A Lab-scale Investigation of the Mars Kieffer Model

Observations with the MGS's MOC and TES revealed a host of relatively dark features that appear on top of the seasonal CO₂ ice layer in spring (Kieffer et al. 2006; Kieffer 2007). "Spots" or "blotches" are radially symmetric round or oblate dark patches that often appear in spider locations in spring (Kieffer 2007; Portyankina et al. 2010; Thomas et al. 2011), while fans are stretched and oriented in the direction of local winds (Kieffer 2007; Aye et al. 2019).

"Halos" were identified as belted regions of uniform brightness surrounding dark spots. Other bright features have been identified related to dust deposition, such as halos surrounding Swiss cheese terrain pits and scarps on the South Polar Residual Cap (SPRC; Becerra et al. 2016) and bright edges surrounding linear dune gully recurring diffusive flows (Pasquon et al. 2016; Mc Keown et al. 2021). Halos, in the context of spots, were originally suggested to be due to metamorphism of the CO₂ slab material because of strain from diurnal flexure caused by basal sublimation (Kieffer 2007). An alternative formation mechanism was proposed by Titus et al. (2007), albeit for bright fans, which used near-infrared observations to show that their material consisted of CO₂ frost. This work suggested that the bright material forms owing to adiabatic cooling of gas spewing downwind from the jets producing CO₂ frost, which settles on the surface of the ice downwind. Pommerol et al. (2011) suggested that they are due to sinking of dust grains into the ice because many halos tended to appear after the original spot deposition. Thomas et al. (2010) proposed that when the pressure is locally raised by CO₂ plume activity, the equilibrium vapor pressure is exceeded for the ambient temperature. Therefore, condensation occurs, and dust drag on the gas is required to reach supersaturation and condensation. Thomas et al. (2010) had not seen supersaturation in their simulation runs, but they had only conducted simulations in the frame of a steady-state solution; it is possible that a transient model is required to allow for supersaturation and subsequent condensation to occur during a jet eruption. Several studies have been carried out with the aim of elucidating the origin and progression of these ringed features (Martinez et al. 2012; Cesar et al. 2022), showing various classifications based on change detection observed in images showing temporal evolution of spots. However, empirical studies of halo formation have not been conducted. Additionally, there has been no definitive evidence of active plumes despite extensive monitoring with the High Resolution Imaging Science Experiment (HiRISE) camera and Color and Stereo Surface Imaging System (Hansen et al. 2019).

Araneiforms compose a family of dendritic features on Mars, classified according to their scale and apparent activity level: spiders (Piqueux et al. 2003), dendritic troughs (Portyankina et al. 2017b), and sand furrows (Bourke & Cranford 2011). All araneiform types are posited to be formed as a result of escaping pressurized CO₂ gas beneath the seasonal ice slab and its interaction with the Martian surface, as outlined in the above description of the Kieffer model. Spiders are striking dendritic, tortuous, often radial networks of negative topography troughs that are native to the "cryptic region" (Kieffer et al. 2006) among the Martian south polar layered deposits and surrounds (Piqueux et al. 2003; Schwamb et al. 2018). Many of their morphologies comprise a central pit and radial "legs" (Hansen et al. 2010), and they range in scale from <50 m to >1 km. Their morphologies range from "thin" to "starburst" to "fat" and may be governed by slope and substrate properties, with many of them appearing in clusters with distinct distances between them (Hansen et al. 2010; Hao et al. 2019; Mc Keown et al. 2022). During southern spring, relatively dark albedo fans and spots (Hansen et al. 2010; Portyankina et al. 2010; Thomas et al. 2011), as well as bright halos (Kieffer 2007; Titus et al. 2007), are observed within their locales. Spiders can often be found within the locales of high-latitude patterned ground. Some of these terrains are suggested to form as a result of thermal contraction, possibly driven by sublimation dynamics in the current climate (Mangold 2005; Levy et al. 2009). Some high south polar araneiforms appear densely organized, overlapping with no distinct central region among interwoven troughs, and have thus been named "lace terrain." It has been suggested that some instances of this terrain may be patterned ground with polygon edges eroded by overlying escaping gas conduits, creating an anastomosing pattern (Hansen et al. 2011).

