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Sublimation-driven erosion on Hyperion: Topographic analysis and landformsimulation model tests

Alan D. Howard a,⇑, Jeffrey M. Moore b,1, Paul M. Schenk c, Oliver L. White c, John Spencer d

a University of Virginia, Department of Environmental Sciences, P.O. Box 400123, Charlottesville, VA 22904-4123, United Statesb NASA Ames Research Center, M/S 245-3, Moffett Field, CA 94035, United Statesc Lunar and Planetary Institute, 3600 Bay Area Blvd., Houston, TX 77058, United Statesd Southwest Research Institute, 1050 Walnut St., Suite 300, Boulder, CO 80302, United States

a r t i c l e i n f o

Article history:Received 6 July 2011Revised 8 May 2012Accepted 8 May 2012Available online 16 May 2012

Keywords:CrateringGeological processesImpact processesSatellites, SurfacesSaturn, Satellites

a b s t r a c t

The unique appearance of Hyperion can be explained in part by the loss to space of ballistic ejecta duringimpact events, as was proposed by Thomas et al. (Thomas, P.C. et al. [2007a]. Icarus 190, 573–584). Weconclude that such loss is a partial explanation, accounting for the lack of appreciable intercrater plainson a saturation-cratered surface. In order to create the smooth surfaces and the reticulate, honeycombpattern of narrow divides between old craters, appreciable subsequent modification of crater morphologymust occur through mass-wasting processes accompanied by sublimation, probably facilitated by theloss of CO2 as a component of the relief-supporting matrix of the bedrock. During early stages of craterdegradation, steep, crenulate bedrock slopes occupy the upper crater walls with abrupt transitions down-slope onto smooth slopes near the angle of repose mantled by mass wasting debris, as can be seen withinyoung craters. Long-continued mass wasting eventually results in slopes totally mantled with particulatedebris. This mass wasting effectively destroys small craters, at least in part accounting for the paucity ofsub-kilometer craters on Hyperion. Surface temperatures measured by Cassini CIRS range from 58 K to127 K and imply a surface thermal inertia of 11 ± 2 J m�2 K�1 s�1/2 and bolometric albedo ranging from0.05 to 0.33. Resulting H2O sublimation rates are only tens of cm per billion years for most of the surface,so the evolution of the observed landforms is likely to require sublimation of more volatile species suchas CO2.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

Hyperion is a unique saturnian satellite in several respects. Itslandscape of sharp-edged, shoulder-to-shoulder strongly concavecraters has been likened to that of a sponge (Thomas et al.,2007a). It is relatively small (270 km mean diameter), highly irreg-ular in shape with an old prominent basin (121 km diameter) occu-pying one side (Fig. 1), and it has an eccentric orbit with chaoticrotation (Black et al., 1995; Cruikshank et al., 2010, 2005; Thomasand Veverka, 1985; Thomas, 2010; Thomas et al., 1995, 2007b). Itsbulk density is about half that of ice, indicating a high porosity.

Based on Cassini high-resolution images of Hyperion acquired in2005 (Thomas et al., 2007a) attributed this sponge-like appearanceto the enhanced preservation of craters in the 2–10 km-diametersize range, relative to the crater size–frequency distribution ofsmaller craters on outer satellite Phoebe (which is about the same

size as Hyperion). They reported that within this size range, Hype-rion has twice the number of craters per unit area as Phoebe.

Several of our studies, (e.g., Howard and Moore, 2008; Mooreet al., 1999, 1996, 2004), have identified the effects of erosion onGalilean satellite landforms and recognized the role of volatile lossand mass redistribution in the evolution of these features. Thesestudies introduce and outline qualitative and semi-quantitativedescriptions of certain aspects of this process. In this report we ap-ply landform evolution modeling originally developed for terres-trial and martian studies (e.g., Howard, 2007), but recentlymodified for outer planet satellite research (Howard and Moore,2008; Moore et al., 2010) in order to heuristically characterizehow the crater morphologies of Hyperion may first express them-selves and then change with time, and what roles that volatile lossand mass wasting play in this evolution.

2. Background and initial working hypotheses

Thomas et al. (2007a) concluded that primary crater morphol-ogy, rather than other modifying processes such as sublimationor mass wasting, is responsible for Hyperion’s unusual appearance.

0019-1035/$ - see front matter � 2012 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.icarus.2012.05.013

⇑ Corresponding author. Fax: +1 434 982 2137.E-mail addresses: ah6p@virginia.edu (A.D. Howard), jeff.moore@nasa.gov (J.M.

Moore), schenk@lpi.usra.edu (P.M. Schenk), white@lpi.usra.edu (O.L. White),spencer@boulder.swri.edu (J. Spencer).

