Compositional Constraints of Ice Lobes at the Edge of Martian South Polar Cap and the Possibility for CO2 Ice

As one of the major ice reservoirs on Mars, the south polar layered deposits (SPLD) are mainly composed of water ice and dust except for the perennial CO2 ice deposits on the surface and within buried layers. At the edge of Planum Australe, the Shallow Radar detected the base of two ice lobes, which can be used to estimate their dielectric properties and analyze the components. These measurements, combined with topographic data, allow for the relative permittivity of the lobe materials to be estimated at 2.73 ± 0.67. Under the constraint of the SPLD density, the permittivity value translates to the existence of CO2 ice depending on the dust content. If the dust content is larger than 24%, the lobes are CO2 free and composed of water ice, dust, and pore space. Whereas, for the dust content of <12%, our results suggest that the lobes must contain a certain amount of CO2 ice, which could be an average volume of 30%. When the dust content is between 12% and 24%, the existence of CO2 ice is undetermined. This study improves the understanding of ice deposits at the Martian south polar.


Introduction
The ice caps in the polar regions of Mars have been observed since the sixteenth century by Huygens and Cassini, but not until the Mariner and Viking spacecraft were the north and south polar layered deposits (NPLD and SPLD, respectively) identified from orbital images (Murray et al. 1972;Cutts 1973;Blasius et al. 1982;Howard et al. 1982).Subsequently, topography data obtained from Mars Orbiter Laser Altimeter (MOLA) on Mars Global Surveyor (MGS) show that the maximum thickness of the SPLD is about 3.7 km, with a volume of >1.60 × 10 6 km 3 (Smith et al. 2001;Plaut et al. 2007).The SPLD is considered the largest reservoir of volatile deposits on Mars and potentially holds the record of past climate changes in the last tens of million years (e.g., Clifford et al. 2000;Becerra et al. 2019).
In the past, it was suggested that large amounts of CO 2 could be stored in the SPLD (Leighton & Murray 1966).Thermal data from the infrared thermal mapper onboard Viking orbiter indicate that the south polar residual cap (SPRC) partially covering the SPLD is mainly composed of carbon dioxide (CO 2 ) ice with a small amount of water ice (Kieffer 1979;Paige et al. 1990).The comparison between Mars Orbiter Camera images in two Martian summers shows few-meter scale retreats of the erosion features which represent the loss of CO 2 from the SPRC (e.g., Malin et al. 2001).However, modeling of the topography based on the three possible flow laws does not support the composition of pure CO 2 ice for the Martian south polar cap (Nye 2000).Based on the modeling of the circular depressions, Byrne & Ingersoll (2003) argue that the etched CO 2 ice layer on the surface of the south polar cap is quite thin (∼8 m thick); further, data from the MGS and Odyssey reveal exposed water ice near the south pole (Titus et al. 2003;Bibring et al. 2004).Later, combined with the results of the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) and other pieces of evidence, the SPLD was interpreted as water ice dominant deposits mixed with 10%-15% by volume of dust (Plaut et al. 2007;Zuber et al. 2007).Tanaka et al. (2007) divide the late-Amazonian layered deposits of SPLD into the Planum Australe 1 to 4 units (Aa 1−4 ).Subsequently, Shallow Radar (SHARAD) detected CO 2 reservoirs that could double the current atmospheric pressure on Mars buried within the Aa 3 unit (Phillips et al. 2011;Bierson et al. 2016;Putzig et al. 2018).The distinct CO 2 ice units capped by thin water ice layers were identified in some regions with nearly radar "reflection-free zones" (RFZ).The depositʼs stratigraphy records the change of evolution of the Martian atmosphere in sync with the cycles of the planetʼs obliquity (Phillips et al. 2011;Bierson et al. 2016;Buhler et al. 2019;Manning et al. 2019).
As it stands, there is no evidence to suggest whether other RFZ or "low-reflectivity zones" (LRZ) might contain CO 2 ice (Whitten & Campbell 2018).MARSIS can penetrate to the base of the SPLD but could not distinguish a component of CO 2 ice in the SPLD materials due to the high density of CO 2 ice and degeneracies in solving for multi-component mixtures of dielectric permittivity and density (Plaut et al. 2007;Zuber et al. 2007).Therefore, the volume fraction of CO 2 in the SPLD material other than Aa 3 unit has not been addressed.In this work, we estimate the relative permittivity values of lobes (Figure 1) at the edges of the Ultimi Lobe region with SHARAD and MOLA data.The characteristics of radar reflections in the study region are identified as LRZ.Our results suggest that the lobes are mainly composed of water ice, which is consistent with previous studies.More significantly, we investigate the existence and quantities of CO 2 ice, which depends on dust content.This finding contributes to our understanding of the formation of SPLD and the evolution of the Martian climate.

