1 Ice In Micro Cold-Traps on Mercury: Implications for Age and
2 Origin
1 2 2 1 3 L. Rubanenko , E. Mazarico , G. A. Neumann & D. A. Paige ,
1 4 University of California, Los Angeles.
2 5 NASA Goddard Space Flight Center, Greenbelt, MD.
6 Key Points:
• 7 Using MLA data and a thermal illumination model, we find evidence for ice trapped
8 in micro cold-traps of scales < 10 m and thickness < 1m.
• 9 Surface micro cold-traps occupy 1% − 2% of the polar region, compared to ∼ 7%
10 occupied by the larger cold-traps.
• 11 A recent comet impact is more likely to explain our findings than continuous deliv-
12 ery by, e.g, solar wind implantation or micrometeorites.
Corresponding author: Lior Rubanenko, [email protected]
–1– 13 Abstract
14 Evidence in radar, reflectance, and visible imagery indicates surface and subsurface wa-
15 ter ice is present inside permanently shadowed regions (PSRs) in the north polar region
16 of Mercury. The origin of this ice and the time at which it was delivered to the planet
17 are both unknown. Finding the smallest, most easily eroded, ice deposits on Mercury can
18 help answer these questions. Here we present evidence for volatiles trapped in cold-traps
19 of scales ∼ 1 − 10 m. We consider two possible delivery methods for these deposits: a
20 gradual, slow accumulation by micrometeorites or solar wind implantation and an episodic
21 deposition, either primordial or by a recent comet impact. We conclude the mechanism
22 that best explains the presence of volatiles in these micro cold-traps is a comet impact that
23 most likely occurred in a last ∼ 100 Ma.
24 1 Introduction
25 It has long been known that high latitude topographic depressions on low obliquity,
26 airless planetary bodies cast shadows that may persist for geologic time periods [Urey,
27 1952]. If sufficiently cold, these permanently shadowed regions (PSRs) may trap and pre-
28 serve volatiles for billions of years inside cold-traps [Watson et al., 1961; Arnold, 1979].
29 On Mercury, thermal models of the surface and subsurface showed water ice may
30 persist inside polar craters [Paige et al., 1992; Ingersoll et al., 1992; Vasavada et al., 1999;
31 Paige et al., 2013]. More recently, evidence for the presence of thick ice deposits near the
32 north pole of Mercury was bolstered by several independent measurements. Earth-based
33 radar observations have found anomalously bright regions suggestive of ice deposits which
34 are at least a few meters thick [Slade et al., 1992; Harmon and Slade, 1992; Butler et al.,
35 1993; Harmon et al., 2001, 2011]. Near infrared (IR) surface reflectance measurements
36 obtained by the Mercury Laser Altimeter (MLA) on board the MErcury Surface, Space
37 ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft detected bright
38 and dark deposits in areas that are sufficiently cold to trap ice according to thermal mod-
39 els [Paige et al., 2013; Neumann et al., 2013]. The bright deposits were identified as ex-
40 posed surface ice, while the darker deposits were suggested to be ice buried under a space
41 weathered thermal lag [Paige et al., 2013; Chabot et al., 2014; Delitsky et al., 2017]. PSRs
42 within craters were imaged by the Mercury Dual Imaging System (MDIS) and were found
43 to contain similar features with distinctive reflectance properties and sharp boundaries
44 [Chabot et al., 2014]. If these features are ice deposits, they could only outlast erosion if
–2– 45 they were relatively young or continuously renewed at a rate that dominates the gardening
46 rate [Chabot et al., 2016].
47 Lately, it was hypothesized that ice may persist in micro cold-traps that form in
48 PSRs cast by craters and random small scale topographic features [Hayne and Aharon-
49 son, 2015]. In this case, the term "micro" does not mean "of microscopic size"; instead, it
50 refers to the Greek word "µικρóς" (mikrós), "small". More recently, Deutsch et al. [2017]
51 found evidence for small ice deposits inside cold-traps on scales ∼ 1 km. Here we show
52 evidence for ice trapped inside much smaller micro cold-traps on scales 1-10 m. We use
53 MLA data to find the surface darkening occurs not only inside the larger, resolved fea-
54 tures, but also in the inter-crater terrain. We interpret this as evidence for water ice micro
55 cold-traps buried under a darkened thermal lag. We fit a model to the reflectance data in
56 order to constrain the lateral size of these cold-traps and their maximum possible thick-
57 ness. Finally, we compare our findings with recent estimates for the volatiles erosion rate
58 in order to constrain the origin and age of the ice trapped within them.
59 2 Evidence for Ice Inside Micro Cold-Traps
60 2.1 Measuring Mercury’s Surface Darkening
61 The surface darkening observed on Mercury’s pole by Neumann et al. [2013] and
62 Paige et al. [2013] is not unique to large impact craters. Inspection of the stretched MLA
63 reflectance map (Figure 1a) shows that the inter-crater terrain darkens in high latitudes
64 as well [Neumann et al., 2017; Rubanenko et al., 2017]. Similar inspection of the radar
65 brightness map [Harmon et al., 2011] (Figure 1b) shows small scale radar-bright features
66 in between the larger resolved cold-traps, indicative of small discontinuous ice deposits.
67 However, the radar map does not show a latitudinal brightening that matches the lati-
68 tudinal darkening observed in the reflectance map. While most the signal was found to
69 spatially correlate with the locations of small craters [Chabot et al., 2012; Deutsch et al.,
70 2016], some of it may still be associated with unresolved features in the inter-crater ter-
71 rain.