1 Fax: +1 650 604 6779.

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They speculated that the absence of crater ejecta, which wouldmantle pre-existing craters, may explain the enhancement of 2–10 km-sized craters. They noted that Hyperion has a very low bulkdensity of 554 ± 50 kg m�3 (hence low surface gravity averaging0.019 ms�2) and suggested that this contributes to the minimal ef-fect of ejecta either by suppressing its production (Housen andHolsapple, 2003), or by enhancing the velocity of ejecta that doesform so that it does not re-accrete (Asphaug et al., 2002). Anoma-lously deep craters could also contribute to Hyperion’s sponge-likeappearance. Thomas et al. (2007a) measured depth-to-diameterratios for 13 craters using shadow lengths and found an averagevalue of 0.21 ± 0.05, larger than for craters on large icy satellites(0.14) (Schenk, 1991), but similar to fresh lunar craters. Consider-ing the potential effects of sublimation, they noted that H2O andCO2 are observed on Hyperion (Cruikshank et al., 2007) althoughit is too cold for any appreciable H2O loss. Thomas et al. (2007a)use the observation of sub-km-sized craters on the floors of largercraters to argue that there has been <20 m of eroded materialtransported out onto these floors, and hence CO2 sublimation, ifacting, may be limited. Brad Dalton et al. (2012) report pure H2Oice, probably as frosts, preferentially located atop topographiccrests (crater rims), which is consistent with local volatile redistri-bution and cold trapping.

We began with the goal of evaluating the hypothesis that themajor landforms on Hyperion can be explained solely though mod-ification of a cratered landscape through volatile sublimation andmass wasting of released dust. From this central starting workinghypothesis we identified several additional questions to be testedby a combination of data analysis and modeling. (1) Has there beenlittle redeposition of ejecta as was concluded by Thomas et al.(2007a)? (2) Are steep lower slopes of larger fresher craters man-tled by mass wasting debris of loose granular material close tothe angle of repose? (3) Is the high proportion of 2–10 km diametercraters relative to smaller sizes the result of preferential destruc-tion of small craters during impacts as suggested by Thomaset al. (2007a)?

Our simulation modeling is intended to determine what mini-mal set of processes, relative process importance, and historicalevolution can replicate the observed topography of Hyperion.Because of the uncertainties concerning the composition ofHyperion and the rate and size distribution of cratering a fullycalibrated model is not possible. In Section 5 we address more fullythe issues of process scaling.

3. Surface morphology

The highest resolution images of Hyperion taken by the CassiniOrbiter are of the region dominated by the big 121-km impact

Fig. 1. Global view of Hyperion. This face of the satellite is dominated by a 121 kmdiameter impact basin with steep interior walls and raised central dome that isdensely covered with subsequent impacts. Some crater floors and depressions arecovered by a shallow, dark-toned mantle. (Cassini ISS Narrow Angle Camera imagenumber N1506383441; solar illumination phase angle 52�; lighting from above)Inset in upper left shows the locations of Figs. 2–4). Note that Hyperion chaoticallyrotates and thus no standard coordinate system has been officially recognized.

Fig. 2. Detail of a part of the interior wall of the 121 km basin, a �30-km-diametersuperimposed impact basin (right center), and numerous smaller craters. The basincrater rim as well as several of the younger craters feature steep, intricately-sculpted (crenulated) upper slopes that we hypothesize are exposures of volatile-cemented particulates (bedrock) undergoing sublimation disaggregation and masswasting. The lower crater interior crater walls are mantled with loose, mass-wasteddebris near the angle of repose. These slopes locally show lobate texturescharacteristic of shallow avalanching. Between the larger craters are much moredegraded craters with rounded rims comprising an apparent saturation population.(This scene is a portion of Cassini ISS Narrow Angle Camera image numberN1506391247; lighting from right).

Fig. 3. Detail of a cratered landscape on Hyperion. Landscape is dominated bysmooth crater depressions of generally concave shape intersecting at narrowconvex ridges displaying a cellular (honeycomb) pattern which we interpret asimpact basins highly degraded by weathering and mass-wasting. A few, probablyyounger, craters exhibit crenulated upper slopes exposing bedrock. Hummockyridges below these crenulated slopes (‘#’) are probably landslides. This scene is aportion of Cassini ISS Narrow Angle Camera image number N1506393074; lightingfrom above.