Sand furrows and dendritic troughs are smaller, less well-developed features that were recently detected on dune lee slopes (Bourke & Cranford 2011; Bourke 2013) and within interdune regions (Portyankina et al. 2017b), respectively, and are also attributed to the Kieffer model in a similar way to spiders. The main difference between spiders, furrows, and dendritic troughs is that the last two have been observed to form and be erased or extended in the present day, whereas spiders have not been observed to grow or newly form over the past two decades of high-resolution change detection imagery with HiRISE (McEwen et al. 2007). The reasons for the differing morphologies and apparent activity levels/lack thereof for all of these features have been largely unconstrained, mainly due to a paucity of Earth analogs or ground-truth data.

For the first time in the laboratory, plumes were formed when the interface between a CO₂ ice layer and Mars regolith simulant was heated, as proposed by the Kieffer model (Kieffer et al. 2006) (Figures 4(c) and 5(a)). However, our method of heat transfer was different to what we expect on Mars in that we did not engender the type of gradual heating expected by insolation receipt and used a small strip heater. In these experiments, the location(s) and number of plumes were stochastic, which was expected since small-scale variation in CO₂ ice layer thickness would cause weaker points in the ice. In all cases, the plume began as a subtle ejection of gas and dust and gradually grew more vigorous in activity. During the start of plume activity, we observed small-scale "cracking" of the regolith surface before the clear emanation of dust.

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For the first three trials, we observed plume dynamics when the heater was activated at full power (Figure 4). In each case, we ran the heater at 100% for ∼20 minutes. After ∼10–15 s, a relatively dark plume was observed to emanate from a corner of the heater; in some experiments a second plume formed from a different edge of the heater. The plume typically grew in power, in some cases hindered in its vertical stretch only by the top of the chamber shroud, approximately 40 cm above the surface of the MMS dust. Broader cracked patterns developed across the top of the square-shaped heater. Eventually, sufficient material was excavated from above and below the heater by the activity for small pits to form within the regolith above the heater. After the plume had died down, which usually took ∼10 minutes, the heater was stopped and the chamber was backfilled. Inspection of the fully defrosted surface showed that the energetic plume activity had erased any surface cracking or other created topography, via a combination of material ejected in the plume falling back down onto the surface and infalling material into the pit generated by the plume.

So as to investigate the influence of heater power level and to attempt to retain some created topography, three trials were run with the heater activated at 20% power. In these experiments, the plumes took longer to appear, were far less vigorous, and appeared as waving long, dark, standing striations in the chamber "atmosphere" (Figure 5). The lower levels of heat impulse also resulted in smaller, less dense cracks. These cracks were still erased if the heater was left running until the plume naturally ended. For the trials at either power level where the heater was stopped early and thus plume activity was cut short, surface morphologies were preserved.

The plume vent, upon first appearance, was a relatively dark spot within the frost as it exposed regolith. After the initial appearance, the vent widened enough to expose the heater, which was much darker than the regolith. Thus, we could not investigate further the appearance of dark spots.

Bright halos (Figures 4(c) and 7) often developed around the heater as the plume advanced. The halo became brighter as the plume activity continued, and it remained visible after plume activity ceased. When the chamber was opened up, the halo was inspected to determine whether its brightness was due to frost-covered material or granular sorting. As the bright material eventually disappeared, there was no change to the surface morphology as the surface completely defrosted, and there was no visible difference between the grains in the halo and the rest of the regolith, we concluded that the halo was bright because of a concentration of frost.

