Crater Density Predictions for New Horizons flyby target 2014 MU69
Sarah Greenstreet, Brett Gladman, William McKinnon, JJ Kavelaars, Kelsi Singer
aa r X i v : . [ a s t r o - ph . E P ] J a n Crater Density Predictions for New Horizons flybytarget 2014 MU69
Sarah Greenstreet
B612 Asteroid Institute, 20 Sunnyside Ave, Suite 427, Mill Valley, CA 94941DIRAC Center, Department of Astronomy, University of Washington, 3910 15th AveNE, Seattle, WA 98195
Brett Gladman
Department of Physics & Astronomy, 6224 Agricultural Road, University of BritishColumbia, Vancouver, British Columbia
William B. McKinnon
Department of Earth and Planetary Sciences and McDonnell Center for Space Sciences,One Brookings Drive, Washington University, St. Louis, MO 63130, United States
J. J. Kavelaars
National Research Council of Canada, Victoria, BC, Canada
Kelsi N. Singer
Southwest Research Institute, 1050 Walnut Street, Suite 300, Boulder, CO 80302, UnitedStates
Abstract
In preparation for the Jan 1/2019 encounter between the New Horizonsspacecraft and the Kuiper Belt object 2014 MU69, we provide estimates ofthe expected impact crater surface density on the Kuiper Belt object. Us-ing the observed crater fields on Charon and Pluto down to the resolutionlimit of the 2015 New Horizons flyby of those bodies and estimates of theorbital distribution of the crater-forming projectiles, we calculate the numberof craters per unit area formed as a function of the time a surface on 2014MU69 has been exposed to bombardment. We find that if the shallow crater-size distribution from 1-15 km exhibited on Pluto and Charon is indeed dueto the sizes of Kuiper Belt projectiles, 2014 MU69 should exhibit a surface
Preprint submitted to Elsevier January 3, 2019 hat is only lightly cratered below 1 km scale, despite being bombarded for ∼ ≃
1. Introduction
The upcoming flyby of the New Horizons spacecraft by the cold classicaltransneptunian object (TNO) 2014 MU69 (hereafter referred to as MU69)will offer the first up-close look (sub-km resolution) of a small outer Solar Sys-tem body in its formation environment, and will provide the first opportunityto observe a high-resolution cratered surface of a TNO other than those inthe Pluto system, imaged by New Horizons in July 2015 (Stern et al., 2015;Moore et al., 2018).The classical Kuiper belt appears to be divided into at least two sep-arate inclination components (Brown, 2001). The ‘cold’ classical Kuiperbelt (Kavelaars et al., 2008) contains the vast majority of the TNOs on low-eccentricity orbits of low inclination in the semimajor axis range 42 . < a <
47 au (Petit et al., 2011). The existence of large separation TNO binariescombined with the low orbital inclination distribution suggests that the coldclassicals represent a reservoir of the primordial proto-planetary disk beyond40 au (Parker and Kavelaars, 2010). This the only sub-population thought tohave been in place since the formation of the Solar System. The low orbital2nclination and eccentricity of MU69’s orbit (Porter et al., 2018) place thisobject firmly within this region and thus MU69 is likely to have formed atthis large heliocentric distance and be the most primitive outer Solar Systembody yet visited. There is considerable structure in the a and eccentricity( e ) space of the cold population, and it is has been split (Petit et al., 2011)into a ‘stirred’ component crossing the whole cold a range, and a much moreconfined ‘kernel’ of cold objects near a = 44 au and e ≃ .
05; MU69 isconsistent with being in this kernel.The other Kuiper Belt sub-populations (characterized by broader orbitalinclination distributions) have been postulated to have formed closer to theSun and transplanted to their current location in the final stages of planetformation (e.g. Levison et al., 2008). The postulated 500 Myr delay in theinstability in the often-cited Nice Model (Gomes et al., 2005) has been re-treated from (Mann, 2018); see Nesvorn´y (2018) for a recent review. Thedesirable implantation properties for creating Kuiper Belt structure, how-ever, still hold even if the instability process occurs early in Solar Systemhistory (Gladman et al., 2012). In the scenario that MU69 has always beennear its current orbit, a hypothetical metastable phase (which was of interestfor Pluto’s early cratering since Pluto is part of the metastable population)is irrelevant because during the early phase the population closer to theSun is not cratering MU69. In either case, the ‘hot’ populations are ulti-mately emplaced during a relatively brief ( <
1% of the Solar System’s age)period in which the cold population must not be dynamically excited (eg.,Dawson and Murray-Clay, 2012). While we thus concentrate our calcula-tions on the last 4 Gyr of bombardment, we argue below that the brief phasein which the objects where scattered out through the Kuiper belt, with somesmall fraction becoming the hot classical Kuiper belt we see today, cannotcontribute a large change in MU69 cratering, especially given that we find3hat the cold populations dominate the impactor flux.The observed crater density on Pluto and Charon by the New Horizonsspacecraft during its flyby of the Pluto system in July 2015 showed a changeto a shallower size distribution (Singer et al., 2019). We assume here that thistransition is caused by a similar paucity of small impactors, and combine thederived impactor size distribution with a Kuiper belt orbit distribution modelto compute the impactor flux, impactor speed distributions, and resultingcrater formation rates on MU69.