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basin (Fig. 1). The interior walls of the basin are steep, with theupper slopes featuring a crenulated surface suggestive of mass-wasting erosion of bedrock or cohesive material that behaves assuch (Fig. 2). The lower slopes are smooth and appear to be an-gle-of-repose accumulations of debris released from the superja-cent steep slopes. This ancient impact basin is densely coveredwith craters, most of which are substantially degraded as well.Most of Hyperion’s craters feature a smooth, strongly concave ba-sin floor (Fig. 3). A few craters feature hummocky floor depositsthat may be landslide debris derived from the crater walls, possiblyoccurring immediately after their formative impact (Figs. 3 and 4).Many of the older craters superimposed on or exterior to the bigbasin appear to be very degraded, with smooth, concave interiorsand sharply rounded rims. These degraded craters often shareexterior walls with adjacent degraded craters forming septa, givingan irregular honeycomb appearance to the landscape (Figs. 3 and4). The occasional craters that exhibit interior wall morphologyof steep, crenulated upper slopes and smoother, less steep lowerslopes appear to be relatively young impacts formed subsequentto extensive degradation of the big basin and most of its superim-posed impacts.

Portions of Hyperion’s surface are mantled with an irregulardark blanket perhaps derived from infalling particulate debris pos-sibly transported from Phoebe or Titan (Figs. 1–4) (Korycansky andZahnle, 2008). This blanketing is primarily but not exclusively con-centrated in basin interiors, but it appears to be a thin, recent man-tle whose origin may be unrelated to the mass wasting landformsinvestigated here. However, the possibility that it is a local detrituscreated by the loss of cementing volatiles upslope cannot be ruledout (Brad Dalton et al., 2012).

Relatively fresh craters on Hyperion exhibit a simple propor-tionality between depth and diameter up to at least 50 km diame-ter (Fig. 5). Data from Hyperion and Phoebe is consistent with aconstant depth-diameter ratio for craters up to several tens ofkm in diameter. This simple-crater proportionality is similar tothat observed on Phoebe yet lacks the transition to complex crater

morphology characteristic of larger saturnian satellites (notablyRhea (White and Schenk, 2011)), Ganymede and the Moon(Fig. 5). Note that surface gravity will affect the slope of thedepth/diameter plot (at least for complex craters).

4. Landform simulation modeling

4.1. Cratering

We have modified a model developed for simulation of terres-trial, martian, and icy satellite landform evolution (Barnhartet al., 2009; Howard, 1994, 1997, 2004, 2007, 2011; Howard andMoore, 2008) to explore the feasibility of the above hypothesesfor the evolution of Hyperion’s surface features. These simulationsuse existing components of the model related to impact cratering,weathering, and mass wasting modified for the assumed condi-tions that pertained on Hyperion.

The initial condition for the simulations is a saturation-crateredsurface (Fig. 6) generated by spatially and temporally randomsimulated impacts using a geometric cratering model reported inForsberg-Taylor et al. (2004) and Howard (2007). The relationshipbetween fresh crater depth and diameter for Hyperion, Phoebeand Mimas is shown in Fig. 5. Crater shape is assumed to followpower–law relationships:

H1 ¼ KH1 Dg1 ; H2 ¼ KH2 Dg2 ; ð1Þ

where H1 is bowl depth relative to surrounding terrain, D, is craterdiameter, H2 is rim height relative to surrounding terrain, andKH1 ;KH2 ;g1 and g2 are scaling parameters. Hyperion and Phoebedepths are consistent with geometric similarity (g1 = 1 over therange of crater sizes up to the largest modeled crater (50 km) whereinterior crater depth, H1 is 0.2 times the crater diameter,DðKH1 ¼ 0:2Þ (Fig. 5). We assume the rim height relative to the sur-rounding terrain, H2, is also a constant fraction of crater diameter(g2 = 1). The interior and exterior of craters are modeled as powerfunctions with interior shape exponents chosen to match Lunarand martian crater geometry (Howard, 2007; Moore et al., 2004):

DH ¼ ðH2 � H1Þ þ H1ð2r=DÞm; ð2Þ

Fig. 4. Image of degraded, cratered landscape on Hyperion with elevation color-coded from stereo-photogrammetry. The two larger craters exhibit crenulatedupper slopes and hummocky floors of probable landslide debris. This is one of thehighest resolution images obtained of Hyperion, with an original resolution of26 m/pixel. Note a few large blocks can be seen near the crater rim just lower rightof center. (Cassini ISS Narrow Angle Camera image number N1506393614; stereotopographic data was derived from this image and from Cassini imageN1506391975; lighting from above).

Fig. 5. Depth-diameter relationship for fresh craters on Hyperion with comparativedata from Phoebe, Mimas, Rhea, the Moon, and Ganymede. Data from Hyperion andPhoebe is consistent with a constant depth-diameter ratio for craters up to severaltens of km in diameter. The surface gravities of Hyperion (0.019 ms�2), Phoebe(0.049 ms�2), Mimas (0.064 ms�2), Rhea (0.264 ms�2), the Moon (1.622 ms�2) andGanymede (1.428 ms�2) give a sense of the relative sizes of these bodies. All targetsurfaces given here are dominated by ice except the Moon. See text for discussion.