We interpret that the halo appeared to be due to deposition of frost-covered dust grains. Due to the plume, these dust grains were lofted into the atmosphere, where, either in the atmosphere or when they fell back down, they served as nucleation sites. CO₂ either froze to them and they fell back down, forming a ring shape around the boundary of the heater, or the heat flux around the edges of the heater caused translucent ice to morph into more triangular crystals. The latter possibility seems more likely owing to the placement of the bright frost around the edges of the heater in many cases. Portyankina et al. (2019) identified triangular crystals at lower temperature ranges than those for translucent slab ice. Figure 7 shows an example of an experiment where a plume was allowed to continue and a halo formed in <10 minutes. These temperature conditions were ∼–160°C, which is consistent with the range within which triangular crystals formed for Portyankina et al. (2017b). We infer that the location of the ring provided the right temperature conditions at our pressure ranges of between 2 and 10 mbar for retention of bright, perhaps triangular crystals (Portyankina et al. 2019) of CO₂—the same type of crystals that were observed to sparkle around the chamber and over the regolith when CO₂ was first condensing. As the frost was concentrated in this deposited ring, it was retained despite proximity to the heater.

In some cases where the plume was allowed to run continuously, we observed small pits and sinuous channels in the aftermath of activity on the surface of the MMS dust (Figure 8), including beneath the heater when it was lifted up after an experimental run. We interpret these as marking the path of trapped gas conduits escaping from beneath the heater.

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Based on the experimental runs where the heater was stopped as soon as surface morphologies were observed to form, we investigated the formation of "cracked," spider-like morphologies (Figures 9 and 4(c)). The activity started with a singular plume, usually at the corner of the heater (a point of weakness), and then a crack developed from the plume, toward the center of the heater. The morphology of these features was different from the morphologies that we expect to form via scouring, based on prior lab studies (Mc Keown et al. 2021) and interpretation of large araneiforms on Mars (Hansen et al. 2011; Hao et al. 2020; Mc Keown et al. 2022), in that they appeared as "cracks" from lateral widening of the regolith as opposed to surface channels, were rectilinear to linear in planform, and did not appear fractal with multiple orders of branching. We hypothesize that the differences are due to the method of heat deposition in these experiments.

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In our experimental setup, it appears that a thin CO₂ slab ice layer overlays a thin layer of regolith with pore-filling CO₂ ice, which itself overlies a layer of dry regolith (Figure 10(a)). The heater is located very near the bottom of the pore-filling CO₂ ice layer. Thus, heat deposition happens on the boundary between the heater and dry regolith/pore-filling CO₂ ice, causing a high-pressure gas pocket to form somewhere above the heater (Figure 10(a)). This overpressure acts on the two layers above (pore-filling CO₂ ice + slab ice layer), and it will crack them both in the polygonal crack pattern, similar to the cracks that are observed in early spring in the CO₂ slab on Mars (Portyankina et al. 2012). The gas will follow along the cracks toward the surface, to escape. However, these cracks may not propagate all the way to the top of CO₂ ice; rather, a hole may form through which the plume vents. In this scenario, erosion of icy regolith happens within these newly formed cracks in regolith held together by an icy matrix (Figure 10(a)). At the scale of our lab experiments, as these cracks and the motion of gas occur predominantly within the thin layer of regolith with pore-filling CO₂ ice, the cracks are likely to be erased as the ice finishes vigorously subliming from that regolith layer, gardening the surface material and any morphological changes caused by ice-rich regolith cracking.

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This is a different process from that what has been, at least so far, described for spider formation on Mars (Piqueux et al. 2003). In that model, a thick slab CO₂ ice layer overlays a thin layer of pore-filling CO₂ ice that in turn overlays dry regolith (which, relative to the experiment setup, can be considered infinite in depth). Solar energy deposition happens on the boundary between the pore-filling CO₂ and slab CO₂, and this is where the pocket of high-pressure gas forms. The pressure bends and breaks the CO₂ slab; as mentioned above, it can create polygonal cracks in the slab ice itself (Portyankina et al. 2012). The gas predominantly moves toward these vent(s) along the boundary between the CO₂ slab ice and the frozen regolith, eroding dendritic channels into the loose regolith. As the regolith lies at the lower boundary of the area of gas motion rather than in the realm of gas motion, these channels are preserved after the activity completes.

To summarize the proposed difference: if the regolith/substrate that is being eroded is embedded into the ice layer around and above the gas conduits, the gas escapes through "cracked" morphologies; if the eroded regolith is below the gas conduits, then dendritic shapes are carved out.