2. The impactor size distribution
Calculating crater formation rates requires a knowledge of the impactorpopulation’s orbital distribution (which determines the impact probabilitiesand impact speed distribution) and its diameter d distribution in order tocompute the scale of the resulting craters of diameter D . The differentialnumber of objects dN as a function of absolute H -magnitude behaves lo-cally as dN ∝ αH , where the exponential index α is also referred to as thelogarithmic “slope” (hereafter referred to simply as the slope). This corre-sponds to a cumulative power law distribution in the projectile diameter with N ( < d ) ∝ d − α . The conversion for objects with absolute g-band magnitude H g and scaling to an albedo p of 5% is d ⋍
100 km r . p . . − H g ) (1)where we see that H g =9.16 corresponds to 100 km. We have chosen tomake a single pre-encounter crater-density prediction, based on telescopicobservations and the results of the New Horizons flyby of Pluto and Charon.We use one size distribution (Fig. 1) for all of the various Kuiper Belt sub-populations. The steep observed Kuiper Belt size distribution for TNOs d >
100 km rolls at this diameter to a “knee” size distribution, as used4 km 10 kmH =14H =19 H =9 log dN
H =24100 m
Knee absent~1 km ~6 km absent
Elbow
100 km Impactor dExpected range of2014 MU69 craters KB direct observations~Crater D
Figure 1: Cartoon schematic of the H g -magnitude differential size distribution. TheKuiper belt observations are well calibrated down to H g ≈
10, but smaller than theknee at H g ∼ α ≃ . α ≃ .
4. Singer et al. (2019) find the impactorsize distribution from craters observed on Charon requires a second change to a slope of α ≃ .
15 for d . d are converted to rough MU69crater diameters D assuming a common impact speed of 300 m/s. The expected range ofcraters observable by New Horizons covers D ≈
200 m to D ≈
20 km (created by cold-beltimpactors ranging from d ≈ . − in Greenstreet et al. (2015, 2016); the slope α =0.4 below this knee extendsdown to another slope change at a scale which Singer et al. (2019) denoteas the “elbow”, visible on both Pluto and Charon. On Charon, this cor-responds to a crater size of D ≈
13 km, which for typical Charon impactspeeds implies projectile d ≈ H g ≈ .
5. We connect the H g < .
16 population estimates from Petit et al. (2011) and Gladman et al.(2012) to the H g < . α ∆ H =10 ((0 . ∗ . − (0 . ∗ . ≈ , α ≃ .
15, and we assume this slope is that comingfrom the impactor size distribution and directly map it back to the projec-tiles. Fig. 1’s horizontal axis also shows the expected crater diameter causedby a typical cold-population impactor striking MU69 (see below). If thiscrater size distribution is in fact present on MU69 it will be a dramatic con-firmation of a shallow Kuiper Belt size distribution in the roughly 0.1–2 kmdiameter range.
3. Methods
The methods for computing the current impact fluxes and cratering ratesonto MU69 are identical to those in Greenstreet et al. (2015, 2016), to whichwe refer the reader for the details; below we only mention any deviationsfrom the methods used in the previous paper.
MU69 sits in the heart of the cold classical Kuiper Belt’s kernel withthe encounter target having a = 44 . e = 0 .
04, and heliocentric J2000orbital inclination i = 2 . o (Porter et al., 2018). We adopted the same or-bital distributions and N ( H g < .
