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Icarus 221 (2012) 262–275

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Origin of small pits in martian impact craters ⇑ Joseph M. Boyce a, , Lionel Wilson a,b, Peter J. Mouginis-Mark a, Christopher W. Hamilton c, Livio L. Tornabene d a Hawaii Institute for Geophysics and Planetology, University of Hawaii, Honolulu, HI 96822, USA b Lancaster Environment Centre, Lancaster University, Lancaster LA1 4YQ, UK c NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA d Center for Planetary Science and Exploration, University of Western Ontario, 1151 Richmond Street, London, ON, Canada N6A 5B7 article info abstract

Article history: We propose a numerical model for the formation of the closely-spaced pits found in the thin, ejecta- Received 26 January 2012 related deposits superposed on the floors, interior terrace blocks, and near-rim ejecta blankets of well- Revised 6 July 2012 preserved martian impact craters. Our model predicts the explosive degassing of water from this pitted Accepted 25 July 2012 material, which is assumed to originally be water-bearing, impact melt-rich breccia at the time of depo- Available online 11 August 2012 sition. This process is analogous to what occurred in the fall-out suevite deposits at the Ries impact structure in Germany. At Ries, impact heating of water-bearing target material resulted in the rapid degassing Keywords: of its water and other volatiles. The martian environment plays an important role in enhancing the effects Mars, Surface of this degassing by increasing the flow-speed of the escaping gas. The high flow-rate of gas through par- Cratering Impact processes ticulate materials, such as suevite, tends to quickly form segregation channels or vent pipes, similar to Geological processes those found in the Ries deposits. These pipes act as conduits for the efficient high-speed escape of the Terrestrial planets gas and small clasts that it entrains. Escaping gas and entrained clasts abraded and eroded the conduit walls, flaring them to form pits above a network of pipes. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction et al., 2007, 2012; Mouginis-Mark and Garbeil, 2007; Morris et al., 2010). The closely-spaced pits have been attributed to subli- Impact craters provide considerable information about the mation (Hartmann et al., 2010), or to undermining and collapse composition and structure of target materials, physical properties (McEwen et al., 2007; Tornabene et al., 2007; Mouginis-Mark and of the impactors, and impact cratering processes. For example, on Garbeil, 2007) caused by removal of water that had seeped or de- Mars, impact structures show evidence of the effects of substantial fused into these deposits following their deposition. This material water in the target material (e.g., Carr et al., 1977; Mouginis-Mark, is found in impact craters that are widely distributed over the sur- 1979). Here, we focus on a recently-identified impact ejecta and face of Mars. Consequently, if the pits require a substantial amount crater-fill facies first discovered by Mouginis-Mark et al. (2003) of water to form, then their occurrence has important implications in Mars Orbiter Camera (MOC) images. These deposits were later for the history of volatiles on Mars (Tornabene et al., 2012). mapped globally by Tornabene et al. (2012). This facies generally Here we present a numerical model of pit formation in this ejec- occurs as thin, heavily pitted deposits in relatively well-preserved ta and crater-fill facies (herein called martian pitted material) that martian impact craters (Fig. 1). The closely-spaced pits found in involves explosive degassing of the water initially contained in the these deposits are morphologically distinct from the larger, single target material. This model is summarized in Fig. 2, which is in- central pit features studied by Wood et al. (1978), Hale (1982), tended to serve as a guide to the reader in the presentation of and Barlow (2010a). In the parent craters that contain both these our model. The model is inspired by evidence that hot materials thin ejecta facies and large single central pits, the thin ejecta facies in the Ries fall-out suevite degassed immediately after deposition appears to overlie the large pits. This thin ejecta facies is thought to (Pohl et al., 1977; Newsom et al., 1986), resulting in fluidization be composed of impact-melt rich breccia impactite similar to sue- of the deposits, elutriation or separation of fine particles and for- vite at the Ries impact structure on Earth, and may have initially mation of vent pipes that carried gas from the deposit. contained substantial water (McEwen et al., 2007; Tornabene

2. Background ⇑ Corresponding author. Fax: +1 808 956 6322. E-mail addresses: [email protected], [email protected] (J.M. Boyce), [email protected] (L. Wilson), [email protected] (C.W. Hamil- The martian pitted material was ﬁrst recognized in MOC images ton), [email protected] (L.L. Tornabene). by Mouginis-Mark et al. (2003) at a resolution of 3–6 m/pixel. As

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Nomenclature

a average radius of spherical clasts q number of tubes cutting vertically through area A A surface area of deposit through which gas escapes Q universal gas constant

Aa average fractional area of void space R radius of spherical space at the center of a cube of side CD drag coefﬁcient length (2L) E kinetic energy r typical radius of gap or tubes between the commonest f friction factor for gas ﬂow past particles from the wall of clast in the layer

the tube rmax radius of largest spherical clast resisting elutriation by Fi mass per unit time passing through any one tube gas at speed Ug Fm gas mass release rate per unit mass of suevite per unit Ta temperature of the gas time Ug ﬂow speed of steam through a pathway at height z Fv gas generation rate above base of layer g acceleration due to gravity v void space fraction L half side length of cube used in void space calculation Z depth below the surface 1 m molecular mass of H2O, 18.0153 kg kmol z height above base of pitted material layer nw water mass fraction in the suevite deposit gg viscosity of the gas P gas pressure at a given depth j thermal diffusivity Pa Mars atmospheric pressure at the surface qg density of the gas P0 pressure at base of suevite layer at depth Z below the qr typical silicate clast density surface

High Resolution Science Imaging Experiment (HiRISE) images paper we show that all of these models are inconsistent with many (25 cm/pixel) became available, workers such as McEwen et al. characteristics of the pits and pitted material. (2007), Tornabene et al. (2007, 2012), Mouginis-Mark and Garbeil McEwen et al. (2007) and Tornabene et al. (2012) listed three (2007), and Morris et al. (2010) studied this material, and con- reasons why the pitted material is impact melt-rich breccia, similar cluded that its morphology and stratigraphic position indicated to the suevite at the Ries impact structure. These reasons include that it is a facies of impact ejecta, probably impact melt-rich brec- (1) the apparent ﬂuid ﬂow of the material unit during emplace- cia (similar to suevite at Ries crater, Germany). They proposed that ment of the host deposit, (2) the presence of blocks embedded in the pits resulted from collapse of voids left in the pitted material by pits walls, and (3) the pitted material’s uppermost stratigraphic escape of water from pockets, or of ice from lenses, at a time well position relative to other impactite deposits. Tornabene et al. after deposition of this material. In contrast, Hartmann et al. (2010) (2012) suggested that the likelihood that the pitted material is im- suggested that the pits are produced by sublimation of ice distrib- pact melt-rich breccia implies the presence of water in the target uted more evenly throughout these deposits. However, in this materials. They based this suggestion on experimental, theoretical

Fig. 1. Examples of pitted material at Tooting crater, a 27 km diameter fresh martian impact crater. (a) Location image for other sub-scenes in this ﬁgure. CTX image P01_001538_2035. (b) Pits on the ﬂoor, segment of HiRISE image PSP_002158_2035. (c) Pits on the exterior rim, segment of HiRISE image PSP_002580_2035. (d) Pits on a terrace block, segment of HiRISE PSP_003569_2035. Author's personal copy

