A brief summary of the concept of thermally-driven ice storage on the Moon. Audience: lunar scientists

1. Lunar Thermal Ice Pump
Norbert Sch¨orghofer
University of Hawaii
2015
N. Schorghofer & O. Aharonson. The lunar thermal ice pump.
Astrophysical Journal 788, 169 (2014).
N. Schorghofer & G.J. Taylor. Subsurface migration of H2O at
lunar cold traps. Journal of Geophysical Research 112, E02010
(2007).

2. Ice storage on the Moon
Proposed storage mechanisms for H2O or volatile H:
Cold trapping, exposed ice Urey (1952), Watson et al. (1961)
Cold trapping, buried ice Paige et al. (2010)
Thermal ice pump Schorghofer & Aharonson (2014)
Adsorption† e.g., Cocks et al. (2002)
Hydration†
Implanted solar wind∗ Starukhina (2001,2006)
& diffusion-limited escape
The “Thermal Ice Pump” is a mechanism for storing water ice,
physically different from cold trapping.
† adsorption is a surface phenomenon whereas hydration is a bulk
phenomenon.
∗ forms H or OH

3. Physics of H2O Migration
Subsurface diffusion. Molecules follow a random walk within
subsurface pore spaces (diffusion)
Thermalization. When a molecule comes in contact with the
surface, it thermally accommodates. Physical justification: Vi-
brational frequency of the bond between the H2O molecule and
the substrate surface is typically 1013 Hz.
A fraction of incident
molecules bounces elasti-
cally: 0–40% at 40–180K
(Haynes et al., 1992)

4. Sublimation Rate into Vacuum
Basic kinetic theory provides relations between
E ... sublimation rate into vacuum
τ ... the mean residence time
psv ... saturation vapor pressure
E =
psv
√
2πkBTm
(1)
E depends on saturation vapor pressure, even in vacuum.
1
τ
=
E
σm
(2)
σm ... number of molecules per area for a monolayer (≈ 1019 m−2)
Adsorbed water molecules are more stronlgy bound than H2O
molecules on ice, e.g. 0.7 eV versus 0.5 eV (Poston et al., 2015).

5. Residence Time of H2O Molecule
60 80 100 120 140 160 180 200 220 240 260
10
−10
10
−5
10
0
10
5
10
10
Temperature (K)
MeanResidenceTime(years)
age of solar system
duration of ballistic flight
diurnal period
10
−5
10
0
10
5
10
10
10
15
MeanResidenceTime(seconds)
1 m/Gyr = 1 nm/yr = 3 monolayers / yr

6. Adsorption Isotherm → Residence Time
0 0.2 0.4 0.6 0.8 1
0
2
4
6
8
10
12
Vapor pressure p/p
0
Adsorbatevolumeθ/θ
m
Cadenhead & Stetter (1974) − adsorption
Cadenhead & Stetter (1974) − desorption
Fit
Measured adsorption isotherms for lunar sample 15565,3G at
15○C (Cadenhead & Stetter, 1974) and an empirical fit (Schorghofer
& Aharonson, 2014). Single monolayer has 1/5th the vapor pres-
sure (and therefore sublimation rate) of bulk ice.

7. Subsurface Diffusion
Molecules follow a random walk within the subsurface pore space
(⇒ diffusion process)
At high temperature: time of flight > surface residence time
at low temperature: time of flight < surface residence time
ice
grain
Transport due to differences
in surface concentration or
due to temperature gradient.

8. Migration Models
σ... areal density (#molecules/area)
zn... depth at site n, zn+1 = zn +
... jump length (mean free path), τ... residence time
The outward flux from any site: σ/τ. The net flux is
J = −(
σn+1
2τn+1
−
σn
2τn
) = −
∂
∂z
(
σ
2τ
) = −
∂
∂z
E(σ,T)
Flux caused by gradient in temperature T or surface concentra-
tion σ.
Three levels of description/models:
Random walk (discrete)
Continuum (diffusion-advection equation)
Boundary-value problem (time average)

9. Loss rate of buried ice
70 80 90 100 110 120 130 140
10
−6
10
−4
10
−2
10
0
10
2
10
4
Temperature (K)
IceLossRate(kg/m
2
/Ga)
buried
exposed
sublimationloss
dash line: ice on
surface
solid line: buried
beneath 10 cm of
75µm grains
In steady state, a gradient of in adsorbate concentration is estab-
lished. Loss rate is reduced relative to sublimation into vacuum
by number of hops it takes to escape: Eburied = ( /∆z)Evacuum.
100 kg/m2/Gyr = 110 K for exposed ice = 130 K for buried ice

10. Pumping Effect
Temperature
Sublimationrate
0
Depthbelowsurface
T(z,t)
Schematic illustration of a
subsurface temperature pro-
file (solid line = instanta-
neous, dashed lines = min-
imum and maximum). A
volatile water molecule has
a probability to hop up or
down. A molecule on the
surface has a higher mobil-
ity than a molecule at depth.
In the long term, this leads
to a net vertical flux of wa-
ter molecules. When suffi-
ciently many H2O molecules
are available on the surface,
this acts as an “ice pump”.

