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Titan’s global crater population: A new assessment
Planetary and Space Science 60 (2012) 26–33
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Titan’s global crater population: A new assessment C.D. Neish n, R.D. Lorenz The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 August 2010 Received in revised form 23 February 2011 Accepted 26 February 2011 Available online 9 March 2011
We report a revised crater population for Titan using Cassini RADAR data through January 2010 (flyby T65), and make a size-dependent correction for the incomplete coverage ( 33%) using a Monte-Carlo model. Qualitatively, Titan’s landscape is more heavily cratered than Earth, but much less than Mars or Ganymede: the area fraction covered by craters is in fact comparable with that of Venus. Quantitative efforts to interpret crater densities for Titan as surface age have been confounded by widely divergent crater production rates proposed in the literature. We elucidate the specific model assumptions that lead to these differences (assumed projectile density, scaling function for simple crater diameter, and complex crater size exponent) and suggest these are reasonable bounding models, with the Korycansky and Zahnle (2005) model representing a crater retention age of 1 Ga, and the Artemieva and Lunine (2005) model representing a crater retention age of 200 Ma. These estimates are consistent with models of Titan’s evolution that predict a thickening of its crust 0.3–1.2 Gyr ago. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Titan Impact craters
1. Introduction Crater counting is a common method for dating solar system bodies (see, for example, Hartmann, 1966). The method assumes a new surface forms with no impact craters, and that craters accumulate at some known rate. Before Cassini arrived at Saturn, Titan’s crater population (and hence its age) was unknown due to the lack of high-resolution images of its surface. Cassini’s first near-infrared (Porco et al., 2005) and radar observations (Elachi et al., 2005) indicated a surface comparatively free of craters. Inspired by the successful characterization of the Venus crater population with only 10% radar coverage, Lorenz et al. (2007) assessed the Titan population with the 10% coverage provided by Cassini synthetic aperture radar (SAR) data through August 2006 (a mere three confidently identified craters, with a handful of probable craters). This was followed 3 years later by an analysis of the 22% of Titan’s surface covered through December 2007, in which a total population of only 49 possible impact craters larger than 3 km was observed (Wood et al., 2010). In a similar surface area on Titan’s neighbor Rhea, we would expect to see 7 104 impact craters of an equivalent size (Kirchoff and Schenk, 2010). This reduction is likely a result of several factors, including shielding of projectiles by Titan’s atmosphere, and erosion and burial of craters by active geologic processes on Titan’s surface, possibly including resurfacing by cryovolcanic activity.
n
Corresponding author. Tel.: þ1 443 778 5874; fax: þ 1 443 778 8939. E-mail address: [email protected] (C.D. Neish).
0032-0633/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2011.02.016
With a surface atmospheric density four times that of the Earth, Titan’s atmosphere has a profound influence on the cratering process. It may completely decelerate or break up small ( 1 km) projectiles and will reduce the impact velocity of even large comets. Using simple models for comet disruption, researchers have estimated the amount of shielding Titan’s atmosphere provides (Artemieva and Lunine, 2003; Engel et al., 1995; Ivanov et al., 1997; Korycansky and Zahnle, 2005). These models often disagree regarding the degree of atmospheric disruption for smaller projectiles, but all show relatively little disruption for craters 420 km in diameter. Yet even in this size range, Titan’s craters are reduced in number. In a similar area on Rhea, we would expect to see 2 103 impact craters of an equivalent size (Kirchoff and Schenk, 2010). Titan therefore appears to have a surface younger than that of Rhea, one of the oldest, most heavily cratered surfaces in the Saturnian system (Kirchoff and Schenk (2008) estimate Rhea’s cratered plains could be as old as 4.56 Ga). But just how young is Titan’s surface? Early attempts to date its surface ranged over almost an order of magnitude, from 100 Ma to as much as 4 Ga (Lorenz et al., 2007; Jaumann and Neukum, 2009; Le Corre et al., 2009; Wood et al., 2010). The principal uncertainty stemmed from the differing crater production rates in the literature, specifically those found in Artemieva and Lunine (2005) and Korycansky and Zahnle (2005). Lorenz et al. (2007) found that the rate of impacts per Gyr quoted in Korycansky and Zahnle (2005) is approximately five times lower than that presented in Artemieva and Lunine (2005). The difference between the two papers has confounded attempts to accurately date Titan’s surface (incomplete coverage is a comparatively modest, and progressively declining, obstacle).
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Constraints on Titan’s surface age are critical for models of Titan’s formation and evolution. For example, Tobie et al. (2006) hypothesize that a major outgassing event occurred 2–2.5 Gyr ago, and thus that Titan’s surface should be neither significantly more nor significantly less than 2 Ga old. Moore and Pappalardo (2008), on the other hand, suggest that Titan might be endogenically inactive, resulting in an ancient surface modified only by exogenic processes over the past 4.5 Gyr. Crater counts also inform us about the history of Titan’s atmospheric density. If Titan’s atmosphere were thicker in the past, we might expect fewer impact craters; if it were thinner, we might expect more, especially at smaller diameters (Engel et al., 1995). In this work, we examine the uncertainties associated with dating Titan’s surface in order to obtain a more robust crater retention age. In Section 2, we discuss the number of craters that have been observed on Titan to date, and predict how many more may be observed in the future. In Section 3, we discuss the differences between the different crater production functions found in the literature. In Section 4, we combine the crater counts with these cratering rates to constrain the age of Titan’s surface.
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seen previously, perhaps because these flybys have more coverage at high latitudes, where densities seem systematically lower (Aharonson et al., 2009; Wood et al., 2010). Given the incomplete coverage of Titan’s surface with the high-resolution RADAR instrument, it is likely that many more craters exist on the surface that have yet to be identified. This is especially true for small craters. First, the effective sampling area of the long, thin RADAR swaths is larger for large craters, since
2. Crater counts To date a surface, one must first count the number of craters. Wood et al. (2010) summarized the crater population for Titan by examining Cassini RADAR images from flybys Ta–T39 (taken between October 2004 and December 2007). In this period, Cassini RADAR imaged 22% of the surface of Titan, and in this data set Wood et al. (2010) identified 5 certain craters, 23 nearly certain craters, and 21 probable craters. Since then, two additional undisputed craters have been discovered, the 80 km diameter crater Selk (Soderblom et al., 2010) and the 115 km diameter crater Afekan, which we include in our data set. We have also surveyed RADAR data from flybys T41–T65 to identify other possible craters. There are many round features on Titan, many of which may not be impact craters, so we limited our search to include only those features that are circular, with a radar-bright, nearly complete rim and/or ejecta blanket. Note that it is likely that only well preserved craters will be observable on Titan. As on Earth, there may be craters for which recognition is difficult due to post-impact erosion, resurfacing, etc. Following Wood et al. (2010), each of the craters is classed on a 1–3 scale, representing our evaluation of the likelihood that its origin is impact related. Class 1 craters are considered to be of certain impact origin; Class 2 features are nearly certain; and Class 3 objects are probable. We identified an additional 4 nearly certain craters, and 4 probable craters (Table 1) in the new 11% of Titan coverage. Nearly certain craters #4 and #5 are shown in Fig. 1. These flybys yield a crater density roughly half of what was
Fig. 1. Nearly certain craters #5 (top) and #4 (bottom) (see Table 1), located on the edge of the Shangri-La Sand Sea, just north of Tortola Facula.
Table 1 Catalog of Titan impact craters T41 through T65. Certaintya
Longitude (1W)
Latitude (1)
Diameter (km)
Radar swath
Description
1 2 3 4 5 6
1 1 2 2 2 2
198 200 150.7 141.8 140.6 147.7
7 26 16.3 11.0 12.1 2.2
80 115 18 22 30 33
T36 T43 T57 T56 T56 T56
7 8 9 10
3 3 3 3
160.2 194.8 162.6 129.7
38.3 0.1 19.1 30.6
11 11 18 19
T57 T61 T43 T41
Selk—broad flat floor, small central peak Afekan—small central peak, rim cut by valleys Dark floor, bright ejecta? Dark floor, bright ejecta, surrounded by dunes Dark floor, bright ejecta Santorini Facula—bright ejecta blanket with prominent cut, dark, dune-filled floor Bright rim in dark area On bright area, dark floor Dark floor, bright rim and ejecta? Bright rim in dark area
Number
a
Certainty: 1¼ certain, 2 ¼nearly certain, 3¼ probable.
