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1 Icarus 214 (2011) Contents lists available at ScienceDirect Icarus journal homepage: The transition from complex crater to peak-ring basin on the Moon: New observations from the Lunar Orbiter Laser Altimeter (LOLA) instrument David M.H. Baker a,, James W. Head a, Caleb I. Fassett a, Seth J. Kadish a, Dave E. Smith b,c, Maria T. Zuber b,c, Gregory A. Neumann b a Department of Geological Sciences, Brown University, Providence, RI 02912, United States b Solar System Exploration Division, NASA Goddard Space Flight Center, Greenbelt, MD , United States c Department of Earth, Atmospheric and Planetary Sciences, MIT, Cambridge, MA 02139, United States article info abstract Article history: Received 17 November 2010 Revised 15 April 2011 Accepted 23 May 2011 Available online 2 June 2011 Keywords: Moon Mercury Cratering Impact processes Impact craters on planetary bodies transition with increasing size from simple, to complex, to peak-ring basins and finally to multi-ring basins. Important to understanding the relationship between complex craters with central peaks and multi-ring basins is the analysis of protobasins (exhibiting a rim crest and interior ring plus a central peak) and peak-ring basins (exhibiting a rim crest and an interior ring). New data have permitted improved portrayal and classification of these transitional features on the Moon. We used new 128 pixel/degree gridded topographic data from the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter, combined with image mosaics, to conduct a survey of craters >50 km in diameter on the Moon and to update the existing catalogs of lunar peak-ring basins and protobasins. Our updated catalog includes 17 peak-ring basins (rim-crest diameters range from 207 km to 582 km, geometric mean = 343 km) and 3 protobasins ( km, geometric mean = 157 km). Several basins inferred to be multi-ring basins in prior studies (Apollo, Moscoviense, Grimaldi, Freundlich Sharonov, Coulomb Sarton, and Korolev) are now classified as peak-ring basins due to their similarities with lunar peak-ring basin morphologies and absence of definitive topographic ring structures greater than two in number. We also include in our catalog 23 craters exhibiting small ring-like clusters of peaks ( km, geometric mean = 81 km); one (Humboldt) exhibits a rim-crest diameter and an interior morphology that may be uniquely transitional to the process of forming peak rings. A power-law fit to ring diameters (D ring ) and rim-crest diameters (D r ) of peak-ring basins on the Moon [D ring = 0.14 ± 0.10(D r ) 1.21±0.13 ] reveals a trend that is very similar to a power-law fit to peak-ring basin diameters on Mercury [D ring = 0.25 ± 0.14(D rim ) 1.13±0.10 ] [Baker, D.M.H. et al. [2011]. Planet. Space Sci., in press]. Plots of ring/rim-crest ratios versus rim-crest diameters for peak-ring basins and protobasins on the Moon also reveal a continuous, nonlinear trend that is similar to trends observed for Mercury and Venus and suggest that protobasins and peak-ring basins are parts of a continuum of basin morphologies. The surface density of peak-ring basins on the Moon ( per km 2 ) is a factor of two less than Mercury ( per km 2 ), which may be a function of their widely different mean impact velocities (19.4 km/s and 42.5 km/s, respectively) and differences in peak-ring basin onset diameters. New calculations of the onset diameter for peak-ring basins on the Moon and the terrestrial planets re-affirm previous analyses that the Moon has the largest onset diameter for peak-ring basins in the inner Solar System. Comparisons of the predictions of models for the formation of peak-ring basins with the characteristics of the new basin catalog for the Moon suggest that formation and modification of an interior melt cavity and nonlinear scaling of impact melt volume with crater diameter provide important controls on the development of peak rings. In particular, a power-law model of growth of an interior melt cavity with increasing crater diameter is consistent with power-law fits to the peak-ring basin data for the Moon and Mercury. We suggest that the relationship between the depth of melting and depth of the transient cavity offers a plausible control on the onset diameter and subsequent development of peak-ring basins and also multi-ring basins, which is consistent with both planetary gravitational acceleration and mean impact velocity being important in determining the onset of basin morphological forms on the terrestrial planets. Ó 2011 Elsevier Inc. All rights reserved. Corresponding author. Address: Department of Geological Sciences, Brown University, Box 1846, Providence, RI 02912, United States. Fax: address: david_baker@brown.edu (D.M.H. Baker) /$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi: /j.icarus

2 378 D.M.H. Baker et al. / Icarus 214 (2011) Introduction Major lines of inquiry in the study of impact craters on the terrestrial planets over the past half-century have focused on the onset and formation of multi-ring basins occurring at the largest crater diameters. Many hypotheses have been developed to explain the formation of rings interior and exterior to the transient cavity of multi-ring basins, including frozen crustal tsunamis (Baldwin, 1981), differential depths of excavation to form nested craters (Hodges and Wilhelms, 1978), the formation of exterior rings by mega-terracing (Head, 1974, 1977; Head et al., 2011), and gravity-driven collapse and formation of tectonic rings due to the contrasting strengths of the lithosphere and aesthenosphere (Melosh and McKinnon, 1978; Melosh, 1982, 1989; Collins et al., 2002). Although these models have provided much insight into the formation of large impact structures on the terrestrial planets (e.g., Melosh, 1989; Spudis, 1993), there is currently no consensus on how the rings of multi-ring basins form. Important to understanding the mechanisms of multi-ring basin formation have been analyses of peak-ring basins and other transitional morphologies between complex craters with central peaks and multi-ring basins. Many crater catalogs of these basin types have been produced (Wood and Head, 1976; Wood, 1980; Wilhelms et al., 1987; Pike and Spudis, 1987; Pike, 1988; Spudis, 1993; Alexopoulos and McKinnon, 1994), which traditionally include measurements of major morphological features such as the diameter of the crater s rim crest, ring, and central peak. Trends in the ring and rim-crest diameters of peak-ring basins