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W1684523249 abstract "Megaregolith accumulation can have important thermal consequences for bodies that lose heat by conduction, as vacuous porosity of the kind observed in the lunar megaregolith lowers thermal conductivity by a factor of 10. I have modeled global average ejecta accumulation as a function of the largest impact size, with no explicit modeling of time. In conjunction with an assumed cratering size-distribution exponent b, the largest crater constrains the sizes of all other craters that significantly contribute to a megaregolith. The largest impactor mass ratio is a major fraction of the catastrophic-disruption mass ratio, and in general the largest crater’s diameter is close to the target’s diameter. Total accumulation is roughly 1–5% of (and proportional to) the target’s radius. Global accumulations estimated by this approach are higher than in the classic Housen et al. (1979) study by a factor of roughly 10. This revision is caused mainly by higher (typical) largest crater size. For b ∼ 2, the single largest crater typically contributes close to 50% of the total of new (nonrecycled) ejecta. Megaregolith can be destroyed by sintering, a process whose pressure sensitivity makes it effective at lower temperature on larger bodies. Planetesimals ∼100 km in diameter may be surprisingly well suited (about as well suited as bodies two to three times larger in diameter) for attaining temperatures conducive to widespread melting. A water-rich composition may be a significant disadvantage in terms of planetesimal heating, as the shallow interior may be densified by aqueous metamorphism, and will have a low sintering temperature. The larger planetesimals, asteroids, and rocky natural satellites are/were invariably blanketed by an accumulation of impact-crater ejecta (megaregolith). The extent of that accumulation is of interest for various reasons. The early bodies underwent rapid thermal evolutions that determined the course of their metamorphic/igneous modification, and ultimately influenced the origin and evolution of the planets. The thermal evolution was determined by a competition: heat generation, probably mainly by 26Al (t1/2 = 0.72 Ma), versus heat loss, which in small bodies occurs mainly by conduction. Megaregolith–ejecta accumulation can have important thermal consequences for such a body. The rate of loss is a function of the thermal conductivity k of the outer layers. Vacuous porosity of the kind observed in the lunar megaregolith lowers conductivity by a factor of approximately 10 (Warren and Rasmussen 1987). Recent thermal models make a range of extreme and, in terms of evolutionary implications, divergent assumptions about k. At one extreme are models (e.g., Ghosh and McSween 1998; Merk et al. 2002; Wilson et al. 2008) that simply assume a solid rock like k. At another extreme, some (Hevey and Sanders 2006; Sahijpal et al. 2007) assume that k is similar to that of lunar surface fines (i.e., lower by a factor of approximately 2000 compared to the solid-rock k: Langseth et al. 1976) prevails until, with rising T, sintering suddenly transforms the material to rock-like k. The megaregolith, for the purposes of this work, is defined as the body’s layer of accumulated impact-crater ejecta, exclusive of material that may have become extensively modified (sintered) to a low porosity. This article is concerned with megaregolith development on bodies of diameter dB between approximately 100 km and Moon-sized (3476 km); i.e., mass between 1018 and 1023 kg. Megaregolith is also important as the outer shell of porous, weak material into/through which later impacts transpire; as the usual context for spall-off of chunks that may become meteorites; and as the context for remote sensing observations. The blast-out and accumulation cycle that produces megaregolith leads to an increase in porosity, by a factor estimated (e.g., Melosh 1989; Richardson 2009) to be approximately 20%. In the context of an atmosphereless planetesimal, this porosity probably tends to be vacuous, like the porosity of the Moon’s regolith and megaregolith. Vacuous porosity leads to a marked diminution of thermal conductivity k (Wechsler et al. 1972; Horai and Winkler 1980). Yomogida and Matsui (1984) found analogous effects with