A Global Catalogue of Ceres Impact Craters&#X202f

Home , Dantu (crater), Haulani (crater), Kerwan (crater), Mondamin (crater), Sintana (crater), Urvara (crater)

Icarus 302 (2018) 296–307

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Icarus

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A global catalogue of Ceres impact craters ≥ 1 km and preliminary analysis

∗ Sheng Gou a,b, Zongyu Yue a, Kaichang Di a,b, Zhaoqin Liu a, a State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China b Lunar and Planetary Science Laboratory, Macau University of Science and Technology—Partner Laboratory of Key Laboratory of Lunar and Deep Space Exploration, Chinese Academy of Sciences, Macau, China

a r t i c l e i n f o a b s t r a c t

Article history: The orbital data products of Ceres, including global LAMO image mosaic and global HAMO DTM with a Received 22 May 2017 resolution of 35 m/pixel and 135 m/pixel respectively, are utilized in this research to create a global cata-

Revised 14 November 2017 logue of impact craters with diameter ≥ 1 km, and their morphometric parameters are calculated. Statis- Accepted 20 November 2017 tics shows: (1) There are 29,219 craters in the catalogue, and the craters have a various morphologies, Available online 23 November 2017 e.g., polygonal crater, ﬂoor fractured crater, complex crater with central peak, etc.; (2) The identiﬁable Keywords: smallest crater size is extended to 1 km and the crater numbers have been updated when compared Ceres with the crater catalogue ( D ≥ 20 km) released by the Dawn Science Team; (3) The d/D ratios for fresh Crater catalogue simple craters, obviously degraded simple crater and polygonal simple crater are 0.11 ± 0.04, 0.05 ± 0.04 Distribution and 0.14 ± 0.02 respectively. (4) The d/D ratios for non-polygonal complex crater and polygonal complex

Density crater are 0.08 ± 0.04 and 0.09 ± 0.03. The global crater catalogue created in this work can be further ap- Morphometric parameters plied to many other scientiﬁc researches, such as comparing d/D with other bodies, inferring subsurface properties, determining surface age, and estimating average erosion rate. ©2017 Elsevier Inc. All rights reserved.

1. Introduction crater catalogue with morphometric properties have significant scientific application potentials for the research of Ceres, which is im- The geologically primitive dwarf planet Ceres, with approxi- possible to accomplish before the Dawn mission. Though studies mately 940 km diameter and a mass of one third of the total mass on craters at a global scale for Ceres have been done by the Dawn of the asteroid belt, is an intact protoplanet since its formation, Science Team ( Hiesinger et al., 2016; Marchi et al., 2016 ), the spa- which is key to understand the origin and evolution of the so- tial resolution of the base map for constructing their crater cata- lar system ( Russell et al., 2004; Russell and Raymond, 2011 ). The logues is about 135 m/pixel ( Roatsch et al., 2016b ). Dawn spacecraft, chiefly equipped with Framing Camera (FC), Vis- In this research, the recently released global LAMO image mo- ible and infrared spectrometer (VIR) and Gamma Ray and Neutron saic and global HAMO DTM derived from FC images with a resolu- Detector (GRaND), has mapped Ceres with Framing Camera at dif- tion of about 35 m/pixel ( Roatsch et al., 2017 ) and 135 m/pixel re- ferent orbital heights during the early approach phase, the Survey spectively are utilized comprehensively to construct a global crater orbit, the High Altitude Mapping Orbit (HAMO) and the Low Alti- catalogue with diameter ≥ 1 km, and crater morphometric parame- tude Mapping Orbit (LAMO) after orbit insertion on March 6, 2015 ters are further measured and calculated. Preliminary analyses of ( Russell et al., 2016 ). their spatial distribution characteristics and morphometric param- FC images reveal the surface of Ceres is heavily cratered with eters are also included in this research. We hope this global crater a large variety of crater morphologies, e.g., bowl shaped craters, catalogue for Ceres can contribute to the community and be used polygonal craters, floor-fractured craters ( Hiesinger et al., 2016 ). broadly in the future. Cratering is one of the most important processes that greatly shaped the surface of Ceres, and the morphology and distribution 2. Datasets and methodologies of the craters can provide insights into geological settings, subsurface properties, and even the evolution history of Ceres. Therefore, 2.1. Datasets

The datasets used in our research are global mosaic prod- ∗ Corresponding author. ucts from the Dawn mission, which is the ﬁrst spacecraft to E-mail address: [email protected] (Z. Liu). orbit separately two extraterrestrial bodies: Vesta and Ceres https://doi.org/10.1016/j.icarus.2017.11.028 0019-1035/© 2017 Elsevier Inc. All rights reserved. S. Gou et al. / Icarus 302 (2018) 296–307 297

