Vacuum Environments III

Observations and Thermal Analysis of Ice Deposits on Mercury and the Moon

Spring 2003

Calculating Surface Temperatures on Mercury and the Moon

Energy balance at the surface

Slowly rotating + no atmosphere = nearly in radiative equilibrium
First-order estimate of temperature is based on a balance between incoming solar energy and outgoing thermal emission (see tutorial):
```
          F cos(i) (1 - A)
          ----------------  =  e · sigma · T⁴
                D²
```
where
- F = solar flux at 1 AU (1370 W/m²)
- A = albedo (reflectivity) of surface
- i = solar incidence angle measured from vertical (e.g., latitude)
- D = ratio of object's distance from the Sun to Earth's
- e = emissivity (ability to radiate)
- sigma = Stefan-Boltzmann constant (5.67 x 10^-8 W/m²/K⁴)
- T = surface temperature
Temperature vs. Latitude - at the Moon's surface (solid) and at shallow depth (other line styles) from Vasavada et al. (1999)
Heat flow from the interior: is it important? Values are 20 mW/m² (estimate for Mercury) and 33 mW/m² (measured on the Moon).

Need for thermal model

What happens at night? Not in radiative equilibrium any more.
Diurnal temperatures - at the equators of Mercury (top) and the Moon (bottom) from Vasavada et al. (1999)
What happens at depth? Temperature at depth (ignoring internal heating) is roughly the average of the variation at the surface. The thermal "wave" penetrates to a characteristic "skin depth" depending on thermal and physical properties of the surface material.
Temperature vs. Depth - Daily maximum, average, and minimum temperatures vs. depth at the equator (left 2 columns) and at 85N (right columns) on Mercury. The top row has a thin inulating layer. The bottom row assumes either a single insulating (dotted) or conductive (dashed) layer. From Vasavada et al. (1999)

Location of cold traps

Where are the coldest places on Mercury or the Moon?
Based on simple thermal modeling above and billiard-ball planets, the polar surfaces of both the Moon and Mercury are too warm (>110 K, see last lecture) to permit the retention of water ice deposits
Low axial tilts (obliquity) of the planets create regions near their poles where sunlight never directly shines. Temperature instead set by reflected and emitted radiation from nearby warm faces.
Predicted for the Moon by WMB, not observed for >30 years.

Observations of Ice Deposits on Mercury and the Moon

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Discovery of Mercury radar features

Goldstone / VLA maps of Mercury - Slade et al. (1992)
unexpected result of radar mapping of Mercury using the Goldstone 70-m dish as a transmitter and the 27-antenna Very Large Array in New Mexico as a receiver.
high radar reflectivity and inverted polarization ratio at 3.5 cm
- a perfectly smooth surface viewed head-on creates a specular reflection and flips the polarization
- a perfectly rough surface creates a broad reflection in both polarizations
- only special processes like the Coherent Backscatter Opposition Effect (COBE) or volume scattering within a non-absorbing medium will return an inverted (more return in the un-flipped sense) polarization ratio
- such effects are noted on the Greenland ice sheet, the North polar ice cap of Mars, and the Galilean satellites
both processes require radar wave to scatter through a surface layer with a thickness up to 10 times the wavelength, with much absorption. Best explained by volume scattering in pure, meter-thick water ice
later analysis by Harmon et al. (1994) linked specific radar features at 13 cm to known impact craters: slam dunk for cold trap hypothesis
1994 Arecibo radar images and Mariner 10 maps from Harmon et al. (1994)
Radar results with crater locations - from Vasavada et al. (1999)
2001 Arecibo radar images - 1.5 km/pix!! from Harmon et al. (2001) Possible ice near poles

Possible Observations of Ice Deposits on the Moon

Clementine attempted a similar radar experiment at the Moon's south pole. When the spacecraft was in the line-of-sight of the pole as seen by Goldstone, it transmitted and Goldstone received. One unconvincing signal was found, which has since been disputed.
Ground-based radar mapping of the Moon's poles have not detected any Mercury-like returns.
Lunar Prospector carried a neutron spectrometer, designed to detect surface hydrogen deposits which mask the background flux of neutrons (originally created by cosmic rays). Feldman et al. (2000) found hydrogen concentrations at both lunar poles. Best interpretation is small amounts of water mixed with regolith.
Neutron Spectrometer results I - epithermal neutron count versus latitude.
Neutron Spectrometer results II - epithermal neutron count in map form.
Lunar cold trap locations - from radar-based topographic mapping by Margot et al. (1999). White & gray areas are permanently shaded from the Sun. Gray areas were shaded from the radar during the observations.