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Fig. 2. Conceptual model for the formation of pitted materials within impact structures on Mars. (a) An impactor strikes the martian surface, which includes H2O distributed in the regolith and cryosphere. (b) Ejecta from the transient crater generate an impact melt sheet and ejecta plume. (c) The expanding ejecta plume, which includes entrained

H2O and lithic materials, becomes gravitationally unstable and begins to collapse. (d) The melt-bearing impact breccia with entrained H2O is deposited within the crater floor and surrounding terrain to form the crater fill and outer ejecta facies. (e) Hot melt-bearing impact breccia almost immediately converts entrained water, and water contained in the melt and hot lithic fragments to steam. (f) Water vapor starts to escape from the deposit and form a series of preferential pathways that transport vapor and fine- grained material to the surface. (g) As gas bubbles coalesces into larger vent pipes, the flow velocities increase, which draws in additional water vapor by the Venturi Effect (Kokelaar, 1983). This helps the flow of gas to begin to entrain larger clasts that help to abrade vent walls. The growth of the pits is enhanced by deepening of the choked flow point within the flaring vent. (h) The eruptions terminate as the volume of gas is depleted within the deposit. The vents pipes fill with collapse material to produce a pitted terrain composed of a network of regularly spaced pits with shared rims that are draped by a topographically subtle layer of interfingered ejecta deposits. Note that (f–h) show a magnified view of the inset identified in (d), and hence are at different scales. and terrestrial field studies (Kieffer and Simonds, 1980; Sheridan and timing of these pits, and specifically, whether they formed and Wohletz, 1983; Stewart et al., 2003; Pope et al., 2004; Stewart by processes that require substantial water in the target materials and Ahrens, 2005; Osinski, 2006; Osinski et al., 2008) implying that at the time of impact. craters formed in volatile-rich targets, like the Earth or Mars, should produce an abundance of this type of material. 2.1. Morphology of the pits Furthermore, while the pitted material is best exposed in the freshest martian single- and multiple-layer impact craters (it is The martian pits (Fig. 1) are bowl-shaped, depressions that rare in double-layer ejecta craters), it is also identified in some old- range in size from a few meters to more than 3 km in diameter, er, but still well-preserved, craters of the same type. This, com- but most pits are [200 m in diameter (see Tornabene et al. bined with their observation that craters containing pitted (2012) for detailed geomorphic descriptions of the pits). These pits material occur everywhere outside the polar regions, led Torna- occur on the floors, terraces, and exterior ejecta deposits of fresh bene et al. (2012) to suggest that abundant H2O (probably in the craters (Tornabene et al., 2012). The pits commonly occur in clo- form of ice) was present in the subsurface of Mars, at least within sely-spaced groups whose individual pits are so close together that the excavation depth of the craters, for much of the planet’s their rims share straight segments situated between individual history. For this reason, it is important to determine the origin pits. The tendency for the pits in these closely-spaced groups to Author's personal copy

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Fig. 3. Comparison of geometry of closely-spaced martian pits in Mojave crater (left) and a schematic diagram of a typical soap froth (right). Note that both types of feature share straight segment boundaries between individual cells. Image on left is segment of HiRISE image PSP_002602_1875; image on the right is typical soap froth based on the work of Glazier and Weaire (1992).

be nearly circular and to share straight rim segments produces a geometry that resembles a 2-D cross-section though soap-froth, or a honeycomb (Fig. 3). There are isolated pits that do not exhibit shared rims (Fig. 4), but in general pits occur within closely-packed groups with rims that do not appear to be raised above the surrounding terrain. In contrast, isolated pits commonly have relatively low, raised rims (Fig. 3). The martian pits commonly exhibit evidence of mantling (flat floors and subdued topography), even in the freshest of craters. However, in some large pits, even those that appear to be mantled, meter-scale, light-toned blocks are embedded in their walls (Fig. 5). McEwen et al. (2007) and Tornabene et al. (2007, 2012) have proposed that these blocks are large clasts within an impact-melt-bearing breccia deposit. Tornabene et al. (2012) found that the size of the largest pits in Fig. 4. On the left is a view of the NE floor of Tooting crater showing the location (box) of the high-resolution image on the right, showing examples (arrows) of pits a given crater generally scales with the diameter of the host crater. with low rims. Note that in the image on the right two areas contain pits of They also found that the largest pits in a particular crater are typ- difference average sizes (upper right portion with larger pits, and lower left and ically located near the center of the pitted materials within that bottom with smaller pits). This difference may be the result of such factors as crater. This relationship of pit diameter to crater size and location difference in thickness of pitted deposits that could cause differences in total may reflect a relationship between pit size and deposit thickness. amount of water available to produce pits, and hence duration of eruption (HiRISE image ESP_014157_2035).

2.2. The pitted material

In this section, we discuss the aspects of the pitted material most relevant to our model for pit formation, including the general morphology of the pitted material, and its physical properties based on knowledge gained from Mars observations, theoretical studies, and terrestrial analog studies (n.b., for more extensive discussion of the morphology and possible origins see Tornabene et al., 2012). We also estimate the volatile content of the pitted material based on models of the martian crust and indirect obser- vational data. This information provides a basis for constructing and testing our model against observed pit characteristics. The pitted material mainly occurs as flat, thin deposits superposed on other impact crater material on the floors of fresh martian craters (Fig. 1). These deposits can be several hundred meters thick in the largest craters containing these materials (e.g., Hale crater). Pitted material also is found within topographic low areas on interior terrace blocks and on ejecta blankets near Fig. 5. Blocks (light colored spots) appear embedded in the walls of these pits on crater rims. Considering the general relief of hummocks in some the SW floor of Mojave crater. The blocks are similar to those found in terrestrial of the ejecta blankets, the deposits found there may only be several suevite deposits. Note material of uniform albedo on the floors of these pits. These meters thick. This material also commonly occurs on interior materials form flat areas that embay or surround hummocks, and also appear to be slopes of craters as thin sheets. These sheets appear to have free of blocks. These materials may be a mantling or pooling of fine-grained material, possibly deposited as rapidly escaping gas separates and removes fine- drained from high places in the crater (e.g., on terrace blocks) to grain particles from the pitted deposit below (HiRISE image PSP_002602_1875). lower elevations (e.g., crater floors) (Fig. 6). They often contain Author's personal copy