have been used as evidence to support a number of peak-ring basin formation models (Pike and Spudis, 1987; Pike, 1988). However, the lack of complete population data for peak-ring basins on the terrestrial planets due to limitations in image and topographic resolution has inhibited accurate interpretations of the relationship between peak-ring basin morphologies and the mechanisms of their formation. With the addition of new and improved spacecraft data, it is important to update the existing catalogs of craters and basins, including observations of their morphological characteristics. This is especially important for the airless bodies, Mercury (Baker et al., 2011) and the Moon, where relatively low erosion and resurfacing rates throughout geologic history have preserved much of their basin populations. We use new topographic data from the Lunar Orbiter Laser Altimeter (LOLA) (Smith et al., 2010), in combination with a global Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) (Robinson et al., 2010) image mosaic at 100 m/pixel resolution to update the current catalog of peak-ring basins and other basin morphologies in the transition from complex craters to multi-ring basins on the Moon. LOLA currently provides gridded topography at better than 128 pixel/degree (235 m/pixel) resolution, a substantial improvement over previous topographic data of the Moon, including the 8 30 km/pixel resolution data from the Clementine Light Imaging Detection and Ranging (LiDAR) instrument (Smith et al., 1997) and the 15 pixel/ degree resolution data from the Kaguya Laser Altimeter (Araki et al., 2009). Our catalog of the lunar peak-ring basin and protobasin populations, including measurements of basin rim-crest, ring, and central-peak diameters, is then compared with catalogs on the other terrestrial planets, including a recent, comprehensive catalog of peak-ring basins and other transitional basins on Mercury (Baker et al., 2011). We then use our lunar basin catalog to test the predictions of one basin formation model, which seeks to explain the formation of peak rings by modification of the crater interior from a growing impact melt cavity. 2. The size-morphology progression Transitional morphologies in the size progression from complex craters to multi-ring basins have traditionally included at least two classes of basins: peak-ring basins (or double-ring or two-ring basins) and protobasins (or central-peak basins) (Pike, 1988; Baker et al., 2011). Peak-ring basins are the most numerous transitional forms and their interior morphologies are characterized by a single, continuous or semi-continuous interior ring of peaks with no central peak. The lunar basin, Schrödinger, (rim-crest diameter, as measured in this study = 326 km) best exemplifies this morphology, showing a nearly continuous ring of peaks (Fig. 1A). LOLA gridded topography shows that Schrödinger has a depth of about 4 km with a peak ring that is tens of kilometers in width and rises about 1 km above the surrounding floor materials (Figs. 1A and 2A). Protobasins posses both a central peak and an interior ring of peaks, but these features are commonly smaller in diameter and have less topographic relief than either central peaks in complex craters and peak rings in peak-ring basins (Pike, 1988). Antoniadi (rim-crest diameter, as measured in this study = 137 km) is a type example of a protobasin on the Moon (Fig. 1B). Its peak ring has less relief ( m) than the peak ring of Schrödinger, and it has a small, but prominent central peak that rises above the surrounding peak ring (Fig. 2B). However, the smoothness of Antoniadi s interior suggests that substantial infilling has occurred, which has certainly affected the relative topography of its central peak and peak ring. A third class of basins, called ringed peak-cluster basins, has also been identified from analysis of recent flyby data of Mercury (Baker et al., 2011). Like peak-ring basins, ringed peak-cluster basins have a single interior ring of peaks without a central peak (Fig. 1C) and overlap in rim-crest diameter with protobasins; however, the relatively small diameter of their peak rings relative to their rim-crest diameter precludes these basins from classification as traditional peak-ring basins. The type example of a ringed peak-cluster basin on Mercury is the 125-km diameter crater, Eminescu, which exhibits a very well-defined interior ring (Schon et al., 2011). On the Moon, many craters with small interior rings of central peak material are identified; however, only one of these craters, Humboldt (rim-crest diameter, as measured in this study = 205 km) overlaps in rim-crest diameter with protobasins and is thus classified as a potential ringed peakcluster basin. Humboldt has a disaggregated ring-like array of central peak elements (Fig. 1C) that is nearly 1 km in relief (Fig. 2C). A central depression in the middle of the array of peaks slopes steeply to about 100 m below the fractured fill material that occupies the floor of Humboldt (Fig. 2C). 3. Methods There have been several comprehensive catalogs of basins on the Moon (Wood and Head, 1976; Pike and Spudis, 1987; Wilhelms et al., 1987; Spudis, 1993), which were based primarily on Apolloera data, including image data from the Lunar Orbiter and Apollo Terrain Mapping Camera. While there are many similarities between these catalogs, there are some disagreements, particularly with identification of multiple exterior and interior rings and central peak plus ring structures. We have elucidated the identification of protobasins and peak-ring basins by analyzing new Lunar Orbiter Laser Altimeter (LOLA) (Smith et al., 2010) global gridded topography and hillshade data at 128 pixel/degree (235 m/pixel) resolution in combination with a Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) (Robinson et al., 2010) global image mosaic at 100 m/pixel resolution. We also used detrended LOLA gridded topography data to remove the effects of long-wavelength topographic variations and to help emphasize local variations in topography such as peak rings. All craters on the Moon greater than 50 km in diameter were analyzed in ArcGIS (ESRI, using a recent catalog of lunar craters (Head et al., 2010) to ensure complete surveying of basin types. Particular scrutiny was given to basins already cataloged, including many