72 Due to the lack of MLA data in the south pole, our analysis is restricted to the north
73 pole of Mercury. To measure the decrease in surface reflectance due to the sub-pixel dark-
74 ening (below the resolution of the binned MLA dataset), we first collect MLA reflectance
75 data gathered between 2011-2015 in bins of 250 m. Then, we discard data below latitude
–3– Figure 1: a. The north pole MLA reflectance map in polar stereographic projection, binned at 250 m px−1. Dark deposits, which are postulated to contain ice trapped under a space weathered thermal lag, appear both inside craters and in the inter-crater terrain. In order to measure the sub- pixel darkening, we remove spots with reflectance < 0.08 and size > 1 pixels (marked in red). Gray pixels indicate missing or discarded data. b. The north pole stretched radar brightness map in polar stereographic projection, adapted from Figure 5 in Harmon et al. [2011] and rebinned at 1 km2. Radar bright regions, which are indicative of pure, thick ice, are apparent both in resolved cold-traps within larger craters but also in smaller craters [Harmon et al., 2011; Deutsch et al., 2016].
76 70°, anomalous measurements (greater than unity) and those obtained at emission angles
77 > 10°. The obtained reflectance distribution, shown in Figure 2, is bimodal with an ex-
78 tended tail. The right and left modes correspond to the mean reflectance of the bare re-
79 golith and the mean reflectance of slopes covered by a darkened deposit, respectively. The
80 extended tail was suggested to be exposed surface ice [Paige et al., 2013].
81 Next, we remove all the larger dark features, such as those inside craters: we begin
82 by reducing the reflectance map into a binary image with threshold 0.08, and remove bi-
–4– Figure 2: The MLA reflectance distribution of the north pole of Mercury (above latitude 70°) binned at 250 m2. The distribution is bimodal with an extended tail; the left mode corresponds to the mean reflectance of the dark surface deposits. The right mode approximately corresponds to the mean reflectance of the surface. The extended tail is thought to represent exposed, and therefore bright, water ice deposits. We use these two representative values (marked by arrows) to model the surface reflectance. The uncertainty we consider when choosing the reflectance of the dark deposits is shown by the two-sided arrow on the left.
83 nary spots larger than 1 pixel. The choice of 0.08 is reasonable considering it separates
84 the two modes of the reflectance distribution shown in Figure 2.
85 Mercury is found at a 3/2 spin-orbit resonance that causes roughly half of its polar
86 region to receive more insolation than the other half [Soter and Ulrichs, 1967]. These two
87 distinct longitude ranges are sometimes termed the "cold pole" (∼ 60°W − 120°W and
88 ∼ 240°W − 300°W) and the "warm pole" (∼ 120°W − 240°W and ∼ 300°W − 60°W),
89 respectively [Paige et al., 1992]. We calculate the zonal mean of the reflectance data in
90 these two longitude ranges (yellow-black and green-black dots, Figure 3). Due to MES-
91 SENGER’s non-polar orbit, the most reliable MLA measurements were gathered between
92 latitudes 75° − 85°. This region is marked in the figure by the dashed vertical lines and
93 filled circles.
94 We find the zonally averaged reflectance decreases from ∼ 0.18 in lower latitudes
95 (75°) to ∼ 0.15 near the edge of the most reliable data region (85°). The reflectance in
96 the cold pole decreases more rapidly than the reflectance in the warm pole. Near the pole
–5– 0.25 0.6 0.25 0.6 =5° =15° =20° s s s Modeled reflectance ( 1 km) ( 10 m) ( 1 m) MLA data (warm pole) MLA data (cold pole) 0.2 0.4 Subsurface cold-traps Surface cold-traps
0.15 0.2 0.2 0.4 Reflectance Cold trap fraction
0.1 0 =10° =25° s s ( 100 m) (<1 m) Reflectance 0.15 0.2 0.2 0.4 Cold trap fraction
0.15 0.2 Reflectance Cold trap fraction
0.1 0 0.1 0 70° 75° 80° 85° 90° 70° 75° 80° 85° 90° 70° 75° 80° 85° 90° Latitude Latitude Latitude
Figure 3: The zonally averaged reflectance (black circles) binned at 250 m px−1, large craters
removed, along with the modeled reflectance of random surfaces with different σs (blue), and the corresponding modeled surface and subsurface cold-trap area fractions (red). The green and yel- low circles indicate Mercury’s "warm pole" and "cold pole", respectively. The reflectance of the cold pole is lower than that of the warm pole, possibly indicating a greater fraction of ice buried under a thermal lag. The measured decrease in reflectance matches that of a random rough surface
with σs = 15 − 20°, corresponding to cold-traps on lateral scales < 10 m. The shaded envelope indicates the uncertainty in the value we chose to represent the reflectance of the dark slopes. The dashed vertical lines mark the region of most reliable data, also emphasized by the filled circles.
We highlight the σs = 20° panel as it described the surface that best fits the observed darkening.
97 (above latitude 85°) the surface reflectance sharply increases, possibly due to the pres-
98 ence of large impact craters such as Prokofiev, which were found to contain many high
99 reflectance deposits [Neumann et al., 2013].
100 2.2 Possible Reasons for Mercury’s Surface Darkening
101 Paige et al. [2013] postulated the MLA dark deposit found in many polar craters is a
102 weathered carbonaceous thermal lag covering a thick layer of ice. Using a thermal model,
103 they showed a spatial correlation between areas in which ice is stable in the subsurface
104 and areas that are MLA dark. Additional analysis conducted by Neumann et al. [2013] and
–6– 105 Chabot et al. [2014] showed a similar spatial correlation between these dark deposits and
106 the boundaries of permanent shadows.