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Fig. 2. The probability that Cassini RADAR would have detected a crater as a function of its size, given the surface coverage through the T65 flyby (January 12, 2010).
only the rim of the crater needs to be seen. This leads to a sampling area correction of the order of (wþD)(D þL)/wL with the swath width and length being w 300 km and L 4000 km, respectively, and D the crater diameter (Lorenz, 1995). A second, slightly more subtle, effect arises from the growing density of these thin swaths on the finite spherical surface of Titan—it becomes ever more difficult to find a patch between swaths that would allow a large crater to ‘hide’. A proper assessment of crater density with the present incomplete coverage (SAR coverage will likely remain less than 50% even at the end of the Cassini Solstice Mission in 2017) requires correction for these effects. We determined the probability of detection for craters of different sizes by conducting a simple Monte-Carlo experiment. We constructed a 360 180 array, with each box representing a 11 11 area on Titan’s surface, and set a flag for those latitudes/ longitudes covered by SAR through the T65 flyby (January 12, 2010). The center location for an impact crater of a specified diameter (30–1200 km) was chosen at random, and spherical trigonometry was used to identify those elements in a separate 360 180 array where a rim would be observed. If the product of the two arrays was non-zero, the crater would have been detected. The experiment was repeated 1000 times at each crater size to determine the probability of detecting a crater through T65 (Fig. 2). An example run, demonstrating how even a 2000 km diameter crater could be hidden between RADAR swaths, is shown in Fig. 3. At small crater sizes, the values returned are roughly equal to the areal percent of RADAR coverage (but slightly larger, due to the limited resolution of the array). At large crater sizes, the probability of detection approaches 100%, since there is no coverage gap large enough to hide the craters. For example, there is only a 25% chance that another Menrva-sized (440 km) crater has gone undetected on Titan’s surface.1 To account for these potentially unseen craters, we have multiplied the actual crater counts by 1/(probability of detection through T65) (Table 2). The resultant observed crater density is shown in Fig. 4, with comparisons to the crater densities of the Earth, Venus, Ganymede, Mars, and Iapetus. Lists of craters were obtained
1 Menrva was in fact detectable in near-infrared imaging early in the Cassini mission (Porco et al., 2005). The apparent lack of other large structures in the nearglobal near-infrared imaging at resolutions better than 15 km supports the argument that no other such structures exist. However, the imaging resolution varies significantly and recognition of impact structures in these data relies on surface albedo variations alone, so we restrict the discussion in this paper to the more uniform RADAR dataset.
Fig. 3. Cassini RADAR coverage of Titan through T65 (in sinusoidal projection) demonstrating how even a 2000 km diameter crater (white circle at bottom left) could remain hidden between the radar swaths.
Table 2 Titan’s differential crater count, corrected for incomplete coverage. Diameter (km)
Number of craters
Probability of detection through T65 (%)
Corrected number of craters
2O2–4 4–4O2 4O2–8 8–8O2 8O2–16 16–16O2 16O2–32 32–32O2 32O2–64 64–64O2 64O2–128 128–128O2 256O2–512
5 4 4 10 2 11 5 8 2 4 2 1 1
33.0 33.0 33.0 33.0 33.0 33.0 33.0 41.4 46.4 50.0 53.7 58.3 76.0
15.2 12.1 12.1 30.3 6.1 33.3 15.2 19.3 4.3 8.0 3.7 1.7 1.3
Fig. 4. Cumulative crater density for Titan (counts in O2 size bins), scaled upward to reflect the portion of the surface that has not been imaged by Cassini RADAR, with ON error bars. Shown for comparison are the cumulative crater densities for Earth, Venus, Ganymede, Mars, and Iapetus.
from the Catalog of Large Martian Impact Craters (Barlow, 1988), from the Venus Crater Database (Herrick et al., 1997), from the Earth Impact Database (2006), from the Ganymede Crater Database (Schenk, 1996), and from Figure 15 in Lissauer et al. (1988) for
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Iapetus. Note that the terrestrial craters encompass all craters known to exist on Earth, including those not recognizable from orbit, and thus represents an upper limit on its relative crater density. The craters were placed in O2 km sized bins, and then summed with craters in all larger bins to produce a cumulative crater distribution. To first order, we can characterize Titan’s cratering as ‘comparable with Venus’, more cratered than Earth, but less cratered than Ganymede or Mars. Although the number of 4150 km diameter craters on Titan (namely one—Menrva) remains the same as it did when that structure was first imaged in February 2005, the increased coverage makes the statistical significance of the paucity of these large structures much more robust. In Lorenz et al. (2007) it was still reasonable to extrapolate that a few other Menrva-sized structures might exist in unobserved areas: this is no longer likely to be the case. The statistics of small numbers permit Menrva’s formation as simply an unlucky accident (like so many others in the solar system). However, an alternative hypothesis is that Menrva formed in the deep past, and that incomplete resurfacing has since obliterated, or at least obscured, craters on much of the crust except for an ‘island’ containing Menrva. This may explain the lack of craters in the 200–400 km diameter range. For a b¼ 2 cumulative power law crater population (typical of a surface saturated with craters), the presence of a 4400 km crater in a uniform global population suggests that four 4200 km craters should also be present. This is increasingly improbable given that 60% of such structures should have been detected by now. For a b¼ 3 cumulative power law crater population (more typical for 85–300 km diameter craters on Ganymede, Schenk et al., 2003), we would expect eight4200 km craters, which is even less probable. The statistics alone suggest such an island should occupy less than one quarter of Titan’s surface area, although such questions may be more tightly constrained by also considering the geographic distribution of craters, as in Wood et al. (2010).
3. Cratering rate The second key piece of information needed to quantitatively date a surface is the impact rate (or rates) throughout the epochs reflected by the cratered surface. Unfortunately, these rates are not well known for the Saturnian system, or for the outer solar system in general. The approach applied to date relies on calculating the impact rate based on observed cometary populations (Zahnle et al., 2003; Dones et al., 2009). Once an impact rate has been determined, it is necessary to include the effects of Titan’s atmosphere on the impact process, which tends to disrupt smaller projectiles. Two recent papers, Artemieva and Lunine (2005, hereafter AL05) and Korycansky and Zahnle (2005, hereafter KZ05) have used calculated impact rates from Zahnle et al. (2003), coupled with models of atmospheric disruption of impactors, to estimate the crater size distribution on Titan. KZ05 assumed that the impact rate NðTÞ was constant with time, whereas AL05 assumed that the impact rate has decreased over time with a 1/t dependence (Holman and Wisdom, 1993). Eq. (1) gives the overall number of impacts since time t0 until the present time T assuming a constant flux. Eq. (2) gives the overall number of impacts since time t0 assuming a 1/t flux.
N1 ¼ NðTÞðTt0 Þ
ð1Þ
N2 ¼ NðTÞT lnðT=t0 Þ
ð2Þ
AL05 used t0 ¼0.1 Gyr, so the number of impacts over 4.5 Gyr in AL05 is presumed to be 15 times the present-day rate of impacts per Gyr.