mildly porous chondritic materials. Models that assume gas pressure is not <<0.1 MPa within the pores (e.g., a model used in planetesimal modeling by Ciesla et al. 2009) vastly overestimate the k of vacuous–porous materials. The lunar data (summarized in Fig. 1) show that vacuous porosity yields a reduction in k along a single exponential relationship, whether the material is a cohesive breccia or a loose soil. Even the igneous (nonfracture) porosity in unbrecciated mare basalt appears to have almost the same effect (regarding sample 70017, see the caption of Fig. 1). Thermal conductivity (k) at 300 K, plotted as a function of vacuous porosity for lunar rocks and soils. Data are from Horai and Winkler (1980) and other sources cited in Warren and Rasmussen (1987), most notably, for the 1 m deep soils, k from Langseth et al. (1976; their fig. 6) and porosity from Carrier et al. (1991). The breccias are mostly impact melt breccias, except for 77017 (porosity = 15%) which is a fragmental breccia, and 10065 (porosity 24%), which is a regolith breccia. The exponential equation for the line between solid rock and (average) surface soil is k = 2e−0.1246ϕ. The one clear deviant from the trend, mare basalt 70017, is unusually coarse-grained, and Horai and Winkler (1976) used an uncommonly small sample for their 70017 measurements. A low-k planetary layer may be analogized to a resistor in an electrical circuit. The thermal resistance of each layer is proportional to (1/ki-o)(1/ri − 1/ro), where ro and ri are the fractional radii of the outer and inner boundaries of the layer (e.g., Sucec 1975). The resistances are additive. As a crude illustration of the potential importance of the insulating layer, the steady-state, internal heat generation neglected, heat flow q out of the body shown in Fig. 2 would be Results from application of Equation 1 to cooling of a megaregolith-covered body (shown in schematic cross section in the inset): relative steady-state heat flow q as a function of the relative conductivity kMR of the megaregolith, shown for a range of assumed megaregolith thickness. The models shown assume the depth to the approximately isothermal deep interior (depth to r1) is 8 km (Wilson et al. 2008; see text) and that the body is approximately 500 km in diameter dB. (Results are not very sensitive to dB; e.g., for megaregolith thickness of 1 km and kMR/krock = 0.1, relative q varies by only a factor of 1.074 as dB ranges from 100 to 1000 km.) The actual situation is never as simple as modeled here, as the body is being heated from within by, e.g., (in the case of an early planetesimal) 26Al. Results from Equation 1 for the relative q implied by various assumptions regarding the megaregolith’s thickness and conductivity are shown in Fig. 2. For example, suppose a body of order 100–1000 km in diameter dB has a 2 km megaregolith, with k = 0.1× solid rock, atop a 6 km conductive solid-rock layer, below which the body is approximately isothermal due to the rapidity of primordial heating in relation to thermal diffusivity. A planetesimal that undergoes rapid, uniform heating will develop an approximately isothermal deep interior (inward of r1 in Fig. 2), as the influence of radiative heat loss from the surface penetrates only to a “skin” depth that according to Wilson et al. (2008) is approximately 8 km (as will be discussed below, the skin depth is a function of time, k, and heat production, but 8 km is a plausible result for a small body heated by 26Al for several Ma). Figure 2 indicates that a 2 km megaregolith layer, with k = 0.1× the deep (solid) interior k, will reduce heat loss from the deeper interior by a factor of 3 in comparison to the rate with the higher k throughout. The same approximate total resistance would result if just 0.02 km of powdery regolith with k = 0.001 × solid rock were separated from the near-isothermal core by a 7.98 km solid-rock layer. For the best known megaregolith-covered body, the Moon, based on an earlier version of Fig. 1, coupled with a compilation of porosities in lunar breccias (average: 17 ± 10%), Warren and Rasmussen (1987) estimated that the kMR of the megaregolith is approximately 0.1 times that of solid rock. In general, porosity is expected to be higher on smaller bodies, with their lower gravity and internal pressure, and