3 D.M.H. Baker et al. / Icarus 214 (2011) Fig. 1. Examples of a peak-ring basin (A), protobasin (B), and ringed peak-cluster basin (C) on the Moon. Top panels show outlines of circle fits to the basin rim crest and interior ring (dashed lines) on LOLA hillshade gridded topography. Bottom panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade gridded topography. (A) Schrödinger (326 km; E, S), a peak-ring basin, exhibits a nearly continuous interior ring of peaks with no central peak. (B) Antoniadi (137 km; E, S), a protobasin, has a less prominent peak ring surrounding a small central peak. (C) Humboldt (205 km; E, S) is a ringed peak-cluster basin with an incomplete, diminutive ring of central peak elements. multi-ring basins where some ring designations were most uncertain (Pike and Spudis, 1987). The diameters of basin features, including rim crests, rings, and central peaks, were measured (where present) by visually fitting circles to the features using the CraterTools extension in ArcGIS (Kneissl et al., 2010). Circle-fits were carefully selected to best approximate the mean diameter value for the features (Baker et al., 2011) (Fig. 1). For example, peak rings were fit by a circle intermediate between circles that inscribe and circumscribe the peak ring. Fits to rim crests were defined by the most prominent topographic divides along the crater rim crest. Central peaks were the most difficult to measure due to their irregular outlines. For those irregular central peaks, we chose circular fits that approximated a diameter that is intermediate between the maximum and minimum areal dimensions of the feature (Baker et al., 2011) (Fig. 1). As in previous catalogs, our confidence in the identification and measurement of peak rings is presented as a scale from 1 (lowest) to 3 (highest) (Tables A1 A3). Most basins are cataloged with the highest confidence, however, three peak-ring basins remain more speculative due to incomplete preservation of interior morphologies or possible mis-interpretation of interior features as primary basin structure. The continuity of observable peak rings are also designated as being greater than or less than 180 of arc (Tables A1 A3). 4. The basin catalog Our catalog is a refinement of earlier catalogs of peak-ring basins and protobasins on the Moon. We have excluded some ambiguous basins and have re-classified several other basins, particularly those near the transition diameters between peak-ring basins and protobasins and peak-ring basins and multi-ring basins. These re-classifications largely reflect our improved ability to recognize genuine basin ring and central peak structures from new LOLA topographic and image data. Our refined catalog includes 17 peak-ring basins (Table A1), 3 protobasins (Table A2), and 1 ringed peak-cluster basin (Table A3). LOLA gridded topography images of each basin in Tables A1 A3 are also included as online supplementary material. Twenty-two craters exhibiting ring-like arrangements of central peak elements are also cataloged (Table A3), but are not classified as ringed peak-cluster basins due to their small (<114 km) rim-crest diameters that fall below the transitional rim-crest diameter range between complex craters and peak-ring basins (see discussion in Section 6.1). All of the peak-ring basins and protobasins cataloged in this study have appeared in earlier catalogs, but have been variously classified as one or multiple basin types based on the available data at the time the catalogs were generated. Our peak-ring basin catalog includes five basins that have been previously classified as multi-ring basins by Pike and Spudis (1987): Apollo, Moscoviense, Grimaldi, Coulomb Sarton, and Korolev. Our catalog also includes Freundlich Sharonov, which was recognized as a candidate multi-ring basin but with only one 600-km diameter ring identified (Wilhelms et al., 1987; Spudis, 1993). Upon careful examination of LOLA topographic data (Fig. 3), we find that all of these basins are fit best by no more than two topographic rings. For example, a possible ring exterior to Apollo (Fig. 3A) appears to be associated with the rim structure of South

4 380 D.M.H. Baker et al. / Icarus 214 (2011) Fig. 2. Radially averaged LOLA topographic profiles of Schrödinger (A), Antoniadi (B), and Humboldt (C) (see Fig. 1 for locations). After Head et al. (2011), the profiles were calculated by averaging 360 great circle transects radiating from the basins centers and separated by 1 of azimuth. The topography along each of the 360 transects was calculated using a bilinear interpolation with the number of data points set to equal the 16 pixel/degree resolution of the LOLA data used for the profiles. Pole Aitken basin and is not concentric to Apollo s main topographic rings. Moscoviense (Fig. 3B) has been traditionally interpreted to be a multi-ring basin (e.g., Pike and Spudis, 1987) due to the presence of three concentric but off-centered ring structures. The offset characteristic of the three rings of Moscoviense to the southwest has suggested that Moscoviense may have formed from an oblique impact (see discussion in Thaisen et al. (2011)). However, a survey of offset peak rings in basins on Venus, for which impact direction could be inferred from ejecta patterns, determined that there was no correlation between ring offset and direction of impactor approach (McDonald et al., 2008). It was suggested that other parameters, such as target rock heterogeneities likely contributed to the offset ring characteristics of these peak rings on Venus. Furthermore, the effects of oblique impacts on basin morphology, especially on the scale of multi-ring basins are still poorly understood (Pierazzo and Melosh, 2000). Alternatively, we favor a scenario whereby the inner two rings of Moscoviense represent a peak-ring basin superposed on a larger, older impact basin (e.g., Ishihara et al., 2011; Thaisen et al., 2011). Several geophysical and morphological characteristics of Moscoviense support a superposed impact scenario. First, the anomalously thin crust and high gravity of Moscoviense is more easily explained by double impacts than a single oblique impact (Ishihara et al., 2011). Second, the prominence and regular outline of the intermediate ring appears much more analogous to a basin rim-crest compared to the more plateau-like, irregular topography of the intermediate rings in multi-ring basins such as Orientale (Head et al., 2011). Finally, the innermost ring of Moscoviense is very prominent and sharp, sharing many similarities with other peak-ring basins on the Moon (Figs. 1A and 2A). Several of the basins (e.g., Grimaldi, Fig. 3C, and Freundlich Sharonov, Fig. 3D) exhibit