0) population estimates for the variousKuiper Belt sub-populations as before and computed the impact fluxes ontoMU69. We added to the analysis the population of TNOs in the 7:4 mean-motion resonance with Neptune (whose population is small and was thus notused for the Pluto/Charon analysis), because the resonant semimajor axisof a ≃ . The ¨Opik collision probability code used in this study is the same as usedpreviously, with the only change being the new target body. MU69’s gravi-tational focusing is negligible, but is included. Unlike computing the impactflux onto Pluto from the various sub-populations, 2014 MU69 is not locatedwithin a mean-motion resonance nor is it undergoing Kozai oscillations. Itwas thus not necessary to provide a correction factor to the collision probabil-ities provided by the ¨Opik collision probability code to take into account howthe dynamics allowed Pluto to avoid orbital intersections with some portionsof some sub-populations. Our code provides the impact probabilities for theensemble of objects in each orbit and the probability-weighted impact speeddistribution onto MU69.The impact speed distribution is remarkable (Fig. 2). Essentially all im-pacts onto MU69 are less than the ∼ p wave speed in solid water ice;thus if MU69 is a coherent body these impacts are subsonic, where the craterscaling laws are less well-established (see discussion below and in Singer et al.(2013)). The most extreme behavior is that, because of their similar orbitsto MU69, the cold classicals have tiny impact speeds, peaking around only300 m/s, similar to the p wave speed in unconsolidated sands - which maybe a better structural analog to MU69’s surface. While such speeds areabove MU69’s escape speed, they are essentially unknown for primary pro-jectiles in the Solar System and would only be seen elsewhere in the contextof non-escaping, secondary projectiles. Fig. 2 shows, as expected, the 7:4resonant objects have a range of encounter speeds including serendipitousclose encounters with MU69 at similarly low velocities due to their very sim-7 igure 2: Impact velocity spectrum onto MU69 for each Kuiper Belt sub-population. Eachsub-population’s distribution is separately normalized. The cold main classical impactvelocity distribution includes both the stirred and kernel sub-components, because theirspeed distributions are similar. The bimodal nature of the (nearly negligible) inner classicalbelt is due to a gap in that population’s orbital inclination distribution (Petit et al., 2011).Almost all impactors on MU69 are travelling less than the speed of sound in coherent waterice. ilar semimajor axes. Unsurprisingly the scattering objects, which have largesemimajor axes, peak at the highest impact velocity ( ≈ ≈ . Table 1 shows the calculated ¨Opik collision probabilities (/yr/TNO) ontoMU69 for each Kuiper Belt sub-population (this collision probability is in-dependent of the projectile size). This is converted to an impact rate bymultiplying by the estimated corresponding population at some scale. To8ick a single number, we have chosen to tabulate the rate of projectiles ofthe size scale of the elbow or larger ( H g < . d & d & <
10% of the impactor flux. The classical inner populationis essentially negligible because many of its members do not intersect theMU69 orbit. Finally, the population of non-resonant TNOs with semimajoraxes beyond the 2:1 resonance (the ‘Classical Outer’ population) contributesabout 6% of the impactors; this population has many orbits with perihe-lion just inside MU69’s perihelion and as Fig. 2 shows these impactors have9edian impact speeds U ∼ Kuiper Belt H g < . ¨Opik d & km % of D > km % ofSub-Population Population Impact Impact Total Cratering TotalType Estimate Probability Rate Impact Rate Cratering(/yr/TNO) (/Gyr) Rate (/Gyr) Rate S.O. (15 AU ≤ a ≤
200 AU)S.O. ( a >
200 AU) 1.8e8 1.0e-22 1.8e-5 0.1 2.1e-3 0.2Classical Inner 5.5e6 5.6e-22 3.1e-6 0.0002 2.6e-4 0.0002
Classical Main H
Classical Outer 1.5e8 6.8e-21 1.0e-3 5.9 9.9e-2 9.3Resonant 3:2 2.5e7 2.7e-20 6.8e-4 4.0 5.8e-2 5.4Resonant 2:1 7.0e6 2.3e-20 1.6e-4 0.9 1.4e-2 1.4Resonant 5:2 2.3e7 1.2e-20 2.8e-4 1.7 2.6e-2 2.4Resonant 7:4 5.5e6 5.0e-20 2.8e-4 1.7 1.8e-2 1.7
Total 0.017 100.0 1.1 100.0
Table 1: ¨Opik collision probability calculations, d & D > H g < . d & p = 5%), which is thelocation of the elbow. Impact probabilities are (/yr/object). Impact rates are (/Gyr) anddetermined using the number of H g < . D >
Our derived impact fluxes, when expressed as impacts per year per km of target (assuming an effective spherical radius of r ≈
10 km), are abouttwice that onto Pluto, reflecting the higher spatial density of the MU69environment. This relative flux is in agreement with JeongAhn et al. (2018,to be submitted) who also conclude that the cold classicals should provide ∼
80% of the impacts.