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In this study, we use the pitted material in the northern portion of the floor of fresh martian impact crater Tooting (28.8 km diameter) to test our model because it contains well-developed pitted deposits and we can reasonably estimate of the average thickness of the deposit at this location. We also use the suevite of Ries impact structure as a terrestrial analog to the pitted material in Toot- ing crater as a way to estimate physical properties of the pitted material (see e.g., Pohl et al., 1977; Stoffler, 1977; Hörz et al., 1983; Newsom et al., 1986; Osinski, 2003, 2008). We contend that this is reasonable because the two craters are approximately the same size (the gravity-scaled diameter of Ries is 32 km; see Stew- art and Valiant, 2006), relatively uneroded, and produced in similar target rock (i.e., water-rich silicate rock). In addition, similarities in ejecta physical properties are suggested by the calculations of Pope Fig. 6. Pitted material (‘‘pm’’) on the terrace blocks shown here in eastern Mojave et al. (2006, Tables 1 and 2) that indicate that, even considering the crater appears to have drained onto the crater floor (‘‘cf’’) through small gaps and effects of differences in targets composition (i.e., basalt verse canyons within the terrace blocks (arrowed). Part of CTX image granite) (Pierazzo et al., 1997, 2005), as well as impact velocities G04_019625_1876_XN_07N032W. (Bjorkman and Holsapple, 1987; O’Keefe and Ahrens, 1994), and gravity (Pope et al., 2000) these two craters should have produced a similar volumes of impact melt (i.e., 11 km3). Furthermore, because the shock fragmentation process follows a power function that is influenced by maximum clast or block size which is related to crater size (Moore, 1971, 1972; Bart and Melosh, 2007), stress history, and the degree of pre-impact fracturing, it should fragment the targets at both craters in a similar way (see Melosh, 1989; Fujiwara et al., 1989; Melosh et al., 1992). Hence, the clasts in their impact melt-rich breccia should have similar size distributions. However, the clast-size distribution for Ries suevite shows some variations, Bringemeier (1994) reported a median particle diameter of 4.5 £ (i.e., 22 mm, whereas Engelhardt (1972) found a median clast size of 2.75 £ (i.e., 6.75 mm). This difference may be the result of the natural inhomogeneity of impact-melt-rich breccia deposits. We consider the effects of these differences in grain size later. Heat is a critical element of our model because it is the driving force behind water loss. A considerable amount of heat is generated by conversion of the kinetic energy of the impact to produce hot ejecta in the form of impact melt and impact melt-rich breccia (Ahrens and O’Keefe, 1972; Melosh, 1989; Pope et al., 2006). These heated materials progressively lose heat from the time they are excavated through transport and deposition. In this study, only Fig. 7. Image showing an example of pitted material flowing (arrowed) onto the the heat remaining in the pitted material after its deposition is floor of south-west Mojave crater from behind a terrace block to embaying already- considered and relevant to our model (Fig. 2d). The temperature formed pitted material (‘‘pm’’). Segment of HiRISE image ESP_017568_1870. of shock melted silicates should be 2000 °C (e.g., see El Goresy, 1968). However, on planets where this melt is mixed with cooler curvilinear ridges and grooves that appear to be flow lines, sug- clasts to produce impact melt-rich breccia rapid cooling occurs, gesting that this material was initially relatively fluid, but solidi- quickly reducing the average temperature (Grieve and Cintala, fied before it could completely drain into the crater floor. In 1992; Cintala and Grieve, 1994). For example, Engelhardt (1990) contrast to the pitted deposits on the floor and in topographic lows, and Engelhardt et al. (1995) estimate that the temperature of the pits are typically rare on these drained sheets. Ries suevite was an average of 750 °C (i.e., 1023 K) at the time In some fresh craters, solidification and stabilization of the sur- of its deposition. We use this value as the initial temperature of face of the pitted material appears to have occurred in some places the pitted material to test our model. before others. For example, fully-formed pits located around the The water content of the martian target material is also a criti- edges of the floors of some relatively large craters appear to be par- cal factor because it dictates the water content of the pitted mate- tially buried by pitted material that flowed from interior walls rial at the time of deposition. Although the water content of (Fig. 7). This overlapping relationship suggests that the surface of martian target material cannot be measured directly, it can be esti- the pitted material on the floor of these craters had stabilized en- mated from indirect observations (Barlow, 2010b) and theoretical ough to allow pit formation, while the pitted material elsewhere calculations (see Clifford, 1993; Carr, 1996). For example, based was still a fluid. The length of time between formation of the floor on layered ejecta morphology and terrain softening Barlow pits and their partial flooding is not clear, but considering cooling (2010b) found that 20–25% ice is likely to reside within the reg- rates and deposit thicknesses it could be quite short, possibly days olith in non-polar regions. This is consistent with calculations (Mouginis-Mark and Boyce, 2012). These observations suggest that based on the approach employed by Clifford (1993) that used the some process rapidly indurated the pitted material (e.g., cementa- lunar impact fracturing model of Binder and Lange (1980) to esti- tion, sintering, or solidification of the melt phase), which is consis- mate pore space in the martian surface target material (i.e., the tent with the observation that the pits appear to have resisted the megaregolith). This calculation provides an estimate of the volume subsequent flow of lobate materials (Morris et al., 2010). of possible storage space for water/ice in the martian target Author's personal copy