While acknowledging the scale differences, if the mechanism that we observed in the lab were to occur on Mars, then it suggests that sunlight would (a) penetrate overlying translucent slab ice and reach ice-rich substrate, warming at the boundary and causing a combination of cracking and surface scouring, depending on energy flux; (b) reach ice-rich terrain that is not covered in slab ice, warming it gradually to cause cracking; or (c) as suggested by Aharonson et al. (2004), stored heat in high thermal inertia terrain could transfer upward, first causing cracking within the top layer of ice-rich regolith and then forming "early" appearances of fans and spots. Due to the observation that this cracking in the laboratory is caused by heat and induced pressure from below the overlying slab and within the ice-rich regolith, we propose that the third scenario is most likely. Further temporal monitoring of fan/spot activity and reconciliation of this timing with corresponding sub-slab morphologies combined with thermal inertia studies, as well as a comparison of the morphologies formed using a solar simulator directed on a layer of thick ice, are needed to further elucidate whether a process similar to that which we observed in the laboratory is plausible for Mars. If such a process were to occur on Mars, certain morphologies may then provide insight as to whether there is ground ice within the topmost layer of substrate, whether composed of CO₂ or H₂O.

We have successfully replicated in the laboratory Stage 1 of the Kieffer model: condensing CO₂ onto a thick layer of granular material. For our laboratory experimental conditions, we observed that CO₂ diffuses into fine (<150 μm) MMS dust substrate down to at least 5 mm while forming a thin, conformal layer on top of this frozen layer of regolith. This consistently occurred as long as the pressure and temperature conditions identified by Portyankina et al. (2019) for the formation of CO₂ slab ice were maintained, despite experiments having slightly different CO₂ flow rates and sometimes varying within an experiment, including a long pause as the gas canister needed to be swapped. It is not clear what is the depth of seasonal CO₂ ice penetration into regolith on Mars. However, our tests show that pore-filling ice may influence the process of spider formation and retention and thus needs to be considered.

Efforts to create a measurably thick layer of frost were hampered by coolant availability and ensuring that we did not stress the coolant venting system, but the formation of an isolated and energetic plume indicates that the layer was thick enough to hold a building gas reservoir. This frost layer was translucent and visibly different from the "sparkling" frost crystals that would initially form.

Our observations suggest that an ice slab layer does not need to be that thick to serve as an impermeable layer and be able to withstand rising pressure. Thus, the formation of jets and their height may depend much more on the quality and purity of the ice rather than ice thickness. Additionally, as typical Martian wintertime pressure and temperature conditions are expected to fall within the range where we were forming slab ice, our experiments show that slab CO₂ ice is likely to form over at least Martian dust grains (< 150 μm) and also is likely to diffuse into the topmost layer of the regolith. Further studies using a wider range of discrete grain size ranges would be needed to investigate how ice deposition modes vary with grain size, as well as how grain size may influence the plume dynamics and any morphologies produced.

We also successfully simulated Stage 2 of the Kieffer model: forming plumes, spots, and halos. When heat was initiated at the interface between the substrate and conformal, condensed CO₂ ice, we formed plumes in the laboratory. As expected owing to differences in heat flux, energetic plumes reaching the ceiling of the chamber were formed when heaters were activated at full power, and more diffuse, gradually growing plumes formed for 20% power.

The spots and halos, as expected, disappeared as the surface completely defrosted, while the cracks were retained as long as plume activity was not too vigorous (which we elaborate on below). This supports the base hypothesis from the Kieffer model that this "zoo" of features are all formed owing to activity during eruptive CO₂ ice sublimation.

Finally, we may have simulated Stage 3 of the Kieffer model: forming spider-like morphologies, though mostly through a mechanism that differs from the traditional Kieffer model. Our plumes created crack morphologies that appeared to be driven by sublimation of interstitial ice within the regolith, rather than scouring of gas within the substrate-frost interface (as was proposed by Piqueux et al. 2003 for spider formation). This activity matches better with the types of processes discussed by Hao et al. (2020) and Pilorget & Forget (2016) that invoke a feedback with permeability and porosity and CO₂ diffusion into regolith pore spaces, respectively. Similar models have been proposed for patterned ground at high latitudes on Mars (Mangold 2005; Levy et al. 2009), citing thermal stress as responsible for polygonal or cracked patterns in the substrate.