( Russell et al., 2016 ). After orbital insertion on March 6, 2015, the framing camera onboard Dawn had imaged Cerean surface through a clear filter and 7 narrow-band filters covering the wavelengths from the visible to the near-infrared, at different orbital heights under various viewing angles and illumination conditions ( Sierks et al., 2011 ). Global image mosaics of different resolutions have been produced from these collected images, including global survey mosaic with a resolution of about 400 m/pixel ( Roatsch et al., 2016a ), global HAMO mosaic with a resolution of about 135 m/pixel ( Roatsch et al., 2016b ), global LAMO mosaic with a resolution of about 35 m/pixel ( Roatsch et al., 2017 ). In addition, about 2350 clear filter images acquired from HAMO in six different cycles, each of which is optimized for stereo photogrammetry, are used to construct digital terrain models (DTMs). A global HAMO DTM, format- ted as image where the DN values give the height in meters above a reference sphere of 470 km, is generated with a lateral spacing of about 135 m/pixel and a vertical accuracy of about 10 m. The DTM covers approximately 98% of Ceres surface, with only few permanently shadowed areas near the poles interpolated ( Preusker et al., 2016 ). Hence, the global LAMO mosaic and global HAMO DTM, both of which provided in equidistant cylindrical projection, are the highest resolution cartographic products available at present, and are the two most important basemaps to map craters on Cerean surface and to calculate their morphometric parameters in this research. The inappropriate illumination geometry and the permanently shadowed areas of the mosaics ( Schorghofer et al., 2016 ) have influence on crater identification on polar regions and will be discussed in Section 3.2.2 .

2.2. Methodologies

2.2.1. Crater identification The crater identification is the basis for further morphometric measurement and analysis. The crater identification procedure over Fig. 1. Flow chart of crater extraction and morphometric measurement. the Cerean surface is performed manually with global LAMO mosaic as basemap in a geographic information system environment by using the CraterTools extension for ArcGIS, which helps to avoid cle center of each crater are drawn starting from north with fixed errors of crater diameters and measurement area sizes related to interval angle 22.5 ° ( Fig. 2 b). map-projection induced distortions automatically ( Kneissl et al., (3) Profile update Taking into account the uncertainty of the ini- 2011 ). The craters are identified by their unique characteristics tial diameter measurement in CraterTools, the local topographic in- (e.g., presence of rim, circularity of the rim, etc.), and they are dig- flection point (local maxima) along the profile is found within 10% itized by a three-point rim fitting method ( Kneissl et al., 2011 ), diameter on both sides of the initial circle ( Fig. 2 c), and the pro- so the resulted diameter is rim diameter in this research. The files are updated by connecting the two local maxima points in basemap for crater identification is shown in polar stereographic each previous profile. During this process, if any of the local max- projection for single hemisphere areas poleward of 60 ° and the ima is within other crater, the relief along this profile is affected other areas is mapped in equidistant cylindrical projection. and the profile is marked as invalid. And if none of the local maxima can be found along the profile, this profile is also marked as 2.2.2. Morphometric measurement invalid. After the completion of crater extraction over Cerean surface, (4) Major axis localization Though the major axis within the up- the morphometric parameters for each crater are measured based dated 8 profiles can be determined, it may be not the real case, on the global HAMO DTM. Because of the limitation of the reso- so it is named as ‘pseudo major axis’. The exact major axis cross- lution ( ∼135 m/pixel) of DTM, the smallest diameter of the crater ing the crater center is searched and localized within the current that can be reliably resolved is ∼ 1 km, or ∼8 pixels across ( Garvin ‘pseudo major maxis’ and its left and right neighbors by binary and Frawley, 1998; Robbins and Hynek, 2012 ). Hence, the morpho- search method with the search threshold is set to 1 ° The major metric measurements are only applied onto those craters with di- axis localization procedure can make morphometric measurement ameter ≥ 1 km by following the algorithm shown in Fig. 1 . more accurate and reliable, especially for fresh craters. (1) Crater selection The craters ≥ 1 km in diameter in previ- (5) Morphometric measurement The diameter of the crater mea- ous identification are selected for morphometric measurements sured by CraterTools is adopted in this research, the depth of the ( Fig. 2 a). Within this step, obvious secondary craters that align crater is defined as the average elevation difference between the in chains or form clusters are excluded for further calcula- rim and the floor of each profile, and the depth-to-diameter ratio tion to preclude possible contamination on crater morphomet- (abbreviated as d/D ) is defined as the ratio of the average depth to ric analysis, especially those secondaries around Occator, Dantu the diameter. During the morphometric measurement procedure, and Yalode identified by Scully et al. (2016) _ENREF_43 and in order to avoid any influence of map projection and terrain re- Schmedemann et al. (2017) . lief, the coordinates of each crater are converted to local coordi- (2) Profile creation Because there are many craters that cannot nate system (the origin is the crater center, x direction is local east, be perfectly fitted by a circle, so 8 profiles crossing the initial cir- y direction is local north, and z direction is perpendicular to the 298 S. Gou et al. / Icarus 302 (2018) 296–307