107 Chemical and physical models explain how these polar deposits accumulate and
108 grow dark [Paige et al., 2013; Delitsky et al., 2017]. At first, comets or other impactors
109 deposit volatile raw materials such as water, methane, carbon dioxide and ammonia on the
110 surface. These volatiles travel to the pole and become cold-trapped inside PSRs [Schorghofer,
111 2015]. Then, magnetic cusps in Mercury’s magnetic field focus energetic particles onto
112 these ices along with galactic cosmic rays and Lyα radiation. This radiation can initiate
113 chemical processes that would eventually create heavier less volatile complex organic C-H-
114 N-O-S molecules that would cover the ices and protect them from sublimation or destruc-
115 tion [Delitsky et al., 2017].
116 Here we suggest the surface darkening we measure between latitudes 75° − 85° is
117 evidence for ice in micro cold-traps: ice deposits trapped in PSRs cast by sub-pixel topog-
118 raphy and buried under the same darkened thermal lag that covers the larger cold-traps.
119 This idea is supported by the difference in reflectance between the cold and warm poles.
120 The cold pole has a greater cold-trap area fraction than the warm pole as it receives less
121 insolation and has a higher PSR fraction due to the smaller angular size of the Sun in the
122 sky. The higher PSR fraction increases the area fraction of cold-traps that are buried un-
123 der a thermal lag, which leads to a lower surface reflectance. Thermal models show bright
124 surface ice is not prevalent on Mercury below latitude 85° due to the high amount of scat-
125 tered and emitted radiation, and thus has little effect on the overall surface reflectance
126 [Paige et al., 2014].
127 Other possible explanations for this surface darkening could be Mercury’s higher
128 surface carbon content [Syal et al., 2015], geologic features related to Mercury’s north po-
129 lar smooth planes [Neumann et al., 2017] or the low reflectance materials (LRM) found in
130 lower latitudes [Robinson et al., 2008]. However, these alternative explanations do not ac-
131 count for the excellent spatial correlation with PSRs and areas in which water ice is cold-
132 trapped under the surface [Paige et al., 2013; Chabot et al., 2014].
133 Next, we constrain the lateral scale of these cold-traps by modeling their reflectance
134 using artificial random topography.
–7– 135 2.3 Modeling the Micro Cold-Trap Area Fraction
136 A common way to model rough topography on airless bodies is to use random Gaus-
137 sian surfaces [e.g. Hagfors, 1964; Smith, 1967; Jamsa et al., 1993; Davidsson and Rick-
138 man, 2014; Bandfield et al., 2015; Rubanenko and Aharonson, 2017]. This artificial real-
139 ization has a Gaussian slope distribution and a power-law power spectrum. The 1-D slope
140 distribution of realistic airless topography sometimes deviates from this idealized model
141 due to the presence of craters. However, the calculated shadow and temperature distribu-
142 tions and the resulting cold-trap fractions of rough surface resemble those observed on the
143 Moon [Smith, 1967; Bandfield et al., 2015; Rubanenko and Aharonson, 2017]. To verify
144 this is also true for Mercury, we compared the modeled north pole cold-trap fraction using
145 real topography to that of a rough random surface with the same RMS slope σs ∼ 7°. The
146 cold-trap area fraction modeled by Paige et al. [2013] is 0.068, in good agreement with
147 the one calculated by our model, 0.07.
148 The exponent of the surface power spectrum describes the dependence of the rough-
149 ness on the lateral scale. The value of this exponent was recently measured on Mercury to
150 be β ∼ 2.9 for lateral scales ∼ 0.5 km, larger than some of the scales we model here [Su-
151 sorney et al., 2017]. However, with no better measurement, we choose to adopt this value.
152 We verified our calculated shadow and cold-trap fractions are largely insensitive to that
153 choice by modeling surfaces with β = 1.9 and β = 3.9. The surfaces we generate are com-
154 posed of N = 100 × 100 facets. This choice of the surface size is a compromise between
155 the model running time, which is squared in N, and the error in the calculated PSR area
156 fraction, which is ∼ 3% (compared to a surface with N = 1000 × 1000 pixels). A more
157 detailed description of the model and the generation of rough random surfaces is provided
158 in Rubanenko and Aharonson [2017].
159 Accurate measurements of the surface roughness are limited to the instrument reso-
160 lution which on Mercury is ∼ 250 m - much larger than our scale of interest. In the ab-
161 sence of better data for Mercury, we adopt measurements conducted on the Moon by the
162 lunar reconnaissance orbiter laser altimeter (LRO LOLA), noting Mercury’s surface rough-
163 ness was found to be slightly lower at lateral scales > 500 m [Fa et al., 2016]. However,
164 as will be explained later, this does not significantly affect our conclusions.
165 On the Moon, higher σs corresponds to smaller lateral scales; the distribution of
166 slopes on scales ∼ 1 − 10 km has σs ∼ 5°, while the distribution of slopes on scales
–8– 40 Moon South Pole 35 Moon North Pole Bandfield et al. (2015) Helfenstein and Shepard (1999) 30
25
20
15
RMS Slope (degrees) 10
5
0 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 10 3 10 4 Lateral Scale (m)
Figure 4: The surface roughness (indicated by the RMS slope) increases with decreasing scale on the Moon. The red and blue dots, which show LOLA data on scales > 10 m, are provided along with the standard deviation. Roughness measurements at smaller scales were obtained by Helfen- stein and Shepard [1999] and Bandfield et al. [2015].