For the purposes of this paper we assume that MU69 is an unconsolidated,low-density body. We convert between crater diameters D and projectile10iameter d via D = 8 . U km/s g cm/s ! . (cid:18) δρ (cid:19) . d . km km (2)where U is the impact velocity (in km/s), d is the impactor diameter, andthe gravitational acceleration on the surface of MU69 is g ≈ . . Weassume both impactor δ and target ρ (at surface) densities are δ = ρ =1 . , although the value is unimportant as long as they are the similar.The coefficients in Eq. (2) are appropriate to unconsolidated sand or theregolith in the gravity regime (Singer et al., 2013), and are based on well-established scaling from laboratory and numerical simulations (Holsapple,1993; Housen and Holsapple, 2011; Greenstreet et al., 2015, 2016; Singer et al.,2019). This procedure should provide a reasonably accurate estimate ofcrater size (to within +/- 50%), provided neither the impact speed northe cratering efficiency (excavated crater mass/impactor mass) are too low.Well-defined secondary craters are seen on icy satellites for speeds downto ≈
200 m/s, so we anticipate that most TNO impacts onto MU69 willform craters; the lowest-speed impactors may be accretionary, however, notcrater-forming. Despite the difference of physical regime, Eq. 2 gives quitesimilar results to those obtained if we use the scaling law we deployed inGreenstreet et al. (2015) appropriate for non-porous coherent surfaces; whenpropagated through the entire analysis the resulting crater densities pre-sented below are nearly identical. Thus, uncertainties in the scaling law is oflittle consequence compared to the much larger uncertainties that we expectto arise because of the sparse crater statistics.First note that for the tiny U ≃ . D ≃ d = 1 km projectile, and thus the crater/projectile ratio is somewhatsmaller than the typical 10-20 common elsewhere in the solar system. Byintegrating the crater production over all speeds of all sub-populations, we11 .1 1 10 1000.00010.0010.010.11 Figure 3: Logarithm of crater density ( ) larger than a given crater diameter D on MU69’s surface versus the logarithm of the crater diameter for an impactor sizedistribution with a both a knee (not visible in this plot) and elbow (shown as the gradualslope change near D ≈
10 km) at various surface ages. The solid black line is the craterequilibrium curve from Melosh (1989). The horizontal line at ≈ − corresponds to 1crater/MU69 surface, and the vertical line is an estimate for the smallest craters that willbe visible in the best MU69 images. The black squares at the 1 crater/MU69 surfaceline correspond to the black squares in Figure 4. The change in slope at D ≈
10 kmcorresponds to the elbow break in the impactor size distribution, but will not be visiblein the crater data; note that this change is gradual because of the large fractional spreadin impact speeds U present. D >
D > D limit, as their craters are smaller than those produced by thehigher-speed populations; the cold population still manages to contributethree-quarters of the D > D ∼
200 m. Even morespectacularly, given that the surface area of MU69 is only ∼ ,the 4 Gyr bombardment predicts only ∼ ∼
200 m resolution limit of MU69, and note that only half of the bodyis likely to get this highest-resolution data. As long as craters are visible,however, this predicted level of cratering would provide strong confirmationthat the paucity of Pluto/Charon craters smaller than the elbow scale (atcrater
D <
13 km for Pluto/Charon or impactor d . Figure 4: Relative crater frequency plot of the same information in Figure 3. The blacksquares correspond to 1 crater/MU69 surface on the cumulative plot (Figure 3), so craterslarger than the dots will likely not be visible on MU69’s post-accretionary terrains, ex-cept by statistical fluctuation. The fact that R values rise for increasing D is due to therelatively shallow projectile size distribution implied by the Pluto/Charon surfaces. As-suming MU69 preserves the craters integrated over all of Solar System history, this levelof cratering in the visible portion will be sparse statistically. Fig. 4 displays our results in ‘R-plot’ formulation, which can be thoughtof as roughly the fraction of the surface covered in craters at each crater scale14 . The rise with increasing diameter over the visible range would be verycharacteristic of the projectile population derived from THE Pluto/Charoncrater data. If the (probably sparse) crater counts do indeed match thesepredicted values, it would strongly argue that the current Kuiper belt size dis-tribution is extremely shallow in the 100 m to 1 km diameter range probed byMU69 and the Pluto-Charon crater counts. This would then offer the strongpossibility that the current Kuiper Belt retains the primordial planetesimal-building size distribution.