Overall, we conclude that the erosion by active CO₂ jets might be more complex than the original Kieffer model describes, and, beyond spiders, it may contribute to formation of other typical Martian morphologies like polygonal terrains. Further study is needed to determine whether active dendritic troughs (Portyankina et al. 2017b) or sand furrows (Bourke & Cranford 2011) may form on present-day Mars via this mechanism. Additionally, in the lab these features were often erased, with preservation achieved only when (i) diffuse plumes operated and (ii) plume activity was abruptly halted. Thus, quantitative characterization of plume strength, along with duration, is needed to estimate the potential modification of such cracks and correlate with remnant geomorphology.

The pressure and temperature constraints outlined in Portyankina et al. (2019) seem to be sufficient within the lab setting for prompting CO₂ slab ice formation, i.e., changes to CO₂ flow rates and duration of the experiment influence the rate of slab ice formation, but not its creation. This is encouraging for alternative laboratory experiment setups and implies a robustness to these conditions within the Martian environment. We also showed for a thick (∼2 cm) layer of MMS that CO₂ ice will deposit first within the pore spaces of cold regolith and then coat over the surface as translucent slab ice.

However, with these first experiments, we can only report surface frost formation and diffusion for simulant grains <150 μm, and it is unclear to what extent this process may occur for different mineralogies or grain size distributions. Further investigation is needed to identify the exact granular properties that enable a CO₂ ice layer to form.

It is also not clear whether the heater depth influenced the depth to which CO₂ diffused into the substrate. Thus, an open question remains about the depth to which the CO₂ ice may infiltrate the substrate, via diffusion, and what controls that depth. Future experiments could aim to investigate frost formation over and within substrate of different grain sizes and types. Additionally, acquiring a thermal profile of the top 1 to a few centimeters would be beneficial in the lab. The same type of thermal profile, along with characterization of grain size range and roughness, would be important within in situ investigation of frost formation on Mars.

Achieving the correct conditions to build a thick layer of CO₂ on a thick, homogeneously cooled layer of regolith remains extremely challenging. Condensing our layer of CO₂ ice on a thick layer of MMS dust was only possible by having a small chamber (but large enough to contain a thick sample of MMS) with a cylindrical shroud that could cool the sky, as well as using a significant amount of coolant. If the sky is not cold enough, then the top layer of regolith can warm beyond the CO₂ frost point; this in turn causes much of the injected CO₂ to freeze onto the cold shroud rather than onto the regolith. We targeted building CO₂ onto our MMS layer by initially putting the CO₂ gas outlet close to the regolith surface, but incoming warm CO₂ quickly heated the surface and prevented the frost from forming in that region. Even with the outlet placed farther from the surface, we needed to carefully modulate flow so as to remain at the temperature ranges where translucent CO₂ condenses (Portyankina et al. 2019). Chilling the line of incoming CO₂ gas and connecting the chamber to LN₂ plumbing instead of individual dewars could increase the efficacy of future experiments.

While insights into the processes shaping the Martian surface may be gleaned by reconciling larger-scale models with our laboratory observations, we caution that our observations are limited by the conditions needed to condense CO₂. In particular, the MMS regolith simulant needed to be cooled throughout, which required cooling from the bottom via the LN₂ cooling plate. The scenario on Mars is different, with the CO₂ ice in vapor equilibrium with the atmosphere and that atmospheric cooling causing the surface to be cold enough to condense CO₂ as ice.

