Cometary and Meteorite Swarm Impact on Planetary Surfaces

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 87, NO. B8, PAGES 6668-6680, AUGUST 10, 1982

JOHN D. O'KEEFE AND THOMAS J. AHRENS

SeismologicalLaboratory, Division of Geologicaland Planetary Sciences California Institute of Technology,Pasadena, California 9! ! 25

The velocity flow fields, energy partitioning, and ejecta distributions resulting from impact of porous (fragmented)icy cometarynuclei with silicateplanetary surfaces at speedsfrom 5 to 45 km/s are different thanthose resulting from the impactof solidice or silicatemeteorites. The impactof ! g/cm3 icespheres onto an atmospherelessanorthosite planetary surface inducescratering flows that appear similar to those induced by normal density anorthositemeteorite impact. Both of these impactors lead to deep transient cratercavities for final craterdiameters less than ---! to ---10 km and for escapevelocities •Moon, Mercury, and Mars. For objectswith escapevelocities in the 0.1 to ! km/s range the accretionalefficiency for silicateand variousporosity ices are similar, whereas for objectswith escapevelocities <0.1 km/s the accretionalefficiency of icy impactorsbecomes significantly lower than for silicate impactors.

INTRODUCTION repeatedsuggestions of Roddyand co-workers[Roddy, 1968; Roddy et al., 1980] that large flat-flooredcraters such as As our knowledgeof planetary surfacemorphologies has that at Flynn Creek, Tennessee,could have been produced increasedto the point where impact cratered terranes have by porous,possibly cometary impactors. Finally, numerous beensuccessively recognized on the Moon [Shoemakeret al., studies have suggested that the largest meteoritical 1970], Mars [McCaulleyet al., 1972], Mercury [Murray et phenomenonyet documentedby man, the Tunguskaexplo- al., 1974], Phobos,Deimos [Veverkaand Duxbury, 1977], sion, was possiblyinduced by the interaction of the earth Callisto,Ganymede [Smith et al., 1979], Amalthea [Veverka with a comet [Krinov, 1966; Petrov and Stulov, 1976; Liu, et al., 1981], and, recently,tentatively on Venus [Campbell 1978]. Althoughit is likely that somecraters on the terres- et al., 1979; Pettengill et al., 1979] the questionhas been trial planets are induced by the impact of icy cometary raised repeatedly of how the initial density of impacting nuclei, it is not clear what the relative role of comets is in objects affects the resultingcrater shape as well as the parti- producingthe observedimpact crater populationon the earth tioning of energy. In part the motivation for studying the and other terrestrial planets. Meteoritical element abun- effects of cometary impact on planetary surfaceshas come dance patterns have recently been used to assigndifferent from the suggestionof Wetherill [1977], who pointedout the meteorite classesto the projectilesthat have producedsome possibility that one half of the terrestrial impact craters 12 large impact craterson the earth [e.g., Palme et al., could have been producedby retrograde comets, and the 1979]. Asidefrom the activecomets, it may be that poten- tial porousimpactors exist in the vicinity of the earth in the Copyright 1982 by the American GeophysicalUnion form of the Apollo asteroids;these may representdevolatized and short-periodcometary cores [Wetherill, 1976]. This Paper number IBI249. latter class of objectscould providean appreciablefraction 0148-0227/82/001 B-! 249505.00 of the impactor flux recorded on the surfaces and the Moon