J.M. Boyce et al. / Icarus 221 (2012) 262–275 267 materials. Using this approach, we calculate that the maximum so closely spaced that they occupy up to 10% of the volume of volume percent of pore water in the target rocks of Tooting crater the deposit (Newsom et al., 1986). We note that such pipes have ranged from 10% to 25% (assuming the upper 150–200 m of the yet to be found in many of the impact melt-rich deposits elsewhere target rock at Tooting crater was dry due to pre-impact diffusion). on Earth (Osinski et al., 2008). This may be due to mineralization in If this volume were filled with water, then it would imply a water the Ries and Stac Fada vent pipes that makes them easier to ob- content of 4 wt.% to 10 wt.% (assuming an average density of serve. Also, it is not clear that a search for vent pipe features within 2400 kg m3 for the target rock). In addition to this source, water other impact structures has yet been specifically conducted. We bound in minerals may add another 4–7 wt.% (e.g., Ming et al., will discuss the implications for vent pipe formation later. 2008; Boynton et al., 2008) making a total of 12 ± 5 wt.%. Target material may not be the only source of water that could 3. Degassing of water vapor from the pitted material invade the pitted material immediately after deposition. Sources such as water-rich basement rock, groundwater emanating from The approach used here for developing a numerical model for the intensely fractured wall rock (Morris et al., 2010), and/or local the origin of the pits through the loss of heat and water from the rainfall from water to vapor released by the impact, may all be pos- martian pitted material borrows from previous work on degassing sible, but we consider them unlikely. For example, the floors of behavior of pyroclastic materials during their transport, deposi- large craters, such as Hale crater (136 km diameter), excavate be- tion, and cooling. This approach was also used to model degassing low the theoretical water/ice-rich layer into dry rock (e.g., Clifford, of the Ries Crater fall-out suevite by Newsom et al. (1986), and has 1993; Carr, 1996) eliminating them as a source of water. Also, im- provided valuable insight. We suggest that, to a first order, the pact craters are commonly so hot, especially on their interiors, that degassing behavior of all of these materials (i.e., martian pitted liquid water is not stable on their surfaces immediately after depo- materials, known terrestrial suevite, and pyroclastic materials) sition. This would prevent the presence of such water for some should be similar because they are all composed of silicate melts time after crater formation, eliminating its infiltration as a source. and water-bearing clasts of a wide range of sizes. The rate and The steam production-rate from the clasts and impact melt in duration of water loss from these hot clastic deposits is mainly a impact melt-rich breccia is also a critical element behind water function of their initial water content, and their physical properties loss. Such loss should be initially quite high because the gas diffu- such as temperature and grain-size distribution. Together these sion-rate is temperature dependent, and that these deposits con- factors control the production rate of gas within the deposit and tain a relative high abundance of small clasts and hot impact its migration through and from the deposit. Below, we outline a melt particles for which the diffusion pathways are short (Sparks numerical-based approach to how these factors control water loss et al., 1999). For this study, like with average temperature and in impact melt-rich breccia on Mars and the probable outcome of median grain-size, we use the steam production rate inferred for this water loss (Fig. 2f–h). the Ries suevite to test our model (Newsom et al., 1986). Furthermore, we test this model to determine if it produces rea- Because our model is tested using the pitted material in the sonable results consistent with observations and morphometric northern floor of Tooting crater, a knowledge of the thickness of measurements, using the pitted material in the northern portion this material in this area is required. We estimate that the mini- of the floor of Tooting crater because of its similarities to Ries (dis- mum thickness is at least that of the depth of largest pits in this cussed in detail above). It should also be noted that even though area, which is 30 m (i.e., based on digital elevation model data these two craters have many similarities, martian environmental shown in Fig. S.10 of Mouginis-Mark and Boyce (2012)). A maxi- factors (in particular the comparatively thinner atmosphere and mum thickness is suggested by the observations of Mouginis-Mark smaller acceleration due to gravity) may have dramatic effects on and Boyce (2012) who noted a 190 m elevation difference be- the escape rate of water vapor from the impact melt-rich breccia tween the higher, heavily-pitted northern crater floor and the of Tooting crater compared with that at Ries crater. Consequently, sparely-pitted southern crater floor. They speculated that this dif- it is important to pay special attention to these environmental ference may be due to the presence of pitted deposits only on the factors. northern floor where it lay above a relatively flat, impact-melt similar to that in complex lunar craters (Howard and Wilshire, 1975; 3.1. Flow rate and volume loss Bray et al., 2010; Denevi et al., 2012a,b). However, Mouginis-Mark and Boyce (2012) also point out that some of this elevation differ- The rate at which water vapor or steam flows through and from ence may be due to buried slide deposits originating from collapse freshly deposited impact melt-rich breccia is a major factor con- of the northern crater wall as suggested by extensive terrace blocks trolling how those deposits behave during degassing. The rate at development and comparatively lower rim elevation (290 m) of which steam escapes is dependent on a number of factors such the northern side. However, the presence of such buried slide as average temperature of the deposit, the rate at which the steam material beneath the pitted material cannot be verified with avail- is generated, the physical properties of the clasts contained in the able data. Consequently, for the purposes of testing our model, we deposit, and the type of flows within and from the deposit. Addi- assume 100 m as a reasonable value for the maximum thickness of tionally, the amount of steam that escapes and how long it takes pitted material in the northern floor of Tooting crater. to escape is dependent on the inventory of water in the materials Although conduction is the dominant mechanism for heat loss of these deposits. Appendix A presents the detailed numerical basis from the solid clasts in impact melt-rich breccia, water is lost for the discussion that follows. mainly by diffusion through and between grains, and fluid flow Like fluids in other clastic deposits, the ease with which the through vent pipes, like those found at Stac Fada, Scotland (Amor steam moves diffusively though particulate materials is strongly et al., 2008; Branney and Brown, 2011) and in the Ries fall-out sue- dependent on the dimensions of pore space and permeability of vite (Newsom et al., 1986; Engelhardt et al., 1995; Osinski, 2004). the material, which depends on the shape and size of the grains. As with volcanic vents and vent pipes in pyroclastic deposits As water vapor is exsolved and diffuses from the impact melts (e.g., Engelhardt, 1972; Pohl et al., 1977; Newsom et al., 1986), and hot clasts, it is released into the pore space between the grains such conduits in impact melt-rich breccia are the most efficient in the deposit (Fig. 2e and f) where it flows through the connected means of releasing large volumes of water vapor from a particulate pore spaces (here approximated as narrow tubes whose size is deposit. For example, at Ries, the fall-out suevite is dissected by determined by the mode of the clast-size distribution). Conse- vent pipes that are typically 2–4 cm wide. In places, the pipes are quently, the steam flow-rate is dependent on the average size Author's personal copy

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Fig. 8. Diagram showing void space idealized as a spherical space of radius R at the center of a cube of silicate material of side length (2L). As long as void spaces are not too close together, so that more than one sphere intersects a typical cube, this geometry allows estimation of the average fractional area of a slice through the void space. and number per unit area of these idealized small tubes (estimated by considering slices through a cube exactly containing a void space approximated by a sphere, shown in Fig. 8). This geometry allows estimation of the average fractional area of void space in a slice, which can then be integrated for the entire deposit (i.e. collectively, the tubes carry the total mass flux passing through the deposit). Consequently, the mass flux can be estimated for any depth below the surface within that deposit. In addition, this mass flux can be related to the pressure gradient (pressure decreases upward as z increases) driving the gas through the tube. Considering this model for the pitted material in Tooting crater, the gas pressure required to support the static weight of this material must be at least equal to the 0.74 MPa equivalent weight of the 100 m deep bed. Using this value for the gas pressure and the corresponding void space v = 0.125 found above, the steam viscosity 5 gg = 6.0 10 Pa s at Ta = 1023 K (from Engelhardt et al. Fig. 9. (a) Variations in pressure (P) with distance (z) above the base of the 100 m- deep pitted material (i.e., suevite) deposit in the floor of Tooting crater. Note that (1995)), an average martian atmospheric pressure of Pa = 700 Pa (n.b. the escaping steam should be rapidly carried away by thermal our model predicts that the pressure gradient is quite steep at shallow depths, having important consequences for the stability of the deposit. (b) Variations in gas convection, diffusion, and cross winds, and as a result have little lo- flow speed (Ug) with z. Note the predicted high gas-flow speed near the surface. cal effect on Pa), assuming a median particle diameter of 4.5 £ (i.e., 22.6 mm, so that the median radius of the particles is no evidence that this happened, suggesting that some other factor r = 11.3 mm) in the deposit from Bringemeier (1994), suggests that also was at play to prevent explosive disruption. the appropriate solution involves turbulent gas flow, with the min- This apparent conundrum can be resolved in several ways. One 3 1 imum value of Fv required being 0.101 kg m s , so that Fm is of these is that small clasts can be vigorously elutriated from much 4.8 105 kg kg1 s1. The resulting variations of pressure and of the deposit without any requirement that the whole deposit be gas flow speed with distance upward from the base of the fluidized (Fig. 2f). This underlines an inevitable limitation of exper- 100 m-deep suevite layer in the floor of Tooting crater are shown iments to simulate the behavior of particulate deposits like suevite in Fig. 9a and b. The steep pressure gradient at shallow depth re- or ignimbrites using fluidized beds to fluidize the whole deposit sults in an enormous gas flow speed close to the surface of nearly layer by passing gas in through the base of the equipment (e.g., Wil- 300 m s1. son, 1980). We suggest that, in nature, impact-generated impact- Clearly this state could not be maintained for an appreciable melt-rich deposits (and also pyroclastic density current deposits) time because at these near-surface gas flow speeds all fine material produce gas from clasts within the flow, not just at its base. So would rapidly be elutriated from the shallow part of the deposit, the gas flux, and hence the gas flow speed, must increase upward destroying the assumption of a uniform grain size throughout in the way found here, and not require that the entire deposit be flu- the deposit and requiring a more elaborate model. We have calcu- idized. For example, if all particles smaller than 100 lm radius are lated the size of the largest spherical clast that can resist being elu- elutriate from a deposit, then (see Appendix B, Eq. (1)) the typical triated with mid-level gas flow speeds from Fig. 9bof50 m s1 gas flow speed must be 1.3 m s1. However, for median size clasts and pressures from Fig. 9aof0.7 MPa, giving a steam density at of r = 11.3 mm (from Bringemeier (1994)), the solution that leads to 3 Ta = 1023 K of 1.5 kg m ; the implied value of rmax is of order the required typical speed involves laminar gas flow with a basal 0.16 m. This is so much larger than the 11 mm median clast ra- gas pressure of 2000 Pa. This is only about three times the dius in the deposit that if these conditions existed the deposit atmospheric pressure, and results in a gas release rate from clasts 5 3 1 8 1 1 would immediately be explosively disrupted. However, there is of Fv = 2.5 10 kg m s (i.e. Fm = 1.2 10 kg kg s ). Author's personal copy