central depressions that have been classified as potential ring structures (Pike and Spudis, 1987). While these depressions may be related to the basin formation process, they are also interior to and are morphologically distinct from peak rings, which have more circular planform shapes and a distinct topographic signature that is raised above the surrounding basin floor material (Fig. 2A). We therefore do not include the rims of these depressions as separate rings in our catalog. Due to its highly degraded nature, our classification of Coulomb Sarton (Fig. 3E) is the most uncertain of the large basins. However, we find that the observed impact structure can be best fit by two rings that are consistent with the rim-crest and ring diameters of other peakring basins on the Moon. The most uncertain basins in our catalog should be a focus during re-examinations using even higher resolution data or improved techniques. Lastly, in contrast to Pike and Spudis (1987), we do not include Amundsen Ganswindt in our peak-ring basin catalog, as the irregular interior topography of the basin does not resemble a ring and is likely to be modified ejecta material. Our catalog includes three protobasins, two of which, Antoniadi and Compton, are unambiguous examples of basins exhibiting a central peak surrounded by an interior ring of peaks. We also include the crater, Hausen, in our catalog. While the interior ring of Hausen is not as well defined as those of Antoniadi and Compton, an incipient ring is observed. The subtlety of Hausen s ring topography may be related to the size of the central peak, as there appears to be a correlation between size of the central peak and prominence of the interior ring (Pike, 1988). Hausen exhibits the largest central peak and least pronounced ring and Antoniadi exhibits the smallest central peak and the most topographically prominent ring (although the center of Antoniadi has been flooded by mare deposits (Fig. 1B), likely reducing the relief of its central peak and peak ring). Although the lunar protobasin population is very small, this correlation between central peak size and ring prominence and size is consistent with observations of the more numerous protobasin population on Mercury (Pike, 1988). Pike and Spudis (1987) include three other craters, Campbell, Fermi, Hipparchus, and Mendeleev in their protobasin catalog. With the exception of Mendeleev, we do not observe topographic rings in all of these craters in the new LOLA topography. For Mendeleev, we observe an interior ring but do not observe a central peak structure; Mendeleev is therefore classified as a peak-ring basin in our catalog. Pike and Spudis (1987) also include craters exhibiting relatively small ring/rim-crest ratios as potential protobasins (although central peak structures were not directly observed in these craters, possibly due to the effects of resurfacing or erosion). However, ring/rim-crest ratios alone cannot be used to recognize protobasins because the trends of ring and rim-crest diameters of protobasins appear statistically indistinguishable from peak-ring basins (Baker et al., 2011). Of the potential protobasins cataloged by Pike and Spudis (1987), we include Bailly, Milne, and Schwarzschild in our peak-ring basin catalog due to the presence of a

5 D.M.H. Baker et al. / Icarus 214 (2011) Fig. 3. Large peak-ring basins on the Moon previously inferred to be multi-ring basins (Wilhelms et al., 1987; Pike and Spudis, 1987; Spudis, 1993). Left panels show dashed outlines of the observed basin rim crest and ring on a Lunar Reconnaissance Orbiter Camera (LROC) Wide Angle Camera (WAC) image mosaic. Middle panels show LOLA colored gridded topography at 128 pixel/degree on LOLA hillshade gridded topography. Right panels show detrended LOLA topography maps. (A) Apollo (492 km; E, S). (B) Moscoviense (421 km; E, N). (C) Grimaldi (460 km; E, 5.01 S). (D) Freundlich Sharonov (582 km; E, N). (E) Coulomb Sarton (316 km; E, N). (F) Korolev (417 km; E, 4.44 S). See text (Section 4) for a discussion of the ring designations of the basins. prominent interior ring and no observable central peak. While it is still possible that small central peaks within these structures have been erased by resurfacing processes, the absence of a central peak precludes them from being classified as a protobasin in our catalog. We do not observe interior rings or central peaks for the remaining possible protobasins classified by Pike and Spudis (1987). Ringed peak-cluster basins have not been included in previous basin catalogs of the Moon. From analyses of recent flyby images of Mercury, Schon et al. (2011) and Baker et al. (2011) interpret at least some ringed peak-cluster craters to be transitional types between complex craters possessing central peaks and peak-ring basins. Support for such a transitional morphology included overlap between the rim-crest diameters of ringed peak-cluster basins with rim-crest diameters of protobasins and small peak-ring basins, the clear ring-like morphology of the peak elements (ringed peak clusters), and similar trends between the diameters of ringed peak clusters and central peak diameters in complex craters. These trends, as well as geological mapping, led the authors to suggest that ringed peak clusters are the product of early development of a melt cavity that directly modifies the centers of central uplift structures. While at least 23 craters >50 km in diameter on the Moon exhibit interior morphologies with ring-like central peaks (Table A3), the diameter range for these craters is large ( km, with all but one between 50 and 114 km) and only one, Humboldt, has a rim-crest diameter (205 km) that overlaps with the rim-crest diameters of protobasins. It is therefore likely that most ring-like central peak structures do not represent unique transitional types in the size-morphology progression from complex craters to peak-ring basins. The association of ring-like central peaks with floor-fractured craters has led to the interpretation that