–9– 167 ∼ 1 − 100 m has a higher σs ∼ 20° − 10° [Rosenburg et al., 2011, 2015; Bandfield et al.,
168 2015, and references therein]. We show this dependence in Figure 4 based on measure-
169 ments obtained by LOLA and previous analyses [Helfenstein and Shepard, 1999; Bandfield
170 et al., 2015]. To measure the slope distribution at lateral scales 10 m, 120 m and 240 m
171 we calculate the 2-D gradient of the LOLA polar (above latitude ±75°) map at the ap-
172 propriate baseline. To measure σs at higher lateral scales we fit a least-squares plane to
173 square groups of pixels on the 120 m map. We use groups of sizes 8 × 8 and 80 × 80 pix-
174 els for lateral scales 960 m and 9600 m, respectively. Finally, we calculate the RMS of the
175 slope distribution of all planes.
176 Higher σs affects the cold-trap area fraction by simultaneously increasing the PSR
177 area fraction and the amount of reflected and thermally emitted radiation from nearby illu-
178 minated, warm slopes. Therefore, higher surface roughness does not necessarily translate
179 into a higher cold-trap area fraction [Rubanenko and Aharonson, 2017]. On Mercury this
180 effect is amplified compared to the Moon due to the higher temperature of illuminated
181 slopes and the consequent higher reflected visible and emitted IR flux. Next, we use this
182 link between the surface roughness and the cold-trap area fraction to constrain the lateral
183 scale of micro cold-traps on Mercury.
184 We calculate the surface and subsurface temperatures accounting for insolation, scat-
185 tering, thermal emission and subsurface conduction. We employ the same model used by
186 Rubanenko and Aharonson [2017], but introduce two improvements: a finite Sun instead
187 of a point-source Sun and temperature dependent thermal parameters. We assume a bolo-
188 metric albedo of 0.08 [Domingue et al., 2011] and an emissivity of 0.95. Previous works
189 considered slightly lower or higher values [Soter and Ulrichs, 1967; Veverka et al., 1988;
190 Paige et al., 1992; Emery et al., 1998] but those do not significantly affect our results.
191 To calculate the subsurface temperatures up to a depth of 1 m we use a modified
192 version of the 1-D heat diffusion model described in Rubanenko and Aharonson [2017];
−2 −1 −1 193 we use a temperature dependent thermal conductivity (of order k ∼ 10 W m K ) and
−1 −1 194 specific heat capacity (of order c ∼ 300 J kg K ), as prescribed in the appendix of
195 Hayne et al. [2017]. For temperatures > 400 K we linearly extrapolate c and k. The error
196 introduced by this extrapolation should not significantly affect our results as only illumi-
197 nated facets, which are anyway found in radiative equilibrium, reach these temperatures
198 [Bandfield et al., 2015]. Finally, we assume a lunar-like power law subsurface density pro-
–10– Figure 5: A demonstration of our reflectance model. First, we calculate the maximum diurnal temperature distribution of the rough surface (left). Then, subsurface cold-traps are assigned with a reflectance of 0.04, corresponding to the left mode in the distribution shown in Figure 2. Surface cold-traps are assigned with a value of 0.23, corresponding to 1 σ above the right mode of the dis- tribution. Non-cold-traps are assigned with a value of 0.18, the mean reflectance between latitudes 70° − 75°. The total reflectance of the surface is a weighted average of the reflectance of the facets composing it. To obtain a statistically significant result, we average five different random surfaces for each latitude and each roughness.
−3 −3 199 file that increases from a value of 1100 kg m at the surface to a value of 1800 kg m
200 at depth [Hayne et al., 2017]. The resulting thermal skin depth is of the order of a few
201 decimeters.
202 As explained in Rubanenko and Aharonson [2017], we find the surface cold-trap area
203 fraction using the well-known relation between the maximum sublimation rate of ice into Û 204 vacuum Emax and the maximum surface temperature Tmax,
Û Pv Emax = p (1) 2πkB µTmax
−23 2 −2 −1 205 where Pv is the equilibrium vapor pressure, kB ≈ 1.38 × 10 m kg s K is the Boltz-
206 mann constant, µ is the mass of a water molecule [Watson et al., 1961; Schorghofer and
207 Taylor, 2007]. Exposed water ice sublimates from cold-traps at any temperature greater
208 than the absolute zero, but for temperatures < 120 K the ice loss rate is likely dominated
−1 209 by impact gardening and space weathering and is ∼ 1 m Ga [Gault et al., 1974; Lanze-
210 rotti et al., 1981; Morgan and Shemansky, 1991; Schorghofer and Taylor, 2007]. To find
–11– Û 211 the subsurface cold-traps area fraction we use a similar model that relates E, the surface
−2 −1 212 sublimation rate, ζ, the burial depth and J, the ice loss rate in kg m s [Schorghofer
213 and Taylor, 2007], µ`EÛ J = (2) 2ζ
−6 214 where ` = 75 × 10 m is the typical regolith grain size [McKay et al., 1974; Heiken et al.,
215 1991]. We find the surface (subsurface) cold-trap area fraction by calculating the fraction
−1 216 of facets whose surface (subsurface) sublimation rates < 1 m Ga . Finally, to obtain a
217 statistically significant result, we average five different random surfaces for every σs and
218 latitude.