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AL05 and KZ05 both report the differential crater size distribution derived from their models (i.e., the number of craters on Titan’s surface in O2 size bins). Lorenz et al. (2007) integrated these two curves (found in Figs. 10 and 8 in AL05 and KZ05, respectively), and found that the cratering rate per Gyr in KZ05 is 5 times lower than that presented in AL05. There is insufficient detail in AL05 and KZ05 to isolate the reasons for this discrepancy. Both papers use the same impact rate from Zahnle et al. (2003), but the full explanation of the crater scaling law (how projectile diameter scales to crater diameter) is missing in AL05. To determine the cause of the difference, we took the stated assumptions from both papers (with additional input from N. Artemieva), and compared the expected crater distribution to the results presented in the two papers. We do not attempt to reproduce the atmospheric disruption models in KZ05 and AL05, opting instead to focus our comparisons on larger craters (D 420 km) where atmospheric disruption is minimal. For KZ05, we used the impact rate (Eq. (3)) given in Zahnle et al. (2003), and the crater scaling law (Eq. (4)) given in Korycansky and Zahnle (2005), assuming a constant impact rate over time. Zahnle et al. (2003) estimated the impact rates in the outer solar system by extrapolating the impact rate on Jupiter by ecliptic comets. They inferred the size–number distribution of projectiles smaller than 20 km from the distribution of impact craters on Europa and Ganymede (Case A) or Triton (Case B), and the size–number distribution of projectiles greater than 50 km from the distribution of Kuiper Belt objects. Zahnle et al. (2003) use two cases to describe the smaller projectiles because the craters on Jupiter’s moons indicate a lack of small projectiles, while the craters on Triton imply a collisional population rich in small bodies. The difference between the two cases decreases with increasing projectile size, and the distributions merge for crater diameters larger than 40 km. We focus exclusively on Case A in this paper, since that was the impactor population used by AL05, but we note that because of the much larger abundance of small comets, a given crater density translates into a younger age for Case B. For Case A, the impactor rate for an arbitrary projectile diameter d is 8 1:0 > > , d o 1:5, > N 1:5 ðd=1:5Þ > > > > 1:7 < N 1:5 ðd=1:5Þ , 1:5o d o 5, N¼ ð3Þ > 1:7 2:5 > N 1:5 ð1:5=5Þ ðd=5Þ , 5 od o30, > > > > > : N ð1:5=5Þ1:7 ð5=30Þ2:5 ðd=30Þ3:2 , d 4 30, 1:5 where the current impact rate on Jupiter by 1.5 km diameter
þ 0:006 comets is N 1:5 ¼ 0:0050:003 per year (Zahnle et al., 2003). There is 5 probability of a comet hitting Titan relative to a PEC ¼5.4 10
Jupiter, for a global cratering rate C ¼ PEC NðdÞ (Zahnle et al., 2003). The final crater diameter D is related to projectile diameter d by ( ðDs oDc Þ Ds ð4Þ D¼ Ds ðDs =Dc Þx ðDs 4Dc Þ where Ds ¼ 1:25
0:217 m0:103 mv2 d0:177 ðcos yÞ0:333 cm g r0:32 t
ð5Þ
The diameter Ds refers to the size of the transient crater formed by a projectile of diameter d, and Dc refers to the transition between simple and complex craters, which for Titan has been assumed to be 2.5 km (Schenk et al., 2003). KZ05 take the power x ¼0.13 (McKinnon et al., 1991) and assume a projectile density of ri ¼0.5 g/cm3 (in order to derive projectile
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mass, m). Titan’s gravity is g¼135 cm/s2, the target density is assumed to be rt ¼0.9 g/cm3, with an average impact velocity of v ¼1.13 106 cm/s. (KZ05 chose impact velocities from a Gaussian distribution with a standard deviation of 4 km/s, but for this simple calculation, we only used the average.) Impact zenith angles are chosen from an isotropic distribution, but for the purposes of this work, we use the average y ¼451. For AL05, we used the impact rate given in Zahnle et al. (2003) for Case A (Eq. (3)), with a 1/t dependence in rate over time. Like KZ05, AL05 used Eq. (4) with Dc ¼ 2.5 km, but they took the exponent x ¼0.176 (Croft, 1985) (N. Artemieva, personal communication). AL05 used a crater scaling law for a water target (unlike KZ05, who used a scaling law for a sand target), similar to that given in Holsapple and Housen (2007): Ds ¼ 1:17 d
2 0:22 0:31 2v ri gd rt
ð6Þ
with a projectile density of ri ¼1.0 g/cm3 and a velocity v ¼11 km/s (N. Artemieva, personal communication). In both cases, the expected crater distribution overlaps with the results presented in the two papers at large crater diameters, where atmospheric effects are minimal (Fig. 5). The small difference between our calculations and the data from KZ05 may reflect a preference for higher impact velocities or lower impact angles in the particular sample they used to generate their Fig. 8. The major discrepancy between the two papers, then, stems from the different crater scaling laws used. In particular, the two papers used (1) different projectile densities (0.5 vs. 1.0 g/cm3),
Fig. 5. (a) Predicted crater distribution extracted from Figure 8 (Case A) in Korycansky and Zahnle (2005) (multiplied by 4.5 to cover the same time range) compared to the Zahnle et al. (2003) projectile population computed for a constant impact rate over 4.5 Gyr. (b) Predicted crater distribution extracted from Figure 10 in Artemieva and Lunine (2005) compared to the Zahnle et al. (2003) projectile population computed for an impact rate that decreases with time as 1/t over 4.5 Gyr.
(2) different scaling relationships for Ds(d) (dry sand vs. water), and (3) a different scaling exponent, x (0.13 vs. 0.176). When viewed side by side, the two scaling laws are not hugely dissimilar (KZ05 is represented by Eq. (7), and AL05 by Eq. (8)): Ds ¼ 1:02
2 0:217 0:32 v ri d0:783 ðcos yÞ0:333 g rt
2 0:22 0:31 v ri d0:78 Ds ¼ 1:36 g rt
ð7Þ
ð8Þ
However, the differences noted above cause the predicted crater diameters to differ by a factor of 2, with the data presented by KZ05 representing a minimum crater diameter, and the data presented by AL05 representing a maximum crater diameter (Fig. 6). When combined with the calculated impactor rate (Eq. (3)), this causes a difference in the predicted crater distribution on Titan that ranges from a factor of 2 (for small craters) up to 30 (for 1000 km craters) (Fig. 7). In effect, AL05 assumes Titan’s crater population was created by more common small impactors (and hence is younger), while KZ05 assumes Titan’s crater population was created by less common large impactors (and hence is older). The difference between the two predicted distributions increases dramatically for craters larger than 15 km, which, due to the effects of its atmosphere, should be the most common size of crater on Titan. There are 25 craters observed on Titan with diameters o15 km, and 34 craters with diameters 415 km. This distribution may make the difference in crater scaling laws more apparent for Titan than for the airless outer solar system bodies, which also have many small craters to aid in age determination. Still, the differences seen here underscore the large uncertainties in quantitatively dating bodies in the outer solar system. In particular, many of the inputs used in the crater scaling laws (such as the bulk density of the impactor) are poorly known, leading to the large differences in predicted crater sizes observed here. As mentioned previously, the projectile populations responsible for outer solar system cratering are also very uncertain, perhaps by as much as a factor of four (Zahnle et al., 2003). Finally, the role of planetocentric bodies in cratering outer planet satellites is unknown, and has not been included in our analysis. However, planetocentric impactors (composed of escaped secondaries from large basins and the remnants of disrupted satellites) were likely only an important source early in Titan’s history, a time seemingly not recorded in its current crater record.
Fig. 6. Crater scaling law used in Artemieva and Lunine (2005) compared to that used in Korycansky and Zahnle (2005). Artemieva and Lunine (2005) predict a maximum crater diameter and Korycansky and Zahnle (2005) predict a minimum crater diameter for a given projectile size.
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Fig. 7. Predicted cratering rate given the projectile flux in Zahnle et al. (2003) and the crater scaling law used in Artemieva and Lunine (2005), divided by the corresponding cratering rate given the crater scaling law used in Korycansky and Zahnle (2005). For an airless world with abundant small craters, the difference between the two models is only 2, but on Titan, where large craters dominate, the difference between the two models is profound.
4. The age of Titan Comparing the predictions of KZ05 to the observed crater distribution on Titan’s surface, the data seem most consistent with a 1 Ga surface (Fig. 8a). Comparing the predictions of AL05 to the observed crater distribution on Titan’s surface, the data seems most consistent with a 200 Ma surface (Fig. 8b). These two values can both be considered reasonable estimates for Titan’s crater retention age, but cannot properly be said to be upper and lower limits, given the factor of four uncertainty in the absolute cratering rate. Rather, they offer two plausible estimates for Titan’s crater retention age, and demonstrate the range of ages one might expect on Titan (and other icy satellites) if the cratering rate were more precisely known. Note that for these calculations, we assumed the impact rate has been constant over the last 1 Gyr. We also calculated distributions assuming the impact rate increased with a 1/t dependence (as suggested by AL05), but found only minor differences for the last 1 Gyr (the two curves being practically indistinguishable). Note that Dones et al. (2009) adopt a slightly smaller cometary impact rate with Saturn than that given in Zahnle et al. (2003). Their calculated cratering rates are typically 0.6 times the rates given in Zahnle et al. (2003). For an airless Titan, they predict time scales for the formation of D 4 20 km craters of 9 Myr (Case A) and 4 Myr (Case B), vs. 5.0 Myr and 2.2 Myr in Zahnle et al. (2003). This would suggest a somewhat older Titan, but one that is still o 1.5 Ga old. In some cases, there are noticeable differences between the predicted and observed crater distributions (Fig. 8). One striking difference between the modeled crater distributions and the data is Menrva, the largest crater on Titan’s surface (D 440 km). Menrva suggests a much older surface than that inferred from smaller craters, from 3.5 (Artemieva and Lunine, 2005) to 10 Ga (Korycansky and Zahnle, 2005; Dones et al., 2009). (Note that an age of 10 Ga does not imply that the crater is older than the age of the solar system, simply that it formed in an early era of heavier bombardment.) As discussed in Section 2, given that we only see one such crater, and there is only a 25% chance another crater of that magnitude will be discovered on Titan, it is possible that Menrva is a statistical anomaly, and does not represent an older surface. A crater count of 17O1 is still consistent with an age o1 Ga. Alternatively, Menrva may represent an older surface
Fig. 8. Titan’s observed crater population (counts in O2 size bins over Titan’s total surface of 81 million km2) is shown with the dashed line with ON error bars. The crater counts have been scaled upward to reflect the portion of the surface that has not been imaged by Cassini RADAR. Predicted impact crater distributions are shown with solid lines from (a) Korycansky and Zahnle (2005) (Case A) for a 1 Ga surface and (b) Artemieva and Lunine (2005) for a 200 Ma surface, assuming a constant impact rate over time.