6668 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES 6669 in the last 3 Gy of their history[Shoemaker, 1977]. Roddy ASSUMPTIONS [1968] has repeatedlysuggested that porousand possibly volatile and cometary objects when impacting terrestrial The two most controversialfeatures of the presentstudy planetary surfacesgive rise to a different type of cratering are the considerationof impact of planets with objectshay- flow than wasfirst computedby Bjork [1961]for the forma- ing densitiesas low as 0.01 g/cm• and the lack of explicit tion of the Barringer,Arizona, crater. Roddy [1977] recog- considerationof an atmosphere. nizeda similarityof the Flynn Creek and Steinheimcraters, The early suggestionby Roddy [1968] did not include to craters produced in wet alluvium by large-surfaceand the possibilityof an extremely low density. However, two abovegroundchemical explosions(Prairie Flat and Snow- recentstudies of the teentry physicsof the meteorwhich pro- ball). Virtually all previouscalculations of the impact into duced the 1908 Tunguska explosionconcluded that if the geological materials involving iron, anorthosite, aluminum, kinetic energy of infall was convertedinto a suddenincrease and, in the presentcase, solid ice yieldeda large transient in thermal energy [Liu, 1978] or the incoming bolide cavity with primarily radial motionsdescribable in terms of transferred its kinetic energy to the atmosphereby ablation Maxwell's[1977] Z model[O'Keefe and Ahrens,1979, 1981; and radiative heating of a boundary layer of highly Thomsenet al., 1980]. One exceptionhas been the caseof a compressedair [Petrovand Stulov, 1976],densities as low as porouswater sphereimpacting a graphitesurface. In this 0.01 g/cm3 are inferredfor the incomingobject. Notably, case a broad, shallowcrater with a deep but narrow central no real constraintson the compositionof the object have deformed area, not unlike Flynn Creek and Ries crosssec- been obtained from Liu's or Petroy and Stulov's analyses. tions,was recentlycalculated [Roddy et at., 1980]. Earlier The discoveryof presumablyextraterrestrial magnetite crateringcalculations of the flow inducedby the 20 ton TNT and/or silicate-bearingspherules in the Tunguskaarea [Kri- Mixed Companyexplosion [Ullrich et al., 1977] demon- nov, 1966;Glass, 1969] doesnot really constrainthe nature strated that the suddenapplication of pressurefrom gaseous of the bolide from being other than essentiallywater with detonation products on a relatively weak sedimentary somesilicate and/or metallicminerals. For thesereasons we sequenceinduced toroidal particle velocity ground motions have examined both the impact of readily volatile (water) (upward and toward the axis of the crater) that were also and refractoryporous objects having a rangeof densities. measuredby in-situ particle velocity gages. This type of Constraintson the constitutionof cometary nuclei, the motion must logically occur if the observedfiat floor and most important of which for the presentpurposes is density, centralpeak featuresresult from the intrinsicshock-induced have been discussedby Whipple [1977]. The apparent cratering flow in contrast with a flow resulting from the brightnessversus time data, which presumablyresult from gravity-inducedcollapse of a large transientcrater [Metosh rotation of the cometarynuclei inducedby nonradialgas and McKinnon,1978]. emissionupon approachto the sun, providean estimateof The objectivesof this study were to characterize the cometary nuclear density. By equating the centripetal cratering flow and infer the morphology of craters that accelerationto the gravitational acceleration and assuming would be producedby the impact of highly porous(possibly constantcomet densitywith depth the critical rotation period fragmented) and/or volatile hypervelocityimpactors. We T, is givenby have sought to test the hypothesisthat the impact of porous projectiles could produce fiat-floored craters with central peaksand multiple rings. These could arise from intrinsic T, (hours)-- 3.3 p-•/-' (1) flow field geometry and/or instabilities at the vaporized projectile-solidtarget interface. Featuressuch as central wherep is givenin g/cm•. In (!) the cometarynucleus is peaks and multiple rings are ubiquitouson many scaleson assumedto be spheroidal and strengthless. More complex the crateredsurfaces of the solid planets. cometary nuclear models have been constructedby Brin Although fiat-flooredcircularly symmetricdeformed, [1980]. Observedcometary spin periods are in the rangeof butnot excavated, craters have been absent in theresults of 3 to 10hours, implying that p isfrom 10 -• to 10øg/cm 3, the previous calculations in relatively homogeneous target latter being the more common value. Fragmentation of materials[Bjork, 1961;O'Keefe and Ahrens, 1975, 1977a; cometarynuclei is frequentlyobserved when cometscome Bryanet at., 1978], suchfeatures have been produced with within severalastronomical units of the sun. This may be specialtarget configurationswhen a weak target layer over- due to the violentescape of volatiles. However,a weak con- lies a strong strata in several decicentimeterscale impact straint on cometary density may also be obtained from the experiments[Quaide and Oberbeck,1968]. stabilityof cometarynuclei with respectto the tidal stresses In the present paper we examine the impact-induced imposedby the sun upon a closeapproach at a distancer, deformation from hypotheticalcometary objects having initial densitiesin the 0.01to I g/cm• and heatsof vaporizationof ---2 kJ/g (corresponding towater) to ---107 J/g r - 2.46R•)(t,o_,,, ix3 (2) range for impacts in the 5 to 45 km/s range. The direct effect of an atmosphere is neglected, although the atmo- where R•)and p•)are the solar radius and mean solar density. spheremay in fact causea cometaryobject to breakup into If p• = •..• g/cm', (2) impliesthat p>• 10-• g/cm'. Thus a showeror equivalentvery porousimpactor. In addition to we concludethat although there is much evidencethat the examiningthe partitioningof impact energy into internal density of cometsis m 1 g/cm•, the physicalconstraints energy of the impacted planet and impacting cometary which may be imposeddo not yet definitively rule out material we have also calculatedthe relativeefficiency of nuclear densitiesas low as 0.01 g/cm'; however,such shock-inducedmelting and vaporizationby cometson plane- extremely low values may be only characteristicof new tary surfacematerials and the massloss from a given planet cometsprior to initial perihelion [Whipple, 1977]. If the for variousescape velocities. tidal interactionwith an earth-sizedplanet is also considered, 6670 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES it may be that very porous objects would be disrupted by planetary tidal stresses. Because cometary atmosphericinteractions are important in the case of the earth [Stulov and Petrov, 1975; Liu, 1978], it is useful to estimatethe smallestcometary nuclear radius at which atmospheric effects are important. Using the criteria that the mass of the atmosphereintersected by the projectile (cometary nucleus) should be of the order of the projectilemass [Henderson-Sellers et al., 1980], it fol- lows that for normal incidence,