6 382 D.M.H. Baker et al. / Icarus 214 (2011) Fig. 3 (continued) some ring-like central peaks result from collapse of the innermost portions of the central peak structure during magmatic intrusion (Schultz, 1976). Regardless of their origin, the small (<114 km) rim-crest diameters over which most craters with ring-like central peaks occur on the Moon suggest that their development is not related to the peak-ring basin forming process. Humboldt, classified here as the only ringed peak-cluster basin on the Moon, is more likely to be a unique transitional basin type; however, the fractured fill that occupies Humboldt s floor suggests similarities with floor-fractured craters at smaller rim-crest diameters. 5. New basin statistics Based on our new rim-crest measurements, we have revised the general statistics for peak-ring basins and protobasins on the Moon (Table 1). The rim-crest diameters of peak-ring basins range from 207 to 582 km, with a geometric mean diameter of 343 km. Our peak-ring basin data have a much larger rim-crest diameter range than the km range from Pike and Spudis (1987) and has a smaller geometric mean rim-crest diameter compared to the mean rim-crest diameter of 335 km from Pike and Spudis (1987). The three protobasins in our catalog give a range from 137 to 170 km with a geometric mean of 157 km, compared to the larger range of values ( km) and larger geometric mean rim-crest diameter (204 km) for protobasins in the catalog of Pike and Spudis (1987). Using our new basin catalog, we also calculate the onset diameter for peak-ring basins on the Moon. The term onset diameter has been defined loosely in previous studies; examples of such usage include the minimum diameter of a population or the diameter at which one crater morphology outnumbers another (see discussions in Pike (1983, 1988) and Baker et al. (2011)). In an analysis of basins on Mercury, Baker et al. (2011) chose to calculate the onset diameter for peak-ring basins based on the rim-crest diameter range where multiple crater morphologies overlap. In

7 D.M.H. Baker et al. / Icarus 214 (2011) Table 1 Statistics of planetary parameters and of peak-ring basins, protobasins, and ringed peak-cluster basins on the Moon (this study, Tables A1 A3), Mercury (Baker et al., 2011), Mars (Pike and Spudis, 1987), and Venus (Alexopoulos and McKinnon, 1994). This table is reproduced from Table 1 of Baker et al. (2011), and is updated using our new lunar basin catalog (Tables A1 A3). Moon a Mercury b Mars c Venus d Gravitational acceleration (m/s 2 ) Surface area (km 2 ) Mean impact velocity e (km/s) Peak-ring basins (N pr ) N pr /km Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km) Onset diameter, method 1 f (km) / / / 8 Onset diameter, method 2 g (km) Protobasins (N proto ) N proto /km Geometric mean diameter (km) Minimum diameter (km) Maximum diameter (km) Ringed peak-cluster (N rpc ) 1 9 N rpc /km Geometric mean diameter (km) 96 Minimum diameter (km) 73 Maximum diameter (km) 133 a Basin data from this study (Tables A1 A3). b Basin data from Baker et al. (2011). c Basin data from Pike and Spudis (1987). d Basin data from Alexopoulos and McKinnon (1994). Calculations exclude the suspected multi-ring basins Klenova, Meitner, Mead, and Isabella. e Mean impact velocity from Le Feuvre and Wieczorek (2008). f After Baker et al. (2011). Peak-ring basin onset diameters determined by first identifying the range of diameters over which examples of two or more crater morphological forms can both be found, and then the onset diameter is defined as the geometric mean of the rim-crest diameters of all craters or basins within this range (see text for a discussion on calculating onset diameter). Uncertainties are one standard deviation about the geometric mean, calculated by multiplying and dividing the geometric mean by the geometric, or multiplicative, standard deviation. Peak-ring basin and protobasin data used for the calculations are from this study (Moon), Baker et al. (2011) (Mercury), Pike and Spudis (1987) (Mars), and Alexopoulos and McKinnon (1994) (Venus). Complex crater rim-crest diameters used for the calculations are from the catalogs compiled by Pike (1988) (Mercury), Barlow (2006) (Mars), and Schaber and Strom (1999) (Venus); diameters of complex craters and peak-ring basin diameters on the Moon do not overlap. g Peak-ring basin onset diameters calculated by taking the 5th percentile of the peak-ring basin population data. See text for the details of this calculation. this method ( onset diameter, method 1, Table 1), the range of diameters is first identified over which examples of two or more crater morphological forms can both be found, and then the onset diameter is defined as the geometric mean of the rim-crest diameters of all craters or basins within this range (Baker et al., 2011). For Mercury, Venus, and Mars, rim-crest diameters for peak-ring basins overlap the rim-crest diameters of both protobasins and complex craters (Baker et al., 2011). However, on the Moon no overlap exists between peak-ring basins and other morphological classes of basins. We therefore take the onset diameter for peakring basins on the Moon to be the geometric mean of the minimum diameter of the lunar peak-ring basin population and the maximum diameter of the next morphologically distinct population with smaller rim-crest diameters. We use the minimum peak-ring basin rim-crest diameter of 207 km (Schwarzschild) and the maximum rim-crest diameter of 205 km for the ringed peak-cluster basin, Humboldt, to obtain an onset diameter of 206 km for peak-ring basins on the Moon. Onset diameters calculated using the overlap method for basins on the other terrestrial planets (Mercury, Mars, and Venus) are presented in Table 1. The overlap method for calculating the onset diameter for peakring basins has the advantage of defining onset diameter of peakring basins by the spectrum of basin morphologies in the transition between complex craters and peak-ring basins and is therefore related to the physical processes resulting in the onset of interior basin rings. A second advantage is that the uncertainty in the estimated onset diameter is also derivable from the calculation. However, there are situations, such as in the Moon, where distinct crater morphological forms (e.g., peak-ring basins and protobasins) share little or no overlap in rim-crest diameter. Also, the robustness and reproducibility of this method is affected by where the worker defines the overlap diameter range, which is usually defined from the use of multiple catalogs from more than one worker. As such, while its use is directly tied to the observed morphological transition, the overlap method s applicability and reproducibility is limited, as it cannot be easily applied to planets with little or no overlap, and it is not able to be reliably reproduced by other workers because of its dependence on multiple crater populations that may not have been compiled using the same survey techniques. Satisfying