than the rest of Titan, an area relatively untouched by whatever processes have modified the rest of Titan’s surface. There is also an excess of small craters on Titan compared to predictions (Fig. 8a). This excess is slightly larger than a 1-sigma deviation, and given the uncertainties in the size distribution of ecliptic comets with do1 km, this may not be a significant discrepancy. However, for a world with active erosion (such as Titan) you would expect the opposite situation—small craters should be more depleted than large craters. This is the case for Earth, where there is a pronounced deficit of craters below 10 km compared to the expected number of craters formed by the impact of NEOs (Stuart and Binzel, 2004). Most researchers attribute this deficit to crater obliteration processes (erosion, infilling, faulting, etc.) that erases them from the crater record (e.g., Grieve and Shoemaker, 1994). Some have argued that the deficit of small craters on Earth is a real feature of the production rate (Hughes, 2000), but this is not consistent with observations of NEOs or the cratering record on the Moon (Stuart and Binzel, 2004). The observed excess of small craters on Titan could be a result of an overcount (implying that some of the probable craters identified in Wood et al. (2010) were not formed by impact processes), or a failure in the atmospheric disruption model in Korycansky and Zahnle (2005) for the smallest crater sizes (their model predicts fewer 2–3 km diameter craters on Venus than are observed). More speculatively, the abundance of small craters may indicate a time in Titan’s history when the atmosphere was thinner, causing less disruption to smaller projectiles (Engel et al., 1995). An additional factor that has not received
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consideration to date is the effectiveness of secondary crater formation in Titan’s dense atmosphere. Despite the above noted differences between the predicted and observed crater distributions, to first order, the predictions by KZ05 match the observed crater population relatively well. In particular, the lack of any obvious deficit of craters at small diameters (compared to the current cratering rate) might suggest that there is very little ongoing crater obliteration on Titan, and that whatever event served to resurface the satellite some hundreds of millions or billions or years ago acted on craters of all sizes. Of course, there are large uncertainties in the calculated projectile size distribution, as well in the subsequent crater scaling, rendering this conclusion tentative at best. Additional observations and modeling are needed to determine the rate at which erosion and infilling may act to destroy craters (see, for example, Moore et al., 2010). In total, these observations suggest that Titan has a relatively ‘young’ surface, and that something more than erosional processes has been acting there to reduce the number of observed craters. Significant numbers of craters would have to be buried by sand or liquid, or eroded beyond recognition to account for the 100-fold reduction we see compared to Rhea at large crater diameters (D 420 km). In fact, this is similar to the reduction seen on the Earth compared to the heavily cratered, ancient surface of the Moon. There are over 5000 craters with D 420 km on the Moon (Head et al., 2010) and only 50 of an equivalent size (D 16 km) on the Earth (Earth Impact Database, 2006). (Given the differing gravities, impact velocities, and simple to complex transition diameters on the Earth and the Moon, a projectile that creates a 20 km crater on the Moon would make a slightly smaller crater on the Earth.) This represents a many hundred-fold decrease in crater density (considering only the area of the Earth covered by land). Of course, Earth’s population of craters has been determined by field study, geophysical surveys, and remote sensing with higher resolution and more uniform coverage than that at Titan, so this reduction factor would be somewhat higher if determined using the same instrumentation we have available at Titan. Tobie et al. (2006) suggest a possible explanation for Titan’s young age. Using a coupled thermal-orbital model, they predict that a major outgassing event occurred 1.7–2.7 Gyr ago at the onset of convection in a silicate core, and thus that Titan’s surface should be neither significantly more nor significantly less than 2 Ga old. Given our estimate of 0.2–1 Ga for Titan’s crater retention age, our conclusion seems inconsistent with this model. However, Tobie et al. (2006) also predict a thickening of Titan’s crust 0.3–1.2 Gyr ago, from a few kilometers in thickness to more than 50 km. This prediction is in line with recent observations of Titan’s long-wavelength topography, which suggest Titan has a floating, isostatically compensated ice shell with a mean shell thickness of 100 km (Nimmo and Bills, 2010). Craters formed in a thin, elastic lithosphere look morphologically quite different from craters with ‘conventional’ topographic expressions, and therefore may be difficult to detect on Titan. For example, there exists a class of impact features on the Galilean satellites that are very flat, circular features that lack the basic topographic structures of impact craters (Schenk et al., 2003). These multi-ring structures are characterized by multiple concentric ridges and outer graben, and lack central structures such as pits or domes. Examples include Callanish and Tyre on Europa. Impact simulations suggest that these morphologies could be produced by impact into an ice layer 10–15 km thick overlying a low-viscosity material such as water (Moore et al., 1998). Such flat features would be more difficult to detect on Titan, given active erosional processes and/or burial by sand or liquid. It is thus possible that large craters with recognizable topographic
expressions, such as Menrva, could only form in the last 0.3–1.2 Ga on Titan. An age of 0.3–1.2 Ga agrees with the estimates obtained by Artemieva and Lunine (2005) and Korycansky and Zahnle (2005), and is consistent with a crater density similar to Venus. Korycansky and Zahnle (2005) assign an age of 7307110 Ma for Venus, though the similarity in crater densities and ages is likely a simple coincidence, since Venus and Titan were almost certainly cratered by different impactor populations (Shoemaker and Wolfe, 1982; Zahnle et al. 2003). Remarkably, six years into the Cassini mission, Titan’s surface appears to be as youthful as it did when Lorenz et al. (2007) estimated an age of 100 Ma–1 Ga based on just three craters.
Acknowledgments CN thanks the organizers of the ‘‘Titan Through Time’’ workshop, held at Goddard Spaceflight Center April 6–8, 2010, for encouraging the publication of this work. Thanks to Clark Chapman and an anonymous reviewer for their thoughtful suggestions, and to G. Mitri, R. Kirk, and E. Turtle for their careful reading of the manuscript. Thanks also to N. Artemieva for providing information regarding the scaling laws used in Artemieva and Lunine (2005). Finally, thanks go to the Cassini project, for returning the data presented here, and partial funding of this work. References Aharonson, O., Hayes, A.G., Lunine, J.I., Lorenz, R.D., Allison, M.D., Elachi, C., 2009. An asymmetric distribution of lakes on Titan as a possible consequence of orbital forcing. Nature Geoscience 2, 851–854. Artemieva, N., Lunine, J., 2003. Cratering on Titan: impact melt, ejecta, and the fate of surface organics. Icarus 164, 471–480. Artemieva, N., Lunine, J.I., 2005. Impact cratering on Titan II. Global melt, escaping ejecta, and aqueous alteration of surface organics. Icarus 175, 522–533. Barlow, N.G., 1988. Crater size-frequency distributions and a revised Martian relative chronology. Icarus 75, 285–305. Croft, S.K., 1985. The modification stage of basin formation: conditions of ring formation. In: Schultz, P.H., Merrill, R.B. (Eds.), Multi-Ring Basin. Proceedings of the 12th Lunar and Planetary Science Conference. Pergamon Press, New York, pp. 227–257. Dones, L., Chapman, C.R., McKinnon, W.B., Melosh, H.J., Kirchoff, M.R., Neukum, G., Zahnle, K.J., 2009. Icy satellites of Saturn: impact cratering and age determination. In: Dougherty, M.K., Esposito, L.W., Krimigis, S.M. (Eds.), Saturn from Cassini-Huygens. Springer, New York, pp. 613–636. Earth Impact Database, 2006. /http://www.unb.ca/passc/ImpactDatabase/S (accessed 20 August 2010). Elachi, C., et al., 2005. Cassini radar views the surface of Titan. Science 308, 970–974. Engel, S., Lunine, J.I., Hartmann, W.K., 1995. Cratering on Titan and implications for Titan’s atmospheric history. Planetary and Space Science 43, 1059–1066. Grieve, R.A.F., Shoemaker, E.M., 1994. The record of past impacts on Earth. In: Gehrels, T. (Ed.), Hazards Due to Comets and Asteroids. University of Arizona Press, Tucson, pp. 417–462. Hartmann, W.K., 1966. Martian cratering. Icarus 5, 565–576. Head, J.W., Fassett, C.I., Kadish, S.J., Smith, D.E., Zuber, M.T., Neumann, G.A., Mazarico, E., 2010. Global distribution of large lunar craters: implications for resurfacing and impactor populations. Science 329, 1504–1507. Herrick, R.R., Sharpton, V.L., Malin, M.C., Lyons, S.N., Feely, K., 1997. Morphology and morphometry of impact craters. In: Bougher, S.W., Hunten, D.M., Phillips, R.J. (Eds.), Venus II. University of Arizona Press, Tucson, pp. 1015–1046. Holman, M.J., Wisdom, J., 1993. Dynamical stability in the outer Solar System and the delivery of short-period comets. Astronomical Journal 105, 1987–1999. Holsapple, K.A., Housen, K.R., 2007. A crater and its ejecta: an interpretation of deep impact. Icarus 187, 345–356. Hughes, D.W., 2000. A new approach to the calculation of the cratering rate of the Earth over the last 125 7 20 Myr. Monthly Notices of the Royal Astronomical Society 317, 429–437. Ivanov, B.A., Basilevsky, A.T., Neukum, G., 1997. Atmospheric entry of large meteoroids: implication to Titan. Planetary and Space Science 45, 993–1007. Jaumann, R., Neukum, G., 2009. The surface age of Titan. In: Proceedings of the 40th Lunar and Planetary Science Conference, abstract #1641. Kirchoff, M.R., Schenk, P.M., 2008. Bombardment history of the Saturnian satellites. Workshop on Early Solar System Impact Bombardment, LPI Contribution 1439, abstract #3023.