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where DH is the change in elevation relative to the pre-crater ter-rain, r is the radial distance from the crater center and the exponent,m is a function of crater diameter:

m ¼ 0:64D0:13: ð3Þ

The value of m varies from 1.59 for a 1 km diameter crater to 2.6 fora 50 km diameter crater

Because we are interested in the morphology of craters lessthan a few tens of kilometers in diameter, we do not model forma-tion of central peaks. We also assume that crater relaxation fromice creep does not occur because of the small crater size and lowgravity.

Exterior shape exponents are calculated to make the nominalvolume of ejecta equal to that of the excavated crater interior.However, fresh craters on Hyperion have rims that are only slightlyraised relative to surrounding terrain. This suggests that, becauseof the low gravity of Hyperion (g �0.02 ms�2) only a fraction ofthe ejecta is ballistically deposited (Thomas et al., 2007a). Someof the remaining ejecta may be lost entirely, but part may bedeposited as a thin, widely-distributed blanket. We assume thatonly 20% of the excavated interior bowl material is deposited bal-listically. In addition, we reduce the rim height relative to sur-rounding terrain by about two-thirds relative to martian craters,inferring that most of the rim on larger planetary surfaces is dueto ejecta deposition as opposed to rim uplift. Specifically,KH2 ¼ 0:1KH1 . The exterior ejecta depth is also modeled as a powerfunction of distance from the rim:

DH ¼ H2ð2r=DÞ�n; ð4Þ

where the exponent, n, varies from 4.91 for a 1 km diameter craterto 4.15 for a 50 km diameter crater. The exponent, n, is automati-cally selected to result in deposition of 20% of the excavated volumeas ballistic ejecta.

The result of assuming a reduced ejecta volume is that rims ofadjacent large craters generally intersect as narrow ridges(Fig. 6), which results, after mass wasting, in the honeycombtexture of narrow septa separating craters which is a dominant fea-ture of Hyperion (Figs. 3 and 7). If a reduced ejecta volume is notspecified, in cratered landscape simulations larger craters rimsgenerally are separated by relatively level intercrater plains (e.g.,Howard (2007, Fig. 2a and c). Such isolated large craters are

characteristic of most planetary landscapes where higher gravityresults in essentially full deposition of ejecta in ballistic deposits.The modeling choice of 20% for the ballistic ejecta retention onHyperion is arbitrary, and is set to a value small enough to resultin the honeycomb morphology. The two-thirds reduction in craterrim height is assumed to give a decay scaling rate (exponent n inEq. (6)) that is within the range of observed ejecta morphologyon other planetary surfaces.

This scaling, which is assumed to represent modified ratherthan transient crater shape, predicts steep maximum slopes onthe interior rim, ranging from 32.5� for a 1 km diameter crater to46.1� for a 50 km crater. Relatively fresh craters on Hyperion oftenfeature a hummocky floor deposit (Figs. 3 and 4) which likely re-sults from collapse of steep interior crater walls. The upper, steepinterior crater walls on Hyperion generally exhibit gullied or cren-elated morphology (Figs. 1–4), which we infer, and model, to resultfrom rapid mass wasting by avalanching of weathered bedrock.

Impacts are simulated by geometric modification of the surfacewith the locations of impacts chosen randomly and crater sizes arerandomly drawn from a population distribution such that thenumber of craters, ND, greater than diameter D follows an inversesquare relationship to diameter (e.g., Melosh, 1996; Hartmannand Gaskell, 1997):

ND / D�2: ð5Þ

Superposition of craters on pre-existing topography, including ear-lier impacts, is governed by an inheritance parameter, I, (0.9 in thepresent simulations) as discussed by Howard (2007).

4.2. Weathering and mass wasting

Starting from the initial cratered landscape we modeled subse-quent landform evolution through weathering by sublimation and

Fig. 6. Simulated saturation-cratered surface serving as initial conditions for thelandform evolution simulations. Image width is 100 km. Elevation scale in meters(arbitrary datum). Boundary conditions are doubly-periodic.

Fig. 7. Cratered landscape from Fig. 6 modified by long period of simulatedsublimation weathering and mass wasting. A few upper crater walls exhibit shortbedrock exposures. Note that interior crater walls have decreased in gradient,becoming smoothed and retreating until adjacent crater walls intersect in ahoneycomb network of ridges. Relief scale same as in Fig. 6. Note that the simulateddegradation does not materially decrease total relief. The simulated craterdegradation has effectively eliminated craters smaller than 10 km in diameter.Upper slopes of some craters exhibit short terraces of exposed bedrock withintervening debris-covered slopes. The persistence of these terraces is due to thesmall assumed difference in maximum gradient of bedrock slopes relative todebris-covered slopes and is a numerical artifact.