lower potential for igneous activity and sintering after the main, late-accretionary era of impact cratering. The near-surface hydrostatic pressure–depth gradient dP/dz is directly proportional to dB, and the P at any given r/rB scales as dB2 (Fig. 3; density variations may alter this nominal P-distribution, but only to a mild extent). On a small (say dB < 100 km) body, the average megaregolith porosity could conceivably be as high as 40%, implying a reduction in k by a factor of 102 relative to the solid-rock k (Fig. 1). Pressures within bodies of uniform 3000 kg m−3 density, calculated using equation 2–64 of Turcotte and Schubert (1982). To scale to a different density, multiply the indicated P times (density/3000) squared. Grey region indicates estimated range of P for deepest, most sinter-densification prone portion of megaregolith as modeled (assuming b = 2 and DL/dB = 0.6–1) in this work. Housen et al. (1979) authored the classic study of the development of asteroidal ejecta accumulations (cf. Housen and Wilkening 1982). However, their approach focused on the issue of crater saturation for a “typical” surface region “exterior to sparsely scattered, large anomalous craters”; and on that region’s evolution, and in particular its elevation evolution, as a function of time (cf. Ward 2002). An approach focused on time and saturation can be useful for application to powdery regolith (sensu stricto) on asteroids, especially asteroids that may have acquired fresh-rocky surfaces at some relatively recent date. But for the more basic purpose of constraining global impact ejecta accumulation thickness, timing is an ancillary issue, and introduces unnecessary complication. It is precisely the few “large anomalous” craters that preponderate in contributions to a global megaregolith. Moreover, in some important respects, such as depth and volume of the excavation/ejection zone, the Housen et al. (1979) model has been superseded by modern cratering physics interpretation. My model builds from the simple premise that impactors, and the craters they produce, conform (approximately) to a power-law size–frequency distribution; which implies that an estimate for the magnitude of the single largest crater implicitly constrains the sizes of all other craters large enough to be significant contributors to the final megaregolith. The key issue of the (typical or average) size of the largest crater is admittedly difficult to constrain. For now, suffice to note that 4 Vesta’s largest crater is a 460 km basin whose transient crater probably had a diameter of approximately 310 km, or 0.58 times the diameter of Vesta itself (Asphaug 1997; Thomas et al. 1997). Depth provenance for ejecta from an individual crater, as implied by Maxwell’s (1977)Z-model assuming Z ∼ 2.9 (a depth/diameter ratio for the excavation zone of precisely 0.1 implies Z = 2.734; however, as explained in the text, the precise choice of Z is not important for this diagram). As indicated by, e.g., Holsapple (2003), in the small-scale “strength” regime at any given impact velocity vi (and an impact angle not extremely far from 45°) the transient crater diameter Dt will be in approximately fixed proportion to the impactor diameter di; e.g., if vi = 5 km s−1 (the typical asteroid–asteroid encounter velocity), Dt will be ≈10di. As the influence of gravity g increases for very large craters, the Dt/di ratio tends to decrease. Still, we can constrain the b of the crater size power law (Equation 4) indirectly by constraining the exponent β for the analogous impactor-size power law: Ncum(d) = cd−β. In general, 2.5 is the canonical value for β in a population that undergoes collision-fragmental selection (Dohnanyi 1969). But the present-day asteroid population shows a complex distribution (e.g., Asphaug 2009), probably as a result of various size dependent, especially g-related, effects. Bottke et al. (2005a; cf. O’Brien and Greenberg 2005) inferred that this population, although greatly reduced in numbers, probably has a size–frequency distribution similar in shape to the population during the late stages of major accretion. In this distribution, β is approximately 2.1 overall, but 1.94 for the d range of 1–50 km, approximately 1.63 for the range of 50–100 km, and it increases toward 3 for d > 100 km. The details of the size