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Kirchoff, M.R., Schenk, P., 2010. Impact cratering records of the mid-sized, icy Saturnian satellites. Icarus 206, 485–497. Korycansky, D.G., Zahnle, K.J., 2005. Modeling crater populations on Venus and Titan. Planetary and Space Science 53, 695–710. Le Corre, L., Quantin, C., Le Mouelic, S., Sotin, C., 2009. Dating Titan’s surface with impact crater count from the Cassini Radar swaths. Proceedings of the European Planetary Science Congress, 319. Lissauer, J.J., Squyres, S.W., Hartmann, W.K., 1988. Bombardment history of the Saturn system. Journal of Geophysical Research 93, 13776–13804. Lorenz, R., 1995. Cassini Mission: radar sensing of craters on Titan. In: Proceedings of the 26th Lunar and Planetary Science Conference, abstract #863. Lorenz, R.D., Wood, C.A., Lunine, J.I., Wall, S.D., Lopes, R.M., Mitchell, K.L., Paganelli, F., Anderson, Y.Z., Wye, L., Tsai, C., Zebker, H., Stofan, E.R., 2007. Titan’s young surface: initial impact crater survey by Cassini RADAR and model comparison. Geophysical Research Letters 34, L07204. McKinnon, W.B., Chapman, C.R., Housen, K.R., 1991. Cratering of the Uranian satellites. In: Bergstralh, J.T., Miner, E.D., Matthews, M.S. (Eds.), Uranus. University of Arizona Press, Tucson, pp. 629–692. Moore, J.M., et al., 1998. Large impact features on Europa: results of the Galileo nominal mission. Icarus 135, 127–145. Moore, J.M., Pappalardo, R.T., 2008. Titan: Callisto with Weather?, 11. American Geophysical Union 6. Moore, J.M., Howard, A.D., Schenk, P.M., Pappalardo, R.T., 2010. Titan: can fluvial erosion patterns tell us anything about initial landforms and regional landscapes? In: Proceedings of the 41st Lunar and Planetary Science Conference, abstract #1533.
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Nimmo, F., Bills, B.G., 2010. Shell thickness variations and the long-wavelength topography of Titan. Icarus 208, 896–904. Porco, C.C., et al., 2005. Imaging of Titan from the Cassini spacecraft. Nature 434, 159–168. Schenk, P.M., 1996. Ganymede crater database. /http://www.lpi.usra.edu/ resources/gc/gchome.htmlS (accessed 20 August 2010). Schenk, P.M., Chapman, C., Moore, J., Zahnle, K., 2003. Ages and interiors: the cratering record of the Galilean satellites. In: Bagenal, F., McKinnon, W.B. (Eds.), Jupiter: The Planet, Satellites, and Magnetosphere. Cambridge University Press, Cambridge, UK, pp. 427–456. Shoemaker, E.M., Wolfe, R.F., 1982. Cratering time scales for the Galilean satellites. In: Morrison, D. (Ed.), Satellites of Jupiter. University of Arizona Press, Tucson, pp. 277–339. Soderblom, J.M., Brown, R.H., Soderblom, L.A., Barnes, J.W., Jaumann, R., Le Moue´lic, S., Sotin, C., Stephan, K., Baines, K.H., Buratti, B.J., Clark, R.N., Nicholson, P.D., 2010. Geology of the Selk crater region on Titan from Cassini VIMS observations. Icarus 208, 905–912. Stuart, J.S., Binzel, R.P., 2004. Bias-corrected population, size distribution, and impact hazard for the near-Earth objects. Icarus 170, 295–311. Tobie, G., Lunine, J.I., Sotin, C., 2006. Episodic outgassing as the origin of atmospheric methane on Titan. Nature 440, 61–64. Wood, C.A., Lorenz, R., Kirk, R., Lopes, R., Mitchell, K., Stofan, E., 2010. Impact craters on Titan. Icarus 206, 334–344. Zahnle, K., Schenk, P., Levison, H., Dones, L., 2003. Cratering rates in the outer solar system. Icarus 163, 263–289.
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Titan’s global crater population: A new assessment C.D. Neish n, R.D. Lorenz The Johns Hopkins University Applied Physics Laboratory, 11100 Johns Hopkins Road, Laurel, MD 20723, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 August 2010 Received in revised form 23 February 2011 Accepted 26 February 2011 Available online 9 March 2011
We report a revised crater population for Titan using Cassini RADAR data through January 2010 (flyby T65), and make a size-dependent correction for the incomplete coverage ( 33%) using a Monte-Carlo model. Qualitatively, Titan’s landscape is more heavily cratered than Earth, but much less than Mars or Ganymede: the area fraction covered by craters is in fact comparable with that of Venus. Quantitative efforts to interpret crater densities for Titan as surface age have been confounded by widely divergent crater production rates proposed in the literature. We elucidate the specific model assumptions that lead to these differences (assumed projectile density, scaling function for simple crater diameter, and complex crater size exponent) and suggest these are reasonable bounding models, with the Korycansky and Zahnle (2005) model representing a crater retention age of 1 Ga, and the Artemieva and Lunine (2005) model representing a crater retention age of 200 Ma. These estimates are consistent with models of Titan’s evolution that predict a thickening of its crust 0.3–1.2 Gyr ago. & 2011 Elsevier Ltd. All rights reserved.
Keywords: Titan Impact craters
1. Introduction Crater counting is a common method for dating solar system bodies (see, for example, Hartmann, 1966). The method assumes a new surface forms with no impact craters, and that craters accumulate at some known rate. Before Cassini arrived at Saturn, Titan’s crater population (and hence its age) was unknown due to the lack of high-resolution images of its surface. Cassini’s first near-infrared (Porco et al., 2005) and radar observations (Elachi et al., 2005) indicated a surface comparatively free of craters. Inspired by the successful characterization of the Venus crater population with only 10% radar coverage, Lorenz et al. (2007) assessed the Titan population with the 10% coverage provided by Cassini synthetic aperture radar (SAR) data through August 2006 (a mere three confidently identified craters, with a handful of probable craters). This was followed 3 years later by an analysis of the 22% of Titan’s surface covered through December 2007, in which a total population of only 49 possible impact craters larger than 3 km was observed (Wood et al., 2010). In a similar surface area on Titan’s neighbor Rhea, we would expect to see 7 104 impact craters of an equivalent size (Kirchoff and Schenk, 2010). This reduction is likely a result of several factors, including shielding of projectiles by Titan’s atmosphere, and erosion and burial of craters by active geologic processes on Titan’s surface, possibly including resurfacing by cryovolcanic activity.
n
Corresponding author. Tel.: þ1 443 778 5874; fax: þ 1 443 778 8939. E-mail address: [email protected] (C.D. Neish).
0032-0633/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.pss.2011.02.016
With a surface atmospheric density four times that of the Earth, Titan’s atmosphere has a profound influence on the cratering process. It may completely decelerate or break up small ( 1 km) projectiles and will reduce the impact velocity of even large comets. Using simple models for comet disruption, researchers have estimated the amount of shielding Titan’s atmosphere provides (Artemieva and Lunine, 2003; Engel et al., 1995; Ivanov et al., 1997; Korycansky and Zahnle, 2005). These models often disagree regarding the degree of atmospheric disruption for smaller projectiles, but all show relatively little disruption for craters 420 km in diameter. Yet even in this size range, Titan’s craters are reduced in number. In a similar area on Rhea, we would expect to see 2 103 impact craters of an equivalent size (Kirchoff and Schenk, 2010). Titan therefore appears to have a surface younger than that of Rhea, one of the oldest, most heavily cratered surfaces in the Saturnian system (Kirchoff and Schenk (2008) estimate Rhea’s cratered plains could be as old as 4.56 Ga). But just how young is Titan’s surface? Early attempts to date its surface ranged over almost an order of magnitude, from 100 Ma to as much as 4 Ga (Lorenz et al., 2007; Jaumann and Neukum, 2009; Le Corre et al., 2009; Wood et al., 2010). The principal uncertainty stemmed from the differing crater production rates in the literature, specifically those found in Artemieva and Lunine (2005) and Korycansky and Zahnle (2005). Lorenz et al. (2007) found that the rate of impacts per Gyr quoted in Korycansky and Zahnle (2005) is approximately five times lower than that presented in Artemieva and Lunine (2005). The difference between the two papers has confounded attempts to accurately date Titan’s surface (incomplete coverage is a comparatively modest, and progressively declining, obstacle).
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Constraints on Titan’s surface age are critical for models of Titan’s formation and evolution. For example, Tobie et al. (2006) hypothesize that a major outgassing event occurred 2–2.5 Gyr ago, and thus that Titan’s surface should be neither significantly more nor significantly less than 2 Ga old. Moore and Pappalardo (2008), on the other hand, suggest that Titan might be endogenically inactive, resulting in an ancient surface modified only by exogenic processes over the past 4.5 Gyr. Crater counts also inform us about the history of Titan’s atmospheric density. If Titan’s atmosphere were thicker in the past, we might expect fewer impact craters; if it were thinner, we might expect more, especially at smaller diameters (Engel et al., 1995). In this work, we examine the uncertainties associated with dating Titan’s surface in order to obtain a more robust crater retention age. In Section 2, we discuss the number of craters that have been observed on Titan to date, and predict how many more may be observed in the future. In Section 3, we discuss the differences between the different crater production functions found in the literature. In Section 4, we combine the crater counts with these cratering rates to constrain the age of Titan’s surface.