11. History and Analogs
The concept of subsurface ice accumulation due to thermally
driven diffusion (an “ice pump”) was originally proposed for Mars,
by Mellon & Jakosky (1993). On Mars, the source of water
molecules is the humid atmosphere.
Animation: https://github.com/nschorgh/Planetary-Code-Collection/
blob/master/Mars/Misc/movie1zooms.wmv
Reproduced in the lab-
oratory (with a static
rather than a periodic
gradient) by Hudson et
al. (2009).

12. Physical Concept of Ice Pumps
110 115 120 125 130
0
0.2
0.4
0.6
0.8
1
x 10
−8 Ideal Ice Pump
surface mean
subsurface
Pumping
Differential
Temperature (K)
EquilibriumVaporPressure(Pa)
110 115 120 125 130
0
0.5
1
1.5
x 10
−9 Lunar Ice Pump
surface mean
subsurface
Temperature (K)
EquilibriumVaporPressure(Pa)
θ/θ
m
=∞
θ/θ
m
=0.1
110 115 120 125 130
0
1
2
3
4
5
6
x 10
−10 Adsorbate Pump
surface mean
subsurface
Temperature (K)
EquilibriumVaporPressure(Pa)
θ/θm
=∞
θ/θ
m
=0.3
θ/θ
m
=0.03
170 180 190 200 210
0
0.05
0.1
0.15
0.2
Martian Ice Pump
surface mean
subsurface
Temperature (K)
EquilibriumVaporPressure(Pa)

13. Surface Population
0 5 10 15 20 25
40
60
80
100
120
140
160
180
200
Time (days)
SurfaceTemperature(K)
0 5 10 15 20 25
0
0.1
0.2
H2
OSurfaceConcentration(monolayers)
Model of population
of H2O molecules on
the surface.
Molecules are most
mobile but also most
easily lost during
warmest time.
w∞ = 1 m/Ga ... space weathering loss for thick ice layer
σ ... area density of volatile water molecules
E ... sublimation rate
dσ
dt
= s − (1 − e−σ/σm)w∞ − E(T,σ)
Stiff ordinary differential equation.

14. 40 60 80 100 120 140
50
100
150
200
250
Mean Temperature (K)
PeakTemperature(K)
Net loss
Strong Pumping
Weak Pumping
Classical
Coldtrap
PumpingDifferential(m/Ga)
0
0.2
0.4
0.6
0.8
1
Pumping differential according to model calculations that as-
sume a supply rate of 1 m/Ga and a space weathering rate of
1 m/Ga. Three nearly-complementary regions: weak pumping
and classical cold trapping (red), strong pumping (blue), and net
loss (grey).

15. -180˚
-150˚
-120˚
-90˚
-60˚
-30˚
0˚
30˚
60˚
90˚
120˚
150˚
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Pumping Differential (m/Ga)
-180˚
-150˚
-120˚
-90˚
-60˚
-30˚
0˚
30˚
60˚
90˚
120˚
150˚
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Pumping Differential (m/Ga)
Polar maps of the pumping differential (∆E), color coded and
plotted only where positive, overlaid on a shaded relief topo-
graphic grid illuminated from the eqatorial direction.

16. Conclusions
Periodic temperature oscillations can drive water molecule
into the subsurface (if enough volatile water molecules are
available on the surface) ⇒ Downward pumping of water
vapor
Alternative ice storage mechanism to classical cold trap-
ping
Temperature regime for classical coldtrapping and strong
pumping is nearly complementary. Strong pumping occurs
for mean surface temperatures lower than 105 K and peak
surface temperature higher than 120 K.
Ice Pump operates at roughly 1% of the lunar surface, but
is inefficient (≲ a few %). Efficiency is higher for large pore
spaces (rocky) than for small pore spaces (dust).
Adsorbate pump also operates on the Moon ⇒ Subsurface
has more adsorbed H2O than the surface.