Data and Method
The orbital radar sounder onboard the Mars Reconnaissance Orbiter, SHARAD transmits a modulated pulse with 10 MHz bandwidth (15-25 MHz) in frequency, which corresponds to a vertical resolution of 15 m in free space and 8.4 m in water ice (Seu et al. 2004(Seu et al. , 2007)).After processing, the horizontal resolution of SHARAD is 0.3-1 km in the along-track direction and 3-6 km in the cross-track direction (Seu et al. 2007).SHARAD was able to detect the base of two lobes located along the edge of the SPLD, ranging from 162°E to 170°E and 71.5°S to 73°S (see Figure 1).Figures 2(a  examples of the radargrams over the study region, whereas Figures 2(b) and (e) are the corresponding cluttergrams (Holt et al. 2006;Choudhary et al. 2016).White arrows denote the subsurface reflectors that appear in the radargrams but not the cluttergrams.
By assuming that the lobes are overlain on a plane in lateral continuity with the surrounding basal unit and that the subsurface reflectors come from that plane, the relative permittivity of the lobes is calculated by: where τ is the two-way time delay between the lobe top and the basal surface, c is the speed of light, and h is the thickness or depth of the lobe inferred from topographic data from MOLA (Figure 1(b) and Figure 3(a)).
By following the method in (Nerozzi & Holt 2019), the 1σ error of relative permittivity is estimated by:   and basal reflector, s h sur =1 m is the 1σ uncertainties in the MOLA measurement of the lobe top elevation, and s h sub = 36.77m is the elevation error between interpolated lobe basal surface and the MOLA 256ppd DEM of the sounding basal unit (Figure 3(b)).The apparent and interpolated depths in Figure 3(b) are consistent with the results in Khuller & Plaut (2021) and Plaut et al. (2007) at this edge of the SPLD.
We extracted the two-way time delays from the radargrams.Then, we estimated the depths of the subsurface reflections based on the geologic context and MOLA data, including our interpolation of surrounding terrain with lobes removed (Figure 1(b) and Figure 3a).Previous research suggests that the errors in the estimation of permittivity can be introduced by the uncertainty of two-way time delay (τ), especially in thin layers (Christian et al. 2013).To eliminate these errors caused by the overestimation of τ, we only use the surface reflectors that are consistent with the nadir, generated with clutter simulation using local topography data, to calculate the relative permittivity.For instance, the yellow lines in Figures 2(c) and (f) denote the actual nadir reflectors of the SHARAD tracks (Holt et al. 2006).The surface reflectors of SHARAD data 04342_01 are consistent with the orbiter nadir in Figure 2(c), whereas the surface reflectors of 10539_01 in Figure 2(f) are not.The mismatch between the nadir and surface reflectors erroneously raises the two-way time delays between surface and subsurface reflections and thus the calculated relative permittivity will be obviously overestimated according to Equation (1).Therefore, an accurate estimation of relative permittivity can be obtained by ruling out SHARAD tracks where the nadir and surface returns are mismatched.Here, we assume that the three-phase power relation in Stillman et al. (2010) and Bramson et al. (2015) is still working when the pore space is replaced with a CO 2 ice term.The compositions of the lobes are derived based on the estimated values of relative permittivity and the three-phase power relation in which exponent 2.7 is used.