219 The maximum annual temperature distribution of an airless surface is affected by the
220 planet’s obliquity and eccentricity. Here we neglect Mercury’s obliquity which is of order
221 a few arcminutes [Yseboodt and Margot, 2006], and model the thermal conditions at its
222 warm pole by fixing the planet’s solar distance at perihelion, 0.307 AU. In Figure 3 we
223 show the surface and subsurface cold-trap area fractions for surfaces with different σs (red
224 lines).
225 2.4 Modeling the Surface Reflectance
226 To model the latitudinal change in reflectance we use values derived from the dis-
227 tribution shown in Figure 2 and the cold-trap area fractions calculated above. As demon-
228 strated in Figure 5, we assign subsurface and surface cold-traps with a reflectance of 0.04
229 (the left mode) and 0.23 (1σ above the mean) and non-cold-traps with a reflectance of
230 0.18 (the mean between latitudes 70° − 75°). The total reflectance of the surface is ob-
231 tained by calculating the weighted average of the reflectance of the slopes composing it.
232 Results are shown Figure 3. Our choice for the reflectance value of the dark slopes is
233 based on the distribution appearing in Figure 2. For robustness, we consider an uncer-
234 tainty that is equal to the width of the left mode of this distribution, indicated by the blue
235 envelope.
236 The modeled reflectance of random surfaces with σs = 20° (slope-scale . 1 m) best
237 fits the zonally averaged MLA reflectance in the warm pole (green-black circles). Surfaces
238 with σs < 15° (slope-scale > 100 m) do not fit the observed reflectance due to their lower
239 subsurface cold-trap area fraction. Above we noted measurements at larger lateral scales
240 indicate the surface roughness on Mercury may be slightly lower than that of the Moon
–12– 0.25 0.6 MLA data CO/Ar − CH ( 1) 4 Compound Q kJ mol Pt (kPa) Tt (K) CO 2 NH (1) (1) (1) 3 CH4 9.7 11.69 90.67 CH OH 0.2 3 0.4 H O (2) (3) (3) 2 NH3 30.96 6.08 195.48
(2) (4) (4) H2O 51.06 0.61 273.16 CO 7.6(1) 15.30(3) 68.09(3) Reflectance ( ) − (6) ( ) 0.15 0.2 Cold trap fraction 5 4 6 CH3OH 44.2 1.08 × 10 175.6 Ar 7.78(7) 68.9(7) 83.80(7)
(8) (9) (9) CO2 27.2 518 216.58
0.1 0 70° 75° 80° 85° 90° Latitude
Figure 6: Left: the MLA reflectance data for the warm pole along with the subsurface cold-trap area fractions and the modeled decrease in reflectance for the most abundant volatiles found in comets [Zhang and Paige, 2009]. We find the presence of water ice cold-traps best explains the zonally mean surface darkening. The dashed vertical lines mark the region of most reliable data, as before. Argon and CO are represented by the same line, as their cold-trap area fractions are zero.
Right: the enthalpy of sublimation Q along with the triple point pressure Pt and temperature Tt used to calculate the cold-trap area fractions for the volatiles shown on the right. References: (1) Stephenson [2012], (2) Dell and Beebe [1955], (3) Staveley et al. [1981], (4) Sato et al. [1991], (5) Lucas et al. [2005], (6) Cheng [1994], (7) Ferreira and Lobo [2008], (8) Bryson III et al. [1974], (9) Chickos and Jr. [2002].
–13– 241 [Fa et al., 2016]. As roughness increases with decreasing lateral scale, this would only act
242 to decrease the scale of the cold-traps we find here and thus should not affect our conclu-
243 sions.
244 The fraction of the surface that can cold-trap a volatile species depends not only on
245 its temperature, but also on the thermochemical properties of the molecule [Watson et al.,
246 1961]. Above we found water ice cold-traps can explain the surface darkening observed
247 on Mercury. We repeat this calculation for other prevalent volatiles found in comets; we
248 derive their cold-trap area fraction and use it to model the surface reflectance, as we did
249 above. As an example, we show in Figure 6 results for a rough random surface with σs =
250 20° (lateral scale ∼ 1 m). We find that volatile species other than water cannot reproduce
251 the observed darkening. While some complex molecules such as methanol nearly fit the
252 measurements, they are much less abundant in comets compared to water ice [Zhang and
253 Paige, 2009].
254 We estimate the total area fraction occupied by micro cold-traps in the north polar
255 region by linearly extrapolating and integrating the red lines in Figure 3 from latitude 75°
256 to the pole. Assuming the scale of all micro cold-traps is ∼ 10 m (σs = 15°), the total
4 2 257 area of surface cold-traps is 2.98 × 10 km , ∼ 2.33% of the polar region. Similarly, if
258 the scale of all micro cold-traps was ∼ 1 m (σs = 20°), their total area would be 2.13 ×
4 2 259 10 km , ∼ 1.66% of the polar region. This is about 20% of the area fraction occupied by
260 the larger, resolved cold-traps [Paige et al., 2013].
261 Since we do not model lateral heat conduction, our results are only valid for lateral
262 scales larger than the thermal skin depth [Bandfield et al., 2015]. Therefore, although we
263 found cold-traps on scales 1 − 10 m can best explain the observed reflectance, we cannot
264 rule out the existence of smaller cold-traps. Additionally, we note it is possible these mi-
265 cro cold-traps do not contain ice at all as it may have already sublimated, leaving behind
266 the thermal lag that once covered it.