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seen previously, perhaps because these flybys have more coverage at high latitudes, where densities seem systematically lower (Aharonson et al., 2009; Wood et al., 2010). Given the incomplete coverage of Titan’s surface with the high-resolution RADAR instrument, it is likely that many more craters exist on the surface that have yet to be identified. This is especially true for small craters. First, the effective sampling area of the long, thin RADAR swaths is larger for large craters, since
2. Crater counts To date a surface, one must first count the number of craters. Wood et al. (2010) summarized the crater population for Titan by examining Cassini RADAR images from flybys Ta–T39 (taken between October 2004 and December 2007). In this period, Cassini RADAR imaged 22% of the surface of Titan, and in this data set Wood et al. (2010) identified 5 certain craters, 23 nearly certain craters, and 21 probable craters. Since then, two additional undisputed craters have been discovered, the 80 km diameter crater Selk (Soderblom et al., 2010) and the 115 km diameter crater Afekan, which we include in our data set. We have also surveyed RADAR data from flybys T41–T65 to identify other possible craters. There are many round features on Titan, many of which may not be impact craters, so we limited our search to include only those features that are circular, with a radar-bright, nearly complete rim and/or ejecta blanket. Note that it is likely that only well preserved craters will be observable on Titan. As on Earth, there may be craters for which recognition is difficult due to post-impact erosion, resurfacing, etc. Following Wood et al. (2010), each of the craters is classed on a 1–3 scale, representing our evaluation of the likelihood that its origin is impact related. Class 1 craters are considered to be of certain impact origin; Class 2 features are nearly certain; and Class 3 objects are probable. We identified an additional 4 nearly certain craters, and 4 probable craters (Table 1) in the new 11% of Titan coverage. Nearly certain craters #4 and #5 are shown in Fig. 1. These flybys yield a crater density roughly half of what was
Fig. 1. Nearly certain craters #5 (top) and #4 (bottom) (see Table 1), located on the edge of the Shangri-La Sand Sea, just north of Tortola Facula.
Table 1 Catalog of Titan impact craters T41 through T65. Certaintya
Longitude (1W)
Latitude (1)
Diameter (km)
Radar swath
Description
1 2 3 4 5 6
1 1 2 2 2 2
198 200 150.7 141.8 140.6 147.7
7 26 16.3 11.0 12.1 2.2
80 115 18 22 30 33
T36 T43 T57 T56 T56 T56
7 8 9 10
3 3 3 3
160.2 194.8 162.6 129.7
38.3 0.1 19.1 30.6
11 11 18 19
T57 T61 T43 T41
Selk—broad flat floor, small central peak Afekan—small central peak, rim cut by valleys Dark floor, bright ejecta? Dark floor, bright ejecta, surrounded by dunes Dark floor, bright ejecta Santorini Facula—bright ejecta blanket with prominent cut, dark, dune-filled floor Bright rim in dark area On bright area, dark floor Dark floor, bright rim and ejecta? Bright rim in dark area
Number
a
Certainty: 1¼ certain, 2 ¼nearly certain, 3¼ probable.
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C.D. Neish, R.D. Lorenz / Planetary and Space Science 60 (2012) 26–33
Fig. 2. The probability that Cassini RADAR would have detected a crater as a function of its size, given the surface coverage through the T65 flyby (January 12, 2010).
only the rim of the crater needs to be seen. This leads to a sampling area correction of the order of (wþD)(D þL)/wL with the swath width and length being w 300 km and L 4000 km, respectively, and D the crater diameter (Lorenz, 1995). A second, slightly more subtle, effect arises from the growing density of these thin swaths on the finite spherical surface of Titan—it becomes ever more difficult to find a patch between swaths that would allow a large crater to ‘hide’. A proper assessment of crater density with the present incomplete coverage (SAR coverage will likely remain less than 50% even at the end of the Cassini Solstice Mission in 2017) requires correction for these effects. We determined the probability of detection for craters of different sizes by conducting a simple Monte-Carlo experiment. We constructed a 360 180 array, with each box representing a 11 11 area on Titan’s surface, and set a flag for those latitudes/ longitudes covered by SAR through the T65 flyby (January 12, 2010). The center location for an impact crater of a specified diameter (30–1200 km) was chosen at random, and spherical trigonometry was used to identify those elements in a separate 360 180 array where a rim would be observed. If the product of the two arrays was non-zero, the crater would have been detected. The experiment was repeated 1000 times at each crater size to determine the probability of detecting a crater through T65 (Fig. 2). An example run, demonstrating how even a 2000 km diameter crater could be hidden between RADAR swaths, is shown in Fig. 3. At small crater sizes, the values returned are roughly equal to the areal percent of RADAR coverage (but slightly larger, due to the limited resolution of the array). At large crater sizes, the probability of detection approaches 100%, since there is no coverage gap large enough to hide the craters. For example, there is only a 25% chance that another Menrva-sized (440 km) crater has gone undetected on Titan’s surface.1 To account for these potentially unseen craters, we have multiplied the actual crater counts by 1/(probability of detection through T65) (Table 2). The resultant observed crater density is shown in Fig. 4, with comparisons to the crater densities of the Earth, Venus, Ganymede, Mars, and Iapetus. Lists of craters were obtained
1 Menrva was in fact detectable in near-infrared imaging early in the Cassini mission (Porco et al., 2005). The apparent lack of other large structures in the nearglobal near-infrared imaging at resolutions better than 15 km supports the argument that no other such structures exist. However, the imaging resolution varies significantly and recognition of impact structures in these data relies on surface albedo variations alone, so we restrict the discussion in this paper to the more uniform RADAR dataset.
Fig. 3. Cassini RADAR coverage of Titan through T65 (in sinusoidal projection) demonstrating how even a 2000 km diameter crater (white circle at bottom left) could remain hidden between the radar swaths.
Table 2 Titan’s differential crater count, corrected for incomplete coverage. Diameter (km)
Number of craters
Probability of detection through T65 (%)
Corrected number of craters
2O2–4 4–4O2 4O2–8 8–8O2 8O2–16 16–16O2 16O2–32 32–32O2 32O2–64 64–64O2 64O2–128 128–128O2 256O2–512
5 4 4 10 2 11 5 8 2 4 2 1 1
33.0 33.0 33.0 33.0 33.0 33.0 33.0 41.4 46.4 50.0 53.7 58.3 76.0
15.2 12.1 12.1 30.3 6.1 33.3 15.2 19.3 4.3 8.0 3.7 1.7 1.3
Fig. 4. Cumulative crater density for Titan (counts in O2 size bins), scaled upward to reflect the portion of the surface that has not been imaged by Cassini RADAR, with ON error bars. Shown for comparison are the cumulative crater densities for Earth, Venus, Ganymede, Mars, and Iapetus.
from the Catalog of Large Martian Impact Craters (Barlow, 1988), from the Venus Crater Database (Herrick et al., 1997), from the Earth Impact Database (2006), from the Ganymede Crater Database (Schenk, 1996), and from Figure 15 in Lissauer et al. (1988) for
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Iapetus. Note that the terrestrial craters encompass all craters known to exist on Earth, including those not recognizable from orbit, and thus represents an upper limit on its relative crater density. The craters were placed in O2 km sized bins, and then summed with craters in all larger bins to produce a cumulative crater distribution. To first order, we can characterize Titan’s cratering as ‘comparable with Venus’, more cratered than Earth, but less cratered than Ganymede or Mars. Although the number of 4150 km diameter craters on Titan (namely one—Menrva) remains the same as it did when that structure was first imaged in February 2005, the increased coverage makes the statistical significance of the paucity of these large structures much more robust. In Lorenz et al. (2007) it was still reasonable to extrapolate that a few other Menrva-sized structures might exist in unobserved areas: this is no longer likely to be the case. The statistics of small numbers permit Menrva’s formation as simply an unlucky accident (like so many others in the solar system). However, an alternative hypothesis is that Menrva formed in the deep past, and that incomplete resurfacing has since obliterated, or at least obscured, craters on much of the crust except for an ‘island’ containing Menrva. This may explain the lack of craters in the 200–400 km diameter range. For a b¼ 2 cumulative power law crater population (typical of a surface saturated with craters), the presence of a 4400 km crater in a uniform global population suggests that four 4200 km craters should also be present. This is increasingly improbable given that 60% of such structures should have been detected by now. For a b¼ 3 cumulative power law crater population (more typical for 85–300 km diameter craters on Ganymede, Schenk et al., 2003), we would expect eight4200 km craters, which is even less probable. The statistics alone suggest such an island should occupy less than one quarter of Titan’s surface area, although such questions may be more tightly constrained by also considering the geographic distribution of craters, as in Wood et al. (2010).