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mass wasting processes. We conducted simulations with a range ofparameters determining morphologic evolution and process rates.We report on a simulation that best matches the observed mor-phology of Hyperion with process rates scaled to a 4 Ga landformevolution time period.

4.2.1. Mass wasting modelDiffusional mass wasting or creep traditionally has been mod-

eled as a linear process whose vector mass flux, qm, is governedby a diffusivity, Km, and the downslope gradient, S expressed asqm = KmS. Recently, with the recognition that rates of mass wastingincrease dramatically as a limiting slope steepness, Sc, is ap-proached, non-linear creep relationships have been proposed by(Howard, 1994; Roering et al., 1999). Roering et al. suggest thatmass wasting is caused by disturbances of equal magnitude inthe upslope and downslope direction. In the upslope directionthe movement is impeded by both friction and gravity, and down-slope it is also impeded by friction but is aided by gravity. The netflow is the addition of upslope and downslope displacementsresulting in Eq. (6).

qm ¼KmS

½1� ðS=ScÞ2�; ð6Þ

where qm is mass flux (m2 yr�1) per unit slope width and Km

(m2 yr�1) is a scaling parameter with the same units. This relation-ship has been verified in laboratory experiments where shallowmass movement occurs by induced vibrations (Roering et al.,2001) and successfully applied to modeling terrestrial (Roeringet al., 1999) and planetary (Howard and Moore, 2008; Richardsonet al., 2004) landscapes.

4.2.2. Bedrock weatheringWe assume that the bedrock of Hyperion consists of a mixture

of frozen volatiles (H2O, CO2 and possibly others (Cruikshanket al., 2007; Brad Dalton et al., 2012)) mixed with non-volatile par-ticulates (e.g. silicates and carbon). The volatiles are postulated toslowly sublimate at a constant rate, W0, perpendicular to the slope.Because of the chaotic rotation of Hyperion we do not include as-pect or latitude effects. The weathering rate is assumed to decreaserapidly where non-volatile particles accumulate on the surface sothat sublimation effectively ceases where the bedrock is coveredby a few meters of particles. If the bedrock becomes re-exposedby mass wasting or impact cratering, sublimation will re-initiate.

As the volatiles escape from steep exposed bedrock, the partic-ulate component cascades downslope until it reaches a slope gra-dient less than the assumed dynamic angle of repose, where itaccumulates and is further subject to slow downslope creep (seebelow). We also assume a finite strength of the volatile-particulatebedrock, with a maximum stable slope gradient, Scb, of 0.8 (38.7�),where the b subscript indicates the value for bedrock slopes. Thisvalue of the limiting gradient is assumed because maximum slopeangles on eroded crater walls of Hyperion are of about this value,as discussed later. As the slope gradient, S, approaches this criticalvalue, Scb, the bedrock is assumed to mass-waste according to Eq.(6). Bedrock mass-wasted by this process also cascades downslopein the same manner as debris from sublimation. Because we do notknow the timescale of weathering or mass wasting on Hyperion,We set the values of W0 and Kmb 1.25 � 10�8 m yr�1 and1.25 � 10�5 m2 yr�1, respectively, to replicate the modern Hype-rion topography over a 4 Ga timescale. These values result in bed-rock exposures being close to the maximum stable slope gradient.The low density of Hyperion (about one-half that of ice (Thomaset al., 2007a,b)) suggests appreciable void space so that the volatilecementing component is likely to represent less than a void-fillingfraction. We accordingly assume for simplicity that weathering is

isovolumetric, that is, that the volume of particulate debris pro-duced equals the volume of the eroded bedrock.

4.2.3. Non-linear creepWhere mass wasted debris accumulates, we assume that fur-

ther downslope creep of this sedimentary regolith occurs underthe influence of gravity. We model non-linear creep following Eq.(6) but with a smaller critical slope gradient (Scr = 0.53 or 28�)and Kmr = 5.0 � 10�5, where the subscript r indicates values for reg-olith-mantled slopes. This critical slope angle is typical of the angleof repose of loose, angular granular material (e.g., Kleinhans et al.,2011). The disturbances exciting creep are envisioned to be pro-duced by such processes as micrometeorite impacts, thermalexpansion and contraction, and ground shaking (from internalforces or from large impacts).