Fig. 2. Demonstration of crater extraction and morphometric parameter calculation on the surface of Ceres: (a) crater extracted by Crater Tools; (b) distribution of 8 profiles; (c) searching buffer zone; (d) profile is corrected from the general slope of the terrain. ground). The effect from the topography is corrected by subtract- 3. Results ing the general slope of the terrain for each profile before morphometric parameter measurement ( Fig. 2 d). 3.1. Crater morphology

2.2.3. Uncertainties The surface of Ceres is peppered with craters of various mor- The accuracy of the crater diameter is related to the positioning phologies, such as simple bowl-shaped crater ( Fig. 3 a), polygonal accuracy of crater rim of ‘Circle by points’ approach in ArcGIS dur- craters ( Fig. 3 b), complex crater with central peak ( Fig. 3 c), com- ing crater identification. We estimate the maximum diameter error plex crater with terraces and central pit ( Fig. 3 d), complex crater D is 2 pixels (1 pixel error per rim) in the global LAMO image with concentric terraces ( Fig. 3 e), degraded crater caused by vis- product, that’s D max = 70 m. The accuracy of depth measurement cous relaxation (Fig. 3f), craters with flow-like features (Fig. 3g), is mainly derived from the elevation difference of each profile floor-fractured craters ( Fig. 3 h), and craters with bright spots on which depends on the vertical accuracy of global HAMO DTM, and the floor or along the rim ( Fig. 3 i). its maximum value can be estimated as d max = 20 m. The d/D Craters on Cerean surface are not necessarily circular, and there uncertainty is estimated as d/D = d/D × ( d/d + D/D ). are many irregular craters. Of interest among above craters of S. Gou et al. / Icarus 302 (2018) 296–307 299

Fig. 3. FC images of craters with different morphologies on the surface of Ceres: (a) unnamed bowl-shaped crater; (b) polygonal crater; (c) complex crater with central peak; (d) complex crater with terraces and central pit; (e) complex crater with concentric terraces; (f) degraded crater caused by viscous relaxation; (g) crater with flow-like features; (h) floor-fractured crater; (i) craters with bright spots on the floor. various morphologies is the polygonal crater, Otto et al. (2016) dis- 3.2. Crater distribution covered 258 polygonal craters with diameter greater than 5 km, which distributes widely across the surface of Ceres. The formation 3.2.1. Global distribution and density of polygonal craters are thought to be related with the preex- Fig. 4 a shows the global distribution of all the identified craters isting subsurface fractures ( Melosh, 1989 ), and their widespread with diameter ≥ 1 km in this research. There are 29,219 craters distribution indicates the crust of Ceres is extensively fractured, with diameter ≥ 1 km in the completed catalogue, regardless of de- which in turn suggests that the subsurface must be both brittle formation and degradation. These craters forms high crater den- enough to fracture and mechanically strong enough to retain sity regions, e.g., areas around Tibong crater ( Fig. 4 b), showing fractures for long time ( Buczkowski et al., 2016; Russell et al., the varying degree of cratering on Ceres. The regions with low 2016 ). crater density are also very obvious from Fig. 4 b, for example, 300 S. Gou et al. / Icarus 302 (2018) 296–307

(a): Global distribution of all craters with diameter ≥ 1 km overlay on the LAMO global shaded relief mosaic

(b) Spatial density of craters with diameter ≥ 1 km

(d) Spatial density of craters with diameter ≥ 50 km

Fig. 4. Crater distribution and spatial density on the surface of Ceres. All maps are shown in equidistant cylindrical projection. S. Gou et al. / Icarus 302 (2018) 296–307 301