267 3 Accumulation and Dissipation of Ice in Micro Cold-Traps
268 After being delivered to the surface, water molecules on airless bodies travel in bal-
269 listic hops whose length depends on their thermal energy [Watson et al., 1961]. For Mer-
270 cury, the mean hop length is ∼ 100−200 km [Schorghofer, 2015] - comparable to the scale
271 of the largest cold-traps (e.g in Prokofiev Crater). Since the residence time of trapped
–14– 272 molecules is much longer than the duration of the hops, ice precipitation into cold-traps
273 can be thought of as rain falling into buckets; the probability that a molecule would be-
274 come trapped in a cold-trap depends on its surface area alone. Additionally, due to the ex-
275 tremely low sublimation rates, volatile redistribution is minimal and all cold-traps should
276 be filled approximately to the same height. Consequently, the accumulation and dissipation
277 of ice inside cold-traps can be thought of as a source-sink problem (per unit area). Con-
278 straining the ice thickness inside the smallest cold-traps on Mercury and comparing it to
279 the modeled erosion rate could help us estimate its deposition time and delivery method.
280 3.1 Constraining the Depth of Ice in Micro Cold-Traps
281 The potential ice thickness inside a cold-trap is limited by the depth of the perma-
282 nent shadow it occupies. If the temperature of the cold-trap is sufficiently low, ice may
283 accumulate inside it until it exceeds the permanent shadow volume (PSV) and becomes ex-
284 posed to solar illumination. However, ice accumulation may cease even before that stage.
285 Significant ice deposits may alter the topography and change the amount of scattered and
286 emitted radiation the cold-trap receives. Consequently, the temperature of the ice may in-
287 crease, inhibiting growth, or decrease, encouraging it. Next, we constrain the maximum
288 thickness of ice trapped in surface micro cold-traps using the depth of the PSVs they cast.
289 To calculate the depth of the PSV cast by the sub-resolution topography we employ
290 our 3-D illumination model used above. First, we find the instantaneous shadow depth:
291 the vertical distance between the surface and the shadow that covers it. The instantaneous
292 shadow depth d at a distance x from the point casting the shadow is,
d = z0 − z − x cot θ (3)
0 293 where θ is the incidence angle, z is the height of the point casting the shadow (relative
294 to the reference plane) and z is the point of interest (Figure 7). If more than one point in
295 the way to the Sun casts a shadow on the point of interest, we use the deepest shadow. To
296 calculate the depth of the permanent shadow, we find the temporal minimum of the instan-
297 taneous shadow depth at every point on the surface. As this calculation is less computa-
298 tionally intensive than the full temperature calculation, we are able to increase the model
299 accuracy by using topographies of size 250 × 250 facets. Relative to surfaces with size
300 N = 1000 × 1000 facets, our model underestimates the permanent shadow area fraction
–15– Figure 7: Our shadow depth model which we use to constrain the ice depth cast by the random topography. In this figure, θ is the solar incidence angle, d is the transient shadow depth, z is the height of the shadowed point and z’ is the height of the point casting the shadow above the refer- ence plane.
301 by ∼ 1.5%. As before, we obtain a statistically significant result by averaging the PSV
302 fractions of five different surfaces.
303 The cumulative distribution of the PSV depth is shown in Figure 8 for the two rough-
304 ness values that match Mercury’s surface darkening, σs = 15°, 20°, and latitudes 80° and
305 85°. We find that for surfaces with σs = 15° and σs = 20° (lateral scales ∼ 1 − 10 m) the
306 median PSV depth is ∼ 1 m and ∼ 25 cm, respectively. This result explains the absence of
307 a strong radar reflectance signal in between craters, that requires the deposit to be at least
308 a few meters thick [Harmon et al., 2001]. Next we discuss several ways in which erosion
309 can affect accumulated surface ice.
310 3.2 Sublimation due to Heat Delivered by Impacts
311 An impact can destroy cold-trapped ice in two ways: it may sublimate it by heating
312 the surface or it may mechanically disperse it into a region in which it will become unsta-
313 ble. Next we show the former is less important than the latter for ice trapped inside micro
314 cold-traps.
–16– Figure 8: (a) The permanently shadowed volume (PSV) depth superimposed on a random topog- raphy with σs = 20° at latitude 85°. The color bar on the right indicates the depth of the PSV above the surface, which is an upper limit for the thickness of the ice trapped within it. (b) A cross section (shown in red) of the topography. The PSV depth above the topography is plotted as the dashed blue line. (c) The cumulative distribution function of the PSV depth, showing most of the ice must be trapped in a layer < 1 m for surfaces with σs = 15° (scale ∼ 10 m) or < 25 cm for surfaces with σs = 20° (scale ∼ 1 m).
–17– 315 Impacts create a shock wave that compresses the regolith and heats it [Melosh, 1989].
316 The mass loss rate Ji due to surface heating by impactors can be estimated using the sim-
317 ple relation, E(D)α Ji = (4) Lsub
318 where E(D) is the cumulative energy delivered to the surface by meteorites of size < D,
319 Lsub is the latent heat for sublimation, α is the heat transfer coefficient taken here to be
320 unity.
321 Brown et al. [2002] used satellite records to measure E(D) for Earth using observa-
322 tions on detonating bollides in the atmosphere. They found the cumulative number N of
323 bollides colliding with Earth with energy E or greater is,
log N = a0 + b0 log E (5)
324 where a0 = 0.5677 ± 0.015 and b0 = 0.90 ± 0.03. For a given bollide size, the energy
325 delivered to Earth per unit area is,
N(E)dE E(D) = 2 (6) 4πRE
326 where RE is Earth’s radius. To obtain a rough estimate of the cumulative energy deliv-
327 ered to Mercury by meteorite impacts, we use the E(D) measured for Earth, correcting for
−1 328 Mercury’s higher mean impact velocity, ∼ 40 km s [Le Feuvre and Wieczorek, 2011].