these criteria is crucial for use in interplanetary comparisons and in understanding how the physical properties of the planets are modulating the basin-forming process. A more reproducible and applicable method for calculating onset diameter is to select a given percentile of the population. We calculate the 5th percentile of the peak-ring basin populations ( onset diameter, method 2, Table 1) to obtain alternative onset diameters for peak-ring basins on the terrestrial planets: 227 km (Moon), 116 km (Mercury), 56 km (Mars), 33 km (Venus). Peakring basin diameter data used in the calculations are from this study (Moon), Baker et al. (2011) (Mercury), Alexopoulos and McKinnon (1994) (Venus), and Pike and Spudis (1987) (Mars). The 5th percentile is chosen as it is an easily reproducible, descriptive statistic that is based on an historical standard of significance in statistical analysis. The method is robust against outliers, as it is defined by the tail of the distribution itself, not a single data point defining the minimum value of the population. The method is applicable to all planets and is independent, as it relies only on a single basin population and is independent of the interplanetary variations encountered in the population distributions of other transitional crater morphologies. In addition, since basin

8 384 D.M.H. Baker et al. / Icarus 214 (2011) Fig. 4. Log log plots of ring diameter (D ring ) versus rim-crest diameter (D r ) for peak-ring basins (red circles), protobasins (blue squares), and ringed peak-cluster basins (green diamonds) on the Moon (A, Tables A1 A3) and Mercury (B, from Baker et al., 2011). Also plotted for the Moon are the ring and rim-crest diameters for craters exhibiting ringlike central peaks (Table A3). Peak-ring basins follow a power law trend of D ring = 0.14 ± 0.10(D r ) 1.21±0.13 (R 2 = 0.96) on the Moon, which is very similar to the power law trend for peak-ring basins on Mercury [D ring = 0.25 ± 0.14(D r ) 1.13±0.10, R 2 = 0.87, Baker et al., 2011)(Table 2). Protobasins occur at smaller diameters, but appear to follow the tail-end of the peak-ring basin trend for the Moon and Mercury. Also shown are the trends for the diameters of central peaks (D cp ) in complex craters on the Moon (D cp = 0.259D r 2.57, Hale and Head, 1979a, and D cp = 0.107(D r ) 1.095, Hale and Grieve, 1982) and Mercury (D cp = 0.44(D r ) 0.82, Pike, 1988). The ringed peak-cluster basin, Humboldt, and craters with ring-like central peaks plot at intermediate values between the two complex crater trends for the Moon. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) populations can now be cataloged based on complete, or nearly complete, data coverage of the planetary surface, we can be confident that we are using populations rather than samples of particular crater and basin morphologies when calculating onset diameters. While the use of the 5th percentile to define peak-ring basin onset diameter does not rely on more than a single basin population and is not directly derived from the observed morphological transition between complex crater and peak-ring basin, peak-ring basin onset diameters calculated by this method consistently fall within the uncertainties of onset diameters calculated using a method based on the diameters of overlapping morphologies, as described above (Table 1). 6. Analysis and interplanetary comparisons Our refined catalog of transitional lunar basin types between complex craters and multi-ring basins permits us to better compare and evaluate several key characteristics of basin populations on the Moon and the terrestrial planets. These characteristics include: (1) ring and rim-crest diameter systematics, (2) surface density of peak-ring basins, and (3) peak-ring basin onset diameter. The airless body, Mercury, has the largest population of preserved peak-ring basins and protobasins in the inner Solar System (Baker et al., 2011), and thus provides an important dataset for comparison with the population of peak-ring basins and protobasins on the Moon. The basin catalogs for Venus and Mars should also be considered in interplanetary comparisons; however, resurfacing, erosion, and the effects of volatiles have influenced the present populations and morphologies of basins on these planets, rendering them less useful in comparison studies. Since the impact record on Earth is largely incomplete and highly modified by erosion, interior structures cannot be accurately identified and therefore present large uncertainties when used in interplanetary comparisons. As such, impact structures on Earth are not used in this study. In the following sections, we analyze our new catalog of basins on the Moon and identify key similarities and differences with the other planetary bodies, especially Mercury. In the next section, these comparisons are then placed in context of the predictions of a model of peak-ring basin formation that explains their morphological characteristics as resulting from the nonlinear scaling of impact melt Ring versus rim-crest diameter trends Following the methods of Pike (1988) and Baker et al. (2011), we plot the ring diameter versus the rim-crest diameter in log log space for lunar peak-ring basins, protobasins, and craters with ring-like central peaks and the ringed peak-cluster basin, Humboldt. Several trends are observed. First, peak-ring basins form a straight-line in log log space at large rim-crest diameters in Fig. 4, and can be fit by a power law trend of the form D ring ¼ AD p r where D ring is the diameter of the interior ring, D r is the basin rimcrest diameter, and p is the slope of the best-fitting line on a log log plot. Power-law fits were calculated in KaleidaGraph (Synergy Software, which uses the Levenberg Marquardt non-linear curve-fitting algorithm (Press et al., 1992) to iteratively minimize the sum of the squared errors in the ordinate. The use of this criterion for minimization implies that fractional errors in the estimates of interior ring diameters are regarded as larger than those for estimates of the rim-crest diameter. We calculate a power law fit of D ring = 0.14 ± 0.10(D r ) 1.21±0.13 (R 2 = 0.96, where R is the correlation coefficient for the given dataset on a log log plot) for lunar peak-ring basins (Table 2). This fit is very similar to a power law fit to peak-ring basins on Mercury ð1þ