distribution have implications that are best evaluated after an assessment of constraints on DL. For bodies of the relevant size range (dB > 100 km), observational constraints on DL/dB are in short supply. As reviewed by Leliwa-Kopystyński et al. (2008), the data set for asteroids and satellites (other than the Moon) includes only one body known to combine rocky mineralogy, dB > 53 km, and a well-determined largest crater size: Vesta, with dB ∼ 530 km and DL/dB ∼ 0.58 (Leliwa-Kopystyński et al. indicate a value of 1.739 for what they call “D/R,” but this ratio involves the diameter of the largest final observed crater, not, as with DL/dB, the largest inferred transient crater). Bodies with dB << 100 km are not only irrelevant; their largest observable craters probably tend to be much smaller than their true largest craters. Asphaug (2008) noted that impact-seismic shaking effectively smoothes the surfaces of smaller bodies, and inferred that the size dependency of this process accounts for a correlation between apparent DL/dB and dB. Resurfacing can also be a problem with larger bodies. Vesta and the Moon were probably hot enough for long enough (a “magma ocean” is often invoked for both) that some of the largest impacts left no manifestation on the present surfaces. Dynamical models indicate that in general, especially during the late stage of accretion (∼2 Ma after its onset) when encounter velocities began to approach modern values even as multi–hundred-kilometer planetesimals became common (Weidenschilling and Cuzzi 2006), which incidentally was at about the same time heat build-up from 26Al climaxed (Hevey and Sanders 2006), planetesimals probably had to endure impacts energetic enough to challenge their ability to survive. Beyond some impact-energy limit, ejected matter begins to escape more than it lands. As for any given target-body size the transient crater diameter Dt scales as the cube root of impact energy, the transition from growth to catastrophic disruption is quite abrupt, in terms of DL/dB. Thus, unless b is much less than 2, DL is probably within a few tens of percent of the catastrophic-disruption crater diameter DC (expressed in this work, like DL, in terms of the transient crater diameter). Housen et al. (1979) estimated that DC is of order 1/3 to 2/3 of dB, depending on the size and mechanical strength of the target body. By contrast, Nolan et al. (2001) suggested that shock-induced fracture in advance of crater excavation flow reduces the potential for catastrophic mass loss, which results in a DC/dB ratio of 1.3 for even a small asteroid (Gaspra, dB modeled as 12.6 km) being impacted at 5 km s−1. As suggested by Bottke et al. (2005a, 2005b), the disruption threshold can be modeled in terms of dC, the diameter of the catastrophic impactor: The critical impactor mass for catastrophic-disruption mC, expressed as the ratio mC/mB, calculated as a function of target-body diameter dB for a range of impact velocities, by extension of the QC model of Bottke et al. (2005a, 2005b). Also shown for comparison is the 5 km s−1mC/mB implied by the lower QC estimate of O’Brien and Greenberg (2005). For translating between dC/dB and the catastrophic-destruction crater diameter ratio DC/dB (and more generally between di/dB and Dt/dB), I developed parameterizations (i.e., a series of polynomial fits) of Dt results for various combinations of di and dB using Holsapple’s (2003) implementation of π-scaling for crater dimensions. Additional inputs were an impact angle of 45°; rocky physical characteristics for both impactor and target, i.e., densities of 3000 and 3200 kg m−3, respectively; and g and escape velocity calculated as a function of dB under the assumption of uniform density ρ within the target; i.e., g = (4/3)πGρBrB and vesc = (2GmB/rB)1/2. π-Scaling indicates that for impact velocity vi of 5 km s−1 the Dt/di ratio is uniformly close to 10 in even the largest of craters on a dB <<100 km body, but decreases to, e.g., 7.4, 5.4, 3.7, 2.5 in Dt/dB ∼ 1.0 events for dB = 100, 200, 400, and 800 km, respectively. Under the assumption that accretion was oligarchical (not runaway), so that the asteroids and planetesimals are/were stochastic survivors from a series of near-catastrophic collisions, Poisson statistics and the power-law size distribution, Ncum(d) = cd −β, can be applied to estimate the probability of dL being smaller than dC by a given factor. The Poisson equation for probability of zero outcomes is simply p0 = e−n, where n is the number expected from ideal sampling of the overall population. By this method (Fig. 6; with relative d translated into relative mass assuming simple d3 proportionality), for β ∼ 2, the most likely outcome is mL/mC ∼ 0.45. This result varies as a function of β; a mL/mC range of 0.35–0.59 is implied by varying β from 1.5 to 3. Figure 7 shows the DL/dB ratios that result from assuming mL/mC = 0.25–0.75. As a rule of thumb, for bodies of the size range under consideration, mL/mC ∼ 0.5 translates into DL/dB ∼ 1.0. Poisson-statistical probability for the largest mass of impactor mL in terms of mL/mC ratio, assuming that the body is a fortunate survivor among many that have been catastrophically disrupted, and that the population of impactors conforms to the power-law size distribution with slope β (the β shown refers to the diameters of the impactors, albeit this chart shows diameter translated into mass). The largest (transient) crater DL/dB, calculated as a function of target-body diameter dB assuming that the largest crater is formed with mL/mC = 0.5; i.e., the impactor mass mL is 50% as massive as the catastrophic-disruption mass mC, as calculated by extension of the model of Bottke et al. (2005a, 2005b). Translation from that mass mL of the largest impactor into (for an assumed impact velocity) its DL is modeled based on Holsapple (2003), assuming “rock” impacts into “hard rock” targets (for further description, see text) at 45° and the indicated velocity. Light-dashed curves show results assuming mL/mC = 0.25–0.75. Returning to the problem of constraining b, the β(di) of the asteroidal size distribution (Fig. 1) (Bottke et al. 2005a) can be translated into a β(mi/mC), by using Equation 5 to derive dC, and thus mC, for any given target-body size and impact velocity. Since β is a measure of slope, seemingly small bumps and dips on the size distribution become magnified, so that results (Fig. 8) for large mi/mC in the relevant dB range are remarkably structured, with a peak at approximately 80 km and β ∼ 2.5, a deep valley at approximately 220 km and β ∼ 1.3, and then a gradual rise toward approximately 800 km and β ∼ 3. One complication is that gravity’s effect of limiting the growth of large craters causes the ratio Dt/di to decrease (for any given vi) with increasing di, so the size–frequency exponent b for transient crater diameters is slightly greater than the corresponding β for impactor diameters (i.e., the distribution’s slope, for large, high-g bodies, is mildly but systematically steeper). I have not attempted to model the minor increase between β and the corresponding b, except by taking mL/mC ∼ 0.5, and DL/dB ∼ 1.0 (rather than 0.45 and ∼0.9), as the most likely outcome implied by the Poisson-statistical approach at the end of the previous paragraph. The size–frequency exponent β implied by the modern asteroids (Bottke et al. 2005a) shown in relation to the target-body diameter dB and five values of the impactor mass ratio, mi/mC, i.e., the mass of an impactor ratioed to the catastrophic-disruption impactor mass (at vi of 5 km s−1) for the given dB. Another complication is that in late-accretionary times the prevailing vi was lower. Weidenschilling and Cuzzi (2006) estimate that even after 2 Ma of accretion, typical impact velocities were still “a few tenths to approximately 1 km s−1.” The implied impactor diameter di to yield a given crater Dt scales as 1/vi0.5. A lower vi shifts the β spectrum’s features to smaller dB; e.g., with vi, = 2.5 km s−1, the β ∼ 1.3 valley shifts to approximately 160 km, and the two peaks shift to approximately 75 and 400 km. In summary, DL/dB is unlikely to be much less than 1. For the near-largest impacts, b ∼ 2 is probably conservatively low as a single value to represent the general populations of craters and target bodies considered in this work. For many of the largest craters on the largest bodies, particularly if the cratering occurred mostly during the late stages of accretion while the prevailing vi was increasing but still much less than 5 km s−1, b may have been closer to 3. Figure 9 shows the final results from this model: average