ing the crater density changed significantly. For example, Occa- tor (19.86 °N, 238.85 °E, ∼92 km) on the Hanami Planum, Dantu (24.21 °N, 137.43 °E, ∼125 km) on the Vendimia Planitia, and Ur- vara (45.66 °S 248.71 °E, ∼163 km) and Yalode (42.23 °S, 290.64 °E, ∼271 km) in the southern hemisphere. The crater distribution by latitude ( Fig. 5 b) shows an overall parabolic concave downward ‘ ∩ ’ trend. The crater numbers decreased drastically towards both polar regions, which may be caused by their smaller covering areas and illumination de- fects mainly due by grazing illumination and self-shadowing ( Schorghofer et al., 2016 ). The red squares in Fig. 5 a and b show the possible crater distribution if all 29,219 craters are distributed evenly on the surface of Ceres, which can be used together with the actual crater distribution as an indication for the heterogeneous crater distribution across the surface. Figs. 4 b and 5 b jointly show that the equator and the north polar regions have about the same spatial density of craters when taking into account for the different surface area. They also show the spatial density of craters in the mid-latitude of southern hemisphere and that in the high-latitude of northern hemisphere is close to or above the average distribution, while that of the south polar regions and the mid-latitude of the northern hemisphere is significantly below. The low density of south polar regions is partially due to the bad illumination condition and self- shadowing that part of the south pole was in the dark when images collected at LAMO cycles that make the crater identification in this research difficult. The low spatial density of the mid-latitude of the northern hemisphere may be caused by large craters such as Occator and Dantu ( Fig. 4 b) that erase or cover the previously existing craters.

3.3. Crater morphometry

≥ Fig. 5. All craters with diameter 1 km on the surface of Ceres: (a) distribution by 3.3.1. Crater diameter longitude; (b) distribution by latitude. The blue bars show the present actual crater distribution, and the red squares show the possible distribution if all the identified The number of craters decreases with the increasing of crater craters in this study are distributed evenly on the surface of Ceres. (For interpre- diameter, which is consistent with other planetary bodies, indicat- tation of the references to color in this figure legend, the reader is referred to the ing small impacts are more prevalent. There are 14,014 and 15,108 web version of this article). craters with diameter ≥ 1 km on the northern and southern hemisphere, respectively ( Table 1 ), indicating the cratering process hap- pened on both hemispheres at almost the same frequency. Small areas around Occator, Abellio, Ikapati, Gaue and Dantu crater in sized craters with diameters of 1.0–3.0 km are dominant, account- the northern hemisphere, and areas around Urvara, Sekhet, Yalode, ing for 85.44% of the total number of craters in the catalogue. Com- Mondamin, Sintana and Kupalo crater in the southern hemisphere. pared with the catalogue released by Hiesinger et al. (2016) (num- Maps of spatial density of craters with diameter ≥ 20 km ( Fig. 4 c) bers in brackets in Table 1 ), the numbers of craters with diame- or ≥ 50 km ( Fig. 4 d) show large craters are mainly distributed in ter greater than 20 km and 100 km in this catalogue are 578 and the northern hemisphere, which is in good agreement with the 21 respectively, indicating the refinement of this work when using work done by Hiesinger et al. (2016) and Marchi et al. (2016) de- global LAMO mosaic with higher resolution. Fig. 6 shows craters rived from HAMO mosaic. (20 ≤ D ≤ 50 km) that are catalogued in this study but not catalogued by Hiesinger et al. (2016) . Fig. 6 e is an obvious degraded 3.2.2. Longitudinal and latitudinal variations crater with diameter about 40 km, which cannot be easily iden- The crater distribution by longitude ( Fig. 5 a) shows an over- tified from HAMO mosaic (135 m/pixel). And the rest are craters all ‘W’ trend, and the highest crater density is found at three with diameters a bit greater than 20 km, which may be identified intervals: 160–180 °W, 0–30 °W and 160–180 °E, while the low- and catalogued as craters with diameters marginally below 20 km est is located within two intervals: 100–130 °W and 110–140 °E. when using HAMO mosaic. It’s likely that those craters were not These two low crater density intervals may be related with missed by Hiesinger et al. (2016) , but simply they have a slightly large craters, which can obliterate the existing craters, caus- lower diameter than that in this work.

Table 1 Statistics of numbers and percentages of craters ( D ≥ 1 km).

Diameter(km) 1.0–1.5 1.5–3.0 3.0–5.0 5–10 10–20 20–50 50–100 10 0–30 0 Total

Northern hemisphere 6468 5040 1226 653 334 310(278) a 68(60) 7(7) 14,106 Southern hemisphere 8262 5193 873 380 212 142(137) 37(37) 14(12) 15,113 Total 14,730 10,233 2099 1033 546 452(415) 105(97) 21(19) 29,219 Percentage 50.41% 35.02% 7.18% 3.54% 1.87% 1.55% 0.36% 0.07% –

a The number in the brackets are crater numbers catalogued by Hiesinger et al. (2016) with diameter ≥ 20 km. 302 S. Gou et al. / Icarus 302 (2018) 296–307

Fig. 6. Craters (20 ≤ D ≤ 50 km) that are identiﬁed in this study but not catalogued by Hiesienger et al. (2016) , shown in equidistant cylindrical projection. (a)–(c), and (g)–(i) are shown in polar stereographic projection, (d)–(f) are shown in equidistant cylindrical projection. S. Gou et al. / Icarus 302 (2018) 296–307 303