Finally, on Mars, interstitial water ice may be found across some terrains (Leighton & Murray 1966; Mellon & Jakosky 1993; Schorgofer et al. 2004) and may also affect the extent to which CO₂ diffuses into the substrate. This may constrain the locations where CO₂ can sublimate from within regolith on Mars, although it is plausible that cracks may also form by H₂O sublimation (Mangold 2005). Future experiments involving a broader range of grain sizes and frozen water ice within regolith should seek to explore this parameter space, enabling reconciliation of these relationships with remote-sensing imagery in order to understand local substrate properties within regions where spiders do (or clearly do not) form on Mars.

A key limitation of our study is that our heaters were unable to simulate the type of gradual and top-down heating achieved by natural sunlight. Additionally, a more quantified control over the creation of diffuse or energetic plumes would be helpful. On Mars, the plume strength has been thought to be primarily influenced by ice thickness, but CO₂ frost type and imperfections/porosity of that ice may be key controls on the strength of the overlying ice layer. Thus, characterizing these qualities of the overlying ice, in addition to its thickness, would be important measurements to collect in the laboratory or on Mars. Additionally, a measurement of the plume strength and duration could be integrated to constrain the amount of gas that built up beneath the ice layer and connected to the extent of disturbed/excavated material.

In the lab, spots were seen at the location of plume activity close to the crack morphologies. In some cases, where the heat influx continued long enough, bright halos were found around the vent in the substrate created by the plume. We interpreted these halos as frost that either nucleated on ejected dust grains, falling back down from the atmosphere in the chamber, at the right temperature and pressure ranges for sparkling CO₂ crystals to form, or formed at the exact temperature and pressure found at the edge of the heater. Our temperature data from near the heater show that the substrate was around –160°C when the halos were forming. Our pressure readings were from the top of the chamber and were not close enough to the plume to ascertain the pressure at the vent. However, from some experiments where the plume top reached close to the pressure sensor, we note that pressure increased by ∼ 3 mbar (Figure 11(b)). Bright halos on Mars have been suggested to form via a variety of processes, including (i) sinking through the ice overburden (Pommerol et al. 2011), (ii) the downward flow of gas produced by drag effects from particles falling from the jet (Thomas et al. 2011), (iii) metamorphism of the CO₂ slab via diurnal flexing (Kieffer 2007), and (iv) adiabatic cooling of gas spewing from the jets producing CO₂ frost, which settles on the surface of the ice downwind (Titus et al. 2007). The surface ice in our experiments was not sufficiently thick for sinking dust grains to be responsible for the halos, and due to vast scale differences, we cannot comment on the implications of our results for drag effects or slab metamorphism. However, the fourth scenario may explain our observations of frost forming in this region. To understand the environments where we observe bright halos on Mars, future experiments or an in situ investigation could use a thermal camera to map surface temperatures as the plume operates and correlate with the presence of halos.

Future experiments with thicker top ice layers will be needed to explore whether the "traditional" Kieffer model with surface scouring of dendritic troughs, as observed in Mc Keown et al. (2021), will occur. However, future in situ measurements are needed to confirm whether and to what extent CO₂ may diffuse into the top layer of substrate on Mars. This work may motivate future modeling efforts to apply our small-scale observations to the relatively large scales (∼tens of meters) observed for sand furrows and dendritic troughs on Mars.

If sublimation from within the regolith is a significant process to form the observed features on Mars, it appears that preservation of surface morphologies requires less vigorous plume dynamics. Thus, timing and longevity of plume activity may be key controls on where spiders, furrows, and dendritic troughs can form and be retained beyond the surface completely defrosting. These factors will be influenced by a combination of ice thickness/quality, translucency, and slope/aspect. Such factors can be explored on a broad scale with existing orbital observations of areas containing spider, dendritic trough, and sand furrow locations on Mars, but better constraints would be derived with the higher resolution and exact timing that can only be acquired with in situ measurements. Efforts to determine these parameters in the lab could guide investigation methods on Mars. Additionally, initial correlative analyses could be completed within small-scale lab studies or broad surveys of these Martian features.

Finally, morphometric measurements of the cracked morphologies created in the lab could be compared with those seen in the much larger spider features on Mars. Insight from these empirical investigations can guide numerical modeling, to determine whether the small-scale activity and features created in the lab are directly analogous to those on Mars.