Results
In the study region, more than 60 SHARAD profiles cross the lobes, and 21 of them show clear subsurface reflections.By comparing radargrams with their cluttergrams, we selected 13 SHARAD data tracks (black lines in Figure 1(b) and Table 1), whose nadir match the surface reflectors, to estimate the value of the relative permittivity.
Imagery data show that the lobes belong to the Planum Australe 2 unit (Aa 2 ) and cover Noachian-aged terrains (Tanaka et al. 2007).Therefore, the subsurface reflections shown in the SHARAD radargram indicate the interface between the lobes and their surrounding terrains.By extrapolation of the surrounding terrain surface beneath the lobes and combining this with the surface elevation of the lobes, we find that the average thickness of the targeted lobes is ∼318 m (Figure 3).Combining our thickness estimates with the twoway delay time measurements, we estimate the relative permittivity of the lobes to range between 2.08 and 3.56, with an average of 2.73 and a standard deviation of 0.25 (Figure 4(a)).The average error in our calculation is 0.67 by following the method in Equation (2) and Equation (3) (Figure 4(b)) (Nerozzi & Holt 2019).Compared to the relative permittivity value of water ice 3.0 ± 0.5 derived in Plaut et al. (2007), the estimated value of 2.73 ± 0.67 is in the low end of this range, implying the potential component of CO 2 ice in the targeted lobes given that the relative permittivity of CO 2 ice is 2.12 ± 0.04 (Pettinelli et al. 2003).Broquet et al. (2021) revealed a density of 1100-1300 kg m −3 with a best-fitting value of 1220 kg m −3 for the SPLD by combining radar, gravity, and topography data.This best-fit density of 1220 kg m −3 was also found by Zuber et al. (2007) using gravity data.According to previous studies, CO 2 ice has a higher density but a lower permittivity than water ice (Simpson et al. 1980;Plaut et al. 2007;Zuber et al. 2007).Therefore, we use the density of SPLD to further constrain the compositions of the targeted lobes (Table 2).Based on the three-phase power relation (Stillman et al. 2010;Bramson et al. 2015), possible compositions of the lobe units can be derived.Considering that the SPLD materials may include water ice, CO 2 ice, lithic material (dust), and pore space, the following two scenarios are discussed.
The first is a CO 2 -free scenario, in which we assume that no CO 2 ice exists in the lobe unit.MARSIS data suggest that the dust fraction in the SPLD is between 0 to 10% (Plaut et al. 2007).The density obtained from the gravity field and topography of the SPLD indicates that the dust content is less than 15% (Zuber et al. 2007;Li et al. 2012).However, in this study, we do not constrain the upper limit of the lithic material in the lobe.When 1σ error is introduced, Figures 5(a)-(c) shows that a composition of the CO 2 -free scenario is consistent with <82% water ice, 4%-60% pore space, and 14%-47% dust.By assuming that the ice mixtures have an upper limit of porosity of 40% (Bossa et al. 2014), we obtain a composition of 20%-82% water ice, 4%-40% pore space, and 14%-40% dust for this scenario.
In the second scenario, we assume that the lobeʼs materials are nonporous and consist of water ice, CO 2 ice, and dust.A permittivity value of 2.73 corresponds to a maximum dust content of <15% (Figure 5(d)), which is consistent with previous studies (Plaut et al. 2007;Zuber et al. 2007).Then, the average volume content of ∼64.5% for water ice and ∼30.5% for CO 2 ice are derived from the three-phase diagram of relative permittivity and density (Figures 5(d)-(f)).
Considering the uncertainties of relative permittivity and density of the lithic materials, we use a group of low and high values of the properties to infer the lobe compositions, respectively (Figure 6).Similar to the previous results in Figure 5, the CO 2 -free scenario reveals a composition of <85% water ice, <40% pore space, and 15%-60% dust and a composition of 28%-77% water ice, 11-40% pore space, and 12%-32% dust for the low and high properties of lithic material, respectively.For the CO 2 -exist scenario, the changes of lithic properties have a strong influence on the dust content but not the water ice and CO 2 when 1σ errors are applied.We find that the dust content can reach up to 24% if the lithic materials have a low permittivity value of 5 and density of 2200 kg m −3 .If the lithic material has a high relative permittivity of 11 and a high density of 3400 kg m −3 , the content of dust in the lobes is reduced to <11%.