accumulated ejecta layer thickness zA (in units of rB, after all 216 craters form) as a function of assumed DL/dB ratio. The sequence of crater formation, although potentially marginally significant, is not crucial. The four main curves in the figure are each based on a set of 10 randomized sequences of formation for the 216 craters. But as the two light-dashed curves indicate, even under the extreme assumption that the craters form in a sequence of size (either smallest to largest or largest to smallest), results are only marginally different from the average randomized-sequence result. The crater-formation sequence is slightly consequential for models assuming a high b; e.g., for b = 3 and DL/dB in the range 0.4–1.0, zA could in principle vary, between the extremes of the decreasing crater size model and the increasing crater size model, over a factor of 1.4. Figure 10 shows the same model results translated, by straightforward conversion from units of rB for zA into units of kilometers, for a range of different target-body diameters. Results for relative thickness of the global ejecta accumulation zA as a function of the size of the largest crater (DL) and the crater size–frequency exponent (b). The heavy-continuous curves represent averages from 10 different models (for each b value in the sequence 1.5, 1.75, 2, 2.25 … 3), each with 65,000 model craters forming in a different random sequence. The thin-dashed curves indicate, for the b = 2 model, results based on extreme variants of crater-formation order: The curve on the high-zA side of the main, random-order curve represents a model with craters forming (implausibly) in sequence from small to large; the curve on the low-zA side of the main, random-order curve is based craters forming (implausibly) in sequence from large to small. Global ejecta accumulation thickness zA expressed in kilometers, as a function of the size of the largest crater (DL) and two different assumed values for the crater size–frequency exponent (b), as calculated for a range of target-body diameter dB. These results were derived from the same averaging of ten 65,000-crater models as described for Fig. 3. Assumptions include target body consisting of Holsapple’s “hard rock” (ρB = 3200 kg m−3), impactor 3000 kg m−3 hitting at vi of approximately 5 km s−1 and 45° impact angle. Also shown on the assumption that b = 2 are the sizes of the largest craters on asteroids Vesta (V), Amalthea (A), Mathilde (M), Ida (I), and Gaspra (G), along with the Moon (crescent symbol) and Phobos (P), as compiled by Asphaug (2008). The Moon is plotted under the assumption that its largest impact basin is South Pole-Aitken, 2500 km in d. Under the hypothesis that Procellarum Basin is also an impact structure whose rim (or main ring) is 3200 km in diameter (Wilhelms 1987), the Moon’s DL/dB would shift to approximately 0.42. In Fig. 11, the same results (9, 10) have been recast with the largest impactor mass ratio mL/mB taking the place of DL/dB for the x-axis. Masses were derived from diameters assuming the same densities as employed in the modeling of Dt/di, i.e., Holsapple’s (2003)“rocky” densities. An interesting effect follows from the decrease in Dt/di (for any given vi) with increasing dB. By Equation 2b, ejecta yield (z1/rB) scales as the cube of Dt/dB. Thus, the factor by which Dt/di decreases with increasing dB (Holsapple 2003) gets cubed in the evolution of zA. The net effect is that even though the modeling implies a uniform ejecta accumulation zA/rB ratio for any given DL/dB (Fig. 9), in terms of absolute thickness (in kilometers) zA remains relatively constant for any given dL/dB (or mL/mB) over a huge range in dB (Fig. 11). Readers with an interest in specific target-body sizes (and trusting the Bottke et al. 2005a model for QC plus their argument that the size–frequency distribution of planetesimals is closely mirrored by the present-day asteroids) may want to fine-tune these results based on the β variations shown in Fig. 8. Global ejecta accumulation thickness zA expressed in kilometers, as a function of the mass of the largest impactor (mL) and two different assumed values for the crater size–frequency exponent (b), as calculated for a range of target-body diameter dB. These results were derived from the same averaging of ten 65,000-crater