4. Discussion and Conclusion
Based on the above results, we conclude that bombardment over the en-tire age of the Solar System is insufficient to more than modestly crater 2014MU69 near the expected resolution limit. That is, if during its formation pro-cess, accretion activity was sufficient to erase any craters that may have beenacquired during its assembly, MU69 will be modestly cratered today. It wouldthus be incorrect to conclude that a lightly cratered surface implies thatMU69’s surface has been recently reset (or more extremely, that MU69 hasbeen recently created as a collisional fragment from a larger TNO). Charon’sextensive cryovolcanic plain (informally named Vulcan Planitia) is an exam-ple of this; it is unsaturated and the observed crater densities correspond tothose expected from bombardment for ≈ ∼
10 km) size. The latterare thought to essentially all be fragments produced after the accretionaryepoch, and thus are not ‘primordial’ objects directly. In contrast, MU69 willnow look very much like it did at its formation epoch (in the sense that im-pact processes have not made global structural changes to the body nor evengreatly affected more than a modest fraction of the surface). Despite MU69’s15ow gravity, even the largest craters that form are unlikely to provide enoughdistant ejecta to erase 200 m craters; ejecta dispersal will be even more lim-ited if MU69 is very porous, as seen at asteroid Mathilde (Veverka et al.,1999).Looking beyond the values of the crater densities themselves, no so-lar system body has ever been studied where the majority of the primarycratering is from significantly subsonic projectiles. This could result incraters with lowered depth/diameter ratios as seen for secondary craters(e.g., Bierhaus and Schenk, 2010), and perhaps produce a morphologicallyvisible difference between craters formed by impactors coming in from thecold-classical population versus those which tend to be in the 3-4 km/s range.Seeing such differences will require well-resolved craters, which we expect tobe modest in number even in the best MU69 images. For the slowest impactspeeds, we do not expect crater formation at all, but rather, accretion ofthe impactor material, either as coherent mounds or dispersed debris fields(“paintball” patterns). In principle these speed differences might be able tohelp distinguish between craters (or other features) formed by cold classical(kernel or stirred) impactors versus those from the other sub-populations.The uncertainty in the details of the dynamical state of the early outerSolar System is only a small concern to our interpretation, due to the domi-nance of the cold component’s impactors. Under a scenario that all the hotpopulations were 100 times more populous for a brief ( ∼
50 Myr) of SolarSystem history (and a 100 × enhancement throughout that entire interval isunlikely), this would still only double hot-population contributions to thecratering rate; Table 1 shows that even in this case the cold classical projec-tiles still dominate and the total cratering only rises by a few tens of percent.This is insufficient to qualitatively alter our conclusions that MU69 will bedominated by subsonic projectiles and modestly cratered. If the object is16eavily cratered, our interpretation would be that this is a crater field pre-served from the initial assembly epoch of MU69 itself during the phase inwhich it accreted from smaller components.Lastly, and most exciting, if the crater density and diameter distributionare consistent with bombardment over the age of the Solar System by theprojectile distribution we derive based on the Pluto and Charon crateringresults, this will serve as convincing proof of a very shallow sub-km sizedistribution in the Kuiper Belt itself (or, at least, in the cold populationwhich dominates the MU69 crater production rate). Although Singer et al.(2019) already argue against the idea that surface geology on Pluto andCharon could create the shallow size distribution near and below the elbowscale (a crater size distribution which is similar across a variety of terrainson both bodies), such crater degradation ideas would be extremely unlikelyto work in the same way on tiny MU69. A signature with crater R values ∼ α ≃ .
15 distribution isso shallow there are not enough projectiles to disrupt the rapidlly shrinkingtargets as one moves down the size distribution. The current Kuiper Beltsize distribution (at least of the cold population) would then be that whichplanetesimal accretion models would have to create, and the cratering recordpreserved on the already-imaged objects is directly providing constraints onthe planet-building process. 17 . Acknowledgements
S. Greenstreet acknowledges support from the B612 Foundation. B. Glad-man acknowledges support from the Canadian Natural Sciences and Engi-neering Research Council. W.B. McKinnon, J.J. Kavelaars, and K.S. Singeracknowledge support from the New Horizons project.