p, R, .-..-.po H (3) where p,. and R, are cometary nuclear density and radius and po and H are the surfacedensity and scale height of the atmosphere.For the earth,poll • 700 g/cm-'. Therefore the critical radius for significant atmosphericinteraction will be <7 m (lff' kg) and <0.7 km (t0 •ø kg) for cometary objectshaving densities of I and0.01 g/cm', respectively. Analysis of the criteria for breakup depend,however, in detail on the entry angle 0 (with respectto the horizontal) and the effective strength of the object. No breakup of objectsis predictedfor atmosphericentry speedsof 30 km/s, 0 -- 30¸, and strengthsof 50 bars, whereasfor objectswith 0 -- 15¸ and strengthof 1 bar (more likely for comets)complete breakup is predicted at all entry velocities (up to 72 km/s) for objectshaving a mass >107 kg (radius --13 m for ice) [Passeyand Melosh, 1980]. This latter situation would result in a cloud of objects according to Passeyand Melosh's[1980] calculationand yet would produce a single crater when the impactor was sufficientlylarge (e.g., > 10•ø kg, or havinga radius--130 m for icy objects). The size of the crater which results would presumably dependon the degree of dispersionof fragments. According to Passey and Melosh the Sikhote-Alin bolide was such a fairly weak (10-bar strength) object. Judgingfrom the total number of --t m craters and assuming,these were produced by drastically deceleratedobjects (--1 km/s impact velocity), a total massof 104 kg reachedthe earth's surface. The observeddispersion of craters observedyields a very low value from effective impactor density. We conclude from this discussion that for large (>t0 kg) weak objects entering the earth's atmosphere, atmosphericbreakup will result in very low effective impactor densities.