models as described for 8, 9. Five color-filled squares indicate (for b = 2 curves) the catastrophic-disruption mass mC/mB as estimated using the Bottke et al. (2005a, 2005b) approach (Fig. 5; assuming vi = 5 km s−1). Assumptions include target body consisting of Holsapple’s “hard rock” (ρB = 3200 kg m−3), impactor 3000 kg m−3 hitting at vi of approximately 5 km s−1 and 45° impact angle. Assuming that the largest event involves a mL that is a large fraction of mC as calculated by the (extended) Bottke et al.’s (2005a, 2005b) model (Fig. 5; for impact velocity vi of 5 km s−1), we arrive at a simple plot of body diameter dB versus expected thickness zA of accumulated ejecta (Fig. 12). Within the overall uncertainty of the modeling, the relationship is essentially linear at zA/dB ∼ 0.04(mL/mC) (valid for mL/mC ∼ 0.25–0.75). Results for the mean global ejecta accumulation thickness zA for a growing planetesimal as a function of the diameter of the body, shown for b = 2 and a range of assumed values for mass of the largest impactor mL in relation to the catastrophic-disruption mass mC; with mC estimated using the approach of Bottke et al. (2005a, 2005b) for vi = 5 km s−1. As illustrated in Fig. 13, the single biggest crater typically contributes a large fraction of the total ejecta accumulation, especially in cases of low b combined with a high DL/dB ratio. Consider, for the nominal b of 2, the case of a largest crater with DL/dB similar to the Dt/dB of Vesta’s great southern basin, approximately 0.58 (Vesta’s dB ∼ 530 km, and per Asphaug 1997, Holsapple 2003, etc., the Drim of approximately 460 km implies Dt ∼ 310 km). This one crater will produce on average (depending, inter alia, on when it forms relative to other large craters) approximately 40% of the body’s total accumulation of otherwise unexcavated ejecta. However, in terms of the present surface layer about to be studied by Dawn (Russell et al. 2004), the basin’s ejecta probably so greatly churned the surface upon landing at distal locations (cf. Haskin et al. 2003) that the basin does not necessarily dominate the mix of surface debris except within ∼2Rt (∼300 km) of its rim. Fraction of accumulated ejecta contributed by the single largest crater, shown as a function of b for three different values of DL/dB (the three corresponding approximate mL/mB ratios for impacts at 5 km s−1 into a 100 km [dB] “rocky” target body are 3.6 × 10−6, 9 × 10−5, and 2.3 × 10−3). These results were derived from the same averaging of 65,000-crater models, with the craters formed in 10 different randomized sequences, as described for Fig. 8. As noted in the figure, these results are not corrected for the greater proportion of launch-off associated with large events, especially important for small bodies. Some caveats are in order. Realistically, for bodies near the smaller (100 km) end of the size range under consideration, dC is probably sensitive to the material properties of the target body, which means that the true uncertainty in mC, as derived by extension of Bottke et al.’s (2005a, 2005b) model for QC and dC/dB, is hard to even estimate. Moreover, for bodies other than growing planetesimals there is no assurance that mL would bear a strong relationship to mC. If Bottke et al.’s (2005a, 2005b) model for estimating dC/dB were applied to the Moon, the predicted diameter of a catastrophic impactor (assuming vi = 20 km s−1) would be approximately 1270 km. For comparison, the biggest definite lunar impact basin, South Pole-Aitken (Dt ∼ 1100 km), probably formed from an impactor with di of roughly 300 km (Holsapple 2003; of course, the Moon’s size and origin as a natural satellite probably led to an unusually prolonged history of resurfacing by igneous activity, in comparison to most planetesimals). The accuracy of the model probably diminishes (most likely tending to underestimate zA; see next section) as DL/dB increases past approximately 1. For a planetesimal evolving during the middle-late stages o" @default.
W1684523249 created "2016-06-24" @default.
W1684523249 creator A5038481114 @default.
W1684523249 date "2011-01-01" @default.
W1684523249 modified "2023-09-24" @default.
W1684523249 title "Ejecta-megaregolith accumulation on planetesimals and large asteroids" @default.
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