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If the pitted deposit in the floor of Tooting crater contains 10% to coalesce into non-bubbling channels (here interchangeably by mass of water (i.e. 0.1 kg kg1) this gas release rate would need called segregation, degassing, or vent pipes) where small, easily- [(0.1 kg kg1)/(1.2 108 kg kg1 s1)] = 8.3 106 s(96 days) to transported particles are carried to the surface by escaping gases release all of the water vapor (using a median clast diameter of to form a vigorously bubbling layer. Newsom et al. (1986) suggest 4.5 £ for Ries suevite from Bringemeier (1994)). However, if that there is evidence of such elutriation of fine material at the top these pitted deposits contained the lowest range of water contents of the Ries fall-out suevite as a result of this process. At high gas of martian target materials estimated in Section 3 (i.e., 4% by mass flow-rates where the drag forces are large enough to propel parti- of water, or 0.04 kg kg1), instead of 10%, then it would take cles, such phenomena as spouting, fountaining and explosive-like 3.3 106 s(38 days) to release all of the water vapor. But, the eruptions may occur at the top of the pipes, producing pit-like actual duration of such release may be much shorter. Engelhardt features. et al. (1995) and Osinski (2003) found that the impact glass at Ries It also should be noted that experimental studies have shown contains about half of the water content of the target material that in deposits of particulate materials that have high content of (6 wt.% water), suggesting that only half of the initial water may fine-grain particles, high temperatures, and/or high shear stresses, have been lost as a result of the impact. If such loss also occurred conditions favor homogeneous fluidization, instead of vent pipe in the pitted material of Tooting crater, then degassing may have formation (Gravina et al., 2004; Druitt et al., 2004, 2007). However, occurred over a factor of 2 less time than calculated above. vent pipes may readily form in the pitted deposits because (1) elu- In addition, the important effect of median clast diameter on triation by the high-speed escaping gas should rapidly decrease the these calculations can be illustrated by changing the median clast fines content, (2) shear stresses are likely to be low in these rela- diameter from 4.5 £ to 2.75 £ (r = 3.365 mm), i.e., the average tively thin and static deposits during pit formation, and (3) median clast size determined for Ries suevite by Engelhardt (1972). although high temperature can eliminate moisture-derived inter- The gas motion is again laminar, but the required basal gas pressure particle cohesion needed for pipe formation, the water vapor-rich is now close to 10,000 Pa. Hence, the required gas release rate is environment expected in the pitted materials during its degassing 5 3 1 8 1 Fv = 6.2 10 kg m s (i.e., Fm = 3.0 10 kg kg s ), and a may counter the drying effect of high temperature. 10% by mass water content would imply 39 days to release all As at Ries, vent pipes in the pitted material probably developed of the water vapor with a 4% by mass water content releasing its at nearly the same time that fine particle elutriation in the deposit water vapor over 16 days. began (Kuni and Levenspiel, 1969; Wilson, 1980, 1984; Newsom Using the values assumed in this analysis, it is clearly possible et al., 1986; Druitt et al., 2004, 2007). However, because these to remove a significant fraction of the small particles from the pit- pipes provided a much more efficient means for gas to escape com- ted material in the floor of Tooting crater on a timescale that is in pared with uniform diffusion, they quickly dominated as the mech- the order of a few days to a few tens of days (Fig. 2h). Fig. 9b shows anism for gas escape from the deposit (Kuni and Levenspiel, 1969; that the gas flow-speed near to the surface of the deposit can read- Wilson, 1980, 1984; Newsom et al., 1986). Furthermore, we sug- ily exceed 300 m s1. This is considerably higher than the gest that this mechanism should be nearly the same as the mech- 1.3 m s1 terminal velocity of particles of 100 lm in size deeper anism that controls behavior of escaping gas and entrained clasts in the deposit, and suggests that particles of this size will be lofted through volcanic conduits during explosive eruptions because both above the surface with essentially all of the gas speed. This gas flow involve high-speed escape of such materials driven by gas expan- speed assumes that the gas stays in close contact with the bulk of sion through pipe-like conduits that vent at the surface. For this the suevite layer and thus stays at the same average temperature reason, we have adopted the numerical approach of Wilson and as the clasts in the layer. We have not taken into account the en- Head (2007) for calculation of the escape speed of products gener- ergy release due to the decompression of the gas, but this would ated by explosive pyroclastic eruptions on Mars and Earth, and ap- increase its flow speed even more than the existing large increase plied it to the calculation of the escape speed of gas and entrained due to the pressure gradient. Just how much the speed would in- clasts from the vent pipes that underlie the martian pits. The es- crease would depend on the mass loading of the fine particles cape speed of these materials is critical to erosion of the deposit being carried with the gas. surrounding the vent pipes, and is especially important to erosion that results in flaring of the vent pipes near the surface. 3.2. Effects of vent pipe formation In theory, expansion of gas through the vent pipes in the pitted material can be accommodated by increasing the speed of the gas/ To a large degree, the conundrum of disruption of the deposit by clast mixture, and flaring of the conduits toward the surface high gas-flow speeds can be solved by another mechanism, i.e., the (Fig. 2g). This is similar to what happens in terrestrial explosive formation of numerous preferred pathways, or vent pipes that pro- volcanic conduits where expansion of gas is accommodated in vide an efficient means for escape of the gas (Fig. 2f and g). Vent the same way (Wilson and Head, 1981, 2007; Glaze and Baloga, pipes are common in some terrestrial suevite and pyroclastic 2002; Mitchell, 2005). Wilson and Head (2007, see Table 1) calcu- deposits and have been shown to provide an efficient means for lated eruption speeds in vents for martian and Earth pyroclastic gas escape from those deposits (see Newsom et al., 1986). We sug- material that originate from basaltic magma with water contents gest that vent pipes are likely to have formed in the martian pitted comparable to those expected for the martian pitted material. material for the same reason they formed in these other particulate Based on their calculations, the eruption speeds range from 360 deposits, and that they not only played a major role in preventing to 410 m s1. We suggest that these speeds are likely to be sim- the explosive disruption of the pitted materials, but also in the for- ilar to eruption speeds from the vent pipes in pitted material con- mation of the pits. taining similar water contents because both situations involve the Vent pipes are produced as a step in a systematic sequence of expansion of gas through a conduit that is accommodated by behavior in particulate deposits that results from increasingly increasing the speed of the gas and the clasts it entrains. higher gas flow-rates through that material (e.g., Kuni and Leven- Considering the gas eruption velocities in the vents calculated spiel, 1969; Rhodes, 1998; Wilson, 1980, 1984). At low flow-rates, by Wilson and Head (2007), and the size of the largest spherical gas merely percolates through void spaces in the material to es- clast in a deposit (Eq. (14)), these flow speeds would easily be en- cape. At increasing flow-rates, fluidization occurs (i.e., when the ough to move spherical clasts on the order of 1–4 cm in diameter drag force from the ascending gas equals the buoyant weight of from the vents. It is clear that such high-speed escape of gas and the bed) followed by bubble formation. In such cases, bubbles tend clasts, no matter whether they originate from volcanic or impact Author's personal copy