3. Cratering rate The second key piece of information needed to quantitatively date a surface is the impact rate (or rates) throughout the epochs reflected by the cratered surface. Unfortunately, these rates are not well known for the Saturnian system, or for the outer solar system in general. The approach applied to date relies on calculating the impact rate based on observed cometary populations (Zahnle et al., 2003; Dones et al., 2009). Once an impact rate has been determined, it is necessary to include the effects of Titan’s atmosphere on the impact process, which tends to disrupt smaller projectiles. Two recent papers, Artemieva and Lunine (2005, hereafter AL05) and Korycansky and Zahnle (2005, hereafter KZ05) have used calculated impact rates from Zahnle et al. (2003), coupled with models of atmospheric disruption of impactors, to estimate the crater size distribution on Titan. KZ05 assumed that the impact rate NðTÞ was constant with time, whereas AL05 assumed that the impact rate has decreased over time with a 1/t dependence (Holman and Wisdom, 1993). Eq. (1) gives the overall number of impacts since time t0 until the present time T assuming a constant flux. Eq. (2) gives the overall number of impacts since time t0 assuming a 1/t flux.
N1 ¼ NðTÞðTt0 Þ
ð1Þ
N2 ¼ NðTÞT lnðT=t0 Þ
ð2Þ
AL05 used t0 ¼0.1 Gyr, so the number of impacts over 4.5 Gyr in AL05 is presumed to be 15 times the present-day rate of impacts per Gyr.
29
AL05 and KZ05 both report the differential crater size distribution derived from their models (i.e., the number of craters on Titan’s surface in O2 size bins). Lorenz et al. (2007) integrated these two curves (found in Figs. 10 and 8 in AL05 and KZ05, respectively), and found that the cratering rate per Gyr in KZ05 is 5 times lower than that presented in AL05. There is insufficient detail in AL05 and KZ05 to isolate the reasons for this discrepancy. Both papers use the same impact rate from Zahnle et al. (2003), but the full explanation of the crater scaling law (how projectile diameter scales to crater diameter) is missing in AL05. To determine the cause of the difference, we took the stated assumptions from both papers (with additional input from N. Artemieva), and compared the expected crater distribution to the results presented in the two papers. We do not attempt to reproduce the atmospheric disruption models in KZ05 and AL05, opting instead to focus our comparisons on larger craters (D 420 km) where atmospheric disruption is minimal. For KZ05, we used the impact rate (Eq. (3)) given in Zahnle et al. (2003), and the crater scaling law (Eq. (4)) given in Korycansky and Zahnle (2005), assuming a constant impact rate over time. Zahnle et al. (2003) estimated the impact rates in the outer solar system by extrapolating the impact rate on Jupiter by ecliptic comets. They inferred the size–number distribution of projectiles smaller than 20 km from the distribution of impact craters on Europa and Ganymede (Case A) or Triton (Case B), and the size–number distribution of projectiles greater than 50 km from the distribution of Kuiper Belt objects. Zahnle et al. (2003) use two cases to describe the smaller projectiles because the craters on Jupiter’s moons indicate a lack of small projectiles, while the craters on Triton imply a collisional population rich in small bodies. The difference between the two cases decreases with increasing projectile size, and the distributions merge for crater diameters larger than 40 km. We focus exclusively on Case A in this paper, since that was the impactor population used by AL05, but we note that because of the much larger abundance of small comets, a given crater density translates into a younger age for Case B. For Case A, the impactor rate for an arbitrary projectile diameter d is 8 1:0 > > , d o 1:5, > N 1:5 ðd=1:5Þ > > > > 1:7 < N 1:5 ðd=1:5Þ , 1:5o d o 5, N¼ ð3Þ > 1:7 2:5 > N 1:5 ð1:5=5Þ ðd=5Þ , 5 od o30, > > > > > : N ð1:5=5Þ1:7 ð5=30Þ2:5 ðd=30Þ3:2 , d 4 30, 1:5 where the current impact rate on Jupiter by 1.5 km diameter
þ 0:006 comets is N 1:5 ¼ 0:0050:003 per year (Zahnle et al., 2003). There is 5 probability of a comet hitting Titan relative to a PEC ¼5.4 10
Jupiter, for a global cratering rate C ¼ PEC NðdÞ (Zahnle et al., 2003). The final crater diameter D is related to projectile diameter d by ( ðDs oDc Þ Ds ð4Þ D¼ Ds ðDs =Dc Þx ðDs 4Dc Þ where Ds ¼ 1:25
0:217 m0:103 mv2 d0:177 ðcos yÞ0:333 cm g r0:32 t
ð5Þ
The diameter Ds refers to the size of the transient crater formed by a projectile of diameter d, and Dc refers to the transition between simple and complex craters, which for Titan has been assumed to be 2.5 km (Schenk et al., 2003). KZ05 take the power x ¼0.13 (McKinnon et al., 1991) and assume a projectile density of ri ¼0.5 g/cm3 (in order to derive projectile
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mass, m). Titan’s gravity is g¼135 cm/s2, the target density is assumed to be rt ¼0.9 g/cm3, with an average impact velocity of v ¼1.13 106 cm/s. (KZ05 chose impact velocities from a Gaussian distribution with a standard deviation of 4 km/s, but for this simple calculation, we only used the average.) Impact zenith angles are chosen from an isotropic distribution, but for the purposes of this work, we use the average y ¼451. For AL05, we used the impact rate given in Zahnle et al. (2003) for Case A (Eq. (3)), with a 1/t dependence in rate over time. Like KZ05, AL05 used Eq. (4) with Dc ¼ 2.5 km, but they took the exponent x ¼0.176 (Croft, 1985) (N. Artemieva, personal communication). AL05 used a crater scaling law for a water target (unlike KZ05, who used a scaling law for a sand target), similar to that given in Holsapple and Housen (2007): Ds ¼ 1:17 d
2 0:22 0:31 2v ri gd rt
ð6Þ
with a projectile density of ri ¼1.0 g/cm3 and a velocity v ¼11 km/s (N. Artemieva, personal communication). In both cases, the expected crater distribution overlaps with the results presented in the two papers at large crater diameters, where atmospheric effects are minimal (Fig. 5). The small difference between our calculations and the data from KZ05 may reflect a preference for higher impact velocities or lower impact angles in the particular sample they used to generate their Fig. 8. The major discrepancy between the two papers, then, stems from the different crater scaling laws used. In particular, the two papers used (1) different projectile densities (0.5 vs. 1.0 g/cm3),
Fig. 5. (a) Predicted crater distribution extracted from Figure 8 (Case A) in Korycansky and Zahnle (2005) (multiplied by 4.5 to cover the same time range) compared to the Zahnle et al. (2003) projectile population computed for a constant impact rate over 4.5 Gyr. (b) Predicted crater distribution extracted from Figure 10 in Artemieva and Lunine (2005) compared to the Zahnle et al. (2003) projectile population computed for an impact rate that decreases with time as 1/t over 4.5 Gyr.
(2) different scaling relationships for Ds(d) (dry sand vs. water), and (3) a different scaling exponent, x (0.13 vs. 0.176). When viewed side by side, the two scaling laws are not hugely dissimilar (KZ05 is represented by Eq. (7), and AL05 by Eq. (8)): Ds ¼ 1:02
2 0:217 0:32 v ri d0:783 ðcos yÞ0:333 g rt
2 0:22 0:31 v ri d0:78 Ds ¼ 1:36 g rt
ð7Þ
ð8Þ
However, the differences noted above cause the predicted crater diameters to differ by a factor of 2, with the data presented by KZ05 representing a minimum crater diameter, and the data presented by AL05 representing a maximum crater diameter (Fig. 6). When combined with the calculated impactor rate (Eq. (3)), this causes a difference in the predicted crater distribution on Titan that ranges from a factor of 2 (for small craters) up to 30 (for 1000 km craters) (Fig. 7). In effect, AL05 assumes Titan’s crater population was created by more common small impactors (and hence is younger), while KZ05 assumes Titan’s crater population was created by less common large impactors (and hence is older). The difference between the two predicted distributions increases dramatically for craters larger than 15 km, which, due to the effects of its atmosphere, should be the most common size of crater on Titan. There are 25 craters observed on Titan with diameters o15 km, and 34 craters with diameters 415 km. This distribution may make the difference in crater scaling laws more apparent for Titan than for the airless outer solar system bodies, which also have many small craters to aid in age determination. Still, the differences seen here underscore the large uncertainties in quantitatively dating bodies in the outer solar system. In particular, many of the inputs used in the crater scaling laws (such as the bulk density of the impactor) are poorly known, leading to the large differences in predicted crater sizes observed here. As mentioned previously, the projectile populations responsible for outer solar system cratering are also very uncertain, perhaps by as much as a factor of four (Zahnle et al., 2003). Finally, the role of planetocentric bodies in cratering outer planet satellites is unknown, and has not been included in our analysis. However, planetocentric impactors (composed of escaped secondaries from large basins and the remnants of disrupted satellites) were likely only an important source early in Titan’s history, a time seemingly not recorded in its current crater record.
