Presentation at a Symposium in honor of Bill Feldman, Los Alamos, 2023

1. Stability of Subsurface Ice
on Planetary Bodies
Norbert Schörghofer
Planetary Science Institute, Hawaii/Arizona
Bill Feldman Symposium – Los Alamos 2023
1

2. Over the past 20 years I’ve been trying to explain the following
observations:
• Moon – Feldman et al. (1998, 2000, 2001)
• Mars – Feldman et al. (2002, 2004, 2007, 2008)
• Ceres – Prettyman et al. (2017)
and I’ve become to appreciate the power of nuclear spectroscopy
(to see in darkness and to see through a desiccated layer)
2

3. Diffusion of Water Vapor in
Porous Layer of Airless Body
E(σ, T) ... desorption rate
T ... temperature; σ ... surface concentration
grain (n)
En
grain (n+1)
En+1
Ice
Regolith
Vacuum of Space
Water Vapor
Flux between two grain surfaces:
J = −
En+1 − En
= −ℓ
∂
∂z
E(σ, T)
ℓ ... grain distance
z ... depth
3

4. The Power of Time Averaging
Diffusive mass flux:
J = −ℓ
∂
∂z
E(σ, T)
Time average over period P (swap
R
dt and ∂/∂z):
Z P
0
J dt = −ℓ
∂
∂z
Z P
0
E dt
Net flux given by time-averaged sublimation rates;
microphysical processes are averaged out!
In stationary situation, this further results in boundary value
formulation:
Z
J dt =
ℓ
∆z
Z
E(surface) dt −
Z
E(ice table) dt
Net flux given by time-averaged sublimation rates at upper and
lower boundary.
4

5. Loss rate of buried ice (on the Moon)
50 100 150 200 250
0
0.1
0.2
0.3
0.4
0.5
Temperature (K)
Depth
(m)
a)
mean(T)
min(T)
max(T)
10
02
10
03
10
04
10
05
10
06
10
07
10
08
10
09
10
10
10
11
10
12
10
13
10
14
0
0.1
0.2
0.3
0.4
0.5
Depth
(m)
Sublimation Loss (kg/m
2
/Gyr)
b)
mean(E)
mean(Ess)
Dramatic reduction of loss rate beyond thermal skin depth;
Neutron spectroscopy sees through devolatilized layer
5

6. Ceres
Extreme contrast between surface and subsurface ice abundance
Surface Subsurface
optical spectroscopy nuclear spectroscopy
Oxo Crater 6.8 km2
- 3.3 km2
Messor Crater 1.4 km2
Juling Crater 3.2–6 km2
all other 2.4 km2
Combe et al. (2019) Prettyman et al. (2017)
∼11–20 km2 with H2O essentially global
Area with ice detected by optical versus nuclear spectroscopy:
105!
6

7. Phoenix Mars Lander 68◦N
Frost-free surface but perennial ice-cemented soil beneath lan-
der; ∼5 cm
7

8. Ground Ice in Diffusive Contact with
Atmospheric Water Vapor
Ground Ice
Soil
Atmosphere
Water Vapor
Ground ice can be stable (last indefinitely) in present-day climate
Leighton Murray (1966); balance of annual mean vapor density
⟨ρatm⟩ = ⟨ρice table⟩
8

9. Comparison of Equilibrium Predictions
with MONS Measurements
MONS = Mars Odyssey Neutron Spectrometer
Figure from Diez et al. (2008)
9

10. Recharge / Vapor Pumping
predicted and studied by Mellon Jakosky (1993)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
4
Ice filling fraction
Depth
(m)
Growing Ice
Receding Ice
Different initial conditions evolve to the same ice table.
10

11. (Theoretical) History of Ice at Phoenix
Landing Site (68◦N)
−8 −6 −4 −2 0
x 10
5
0
0.05
0.1
0.15
Time (years)
Depth
(m)
dry soil
pore ice
ice sheet
Ice retreats and reforms in response to Mars’ Milankovitch cycles
Schorghofer Forget (2012) Note: period of precession cycle
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12. Can Vapor Pumping occur on the
Moon?
Temperature
Sublimation
rate
0
Depth
below
surface
T(z,t)
Temperature profiles:
solid line = instantaneous,
dashed lines = min and max
Any volatile water molecule
has a probability to move up
or down. A water molecule
on the surface (upper dot)
has a different mobility than
a molecule at depth (lower
dot). In the long term, this
leads to a net vertical flux of
water molecules.
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13. The Moon:
Pumping from Temporary Ice Cover
0 0.5 1 1.5 2
x 10
6
0
2
4
6
8
10
12
14
16
18
x 10
21
Time (years)
Ground
Ice
Mass
(#
molecules/m
2
)
Diffusion
dominated
Pumping
dominated
Loss of
icy layer
Loss of last
monolayer
0
2
4
x 10
−4
Ground
Ice
Mass
(kg/m
2
)
Vapor Pumping occurs, but ice is quickly lost again (Schorghofer
Taylor, 2007)
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14. Vapor Pumping in Lunar Polar Regions
Pumping differential ∆E = ⟨E(surface)⟩ − ⟨E(ice at depth)⟩
Schorghofer Aharonson (2014); Schorghofer Williams (2020);
Schorghofer et al. (in prep.)
14

15. Vertical Profile for Pumping of
Adsorbed Water
86.79◦S 21.1◦W (West of Haworth Crater)
50 100 150 200 250
0
0.2
0.4
0.6
0.8
1
Temperature (K)
Depth
z
(m)
0 1 2 3 4 5
0
0.2
0.4
0.6
0.8
1
Monolayers
Depth
z
(m)
100 kg/m
2
/Gyr
1000 kg/m
2
/Gyr
Subsurface Cold-Trapping ⟨E(surface)⟩ ≥ ⟨E(ice at depth)⟩
Figure from Schorghofer (2022)
Excess hydrogen is buried (Feldman et al., 1998)
Lawrence et al. (2006): “likely buried by 10 ± 5 cm of dry lunar
soil”
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16. Notions of Ice Stability
1. Influx of H2O ≥ Sublimation Loss
• Cold traps when viewed on long time scales
• Subsurface cold traps supplied by vapor pumping
2. Long-lived ice (slow loss); “meta-stable”
• Cold traps when viewed on short time scales
• Relic buried ice (sometimes called “subsurface stability”)
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17. Conclusions
• Thermal skin depth volatilizes surface layer — neutron spec-
troscopy reaches beyond this depth
• Ceres provides example of devolatilized surface layer;
Extreme contrast of ice concentration on the surface versus
the sub-subsurface;
Nuclear spectroscopy revealed 105 more area with H2O than
optical spectroscopy.
• Vapor exchange equilibrium explains ice distribution on Mars
in the top ∼0.5 m mapped by MONS.
• Vapor pumping can operate in the lunar polar regions if
sufficient adsorbed water is routinely available; it can sup-
ply subsurface cold traps and explains the desiccated layer
and H excess outside of cold traps observed by neutron spec-
troscopy.
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