3.3.2. Crater depth and Rhea) are 0.13 ± 0.01, 0.11 ± 0.02,0.09 ± 0.02,0.12 ± 0.02 respec- Because the estimated maximum uncertainty on calculated tively ( Schenk, 1989 ). crater depth is 20 m, only the craters with depth greater than 20 m It can be noticed that the d/D of the fresh simple craters are included in this analysis. Statistics show among these 11,401 (0.11 ± 0.04) on Ceres is somewhat similar to that of sec- crater, 34.63% of the crater depth is shallower than 50 m, and there ondary craters on the Moon and Mars, and more akin to are only 13 craters deeper than 4 km. the icy bodies. As to the d/D of complex craters on Ceres, Hiesinger et al. (2016) found a best fit for the ratio is 0.13, but the ratio 0.08 ± 0.03 in this work also is more akin to that on icy 3.3.3. Crater depth-to-diameter ratio bodies which decreases to slightly below 0.1 for complex craters Statistics on depth-to-diameter ratio (abbreviated as d/D ) are ( Schenk, 2002 ). The possible reasons for the slight difference of also computed only on these 11,401 craters deeper than 20 m. The average d/D ratios between Ceres in this study and the other bod- d/D value of all the craters is in the range of 0.004–0.24, with mean ies can be classified into 4 categories: (1) The errors and uncer- d/D of 0.06 ± 0.04. 79.58% of the d/D are less than 0.10, and only tainties introduced by depth measuring methods used in previous 0.19% is larger than 0.2. studies. Shadow technique tends to overestimate the crater depth The simple-to-complex crater transition on Ceres occurs at di- while photoclinometry underestimates the depth, especially for the ameters of about 7.5–12 km ( Hiesinger et al., 2016 ), here we choose smallest craters, and stereo-photogrammetry is the most accurate 10 km as intermediate delimiter to classify these 11,401 craters on technique, but requires multi-imaging of the surface ( Marchi et al., Ceres and discuss their d/D separately. This division leads to 10,387 2015 ). The elevation for measuring crater depth used in this study craters are classified as simple crater and the rest 1014 are complex is based on stereo-photogrammetric processing ( Preusker et al., craters. 2016 ), while most of the others are not, so the ratios here should The 10,387 simple craters include 1377 fresh simple craters, be more reliable. (2) The lack of enough crater samples for deriving 8996 obviously degraded simple craters and 14 polygonal simple average d/D accurately. For example, the d/D on Phobos and Lute- craters, the mean d/D for above different type simple craters are: tia is derived from 6 and 125 craters respectively ( Shingareva et al., 0.11 ± 0.04, 0.05 ± 0.04 and 0.14 ± 0.02 respectively. 2008; Vincent et al., 2012 ). If high resolution images that cover the The 1014 complex craters are composed of 766 non-polygonal entire surface of these bodies can be collected, more craters should complex craters and 248 polygonal complex craters, and the aver- be identified and measured for a better d/D evaluation, which may age d/D values for them are 0.08 ± 0.04 and 0.09 ± 0.03. decrease the average ratio. (3) The correction of topographic effect in this research. Topographic effect is not considered and corrected 4. Discussions when measuring crater depth in many previous studies, which can lower the d/D ratio greatly, especially for the craters on the irregu- 4.1. Comparison of d/D with other bodies lar bodies. For example, the elongated asteroid Eros ( Veverka et al., 1999 ). (4) The influence of subsurface ice on Ceres’ crater mor- The crater d/D is widely used to describe crater shape, and it phologies. Bland et al. (2016) concluded Ceres’s shallow subsur- has been measured on many other bodies ( Table 3 ). For exam- face is no more than 30–40% ice by volume, with a mixture of ple, the ratio of fresh lunar craters less than 15 km is about 0.2 rock, salts and/or clathrates accounting for the other 60–70%. The ( Pike, 1974 ), which is also found on other terrestrial planets like slightly shallower d/D on Ceres than the other rocky bodies indi- Mars ( Pike, 1980 ) and Mercury ( Barnouin et al., 2012; Pike, 1988 ). cates the crust’s mechanical property that controls the final crater Daubar et al. (2014) even further reported the average d/D of new morphology is affected by the ice content. meter- to decameter-scale Martian craters formed in the last ∼20 years is 0.23. However, the d/D is ∼ 0.11 for the fresh secondary 4.2. Implications for subsurface craters on the Moon ( Pike and Wilhelms, 1978 ) or ∼0.08 on Mars ( McEwen et al., 2005 ). The transition diameter between simple and complex craters The general distribution of d/D of fresh simple craters on Ceres occurs is dependent on the gravity of the planetary body (0.11 ± 0.04) is slightly below that had been measured on many ( Melosh, 1989 ). If the crust of Ceres is mainly made of rock, then other rocky or icy bodies except the rocky Itokawa and Steins and the transition diameter could be ∼50 km and if it’s an ice–rock icy Ariel ( Table 3 ). The depth and diameter plot for fresh craters mixed body, the transition should be ∼10.3 km ( Hiesinger et al., on Gaspra indicates the d/D is close to 0.125 ( Carr et al., 1994 ). 2016 ). Fig. 7 a shows the crater depth increases quasi-linearly with Sullivan et al. (1996) concluded the ratio for fresh craters on Ida is the diameter gradually, however, when the diameter reaches about about 0.154 by photoclinometry method. Thomas et al. (1999) re- 10 km, the depth does not increase as significant as before, which ported the ratio for intermediate sized craters on Mathilde (di- is inconsistent with a pure rocky outer shell. This phenomena, to- ameters about 1–5 km) ranges from 0.12 to 0.25 by shadow mea- gether with morphologies of crater with viscous relaxation ( Fig. 3 f) surements. Robinson et al. (2002) found the ratio on Eros is about and crater with flow-like feature ( Fig. 3 g), suggests that the outer 0.13 ± 0.03, and the freshest craters approach lunar values of 0.2. shell is mixed with materials that has a rheology weaker than that Shingareva et al. (2008) derived d/D on Phobos to range from of pure rock. Both pre-Dawn mission ( Küppers et al., 2014 ) and 0.15 to 0.24 by measuring 6 craters from 1.8 to 8.6 km in di- present orbital observations support the widespread of water ice ameter. The average ratio for 38 identified craters on Itokawa is on the subsurface of Ceres, especially the high latitude polar re- 0.08 ± 0.03( Hirata et al., 2009 ). The typical d/D derived from shad- gions ( Prettyman et al., 2017 ), so the outer shell is an ice–rock ows on Lutetia is 0.12 ( Vincent et al., 2012 ). The derived d/D for mixture that allows for limited viscous relaxation. This inference craters from 0.15 to 2.1 km on Steins varies from 0.04 to 0.25, with have been verified by the gravity field and shape model deduced the mean value of 0.10 ( Besse et al., 2012 ). The d/D from the global from gravity and topography data acquired by the Dawn spacecraft statistics on Vesta is 0.168 ± 0.01 ( Vincent et al., 2014 ). The sim- ( Park et al., 2016 ). The plot of d/D versus diameter scatter ( Fig. 7 b) ple to complex transition is similar on the three icy Galilean satel- demonstrates a tendency of increase first and then decrease, and lites (Europa, Ganymede, Callisto) and the d/D for the unmodified the ratio value reaches maximum of 0.24 around 6 km in diame- and unrelaxed fresh craters is on the order of ∼ 0.2 ( Schenk, 2002; ter, corresponding to 1.4 km in depth, which may be attributed to Schenk et al., 2004 ). The d/D derived by photoclinometry method differences in regional terrain and subsurface properties, e.g., the for the 4 icy satellites of Uranus and Saturn (Miranda, Dione, Ariel variations of water ice and rock in Ceres’ outer layer. 304 S. Gou et al. / Icarus 302 (2018) 296–307