The rate of surface elevation change by creep, @zmr/@t is propor-tional to the spatial divergence of the creep vector:

@zmr

@t¼ �rq: ð7Þ

Eq. (7) is solved by substitution of Eq. (6) into Eq. (7) using finite dif-ference techniques that assure mass conservation. This same equa-tion is used to model diffusion of mass-wasted bedrock.

The values of the weathering and mass-wasting coefficients, W0,Kmb, Kmr, Scb, and Scr determine the rates of landscape evolution. Wedo not know the absolute values of these coefficients, but we havechosen their relative values to best match the landform morphol-ogy of Hyperion. We revisit the question of absolute rates in Sec-tion 5.

4.3. Simulation scenario

Because the surface of Hyperion appears to comprise a popula-tion of highly-degraded craters with a superimposed population ofless-degraded craters, we have undertaken a two-stage simulation.Our initial surface is a saturated cratered surface. We have selecteda square simulation domain 100 km on a side with square grid cells

Fig. 8. Further evolution of the landscape shown in Fig. 7 by addition of a sub-saturation population of new impacts followed by simulated weathering and mass-wasting. The larger added craters exhibit steep, crenulated upper walls. Theresulting mixed population of highly degraded older craters and less degradedyounger craters strongly resembles the landscape of Hyperion (cf. Figs. 2–4). Graylines show profiles used to sample slope–frequency shown in Fig. 10, collectedusing the same procedure used to sample the Hyperion DEM (Fig. 9).

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100 m on a side. The boundaries are periodic, matching acrossboundaries in both the horizontal and vertical direction. The simu-lation starts with a saturation-cratered surface (Fig. 6). The firststage of modification comprises a long period of bedrock weather-ing and mass wasting that is continued to the point that only smallareas of bedrock are exposed and the majority of the surface is cov-ered with loose debris that has been reworked into a smooth sur-face consisting of concave basin floors and slightly rounded craterrims (Fig. 7). Note that weathering and backwasting have causedinterior crater walls to retreat to the point that adjacent craterwalls merge into thin, slightly rounded septa. Because of a high de-gree of uncertainty about weathering and backwasting rates(whether driven by sublimation or not), the time required to reachthis state of degradation is also uncertain.

The second stage of modification consists of superimposing anon-saturated population of new impacts followed by weatheringand mass wasting that do not entirely eliminate bedrock exposureson the upper interior crater rims (Fig. 8). Relative to the time re-quired to create the degraded surface from the first step of the sim-ulation (i.e., going from Figs. 6 and 7), the time required to partiallydegrade the craters to that of Fig. 8 is about two-thirds smaller.

5. Discussion

The qualitative resemblance of the composite simulation toHyperion’s surface is striking (compare Fig. 7 with Figs. 1–4). Thisresult is consistent with our initial hypothesis that mass wasting ofbedrock and regolith explains Hyperion’s surface morphology. Thecritical components of the model that produce Hyperion’s uniquemorphology are the non-retention on the surface of most of the im-pact bowl debris coupled with low crater rim heights compared tothe surrounding terrain. The initial stage of degradation by subli-mation weathering and mass wasting is highly effective in reduc-ing the number of small craters on the surface of Hyperion(compare Figs. 6 and 7). The effectiveness of diffusive mass wastingin erasing surface features decreases with the square of the land-form size. A low frequency of craters on Hyperion less than 2 kmin diameter relative to a production population (as in Figs. 7 and8) was noted by Thomas et al. (2007a) and can be explained bymass wasting obliteration.

The upper interior crater walls of the larger craters in Fig. 6 re-treated about 2–4 km during the erosion producing Fig. 7. The

steep upper walls of the craters (e.g., the crater walls crossed bythe profiles in Fig. 8) continuously expose bedrock, and the rate-controlling step in scarp retreat is the sublimation rate governedby W0. The mass wasting of bedrock using Eq. (6) governed bythe parameter Kmb has a subsidiary role, only becoming quantita-tively important when sublimation steepens the bedrock slopesto near the assumed maximum stable angle of Scb = 0.8.