270 J.M. Boyce et al. / Icarus 221 (2012) 262–275 melt-rich breccia sources, not only can eject particles great dis- martian impact craters (Fig. 2). The material in which these pits tances, but can substantially erode the walls of the conduits that have formed is likely to be composed of impact melt-rich breccia carry them, as well as the vents at the surface. derived from water-rich target materials (Fig. 2a–d). In contrast to previous models of formation of these pits by sublimation or col- 3.3. Pit formation lapse, our model predicts that, as in the Ries suevite, impact-induced heating of the water-bearing components in the pitted Insight into the morphologic effects of the high-speed escape of material caused them to rapidly release their water as steam steam from the vent pipes in the pitted materials is offered by the (Fig. 2e–h). Our model predicts that degassing of the martian pitted modeling of Mitchell (2005). Mitchell (2005) considered the cou- material should be more explosive and have greater morphologic pling between high-speed gas flow in an explosive volcanic conduit effects on the surface compared with degassing of terrestrial and the shape of the vent. He found that abrasive erosion by escap- suevite deposits because of the effects of the lower atmospheric ing high-speed gas and clasts results in conduit flaring near the sur- pressure and lower acceleration due to gravity of Mars. These dif- face to produce a pit. His model was based on the work of ferences act to increase the escape velocity of the steam from these Macdeonio et al. (1994) who derived the abrasion-rate of wall rock deposits. In addition, water-rich, impact melt-rich breccia pro- as a function of the mechanical properties of the wall material, and duced by martian craters of a broad range in sizes should degas the vertical flow-speed of solid particles within the conduit. Mitch- similarly even if the average grain-size (Moore, 1971, 1972; Bart ell (2005) calculated the probable effects of abrasive erosion on and Melosh, 2007) and proportions of impact melt to clasts (Pope conduit shape, and how these changes in shape feedback to affect et al., 2006) in these particulate deposits vary somewhat with cra- the flow parameters. He started with parallel-sided circular geom- ter size. This is because the physics that controls the degassing etry, setting the choking point at the surface, allowing a unique first behavior of such particulate deposits as the impact melt-rich solution for a given mass flux, and proceeded in a step-wise man- breccia on Mars should produce generally similar results (Kuni ner, recalculating the conduit shape at every iteration. Fig. 10 shows and Levenspiel, 1969; Wilson, 1980, 1984; Druitt et al., 2004, the generalized results based on his analysis of the evolution of con- 2007). This behavior is in contrast to that in impact generated duit radius and wall stress as a function of depth for a terrestrial hydrothermal systems where water vapor slowly escapes through basaltic eruption (also see Fig. 5d in Mitchell (2005)). fractures produced by impacts that radiate outward into water- In comparison with Mitchell’s (2005) finding, the higher water bearing rock (Abramov and King, 2005). content of the martian impact-melt-rich breccia deposits, com- Escape of the steam released by these hot, water-rich materials bined with the lower acceleration due to gravity and atmospheric should predominantly be through a network of vent pipes, a natu- pressure of Mars, should increase the velocities of the escaping ral consequence of the high-flow rate of gas through particulate steam/clasts mixture from this material, and duration of flow to materials. The high-speed flow of steam and the clasts it entrains enhance conduit wall erosion and pit growth. These environmental through these pipes should result in abrasive erosion of the pipe differences have the effect of increasing the rate of pit growth on walls, and flaring of these walls near the surface to form pits. Mars compared with Earth given the same escape velocities, but Using the pitted material on the floor of Tooting crater to test do not change the general form of pit growth. However, many our model, we calculate that the gas-flow speeds through the vent other parameters may cause small secondary effects on the quan- pipes could readily exceed 300 m s1 at the vent, and may be as 1 titative calculations based on Mitchell’s (2005) model. Conse- high as 410 m s . At these gas-flow speeds the rate of gas loss quently, Mitchell’s erosion model’s main value to our work is to from the deposit would have expended the gas supply in only a show that substantial flaring of the pipes near the surface is ex- few days to a few weeks, depending on the water content of the pected to result from erosion of the vent pipe walls in the martian pitted material. Even though the eruption of gas and entrained pitted material by the high-speed escape of the steam and its en- clasts may have lasted only a short time, the gas-flow speeds are trained clasts. easily high enough to cause substantial abrasion and erosion of the vent pipe walls to produce the observed pits. These speeds are high enough to eject particles as large as a few centimeters 4. Discussion diameter to very great distances, leaving little trace of these materials around the pit rims. Fine-grain particles ejected from these We have developed a model for the formation of the closely- vents are likely to be carried upward by the escaping hot steam spaced pits found in thin deposits in and around well-preserved to form a turbulent, convecting cloud above the deposit. This cloud would interact with the atmosphere at its outer edges, sharing all the properties of the fine ash plumes that form over pyroclastic density currents, such as those seen at Mount St. Helens and Mont- serrat, and produce so-called co-ignimbrite fall deposits. Depend- ing on local conditions, the fine particles in these plumes could be blown sideways to significant distances by the wind; alter- nately, under low-wind conditions they could settle into the parent crater to form a mantle of fine materials on what otherwise would be the coarse upper part of the deposit from which the fines were stripped. The location, spacing, and size of the pits are reflections of conditions in the pitted material during eruption (e.g., porosity, permeability, and deposit thickness). Vent pipes probably form initially in the pitted deposits as a closely-spaced network of Fig. 10. Flaring of conduit with time for a terrestrial basalt eruption (with volatile nearly vertical tubes like those at Ries (Kuni and Levenspiel, contents 0.5 wt.% CO2, and 0.5 wt.% CO2 plus 2.0 wt.% H2O) due to abrasive erosion 1969; Rhodes, 1998; Wilson, 1980, 1984; Newsom et al., 1986). of vent by escaping high-speed gas and entrained pyroclasts Curve on the right Following their formation, and as steam begins to rapidly escape marks first step in the time series with later times progressively to the left showing the broadening of the vent at the top of the conduit (see Mitchell (2005, Fig. 15d) through them, some of these pipes should begin to grow at the ex- showing results using finer time steps calculations). pense of others. This is a result of a low-pressure zone that should Author's personal copy