329 We find the energy delivered by bodies with diameters < 1 m will sublimate ice at a rate
−1 330 of ∼ 1 mm Ga - much lower than the mechanical gardening rate or the sublimation rate
−1 331 at 120 K, which is ∼ 1 m Ga [Watson et al., 1961; Schorghofer and Taylor, 2007].
332 3.3 Erosion due to Mechanical Impact Gardening
333 Compared to sublimation due to impact delivered heat, mechanical gardening is a
334 more significant erosive process. Recently, Speyerer et al. [2016] found that the impact
335 turnover rate of the lunar surface may be much higher than previously thought due to the
336 contribution of secondaries. Observations of rayed craters on Mercury have suggested sec-
337 ondaries may play an even greater role compared to the Moon [Neish et al., 2013]. While
338 previous models have shown the time in which the top few decimeters are overturned due
339 to gardening is at least ∼ 1 Ga [Gault et al., 1974; Hurley et al., 2012], more recent mod-
340 els for both the Moon and Mercury [Costello et al., 2017a,b] find a much higher rate of a
341 few decimeters in 10 Ma.
–18– 342 While impact gardening does not necessarily accelerate sublimation, it causes lat-
343 eral and vertical regolith turnover. With time this turnover may erode the ice, if it is ex-
344 posed, or the thermal lag that covers it. Above we showed the modeled surface darkening
345 matches the MLA observations, indicating this thermal lag, which is most likely about
346 a decimeter thick [Paige et al., 2013], is more or less intact. If we take into account the
347 overturn models mentioned above, we see a significant fraction of this thermal lag should
348 have been eroded in less than 100 Ma (according to the more conservative, traditional
349 models) or in < 10 Ma (according to the more recent models). Other models that include
350 lateral mixing predict an even shorter erosion time scale [Hurley et al., 2012]. This in-
351 dicates the ice on Mercury was either recently deposited or that its accumulation rate is
352 much greater than its dissipation rate. This observation agrees with previously obtained
353 images that showed the dark deposits have sharp, unperturbed boundaries [Chabot et al.,
354 2014, 2016].
355 3.4 Sublimation Due to Space Weathering
356 The loss rate of exposed ice consists of temperature-dependent sublimation and
357 temperature-independent space weathering [Schorghofer and Taylor, 2007]. The latter
358 occurs mainly due to gardening, solar-wind sputtering and Lyα radiation from the local
359 interstellar medium (LISM), estimated to be a few decimeters per Ga [Lanzerotti et al.,
360 1981; Morgan and Shemansky, 1991; Westley et al., 1995]. While ice deposits in deep
361 craters (depth/diameter ratio ∼ 0.2) might be less affected by sputtering [Feldman et al.,
362 2001], micro cold-traps in the random topography have a generally higher sky visibility
363 [Rubanenko and Aharonson, 2017]. Additionally, while solar sputtering may be a net hy-
364 drogen source, significant quantities of surface ice, like on Mercury, should be more af-
365 fected by sputtering compared to an admixture of ice and soil Crider and Vondrak [2003].
366 4 Discussion
367 Ice persists inside cold-traps formed within permanent shadows on the north pole of
368 Mercury [Harmon et al., 2001; Neumann et al., 2013; Chabot et al., 2014; Deutsch et al.,
369 2017]. Many of these cold-traps were found to be covered by a dark deposit thought to
370 be a space weathered carbonaceous thermal lag [Paige et al., 2013]. Here we show this
371 surface darkening occurs also outside of the larger, resolved features, and find it can be
372 explained by water ice trapped under a thermal lag in micro cold-traps of lateral scales
–19– Pristine Boundaries Micro Cold-Traps radar signal Dark Thermal Lag Theory [Chabot et al., 2014] (this work) [Harmon et al., 2001] [Paige et al., 2013]
Primordial origin x x X X Steady accumulation X x x Only micrometeorites Recent comet impact X X X X
Table 1: Three ice accumulation mechanisms explaining the origin of ice in micro cold-traps on Mercury, and the evidence bolstering/refuting them.
373 ∼ 1 − 10 m. This result is consistent with the model developed by Delitsky et al. [2017],
374 that found both water and simple organics are necessary in order to form the darkened
375 thermal lag. By describing the sub-pixel topography using random Gaussian surfaces, we
376 find the median depth of the permanent shadows harboring these micro cold-traps, which
377 limits the amount of ice accumulated in them, to be < 1 m. This explains the latitudinal
378 sub-pixel darkening, which does not require thick ice [Paige et al., 2013], and the absence
379 of a matching continuous sub-pixel radar reflectance signal, which requires an ice layer at
380 least few meters thick (Figure 1).
381 To first order, four factors affect the purity of an ice deposit and the darkened ther-
382 mal lag covering it: volatile accumulation, volatile destruction, vertical regolith turnover
383 and lateral regolith mixing. By considering these factors we can put further constraints
384 on the origin and age of the ice inside micro cold-traps. We discuss two possible scenar-
385 ios that may explain the presence of ice in these shallow micro cold-traps: a steady gain
386 which is greater than the steady loss or an episodic deposition (primordial or recent) fol-
387 lowed by a steady loss (Table 1).