Thermal Modeling of Ice Deposits on Mercury and the Moon

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Thermal modeling method

the temperature of cold traps is the key factor which determines where ice deposits will form, and how long they will be retained
goal: model the scattering of visible and thermal radiation within closed depressions near the poles of Mercury and the Moon
temperatures within permanently shaded areas are determined by their ability to "see" warm reions. It becomes important to accurately model the orientations of the surface and surrounding topography
polar impact craters are the obvious topographic features
a finite-element scattering model coupled to a 1-D subsurface thermal conduction model used to calculated temperatures within impact craters of appropriate size, shape
Temperatures in Crater C on Mercury - shows maximum (top) and average (bottom) surface temperatures. From Vasavada et al. (1999)
cold regions are bounded by steep temperature gradients; coldest regions are crescent-shaped areas bounding the equatorward rims
temperatures at shallow depth colder, and colder temperatures cover a larger area

Thermal modeling results

Temperature vs. latitude in a 40-km crater - on Mercury (left side) and the Moon (right side). Each pair of columns shows maximum (left) and average (right) surface temperatures. From Vasavada et al. (1999)
Temperature within observed craters on Mercury - Each pair of columns shows maximum (left) and average (right) surface temperatures. From Vasavada et al. (1999)
water stable in near-polar, permanently shaded cold traps, within 10 degrees of Mercury's poles and 13 degrees of the Moon's
comparison of the shapes of modeled cold traps with the radar features suggests that Mercury's cold traps are full
radar features observed at even lower latitudes (higher surface temperatures) on Mercury

Nature of the Ice Deposits on Mercury

physical nature of the deposits - dust cover?
shields the ice from maximum surface temperatures, protects from Ly-alpha, sputtering, etc.
needed to explain the lowest-latitude deposits on Mercury (yet must be a layer of pure ice to be detectable by radar)
more consistent with a catastrophic source (e.g., comet) than a gradual source (e.g., meteoroids, outgassing)
different radar reflectivities at 3.5 and 13 cm consistent with regolith cover of a few cm thickness
Latest Goldstone Mercury Results - at 3.5 cm from Slade et al. (2000)

Nature of the Ice Deposits on the Moon

similar thermal environment on Mercury and Moon--why no radar features?
how important are obliquity history, sources, geotail?
small amount of water ice is mixed with lunar regolith (not buried) would be consistent with neutron signature and lack of radar signature

References for this Lecture:

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Butler, B. J., D. O. Muhleman, and M. A. Slade 1993. Mercury: Full disk radar images and the detection and stability of ice at the north pole. J. Geophys. Res. 98, 15003-15023.

Feldman, W. C. et al., Polar hydrogen deposits on the Moon, J. Geophys. Res., 105, 4175, 2000.

Hapke, B. 1990. Coherent backscatter and the radar characteristics of outer planet satellites. Icarus 88, 407-417.

Harmon, J. K., M. A. Slade, R. A. Velez, A. Crespo, M. J. Dreyer, and J. M. Johnson 1994. Radar mapping of Mercury’s polar anomalies. Nature 369, 213-215.

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

Ingersoll, A. P., T. Svitek, and B. C. Murray 1992. Stability of polar frosts in spherical bowl-shaped craters on the Moon, Mercury, and Mars. Icarus 100, 40-47.

Margot, J.-L., D. B. Campbell, R. F. Jurgens, and M. A. Slade, 1999. Topography of the lunar poles from radar interferometry: A survey of cold trap locations. Science 284, 1658.

Paige, D. A., S. E. Wood, and A. R. Vasavada 1992. The thermal stability of water ice at the poles of Mercury. Science 258, 643-646.

Rignot, E. 1995. Backscatter model for the unusual radar properties of the Greenland Ice Sheet. J. Geophys. Res. 100, 9389-9400.

Slade, M. A., B. J. Butler, and D. O. Muhleman 1992. Mercury radar imaging: evidence for polar ice. Science 258, 635-640.

- A. Vasavada -

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