J.M. Boyce et al. / Icarus 221 (2012) 262–275 271 develop in the material surrounding the pipes, with the best-developed of these pipes tending to draw the greatest volumes of steam to them. This produces an even lower pressure zone around these pipes that acts to draw even more steam toward them (see Kok- elaar, 1983). These pipes are likely to produce the largest and deep- est pits because they tend to carry the most steam. This also implies that the largest pits should develop in the thickest pitted deposits because these thick deposits are likely to harbor greater volumes of steam, and have more vertical space for the pits to grow deeper before the escaping steam shuts off. This supposition is consistent with the observation of Tornabene et al. (2012) that the largest pits are in the largest craters, and the largest pits in a particular crater are in places that would be expected to have the thickest deposits (i.e., the floors). The model presented here also provides an explanation for why isolated pits commonly have low, raised rims, whereas the pits in closely-spaced groups typically lack rims that rise above the surrounding terrain. It is clear that the presence of raised rims is an important morphologic feature suggesting involvement of con- structional processes, which is not expected for pits of collapse or sublimation origin. However, even though solitary martian pits have low, raised rims, they typically lack evidence of substantial ejecta deposits. This lack of thick ejecta deposits, together with the presence of low rims, gives these pits a morphologic appear- ance resembling hydroeruption pits at Mount St. Helens (Fig. 11). These hydroeruption pits were produced by steam-driven explosive eruptions caused when hot pyroclastic flows covered a wet substrate. The rims and ejecta of these hydro-eruption pits are so subdued that they are difficult to identify even in aerial photo- graphs (Moyer and Swanson, 1987). Consequently, it is not surpris- ing that ejecta deposits around martian pits produced by similar explosive degassing processes would be difficult to identify in orbi- tal images. Furthermore, we suggest the reason that the closely-spaced groups of martian pits lack raised rims between individual pits is a result of their close-packing combined with their simultaneous formation. The pits in these closely spaced groups are commonly packed so close together that their rims butt against each other, resulting in shared straight rim segments between individual pits (Fig. 2). Their close packing probably is a reflection of the spacing of vent pipes beneath. This close spacing has produced a geometry pattern that resembles a 2-D cross-section through soap froth that is the result of the balance of pressure between adjacent bubbles (e.g., see Glazier and Weaire, 1992; Li et al., 2007; Vasconcelos et al., 2003). We suggest that the geometry of the pits in these closely-spaced groups is likely to be a result of the simultaneous Fig. 11. Oblique views of a an example of relatively large martian pits in the floor of degassing of nearly all pits in a group with individual pits growing Tooting crater (a) with a particularly large complex pit characterized by scalloped so large that their rims intersect the rims of adjacent pits. With rims and containing smaller pits. The pits shown in the middle image (b) exhibits a continued degassing and pit growth, an equilibrium point would similar morphology to the large complex martian pit, but is a complex hydroeruption pit at Mount St. Helens caused by explosive degassing of water after deposition be reached where outward growth of an individual pit is counter- of pyroclastic flows over a wet surface. The bottom image (c) is an oblique view of balanced by growth of the adjacent pits. After this equilibrium is simple, nearly circular hydroeruption pits at Mount St. Helens. Like the single pits reached, and as degassing continues, all but the largest size-frac- (see Fig. 1c) in the martian pitted deposits, the pits in image (c) show little evidence tion of particles in the ejecta are likely to be removed from around of rims or ejecta. Top image is part of HiRISE PSP_007406_2035, middle (b) image is MSH80-235, and bottom images (c) is MSH80-021 (images b and c are courtesy M. the pits by the high-speed eruption of material from adjacent pits. Malin, MSSS). This process prevents substantial raised rims from forming between pits in the closely-spaced groups and leaves only relatively low rim ridges at the equilibrium distance between the pits. These rim ridges should be composed dominantly of coarse-grain clasts above (Shipton et al., 2005). This allows all mud pots to form such as those shown in Fig. 5. simultaneously, which influences the formation and geometry of The morphological expression of simultaneously formed pits in adjacent mud pots. This reinforces our conjecture that the pits of martian impact breccia is analogous to the formation of mud pots the martian pitted material are likely to have formed nearly found in some locations on Earth, such as those at Crystal Geyser, simultaneously. Utah (Fig. 12). The geometry of these closely-spaced mud pots re- Although rare, the morphology of these pits and closely-spaced sults from simultaneous venting of pulses of CO2-rich water from a groups of pits is not unique to Mars. For example, recently pits and deep source. These pulses travel through multiple near-surface closely-spaced groups of pits that appear to be morphologically fractures that act as vent pipes that propagate into the mud deposit indistinguishable to the martian pits have been discovered in and Author's personal copy

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Tooting crater may have a total volume of 22 km3. As a result, it initially may have contained 22 1011 kg of the water. How- ever, considering the evidence that only about half of the original water content of the target material is found in Ries suevite sam- ples (Engelhardt et al., 1995; Osinski, 2004) these estimates may be a factor of 2 greater that the actual value. These values may provide useful input parameters to models of the effects of such rapid water vapor release on the local martian atmosphere (Segura et al., 2002; Toon et al., 2010; Kite et al., 2011). This is in contrast to the slow escape of water vapor from impact-generated hydrothermal systems that may develop in water-bearing fractured rock surrounding impact craters (Abramov and King, 2005).

5. Conclusion

We propose that the martian pits formed by rapid degassing of water from the pitted material in a way that is similar to the degassing of the fall-out suevite of the Ries impact structure. We calcu- Fig. 12. Oblique view of mud pots during dry period at Crystal Geyser in Utah. late that the escaping high-speed gas and entrained clasts Similar to the martian pits, these pits share rims. substantially eroded walls of the numerous vent pipes in the pitted material to produce flaring of the vents at the surface, thereby forming pits. Furthermore, the honeycomb-like geometry of the around impact craters on the asteroid Vesta (Denevi et al., closely-spaced pit groups is likely to have been produced by erup- 2012a,b). Denevi et al. (2012a,b) speculate that these pits also tive degassing across the deposits that caused simultaneous may be caused by degassing of volatile-rich impactite in the low- growth of pits until they eventually reached an equilibrium point gravity, low-atmospheric pressure environment of the asteroid. where their outward growth was counterbalanced by growth of We note that there are other types of closely-spaced groups of the adjacent pits. pits found on Mars and other planets that only superficially resem- If this model is correct, it provides a new method for investigat- ble the pits and pit groups of the martian pitted material. These ing the distribution of subsurface volatiles at the time of crater for- other types of pit groups owe their origin to a variety of different mation. Previous studies of martian impact craters have processes including volcanic (Frey and Jarosewich, 1982; Greeley concentrated on the analysis of the layered ejecta materials (Carr and Fagents, 2001; Keszthelyi et al., 2010; Hamilton et al., 2011; et al., 1977; Mouginis-Mark, 1979; Barlow, 2010b). Future analysis Ghent et al., 2012), sedimentary (Greeley and Iversen, 1987; Burr of the morphology and distribution of pitted material as a function et al., 2009), glacial (Burr et al., 2009), or impact (Oberbeck and of target material and location on the planet appears to be Morrison, 1973) processes. These pit groups are distinguished from warranted to further understand the role of volatiles in the impact the pits in the martian pitted material by the geometric relation- cratering process on Mars. ships between their individual pits (Boyce et al., 2011), or by their occurrence in material and terrain that is clearly produced by non- Acknowledgments cratering parent processes. In the case of secondary cratering, pits can cross geologic boundaries, unlike pits in the martian pitted We thank Drs. Nadine Barlow, Veronica Bray, and an anony- material. mous reviewer for their thoughtful comments on this work, which Finally, our calculations suggest that degassing of the pitted was supported under NASA/ASU THEMIS Team Contract A2910. material on Tooting crater may have released a substantial amount C.W.H. is supported by an appointment to the NASA Postdoctoral of water vapor into the atmosphere in a relatively short time (i.e., Program at the Goddard Space Flight Center, administered by hours to a few tens of days). A first-order estimate of the amount of Oak Ridge Associated Universities through a contract with NASA. water vapor can be calculated by multiplying the volume of pitted This is HIGP contribution 1979 and SOEST contribution 8700. material at Tooting crater by the average water content of the pitted material (10 wt.%), assuming all water was released. The volume can be estimated by multiplying the area of pitted material Appendix A. Flow rate and volume loss (i.e., 177 km2) mapped by Mouginis-Mark and Boyce (2012) by the average thickness of the pitted material. The average thickness In our treatment of steam release from the freshly-deposited can be approximated by averaging the maximum thickness of impact melt-rich deposits, we let Fv be the steam generation rate, 100 m (estimated in Section 3) with the minimum thickness expressed as the gas mass released from the clasts per unit volume 3 1 based on the likely thickness of the numerous small patches of pit- of the deposit per unit time (in units of kg m s ). Fv can be re- ted material pooled in topographic lows on the rim and terraces lated to the gas mass release rate per unit mass of silicate material (judged from the typical topographic relief in those areas), and per unit time, Fm, via the void space fraction, v, and the typical sil- the thin sheets of this material found on the rim. Employing this icate clast density qr: approach results in an average thickness values of 55 m, a vol- Fv ume of 9.7 km3, and a maximum amount of water released of F ¼ : ð1Þ m q ð1 Þ 9.2 1011 kg. Alternatively, the volume can be estimated using r v theoretical calculations. Stoffler et al. (2002) and Pope et al. Like fluids in other clastic deposits, the ease with which the (2006) calculated that a volume of 11 km3 of impact melt would steam moves diffusively though particulate materials is strongly be produced by formation of martian impact craters the size of dependent on the pore space and permeability of the material, Tooting crater and Ries crater on Earth. Using the approximate ra- which depends on the shape and size of the grains. As a basis for tio of impact melt to clasts in the Ries suevite of approximately 1–1 calculating the flow rate of steam through the pitted deposits (Engelhardt and Graup, 1984) we suggest the pitted material at (Fig. 2f), we consider that the total mass flux of gas passing through Author's personal copy