A series of topographic profiles were constructed through sev-eral prominent craters in a high-resolution Digital Elevation Model(DEM) of part of Hyperion’s surface constructed by stereophoto-grammetry (Fig. 9) (see Schenk, 2002 for details on DEM generat-ing technique). The frequency of slopes measured along-profile isshown by the black line in Fig. 10, normalized to a total area ofunity below the curve. Slope gradients up to 55� were found. Theslope distribution for the simulated saturation-cratered surface isshown by the orange line in Fig. 10. Note that a wide range of slopegradients were simulated, with a few exceeding 80�. We evaluatedthe slope–frequency characteristics of the simulation using a tech-nique similar to that used to evaluate slopes in the natural DEM.We centered radial transects on two of the larger craters with steep(bedrock) upper walls similar to those in the natural landscape(compare Figs. 8 and 9). The combination of simulated long-termsublimation weathering and mass wasting (Fig. 7) and partial sub-sequent sublimation weathering and mass wasting of the non-sat-uration crater population superimposed on the degraded surface(green2 line in Fig. 10) produces a slope distribution that, like theobserved gradients, is dominated by gradients less than 30� to-gether with a small population of slope segments in the range from30� to 50�, primarily along the upper ‘‘bare bedrock’’ walls of thelarger craters of the younger impacts. The slope–frequency charac-teristics of the Hyperion DEM and the simulation are reasonablysimilar. The slightly larger Hyperion DEM grid size (0.16 km com-pared to the 0.1 km simulation grid) may account for the lowernumber of observed slopes greater than 40� in the former.

An alternative scenario of degradation processes might alsoproduce a similar suite of landforms. Specifically, it is possible thatthe ‘‘bedrock’’ is only weakly cohesive (if at all) and that the steep,crenulated upper slopes on fresh craters are at the static angle ofrepose whereas the steepest subjacent slopes do not exceed a con-

Fig. 9. Profiles through the two Hyperion craters. Profiles are derived from the stereo DEM shown in Fig. 4. Elevation datum is arbitrary and profiles from the two craters areoffset by 2 km. Resolution of the profiles is not great enough to clearly show the slope transition from steep, crenulated slopes to the slightly gentler mass wasting slopes. Theapproximate elevation of this transition is shown by ‘#’ symbols for the high crater rim in profiles A–D. The profiles exhibit the hummocky topography of the inferredlandslide debris in the two craters.

2 For interpretation of color in Figs. 4, 10, and 11, the reader is referred to the webversion of this article.

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siderably lower dynamic angle of repose. Recent laboratory simu-lations have indicated that the difference in surface inclinationfor dynamic versus static angles of repose can be quite large underlow gravity situations (Kleinhans et al., 2011). Under this scenariothe ‘‘bedrock’’ could be porous mixtures of ice particles and min-eral dust (consonant with the low bulk density of Hyperion) whichmight be highly pulverized by impact cratering processes. A coun-ter argument to this hypothesis is the observation that large,undoubtedly ejected, blocks can be seen on the surface (Fig. 4). Itis difficult to reconcile such blocks with highly pulverized, low-density pseudo-bedrock.

5.1. Landform evolution timescales: mass wasting

Our simulation modeling is scaled by the rate-controllingparameters sufficient to produce the landscape of Hyperion overa 4 Ga timescale. We briefly address absolute process scaling. Themass wasting diffusion that produces the dominantly smooth sur-face textures of Hyperion could be driven by a variety of processes,

including thermal cycling, seismic shaking from impacts, and di-rectly from small impacts. Impact cratering is a diffusive process(e.g., Soderblom, 1970; Howard, 2007). Modeling of Lunar diffusivecrater degradation by small impacts (data from Craddock andHoward, 2000) is consistent with a diffusivity, Kmr, of about0.0004 m2 yr�1. Much crater degradation on the Moon is from sec-ondary impacts, which would not occur on Hyperion. Size–fre-quency characteristics of saturnian satellites (and Hyperion inparticular) show a pronounced deficiency in craters less than10 km diameter as compared to the Moon (Zahnle et al., 2003;Thomas et al., 2007a; Dones et al., 2009). The impact frequencyof objects producing very small craters is highly uncertain. Thusit appears that a priori estimation of mass wasting diffusivity onHyperion is not possible. Our assumed mass wasting timescale ofKmr = 5.0 � 10�5 m2 yr�1 is about one order of magnitude lowerthan the estimated Lunar value, suggesting either slower rates orthat evolution of Hyperion’s surface has occurred over a shortertimescale the assumed 4 Ga.

5.2. Landform evolution timescales: sublimation

The Cassini Composite Infrared Spectrometer (CIRS) instrument(Flasar et al., 2004) observed daytime and nighttime thermal emis-sion on Hyperion during the 26 September 2005 flyby, allowingderivation of surface temperatures, albedos, and thermal inertiaswhich can be used to directly constrain sublimation rates for ex-posed volatiles (Fig. 11). Thermal emission spectra closely approx-imate blackbodies, and we use the temperature of the best-fitblackbody curve as an estimate of surface temperature, assumingunit emissivity. Using CIRS 20–100 lm data, measured nighttimetemperatures were quite uniform at 58 ± 2 K near the center ofthe night side, and daytime temperatures on the average surfacereached about 115 ± 2 K near the center of the day side. Assumingthese numbers represent the low-latitude diurnal temperaturerange, and using the instantaneous angle between the spin poleand the Sun (79�) and the rotation period (5.00 days) for Hyperionat the time of the flyby from Harbison et al. (2011), we can fit thesedata with a bolometric albedo of 0.33 ± 0.05 and thermal inertia of11 ± 2 J m�2 K�1 s�1/2. This thermal inertia is comparable to that of

