor (hopping) phase

• gases subject to thermal (Jeans) escape, sputtering, photoionization, and photodissociation, with the latter being dominant
• timescales are short: survival of H₂O is ~1 day
• present constituents must be continually resupplied
• such efficient removal implies that volatiles cannot be retained

Paradigm shift: Watson, Murray and Brown (1961)

• previously it was assumed that the stability of volatiles is controlled by vapor-phase loss process
• WMB: condensable volatiles will migrate to coldest locations and become "cold-trapped" there; stability then determined by sublimation from those regions
• So, the limiting loss rate is sublimation, not fast "atmospheric" processes

Thermal sublimation and other losses from cold traps

• temperature of cold traps becomes the decisive factor--more on this later
• sublimation rate is a characteristic physical property of any solid that depends only on the surface temperature
• the partial pressure of a vapor over a condensed phase is equal to the vapor pressure, f(T), when in equilibrium. The maximum sublimation can be calculated by assuming that all evaporated molecules re removed before they re-condense.

  
                      [µ]1/2
          S  =  P  ----------
                   [2 pi R T]1/2
  

  where
  • S = sublimation mass flux (kg/m²/s)
  • P = vapor pressure (N/m²)
  • [ ] = 1 / rms velocity away from surface
• can calculate a critical cold trap temperature by assuming a loss rate
• Loss rates from Vasavada et al. (1999)
• may be vaporized by micrometeoroids and larger impactors
• exposed to solar wind, UV, X-ray, and cosmic ray bombardment

Migration of condensable volatiles (WMB; Butler 1997)

• ballistic hops until lost to photodissociation or a cold trap
• molecules accommodate to surface, emerge with appropriate v(T) and angle
• Monte Carlo simulation
• photodissociation and cold trap "loss" timescales are similar, ~1 day. Average hop length is ~100 km, on the order of 10 hops before loss.
• maximum in atmosphere = vapor pressure(T_coldtrap). Minimum = 0.
• results: 5-15% of randomly place water molecules will find the cold traps on Mercury, 20-50% on the Moon. For CO₂: about 3% on Mercury, 13% on the Moon.
• molecules from all latitudes can find polar cold traps

Summary of sources and sinks of volatiles on Mercury

• Figure from Killen et al. (1997)  
• There are two ways of estimating the critical temperature for the retention of water ice from the above figure:
• For example, one meter of water ice can survive for one billion years if the loss rate is 10⁸ cm^-2 s^-1 or less. Using the curve labeled "sublimation of cubic ice," we see that this occurs for surface temperatures less than 110 K.
• We can also balance the fastest loss rate (sublimation) with the fastest supply rate (meteoritic delivery). These curves cross at 114 K.

References for this Lecture:

Butler, B. J., 1997. The migration of volatiles on the surfaces of Mercury and the Moon. J. Geophys. Res. 102, 19283-19291.

Hodges, R. R. Lunar cold traps and their influence on argon-40, 1980. Proc. Lunar Planet. Sci. Conf. 11th, 2463-2477.

Killen, R. M., J. Benkhoff, and T. H. Morgan. Mercury's polar caps and the generation of an OH exosphere. Icarus, 125, 195-211, 1997.

Moses, J. I., K. Rawlins, K. Zahnle, and L. Dones, 1999. External sources of water for Mercury's putative ice deposits. Icarus, 137, 197-221.

Vasavada, A. R., D. A. Paige, and S. E. Wood, 1999. Near-surface temperatures on Mercury and the Moon and the stability of polar ice deposits. Icarus, 141, 179-193.

Watson, K., B. C. Murray, and H. Brown, 1961. The behavior of volatiles on the lunar surface. J. Geophys. Res, 66, 3033-3045.

- A. Vasavada -

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