Fig. 6. Crater scaling law used in Artemieva and Lunine (2005) compared to that used in Korycansky and Zahnle (2005). Artemieva and Lunine (2005) predict a maximum crater diameter and Korycansky and Zahnle (2005) predict a minimum crater diameter for a given projectile size.
C.D. Neish, R.D. Lorenz / Planetary and Space Science 60 (2012) 26–33
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Fig. 7. Predicted cratering rate given the projectile flux in Zahnle et al. (2003) and the crater scaling law used in Artemieva and Lunine (2005), divided by the corresponding cratering rate given the crater scaling law used in Korycansky and Zahnle (2005). For an airless world with abundant small craters, the difference between the two models is only 2, but on Titan, where large craters dominate, the difference between the two models is profound.
4. The age of Titan Comparing the predictions of KZ05 to the observed crater distribution on Titan’s surface, the data seem most consistent with a 1 Ga surface (Fig. 8a). Comparing the predictions of AL05 to the observed crater distribution on Titan’s surface, the data seems most consistent with a 200 Ma surface (Fig. 8b). These two values can both be considered reasonable estimates for Titan’s crater retention age, but cannot properly be said to be upper and lower limits, given the factor of four uncertainty in the absolute cratering rate. Rather, they offer two plausible estimates for Titan’s crater retention age, and demonstrate the range of ages one might expect on Titan (and other icy satellites) if the cratering rate were more precisely known. Note that for these calculations, we assumed the impact rate has been constant over the last 1 Gyr. We also calculated distributions assuming the impact rate increased with a 1/t dependence (as suggested by AL05), but found only minor differences for the last 1 Gyr (the two curves being practically indistinguishable). Note that Dones et al. (2009) adopt a slightly smaller cometary impact rate with Saturn than that given in Zahnle et al. (2003). Their calculated cratering rates are typically 0.6 times the rates given in Zahnle et al. (2003). For an airless Titan, they predict time scales for the formation of D 4 20 km craters of 9 Myr (Case A) and 4 Myr (Case B), vs. 5.0 Myr and 2.2 Myr in Zahnle et al. (2003). This would suggest a somewhat older Titan, but one that is still o 1.5 Ga old. In some cases, there are noticeable differences between the predicted and observed crater distributions (Fig. 8). One striking difference between the modeled crater distributions and the data is Menrva, the largest crater on Titan’s surface (D 440 km). Menrva suggests a much older surface than that inferred from smaller craters, from 3.5 (Artemieva and Lunine, 2005) to 10 Ga (Korycansky and Zahnle, 2005; Dones et al., 2009). (Note that an age of 10 Ga does not imply that the crater is older than the age of the solar system, simply that it formed in an early era of heavier bombardment.) As discussed in Section 2, given that we only see one such crater, and there is only a 25% chance another crater of that magnitude will be discovered on Titan, it is possible that Menrva is a statistical anomaly, and does not represent an older surface. A crater count of 17O1 is still consistent with an age o1 Ga. Alternatively, Menrva may represent an older surface
Fig. 8. Titan’s observed crater population (counts in O2 size bins over Titan’s total surface of 81 million km2) is shown with the dashed line with ON error bars. The crater counts have been scaled upward to reflect the portion of the surface that has not been imaged by Cassini RADAR. Predicted impact crater distributions are shown with solid lines from (a) Korycansky and Zahnle (2005) (Case A) for a 1 Ga surface and (b) Artemieva and Lunine (2005) for a 200 Ma surface, assuming a constant impact rate over time.
than the rest of Titan, an area relatively untouched by whatever processes have modified the rest of Titan’s surface. There is also an excess of small craters on Titan compared to predictions (Fig. 8a). This excess is slightly larger than a 1-sigma deviation, and given the uncertainties in the size distribution of ecliptic comets with do1 km, this may not be a significant discrepancy. However, for a world with active erosion (such as Titan) you would expect the opposite situation—small craters should be more depleted than large craters. This is the case for Earth, where there is a pronounced deficit of craters below 10 km compared to the expected number of craters formed by the impact of NEOs (Stuart and Binzel, 2004). Most researchers attribute this deficit to crater obliteration processes (erosion, infilling, faulting, etc.) that erases them from the crater record (e.g., Grieve and Shoemaker, 1994). Some have argued that the deficit of small craters on Earth is a real feature of the production rate (Hughes, 2000), but this is not consistent with observations of NEOs or the cratering record on the Moon (Stuart and Binzel, 2004). The observed excess of small craters on Titan could be a result of an overcount (implying that some of the probable craters identified in Wood et al. (2010) were not formed by impact processes), or a failure in the atmospheric disruption model in Korycansky and Zahnle (2005) for the smallest crater sizes (their model predicts fewer 2–3 km diameter craters on Venus than are observed). More speculatively, the abundance of small craters may indicate a time in Titan’s history when the atmosphere was thinner, causing less disruption to smaller projectiles (Engel et al., 1995). An additional factor that has not received
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consideration to date is the effectiveness of secondary crater formation in Titan’s dense atmosphere. Despite the above noted differences between the predicted and observed crater distributions, to first order, the predictions by KZ05 match the observed crater population relatively well. In particular, the lack of any obvious deficit of craters at small diameters (compared to the current cratering rate) might suggest that there is very little ongoing crater obliteration on Titan, and that whatever event served to resurface the satellite some hundreds of millions or billions or years ago acted on craters of all sizes. Of course, there are large uncertainties in the calculated projectile size distribution, as well in the subsequent crater scaling, rendering this conclusion tentative at best. Additional observations and modeling are needed to determine the rate at which erosion and infilling may act to destroy craters (see, for example, Moore et al., 2010). In total, these observations suggest that Titan has a relatively ‘young’ surface, and that something more than erosional processes has been acting there to reduce the number of observed craters. Significant numbers of craters would have to be buried by sand or liquid, or eroded beyond recognition to account for the 100-fold reduction we see compared to Rhea at large crater diameters (D 420 km). In fact, this is similar to the reduction seen on the Earth compared to the heavily cratered, ancient surface of the Moon. There are over 5000 craters with D 420 km on the Moon (Head et al., 2010) and only 50 of an equivalent size (D 16 km) on the Earth (Earth Impact Database, 2006). (Given the differing gravities, impact velocities, and simple to complex transition diameters on the Earth and the Moon, a projectile that creates a 20 km crater on the Moon would make a slightly smaller crater on the Earth.) This represents a many hundred-fold decrease in crater density (considering only the area of the Earth covered by land). Of course, Earth’s population of craters has been determined by field study, geophysical surveys, and remote sensing with higher resolution and more uniform coverage than that at Titan, so this reduction factor would be somewhat higher if determined using the same instrumentation we have available at Titan. Tobie et al. (2006) suggest a possible explanation for Titan’s young age. Using a coupled thermal-orbital model, they predict that a major outgassing event occurred 1.7–2.7 Gyr ago at the onset of convection in a silicate core, and thus that Titan’s surface should be neither significantly more nor significantly less than 2 Ga old. Given our estimate of 0.2–1 Ga for Titan’s crater retention age, our conclusion seems inconsistent with this model. However, Tobie et al. (2006) also predict a thickening of Titan’s crust 0.3–1.2 Gyr ago, from a few kilometers in thickness to more than 50 km. This prediction is in line with recent observations of Titan’s long-wavelength topography, which suggest Titan has a floating, isostatically compensated ice shell with a mean shell thickness of 100 km (Nimmo and Bills, 2010). Craters formed in a thin, elastic lithosphere look morphologically quite different from craters with ‘conventional’ topographic expressions, and therefore may be difficult to detect on Titan. For example, there exists a class of impact features on the Galilean satellites that are very flat, circular features that lack the basic topographic structures of impact craters (Schenk et al., 2003). These multi-ring structures are characterized by multiple concentric ridges and outer graben, and lack central structures such as pits or domes. Examples include Callanish and Tyre on Europa. Impact simulations suggest that these morphologies could be produced by impact into an ice layer 10–15 km thick overlying a low-viscosity material such as water (Moore et al., 1998). Such flat features would be more difficult to detect on Titan, given active erosional processes and/or burial by sand or liquid. It is thus possible that large craters with recognizable topographic
expressions, such as Menrva, could only form in the last 0.3–1.2 Ga on Titan. An age of 0.3–1.2 Ga agrees with the estimates obtained by Artemieva and Lunine (2005) and Korycansky and Zahnle (2005), and is consistent with a crater density similar to Venus. Korycansky and Zahnle (2005) assign an age of 7307110 Ma for Venus, though the similarity in crater densities and ages is likely a simple coincidence, since Venus and Titan were almost certainly cratered by different impactor populations (Shoemaker and Wolfe, 1982; Zahnle et al. 2003). Remarkably, six years into the Cassini mission, Titan’s surface appears to be as youthful as it did when Lorenz et al. (2007) estimated an age of 100 Ma–1 Ga based on just three craters.
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