Fig. 10. Gradient-frequency histograms for Hyperion (‘‘Observed’’) and for simulated landscapes. All curves are normalized to unit area under the curve. The ‘‘Initial Cratered’’curve shows the gradient-frequency for the saturation-cratered population of Fig. 6. The ‘‘Simulated’’ curve shows the gradient frequency for Fig. 8, exhibiting the smallpopulation of steep, crenulated slopes steeper than 30�.

Fig. 11. Color-coded daytime surface temperatures and uncertainties, derived fromblackbody fits to CIRS 9–17 lm measurements of surface thermal emission in andaround dark-floored craters on Hyperion, superposed on a near-simultaneous ISSimage (N1506393257). The squares show the size and location of the CIRS field ofview, and are 1.9 km across.

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several other icy saturnian satellites (Howett et al., 2009, 2011)and implies that the upper centimeter of the surface is highly por-ous and unconsolidated. High (�2 km) spatial resolution CIRS ther-mal data at shorter wavelengths (9–17 lm) reveal locally higherdaytime temperatures, up to 127 K, in the bottoms of dark-flooredcraters (Fig. 11). Derived bolometric albedo of the dark crater floormaterial is only 0.05 ± 0.05.

From these albedos and the thermal inertia, time-averaged sub-limation rates for H2O and CO2 frost can be estimated, thoughHyperion’s chaotic rotation adds uncertainty. To calculate the dis-tribution of surface temperatures with time, we assume that the2005 rotation rate is typical, and that the spin axis orientation var-ies randomly (on timescales longer than the rotation rate) in bothinertial space and body-fixed space, and also account for the eccen-tricity of Saturn’s orbit. From the distribution of the resulting tem-peratures we obtain mean H2O ice sublimation rates of 11.5 m/GAfor material with the 0.05 albedo of the dark crater floors, and0.15 m/GA for the average surface (albedo 0.33), assuming subli-mation is not inhibited by development of a surface lag deposit.These rates are high enough to affect surface albedo, and may beresponsible for the observed low albedo of crater floors, becausethe expected higher temperatures in craters, due to topographicheat trapping, will result in higher sublimation rates there, andmore rapid development of a dark, non-volatile, lag deposit. How-ever, as noted by Thomas et al. (2007a,b), who estimated similarH2O sublimation rates by analogy with other bodies, these ratesare still probably too low to affect the surface morphology onCassini image scales, particularly for the high-albedo material.Sublimation rates for surface CO2 ice are however dramaticallyhigher (measured in kilometers per thousand years), so any freeCO2 ice in the surface will be lost rapidly, with potentiallyimportant consequences for evolution of Hyperion’s topography.We thus infer that if, as hypothesized, scarp backwasting isdriven by volatile sublimation, either (1) H2O acting as a bedrockcementing agent constitutes only a very small proportion ofthe bedrock volume or (2) more rapidly sublimated CO2 is thedominant mechanism for bedrock cohesion.

6. Conclusions

Thomas et al. (2007a) proposed that the unique appearance ofHyperion could be explained by the loss to space of ballistic ejectaduring impact events (Hypothesis 1 from Section 2). We concludethat such loss is a partial explanation, accounting for the lack ofappreciable intercrater plains on a saturation-cratered surface(e.g., Fig. 6). The smooth surfaces and the reticulate, honeycombpattern of narrow divides between craters (Figs. 1–4) occursthrough slope erosion governed by diffusive mass wasting of theregolith at the base of the crater headwall scarps. Sublimation-induced retreat of crater headwalls, probably involving CO2 loss,locally exceeds 2 km. (e.g. Figs. 7 and 8). During early stages of cra-ter degradation steep, crenulate bedrock slopes occupy the uppercrater walls with abrupt transitions downslope onto smooth slopesnear the angle of repose mantled by mass wasting debris (Figs. 2, 3and 8) as suggested by Hypothesis 2 (see Section 2). Long-contin-ued erosion eventually yields slopes totally mantled with particu-late debris (Figs. 2–4 and 7). The mass wasting effectively destroyssmall craters, accounting for the paucity of sub-kilometer craterson Hyperion (Hypothesis 3, given in Section 2).

Acknowledgments

This study was supported by the NASA Cassini Data AnalysisProgram. Two anonymous reviews were beneficial to enhancingmanuscript clarity.

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