388 In the first scenario, the volatiles influx is greater than the outflux and Mercury’s
389 ice budget is dominated by slow, continuous delivery. Among the possible sources we
390 consider solar wind implantation, which was shown to be an important source on the
391 Moon [Crider and Vondrak, 2000; Liu et al., 2012], and a constant flux of micrometeorites
392 [Moses et al., 1999; Syal et al., 2015]. While we cannot completely rule out the contribu-
393 tion of solar wind to Mercury’s ice budget, we find it unlikely it is a significant source;
–20– 394 to explain Mercury’s surface darkening, the accumulated volatiles must contain organic
395 compounds that only exist in comets or meteorites and not in pure hydroxyl.
396 Due to their thinness, micro cold-traps can only remain visible on the surface if
397 the delivery rate is much greater than the overturn rate [Zhang and Paige, 2009]. How-
398 ever, Moses et al. [1999] and Syal et al. [2015] found the average ice delivery rate from
−1 399 micrometeorites is at most a few m Ga (using recent estimates for the cold-trap area
400 fraction, [Paige et al., 2013; Chabot et al., 2018]), same order of magnitude as the lat-
401 eral regolith mixing rate [Hurley et al., 2012] and lower than the mixing rate in the upper
402 few centimeters [Gault et al., 1974; Speyerer et al., 2016; Costello et al., 2017b]. Monte-
403 Carlo simulations conducted on the Moon [Hurley et al., 2012] and Mercury [Crider and
404 Vondrak, 2003] show only 50% of an initially 10 cm thick ice deposit will survive af-
405 ter 10 Ma, preventing it from developing a thermal lag or stay pure enough to be radar
406 bright. Exposed volatiles on Mercury were found to be covered by regolith at a rate of
−1 407 ∼ 0.5 cm Ma , further reducing the purity of the precipitating volatile [Crider and Von-
408 drak, 2003]. Therefore, it is unlikely volatiles delivered by micrometeorites alone are suf-
409 ficient to explain the presence of a darkened thermal lag covering ice trapped in micro
410 cold-traps, or the presence of a pure, radar bright ice layer in the larger cold-traps.
411 Over long time periods, the amount of ice delivered episodically, e.g in a volcanic
412 eruption or a comet impact [Butler, 1997; Moses et al., 1999; Kerber et al., 2009], is not
413 significantly different from the amount of ice delivered by micrometeorites over long time
414 periods. However, over short time periods, episodic events deliver large quantities of volatiles.
415 Of the two episodic mechanisms listed above, comets contain all the carbonaceous materi-
416 als that may potentially form a thermal lag over volatiles deposits [Zhang and Paige, 2009;
417 Delitsky et al., 2017]. Recent hydrocode simulations [Ong et al., 2010; Stewart et al., 2011]
418 showed that the volatile retention rate following a comet impact on the Moon is ∼ 0.1%.
419 Previous models [Butler, 1997; Moses et al., 1999] found higher retention rates for Mer-
420 cury, 5% − 15%. Adopting lunar models for Mercury may be inaccurate due to the higher
421 gravity, that helps preserve the volatile molecules, and the higher surface temperatures,
422 that encourage loss through sublimation. However, we can use these retention rates to ob-
423 tain an order of magnitude estimation for the amount of ice trapped in cold-traps follow-
424 ing a comet impact.
–21– 425 For example, a 5 km comet will deposit a layer of ice that is a few cm (0.1% reten-
426 tion) up to a few decimeters (5% retention) thick - enough to fill a significant portion of
427 the micro cold-traps. This amount of ice should better outlast space weathering [Morgan
428 and Shemansky, 1991] and impact erosion and eventually develop a thermal lag that will
429 further protect the ice. Therefore, we conclude an episodic deposition, such as a comet
430 impact, is more likely to dominate ice accumulation on Mercury. This observation agrees
431 with the recently measured uneven distribution of ice inside PSRs [Chabot et al., 2018].
432 Finally, the relative shallowness of these micro cold-traps shows this emplacement
433 could not have been primordial, as gardening would have eroded the thermal lag covering
434 the trapped ices. We can constrain the age of the ice trapped in these cold-traps, assuming
435 its origin is a comet impact. As mentioned above, the median permanent shadow depth
436 of micro cold-traps of lateral scales 1 m is lower than a few decimeters. In that case, and
437 considering traditional overturn rates for the Moon as a first order estimate [Gault et al.,
438 1974; Hurley et al., 2012], the most recent deposition must have occurred within the last
8 439 10 years. Evidence shows [Neish et al., 2013] the gardening rate on Mercury may be
440 faster than on the Moon, possibly indicating a more recent deposition. Recently acquired
441 observations and models that account for secondary impacts predict a much higher ero-
442 sion rate on both the Moon and Mercury [Speyerer et al., 2016; Costello et al., 2017b].
443 In this case, micro cold-traps could only outlast if the deposition occurred within the last
6 7 444 10 − 10 years. For cold-traps of lateral scales 10 m, the maximum permanent shadow
9 8 445 thickness is < 1 m, changing the time of deposition to 10 years and 10 years, respec-
446 tively. Lateral mixing should further decrease these timescales.
447 5 Acknowledgements
448 The MLA reflectance and topography data used in this manuscript are available
449 from the Planetary Data System (PDS) and the Arecibo radar images are publicly avail-
450 able here. The north pole maximum temperature binary files used to determine ice sta-
451 bility are available here. The modeled cold-trap fractions and permanent shadow depth
452 distributions used to produce Figures 3 and 6 and 8 may be downloaded here.
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