9 D.M.H. Baker et al. / Icarus 214 (2011) Table 2 Comparison of the values for the coefficients (A and p) of power-law fits to peak-ring basins on the Moon (this study) and Mercury (Baker et al., 2011). Power laws are of the form given in Eq. (1) in the text. Coefficients of power-law fits to protobasins and ringed-peak cluster basins on Mercury from Baker et al. (2011) are also given, but none are given for the Moon due to the statistically small populations. Coefficients from the power law model of an expanding melt cavity (Eq. (2), Section 7) on the Moon (this study) and Mercury (Baker et al., 2011) are given for calculations using the Croft (1985) and Holsapple (1993) scaling relationships. Power-law coefficients a A p R 2 Peak-ring basins Moon b 0.14 ± ± Mercury c 0.25 ± ± Protobasins (P90 km) Moon Mercury 0.26 ± ± Ringed peak-cluster basins Moon Mercury 0.18 ± ± Model (Croft, 1985) Moon / ± 0.05 Mercury / / 0.06 Model (Holsapple, 1993) Moon Mercury a Power laws are of the form D ring = A(D r ) p, where D ring is the ring diameter and D r is the final (observed) rim-crest diameter. Uncertainties for power-law fits to peakring basins, protobasins and ringed peak-cluster basins are at 95% confidence. b Coefficients to fits and models for the Moon are from this study. No fits were made to the protobasin and ringed peak-cluster data for the Moon because of the statistically small populations. c Coefficients to fits and models for Mercury are from Baker et al. (2011). (D ring = 0.25 ± 0.14(D r ) 1.13±0.10, Fig. 4B and Table 2), and both fits are consistent with analyses of previous peak-ring basin catalogs (Pike, 1988). Since the population of protobasins on the Moon is statistically small (N = 3), fits to the protobasin data were not conducted. However, protobasins occur at smaller diameters than all peakring basins but overlap in rim-crest diameter with the largest complex craters on the Moon (Fig. 4A). The trend in ring diameter and rim-crest diameter for protobasins is aligned with the tail-end of the peak-ring basin trend (Fig. 4A). This supports the view that peak-ring basins and protobasins are parts of a continuum of basin morphologies. A similar observation is identified between protobasins and peak-ring basins on Mercury (Fig. 4B), where the power law fits to protobasins and peak-ring basins are found to be statistically indistinguishable (Table 2) (Baker et al., 2011). However, protobasins on Mercury are more numerous, and protobasins <90 km have anomalously smaller ring diameters than what is predicted by extrapolation of a power law fit to protobasins P90 km. The one lunar ringed peak-cluster basin, Humboldt, occurs at smaller rim-crest and ring diameters than peak-ring basins but is larger in rim-crest diameter than all three protobasins (Fig. 4A). Humboldt has an atypically small interior ring diameter relative to its rim-crest diameter and thus plots on a trend that is more aligned with the trend for central peak diameters in complex craters than the interior rings of peak-ring basins (Fig. 4A). Other craters with ring-like central peaks also plot near the trend for central peak diameters in lunar complex craters. Fig. 4A shows two trends for central peak diameters in lunar complex craters. The first is the least squares, linear regression of Hale and Head (1979a) (D cp = 0.259D r 2.57, where D cp is the diameter of the central peak and D r is the diameter of the crater s rim crest), which was based on measurements of circular fits to the maximum diameter of central peaks in fresh complex craters on the Moon. Because the measurements were of the maximum diameter of central peaks, the trend of Hale and Head (1979a) is taken to represent an upper limit to central peak diameters on the Moon. The second trend is a power law [D cp = 0.107(D r ) ] determined using the planform areas enclosed by the irregular perimeters of central peaks calculated by Hale and Grieve (1982). We then assume a circular geometry for this area, from which a central peak diameter is derived. These central peak diameters are taken to represent an average value, and should produce results that are comparable to our method for measuring the average diameters of basin features on the Moon. Craters with ring-like central peaks appear to fall on a scattered trend that is intermediate between the Hale and Head (1979a) linear regression and the Hale and Grieve (1982) power law (Fig. 4A), indicating that these ring-like central peaks do not depart substantially from the trend in central-peak diameter observed from complex craters. Humboldt falls near the Hale and Grieve (1982) trend, suggesting a similarity with complex craters with central peaks. However, the clear ring-like arrangement of its interior peaks, its large rim-crest diameter compared to other craters with ring-like central peaks, and its overlap with the rimcrest diameters of protobasins, suggest that Humboldt represents a unique transitional type in the size-morphology progression from complex craters to peak-ring basins. The fact that there is only one ringed peak-cluster basin on the Moon (5% of the total basin population cataloged in this study) is expected as it is likely to be related to the overall smaller numbers of protobasins and peakring basins on the Moon. For comparison, ringed peak-cluster basins account for only 8% of the total cataloged basin population on Mercury (Baker et al., 2011), and also fall along the trend for complex craters on Mercury (Fig. 4B) Ring/rim-crest ratios Rim-crest/ring ratio (or the inverse, ring/rim-crest ratio) plots (Fig. 5) have been used to suggest that protobasins and peak-ring basins represent a continuum of morphologies (Alexopoulos and McKinnon, 1994), in contrast to the view of Pike (1988), who favored a statistical distinction between peak-ring basins and protobasins. Alexopoulos and McKinnon (1994) identified a general trend of continuous, non-linearly decreasing rim-crest/ring ratios with increasing rim-crest diameter for protobasins and peak-ring basins on Venus. The basin catalogs of Wood and Head (1976), Hale and Head (1979b), Wood (1980), Hale and Grieve (1982), and Pike (1988) were also used to suggest similar trends for basins on Mercury, the Moon, and Mars, although the Moon and Mars data appeared with greater scatter (Alexopoulos and McKinnon, 1994). A recent comprehensive survey of 74 peak-ring basins and 32 protobasins on Mercury (Baker et al., 2011) further emphasized these observations by examining the inverse, ring/rim-crest ratios, and noted that peak-ring basins flatten to an equilibrium ring/rim-crest ratio value of around As in Baker et al. (2011), we also calculate ring/rim-crest ratios (in contrast to the convention of using rim-crest/ring ratios from Alexopoulos and McKinnon (1994)), for consistency with earlier studies (Wood and Head, 1976; Pike, 1988) and to avoid magnifying the effects of errors in small denominators. Ring/rim-crest ratios from our refined lunar basin catalog (Fig. 5A) have less scatter than the catalogs used in Alexopoulos and McKinnon (1994), and reveal a trend that is very similar to that observed for Mercury (Fig. 5B) (Baker et al., 2011) and Venus (Fig. 5C) (Alexopoulos and McKinnon, 1994), although at larger rim-crest diameters. The ring/rim-crest ratios for peak-ring basins on the Moon range from 0.35 to 0.56 (arithmetic mean = 0.48), with smaller rim-crest diameters generally having smaller ratios than larger rim-crest diameters (Fig. 5A). The ring/rim-crest ratios on the Moon also flatten to a value of around 0.5 for the largest peak-ring basins. Protobasins have smaller ratios, ranging from