J.M. Boyce et al. / Icarus 221 (2012) 262–275 273 a surface of area A at height z above the base of the layer is the sum those given by Eqs. (6a) and (6b) we can find dP/dz as a function of of all the gas generated at heights less than z,(FvAz). This gas flows z, and hence P as a function of z and the flow speed of the steam through the connected pore spaces, approximated as narrow tubes through any one pathway, Ug as a function of z, for each gas flow re- of equivalent mean radius r, where r represents the typical radius gime. The decision as to which flow regime is relevant hinges on the of gaps between the most common clast-size in the layer, deter- gas flow speeds found for the two assumptions, and whichever is mined by the mode of the clast-size distribution. To calculate the the smaller is the relevant one. rate of gas flowing through these connected pore spaces, we esti- In the case of laminar flow, using Eqs. (5) and (6a), we find mate the number per unit area of the idealized small tubes through dP 8Fvg QT which the gas flows by noting that if there are q tubes cutting ver- g a : P ¼ 2 z ð7Þ tically through the area A, the fractional area they represent, dz vmr 2 [(qpr )/A], is equal to the average cross-sectional area correspond- Performing the integration, with the boundary conditions that ing to the void space fraction, . By considering slices through a v the pressure is equal to Pa, the Mars atmospheric pressure at the cube exactly containing a void space approximated by a sphere surface, and some prescribed value P0 at the base of the suevite (Fig. 8), this average area fraction of void space is found to be ex- layer at depth Z below the surface, we have: actly equal to v as long as the void space fraction does not become 8Fv g QTa so large that any random cube contains parts of more than one P2 ¼ P2 þ g Z2; ð8Þ sphere; hence [(qpr2)/A]=v, and the number of tubes per unit area 0 a vmr2 is q/A = v/(pr2). This geometry allows estimation of the average which enables the value of Fv required to produce a given value of P0 fractional area of a slice through the void space idealized as a to be found. The pressure P as a function of z is obtained by integrat- spherical space of radius R, at the center of a cube of silicate mate- ing Eq. (7) between P0 and P: rial of side length (2L). The fractional area of void space in a slice of 2 thickness dx is zero between x = 0 and x =(L R), and is [(pr )/ 2 2 8Fv ggQTa P ¼ P z2; ð9Þ (2L)2] between x =(L R) and x = L. The average fractional area, 0 vmr2 A , between x = 0 and x = L (by symmetry the same as the average a Using the Poiseuille flow law: U =(r2 dP/dz)/(8g ), U can be found fractional area between x = 0 and x =2L) is therefore given by g g g Z Z at any height z above the base of the layer. Using Eq. (6) to express 1 x¼LR x¼L pr2 A ¼ dx þ dx : ð2Þ dP/dz as a function of P and z gives Ug as a function of z: a 2 L x¼0 x¼LR 4L FvQTa 2 2 2 Ug ¼ z: ð10Þ Fig. 8 shows that R = r +(L x) , i.e., Pvm r2 ¼ R2 L2 þ 2Lx x2; ð3Þ In the case of turbulent flow, using Eq. (5) and (6b), we find "# and so dP F2fQT Z Z P ¼ v a z2: ð11Þ x¼L x¼L dz v2mr 1 p 2 p 2 2 2 Aa ¼ 2 r dx ¼ 3 ðR L þ 2Lx x Þdx L 4L x¼LR 4L x¼LR Performing the integration with the P0, Pa, and Z boundary pr3 conditions, ¼ : ð4Þ 6L3 "# 2F2fQT P2 ¼ P2 þ v a Z3; ð12Þ But note that the void space fraction, v, is by definition equal to [(4/ 0 a 3v2mr 3)pR3]/(8L3), which reduces to (pR3)/(6L3), and so we have the sur- prisingly simple result that Aa is exactly equal to v. which again enables the value of Fv required to produce a given va- Collectively, the tubes carry the total mass flux (FvAz) passing lue of P0 to be found. The general expression for the pressure P as a through the area A at height z above the base of the layer and so function of z is now the mass per unit time passing through any one tube, Fi, must be "# equal to (F Az)/q, i.e., 2 v 2 2 2FvfQTa 3 P ¼ P0 z ; ð13Þ 2 3 2mr Fvzpr v Fi ¼ : ð5Þ v and differentiating this to find dP/dz as a function of P and z, the tur- 1/2 The mass flux calculated in Eq. (5) can be related to the pressure bulent gas flow speed, Ug =[(rQTa dP/dz)/(fmP)] , is found (entirely gradient, dP/dz (pressure decreases upward as z increases) driving predictably since it only involves the gas density, void space frac- the gas through the tube. If the gas motion is laminar, the required tion and gas volume production rate) to be given by the same relationship is the Poiseuille flow law; in terms of mass flux: expression as that found for laminar flow and given by Eq. (10). "# pmPr4 dP Fi ¼ ; ð6aÞ Appendix B. Radius of the largest spherical clast that can resist 8ggQTa dz being elutriated where gg is the viscosity of the gas, Q is the universal gas constant, The radius, r , of the largest spherical clast that can resist 1 1 max 8314 J kmol K , m is the molecular mass of H2O, being elutriated by gas flowing at speed U can be found by equat- 1 g 18.0153 kg kmol , and it is assumed that the perfect gas law ap- ing the downward weight of the clast to the upward drag force ex- plies, so that the density of the gas, qg, is equal to [(mP)/(QTa)]. If erted on the clast by the gas flow. When the gas flow around the the gas motion is turbulent, the relationship is clast is turbulent, the drag force is given by ð1=2Þq C pr2 U2, g D max g mP 1=2 dP 1=2 where CD is a drag coefficient, dependent on clast shape but of order F r5 ; 6b 3 i ¼ p ð Þ unity. Equating this force to the clast weight, ð4=3Þprmaxqrg, we find fQTa dz "# 2 3qgCDUg where f is the friction factor for gas flow past particles from the wall rmax ¼ : ð14Þ 8qrg of the tube. By equating the expression for Fi given by Eq. (5) with Author's personal copy

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