Discussions
The lobes are at the edges of Ultimi Lobe, and are thought to have formed during the late-Amazonian period (Kolb & Tanaka 2001;Whitten & Campbell 2018).According to the geological map by Tanaka et al. (2007), the study area belongs to the Planum Australe 2 unit (Aa 2 ) that consists of evenly bedded planar SPLD sequences with thicker individual layers than those of unit Aa 1 .The estimated permittivity of 2.73 ± 0.67 (1σ error) in this paper is consistent with the low end of 3.0 ± 0.5 (1σ error) obtained by Plaut et al. (2007), which interpreted that the composition of SPLD is nearly pure water ice.Recently, Broquet et al. (2021) considered the effect of the flexure lithosphere under stresses caused by SPLD and constrained the relative permittivity with radar, gravity, and topography data to be 2.5-3.4,which does not exclude the presence of CO 2 , and our estimated permittivity value is also similar to that range.
The existence of CO 2 ice depends on the dust content in the lobes.If the amount of dust is larger than 24%, the lobes are CO 2 free and their porosity increases rapidly with the increment of dust content (Figures 6(f) and (c)).For the dust content of <12%, CO 2 ice must exist to reach the relative permittivity of 2.73 ± 0.67 and density of 1220 kg m −3 with 1σ error of 1100-1300 kg m −3 .If the content of dust is between 12% and 24%, CO 2 ice may or may not exist.Note that the mentioned two scenarios we discuss here only consider three components at a time, rather than all four (H 2 O, CO 2 , air, and lithics).One may expect some pore space within the ice lobe, potentially up to >50% if the SPLD was atmospherically deposited as snow; although compaction and sintering processes work to decrease porosity post deposition.For the lobes mixing with dry ice (i.e., CO 2 ice), water ice, pore space, and dust, the presence of pore space will increase the content of water ice and dry ice together by assuming that the dust content is less than 15% (Zuber et al. 2007).Moreover, previous studies indicate that the dust content in the north polar cap is about 6% (Nerozzi & Holt 2019;Broquet et al. 2020).Thus, we argue that the existence of CO 2 ice in the two lobes is quite possible unless the dust content is very high.Bierson et al. (2016) interpret that the massive CO 2 ice within the RFZ zones in the Australe Mensa Region of the SPLD was accumulated several times at low obliquity.However, the CO 2 ice can be deposited over large regions with low obliquity.The dry ice in the studied lobes could form during the same periods.Though parts of them had resublimated due to the relatively low latitudes, it is possible that there are residuals exist.The remaining CO 2 ices are thin and irregular, which can be the reason why SHARAD does not detect internal layers in the lobes.Moreover, MARSIS detected anomalously bright basal reflectors in an area centered at 193°E , 81°S in Aa 2 unit and LRZ, interpreted as the presence of liquid water (Orosei et al. 2018).The studied lobes also belong to the Aa 2 geologic unit mapped in optical imagery and the Promethei Lingula layer sequence based on stratigraphical analysis of the outcrop wall images (Tanaka et al. 2007;Milkovich & Plaut 2008).If the CO 2 ice does exist in the Aa 2 unit, the geothermal requirement to melt ice at the base of SPLD will be reduced to generate a brine (Sori & Bramson 2019).5 The Astronomical Journal, 166:238 (8pp), 2023 December