Table 3 Statistics of d/D of simple craters for different bodies.

Object d/D Reference

Rocky Moon, Mars, 0.2 ( Barnouin et al., 2012; bodies Mercury Pike, 1974; Pike, 1980 ) Gaspra 0.125 ( Carr et al., 1994 ) Ida 0.154 ( Sullivan et al., 1996 ) Mathilde 0.12–0.25 ( Thomas et al., 1999 ) Eros 0.13 ± 0.03 ( Robinson et al., 2002 ) Phobos 0.15–0.24 ( Shingareva et al., 2008 ) Itokawa 0.08 ± 0.03 ( Hirata et al., 2009 ) Lutetia 0.12 ( Vincent et al., 2012 ) Steins 0.10 ( Besse et al., 2012 ) Vesta 0.168 ± 0.01 ( Vincent et al., 2014 ) Ceres 0.11 ± 0.04 This study Icy bodies Europa, Ganymede, ∼0.2 ( Schenk, 2002; Schenk Callisto et al., 2004 ) Miranda 0.13 ± 0.01 Dione 0.11 ± 0.02 ( Schenk, 1989 ) Ariel 0.09 ± 0.02 Rhea 0.12 ± 0.02

4.3. Determining macroscopic surface age

According to the theories of crater size-frequency distribution ( Neukum et al., 1975 ), the cratering processes on the surface of planetary body are randomly and the erosion rate of craters is much smaller than the forming rate before saturation reached. Therefore, the older the geological unit is, the denser the craters are. In principle, the ages of areas with higher crater density may be older, while the lower crater density regions are relatively younger. Fig. 7. Craters ( D ≥ 1 km and depth > 20 m) on the surface of Ceres, regardless of deformation and degradation: (a) depths versus diameters; (b) depth-to-diameter The crater degrades gradually with time due to erosion, such ratios versus diameters, which shows that simple craters ( D ≤ 10 km) cover all the as rim collapse, infill, seismic shaking, etc., resulting in shallower range of d/D . depth, which can be reflected by the decrease of d/D value. Though the d/D ratio is also influenced by other factors, e.g., impact hap-

Table 2 pens on loose eject blanket around large crater always favor the Statistics of d/D of different crater types ( D ≥ 1 km and depth > 20 m). formation of deep crater, the global distribution and variation of d/D can be used as a ﬁrst order estimation of the geological age Crater type Numbers in Average d/D

the catalogue of Cerean surface. Both global crater density shown in Fig. 4b and global variations of d/D shown in Fig. 8 exhibit apparent di- All craters 11,401 0.06 ± 0.04

All simple craters ( D ≤ 10 km) 10,387 0.06 ± 0.04 chotomy over Cerean surface; however, there seems to be an anti- All complex crater ( D > 10 km) 1014 0.08 ± 0.03 correlation between the two maps. The crater density is lower but Fresh simple crater 1377 0.11 ± 0.04 the average d/D is higher in the northern hemisphere, and the Degraded simple crater 8996 0.05 ± 0.04 crater density is higher while the d/D is relative lower in the south- Polygonal simple crater 14 0.14 ± 0.02 ern hemisphere. Non-polygonal complex crater 766 0.08 ± 0.04

Polygonal complex crater 248 0.09 ± 0.03 In addition, the cumulative distribution function (CDF) of d/D also illustrates that a slightly larger number of shallow craters remained in the southern than that in the northern hemisphere ( Fig. 9 ). For example, 66.6% of the craters in the southern hemi- Polygonal craters have been discovered on a variety of plan- sphere have d/D value less than 0.06 (mean value for all the etary bodies, for example, Mars ( Ohman et al., 2006 ), Mercury craters), while 57.3% of that in the northern hemisphere. Though ( Weihs et al., 2015 ), Venus ( Aittola et al., 2007 ), and Dione we cannot completely exclude the influence of massive deposits of ( Beddingfield et al., 2016 ). Among the 276 polygonal craters iden- ejecta from forming deep new crater but shallowing or obliterat- tified on Cerean surface in this research, 90% of them are greater ing existing craters, especially those regions around Haulani, Dantu than 10 km with depth greater than 20 m. The average d/D value and Occator crater in the north, the general trend of both crater for the polygonal craters is somewhat higher than their corre- density and CDF of d/D support the macroscopic interpretation that sponding counterparts as shown in Table 2 , for example, polygonal geological age of the southern hemisphere may be older. simple crater (0.14 ± 0.02) versus fresh simple crater (0.11 ± 0.04), Though spatial density of craters larger than 20 km ( Fig. 4 c) polygonal complex crater (0.09 ± 0.03) versus non-polygonal com- demonstrates there are more large craters in the northern than the plex crater (0.08 ± 0.04), indicating (hidden) fractures of subsur- southern hemisphere, however, Marchi et al. (2016) inferred the face or surface not only favor the formation of irregular polygonal northern hemisphere has reached a level of crater spatial density craters, but also may alter the physical properties (such as the in- compatible with saturation in the range 20–70 km. The inference crease of porosity) of the target strata, resulting in excavating a bit on macroscopic surface age comprehensively from both crater spa- deeper during the cratering process ( Wünnemann et al., 2006 ). tial density ( D ≥ 1 km) and cumulative distribution function (CDF) S. Gou et al. / Icarus 302 (2018) 296–307 305

Fig. 8. Variations of d/D value over the surface of Ceres. The d/D value in each 10 ° latitude × 10 ° longitude grid is the mean value of all d/D in the grid. Map is shown in equidistant cylindrical projection.