10 386 D.M.H. Baker et al. / Icarus 214 (2011) et al., 2011), which appear distinct from the general continuum of ring/rim-crest ratios between protobasins and peak-ring basins. The ring/rim-crest ratios for craters with ring-like central peaks are also at very low values (range = and arithmetic mean = 0.17) and are similar to the ratio of Humboldt, although they occur at much smaller rim-crest diameters Onset diameter of peak-ring basins Fig. 5. Ring/rim-crest diameter ratios for peak-ring basins (red circles), protobasins (blue squares), and ringed peak-cluster basins (green diamonds) on the Moon (A), Mercury (B), and Venus (C). Basin data are from this study (the Moon, Tables A1 A3), Baker et al. (2011) (Mercury), and Alexopoulos and McKinnon (1994) (Venus). The 0.5 ratio line is drawn in each panel for reference. Also note the change in scale of the x-axis between the Moon (A) and Mercury (B) plots. Nonlinear, curved trends are observed for protobasins and peak-ring basins for each of the planets. The trend is steeper at smaller rim-crest diameters and then flattens to values of for the Moon and Mercury (A and B) and to 0.7 for Venus (C). The continuity between the ring/rim-crest ratios of protobasins and peak-ring basins suggest that they form a continuum of basin morphologies that is a direct result of the process of peak-ring basin formation. Ringed peak-cluster basins appear to diverge from the continuous trend shared by protobasins and peak-ring basins. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) 0.33 to 0.44, with an arithmetic mean of Since there are very few protobasins on the Moon, the lower rim-crest diameter end of the trend is not as well-defined as Mercury (Fig. 5B) and on Venus (Fig. 5C). The ring/rim-crest ratio (0.16) of the lunar ringed peakcluster basin, Humboldt, is much smaller than protobasins and peak-ring basins of similar rim-crest diameter (Fig. 5A). This is consistent with similarly small (arithmetic mean = 0.20) ring/rimcrest ratios for ringed peak-cluster basins on Mercury (Baker Comparisons of the onset diameter for peak-ring basins on the terrestrial planets have been complicated due to the lack of a standard method for calculating this metric. Some authors have compared only transitional diameter ranges, noting that the transitional diameters decrease from the Moon to Mercury and Mars (Wood and Head, 1976; Pike, 1988). Others have used the minimum diameter of the peak-ring basin populations on the terrestrial planets to define onset diameter, yielding a similar decreasing onset diameter ordering from the Moon (140 km) to Mercury (75 km), Mars (45 km), and Venus (40 km) (Pike, 1983; Alexopoulos and McKinnon, 1994). Our calculations for the onset diameter of peak-ring basins (Table 1) do not change this general ordering, but provide new values that are based on the most recent and complete basin catalogs of the terrestrial planets and that are statistical more robust compared with previous values. While the onset diameters for the Moon and Mercury are the most reliable due to relatively complete preservation of their crater populations, the onset diameters for Mars and Venus are more speculative due to the prevalence of erosional and resurfacing processes and effects of differing target properties (e.g., volatiles and temperature) on these planets. Mars smaller onset diameter for peak-ring basins compared with Mercury, which has a similar gravitational acceleration, has traditionally been attributed to the effect of different target materials, including volatiles (e.g., Pike, 1988; Melosh, 1989; Alexopoulos and McKinnon, 1992). Mars is also anomalous in its large range of peak-ring basin diameters ( km), suggesting that additional parameters other than gravity and impact velocity alone are influencing Mars population of peak-ring basins. The surface of Venus has also been globally resurfaced either in a catastrophic manner or at a rate equal to the crater production rate, and thus preserves only a 0.5 Ga crater retention age (Schaber et al., 1992). For these reasons, we exercise caution when interpreting the peak-ring basin and protobasin populations of Mars and Venus in context of the basin populations on the other planets. We also do not calculate an onset diameter for the Earth due to the obvious incompleteness of its impact basin record and the large uncertainties associated with interpreting highly eroded basin structures. It has long been recognized that there is an inverse relationship between the onset diameter of peak-ring basins and the surface gravitational acceleration (g) of the planetary body (Pike, 1983, 1988; Melosh, 1989; Alexopoulos and McKinnon, 1992). This relationship has been used to suggest that the formation of peak rings is largely the result of a gravity-driven process. Gravity-induced collapse of the transient cavity has thus served as the foundation for many current models of peak-ring basin formation, including hydrodynamic collapse of an over-heightened central peak (Melosh, 1982, 1989; Collins et al., 2002). The dependence of peak-ring basin onset diameter on planetary impactor velocity has been more uncertain. Pike (1988) demonstrated that the geometric mean diameters of peak-ring basins do not correlate with the approach velocity of asteroids and short period comets (V 1 ) on the terrestrial planets. An improved correlation was found when approach velocity was combined with g (i.e., g/v 1 ), although g alone still provided the best correlation with the geometric mean diameter of peak-ring basins.