Conclusions
SHARAD detected the base of lobes at the edge of the SPLD.Based on these reflections and combined with topography, the relative permittivity of lobe materials can be estimated as 2.73 ± 0.67.Under the additional constraint imposed by SPLD density measurements from the literature, we propose two scenarios to interpret the possible compositions of the lobes.The CO 2 -free scenario requires the dust content to be no lower than 14% assuming the lithic material with relative permittivity of 8 and density of 2800 kg m −3 , which is at the upper limit of previous studies (Plaut et al. 2007;Zuber et al. 2007).If the CO 2 ice exists, the content of dust with moderate dielectric properties is calculated to be less than 15%.When the four compositions are all considered, porosity within the lobes would raise the content of the lithic material and/or the content of ice (both water ice and CO 2 ice).We conclude that CO 2 ice probably exists in the lobes because no evidence proves that the SPLD contains high amounts of dust.These CO 2 ice may be the residuals that formed during the low obliquity periods.In the future, lobes or other landforms at the edge of SPLD will be carefully studied to find more evidence of the existence of CO 2 ice in the Aa 2 unit.If confirmed, the findings would imply that an appreciable mass of CO 2 might be stored in the SPLD, significantly increasing the CO 2 budget on Mars.Additionally, the presence of CO 2 ice would change the thermophysical properties and reduce the local heat flow requirement for the scenario of liquid water buried in the south polar region.
) and (d) show two

Figure 1 .
Figure 1.The topographic map of the study region.(a) Topographic map of Mars south polar cap (image credit: NASA/JPL/ASI/ESA/Univ. of Rome/MOLA Science Team/USGS).The black line outlines the south polar layered deposits (SPLD) on Mars.The study region is located at the edge of the polar cap, as indicated by the rectangle (white-dash lines).(b) The ground tracks of SHARAD detected subsurface reflectors (white lines).Black lines indicate the ground tracks of radargrams used to estimate relative permittivity.

Figure 2 .
Figure 2. Examples of SHARAD Radargrams in the study region.SHARAD observations of (a) 0434201 and (d) 1053901, white arrows point to the detected base of the lobes.SHARAD cluttergrams of (b) 0434201 and (e) 1053901.(c) and (f) are enlarged cluttergrams indicated by the white frames in (b) and (e).Yellow lines mark the SHARAD nadir locations.

Figure 3 .
Figure 3. (a) Topographic map of the study area in which the two lobes were removed by interpolating the surrounding terrain surface beneath the lobes.(b) Plot of the depth of the lobes based on interpolated topographic map and MOLA topography vs. the apparent depth derived from the delay time of subsurface reflections and an assumption of relative permittivity of 1.By applying the least absolute deviation method, the black line indicates the best-fit line of which the slope is 1.54 and R-square is 0.78.The y-intercept is equal to 36.77 and represents the uncertainties of the basal topography (Orosei et al. 2017).

Figure 5 .
Figure 5. Compositions of the ice lobes by assuming the lithic components have moderate properties.(a)-(b) Ternary diagram of relative permittivity and density calculations for the mixtures of H 2 O ice, lithic material, and air.(c) Combination of (a) and (b).(d)-(e) Ternary diagram of relative permittivity and density calculations for the mixtures of H 2 O ice, CO 2 ice, and lithic material.(f) Combination of (d) and (e).The values of relative permittivity and density are 8 and 2800 kg m −3 , which can be found in Broquet et al. (2021) and Zuber et al. (2007; Table 2).Dashed lines in (a)-(b), (d)-(e) and colored regions in (c) and (f) indicate the 1σ errors.

Figure 6 .
Figure 6.Compositions of the ice lobes by assuming the lithic components have low and high properties (Table 2).(a)-(b) Ternary diagram of relative permittivity and density based on relative permittivity of 5 and density of 2200 kg m −3 .(c)-(d) Ternary diagram of relative permittivity and density based on relative permittivity of 11 and density of 3400 kg m −3 .Colored regions indicate the 1σ errors.

Table 1
SHARAD Data in the Permittivity Calculation