Fig. 9. Cumulative distribution function of d/D for the northern and southern hemisphere and the entire Ceres. Fig. 10. Depths versus diameters for Kerwan crater and its surroundings. The region outlined for this scatter and age estimation is defined by Hiesinger et al. (2016) and the revised age is from Williams et al. (2017) . of d/D with the exclusion of possible contamination from secondary craters in this work is in good agreement with the latest geologic mapping work done by Williams et al. (2017) , who found The revised absolute model age for the smooth region associated Kerwan, Urvara and Yalode impact basins on the southern hemi- with Kerwan crater from lunar-derived model and asteroid-derived sphere are the oldest terrains, which defines much of Cerean ge- model is > 1.3 Ga and > 280 Ma respectively ( Hiesinger et al., 2016; ological time scale, and the faculae-containing Occator crater and Williams et al., 2017 ). And a general depth difference between bright rayed craters such as Haulani on the northern hemisphere deep and eroded craters of similar size (e.g., ∼10 km) is ∼500 m are the youngest. which is found in the vertical dispersion shown in Fig. 10 . Hence an estimation of average erosion rate of > 0.38 m/Ma or > 1.8 m/Ma 4.4. Estimation of erosion rate around Kerwan for this region can be deduced, depending on which chronology model is applied. Though the average erosion rate on Ceres are The variations of depth for craters of similar age and size still much faster than that (2 × 10 −4 m/Ma) on the Moon ( Craddock and can bring some constraints on the erosion rate of the surface Howard, 20 0 0 ), it’s still comparable to that found on other bod- ( Vincent et al., 2014 ). As the oldest and largest confirmed impact ies from the main asteroid belt. For example, average erosion rate crater on Ceres, Kerwan crater and its surroundings is selected as on Vesta is 0.35 m/Ma ( Vincent et al., 2014 ), and on Gaspra is the region of interest in this research for erosion rate estimation. 0.1 ∼1.0 m/Ma ( Carr et al., 1994 ). And the slight discrepancy of aver- 306 S. Gou et al. / Icarus 302 (2018) 296–307 age erosion rate between Ceres and other asteroids may be related Bland, M.T. , et al. , 2016. Composition and structure of the shallow subsurface of with the viscous relaxation on Ceres ( Bland et al., 2017 ). Ceres revealed by crater morphology. Nat. Geosci. 9, 538–542 . Buczkowski, D.L. , et al. , 2016. The geomorphology of Ceres.. Science 353, aaf4332 . Carr, M.H. , et al. , 1994. The geology of gaspra. Icarus 107, 61–71 . 5. Conclusions Craddock, R.A. , Howard, A.D. , 20 0 0. Simulated degradation of lunar impact craters and a new method for age dating farside mare deposits. J. Geophys. Res. 105, 20387–28362 . A global crater catalogue with diameter ≥ 1 km across the en- Daubar, I. , Atwoodstone, C. , Byrne, S. , Mcewen, A.S. , Russell, P.S. , 2014. The mor- tire Cerean surface has been created in this work, which consists phology of small fresh craters on Mars and the Moon. J. Geophys. Res. 119, 2620–2639 . of 29,219 entries. The crater morphology and distribution are an- Garvin, J.B. , Frawley, J.J. , 1998. Geometric properties of Martian impact craters: pre- alyzed, and their morphometric parameters are calculated, which liminary results from the Mars orbiter laser altimeter. Geophys. Res. Lett. 25, shows that: (1) Craters forms high crater density regions, such 4 405–4 408 . as areas around Tibong crater. The crater distribution by longi- Hiesinger, H., et al., 2016. Cratering on Ceres: implications for its crust and evolution. Science 353, aaf4759 . tude and latitude shows an overall ‘W’ trend and parabolic con- Hirata, N. , et al. , 2009. A survey of possible impact structures on 25,143 Itokawa. cave downward ‘ ∩ ’ trend respectively. (2) The identifiable smallest Icarus 200, 486–502 . crater size is extended to 1 km and the crater numbers have up- Küppers, M., et al., 2014. Localized sources of water vapour on the dwarf planet (1) Ceres. Nature 505, 525–527 . ≥ dated when compared with the crater catalogue (D 20 km) re- Kneissl, T. , Van Gasselt, S. , Neukum, G. , 2011. Map-projection-independent crater leased by the Dawn Science Team. (3) The d/D ratios for fresh size-frequency determination in GIS environments—New software tool for Ar- simple craters, obvious degraded simple crater and polygonal sim- cGIS. Planet. Space Sci. 59, 1243–1254. Marchi, S. , Chapman, C.R. , Barnouin, O.S. , Richardson, J.E. , Vincent, J.B. , 2015. In: ± ± ± ple crater are 0.11 0.04, 0.05 0.04 and 0.14 0.02 respectively. Michel, P., DeMeo, F.E., Bottke, W.F. (Eds.), Cratering on Asteroids. Asteroids IV (4) The d/D ratios for non-polygonal complex crater and polygonal University of Arizona Press, Tuscon, pp. 725–744 . complex crater are 0.08 ± 0.04 and 0.09 ± 0.03 respectively. Marchi, S. , et al. , 2016. The missing large impact craters on Ceres. Nat. Commun. 7, 12257 .

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