CALCULATIONAL METHOD

In carrying out the presentcalculation, the pressureP, volume V, and energy E equation of state representationof the planetary surface was applied in the form of a modified Mie-Gruneisen equation of state of the Tillotson form given by [Tillotson,1962; Ahrens and O'Keefe,1977]

p E + An + Bg,TM v a+ ( e/( b+ ) (4)

where • -- Vo/V,•t - • - 1, and a - 0.5 is the polytro- pic constantminus 1, at high temperature. The constantb is defined such that (a + b) is the STP Gruneisen parameter, • -- V (SP/SE)• and ,4 is the bulk modulus. The con- O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES 6671

35O In carrying out a seriesof finite difference calculations using the algorithmsof Hageman and Walsh [1970] in 300•/ cylindricallysymmetric geometry, icy (water) sphericalpro- jectiles, bearing no strengthand having initial densitiesvary- ing from0.01 to I g/cm3, wereassumed to impactplanetary surfacesvertically at speedsvarying from 5 to 45 km/s, 200 •/ Although the initial density of these icy projectiles was varleci, tl•elr lmUal internal energy density per unit mass was • 150 •h identical. Thus water melting, surface, and crush-up ener- gies were neglected. The actual material constantspertinent for gabbroic anorthosite,water, and ice in the high-pressure regimes[Ahrens and O'Keefe, 1977] are given in Table 1 and representative pressure-particle velocities Hugoniots from solutionsof (4) and (5) are shownin Figure 1. All of the present calculationsdeal with the energetics 4 8 12 16 20 24 28 32 36 40 44 PARTICLE VELOCITY (KM/SEC) of the initial partitioning of energy and hence apply to both Fig. 1. Pressure-particlevelocity Hugoniotsfor high-pressureregion the large Froude (Fr) and Reynolds(Nr) regimes: propertiesof gabbroicanorthosite, water (25øC), and single-crystal (0.917 g/cm3) andporous (0.1 g/cm3) iceat -10øC. Fr ----u2/gl >> I (8) stantsb, B, and E0 are obtainedby fitting Hugoniotdata up Nr -- olu /• >> I (9) to ---1 Mbar and Thomas Fermi calculations in the 102 Mbar region. The phase transitionswhich occur at approx. 0.15 Mbar in silicates or in ice below 0.02 Mbar are taken where u and I are the characteristic particle velocity and into account by defining the high-pressurephase regime such length scale of the flow, g planetary gravity, p density of the that the Rankine-Hugoniot energy is given by flow, and/• the absoluteor dynamic viscosity. As a result of these conditions, we have used hydrodynamics%aling and discusspartitioning energetics in terms E -- P(Voo - V)/ 2 - ET• (5) of normalized distance d, where Voois the specific volume of the starting material or d -- x/D (10) low pressurephase (lpp) and ErR is the increasein internal energy going from the lpp to hpp at STP [Ahrensand O'Keefe, 1977]. For the low pressurephase, E --0 at where x is actual distance and D is projectile diameter. STP. Normalized time r is defined as At high temperatures and low pressures where V/Voo > 1 for E > Ecv, whereEcv is the energyat stan- r = t v/D (11) dard pressurefor complete vaporization, the complete equation of state is given bv where t and v are time and impact velocity, respectively. Although we have carried out certain of our earlier cal- culationswith finite strengthsilicate materials [O'Keefe and p_.aEV +[ (E/(Eor12))'t bE/V- A/•exp[/5' (1- V/Vo) ]} x exp[-.(V/Vo-!)2 ] 5 KM/s• ,,= Impocto_•_•4 (6) diameter where the parametersused in (4) and (6) for gabbroic anorthosite,andesite, water, and ice Ih are given in Table I. In the partial vaporizationregime,

Vo/V < 1 Ew < E < Ec• where Etv is the energy required to bring a material from normal temperature to incipient vaporization at atmospheric pressure,we use the interpolationrelation

(E-Etv)Pe + (Ec•-E )Pc p -- (Ec•-Ew) (7) where P• and Pc are the pressurecalculated from (6) and Fig. 2. Particlevelocity flow field at r -- 2.05 for 1.0 g/cm3 ice (4), respectively. projectileimpacting a gabbroicanorthosite surface at 5 km/s. 6672 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES

Ahrens,1977a], we assumedfluidlike rheologyfor mostbut ,5 KM/s Impactor not all of the presentcalculations. Later in this paper, after d•ameter we describe the initial, inertially controlled flow field, we take these resultsand apply them in making somegenerali- zationsregarding impact ejecta from cometaryversus silicate impactors. We also assumed in some cases that the gabbroic anorthositerheology was elasto-plasticand possesseda finite strength Y, given by '<•ii Ejecto Y (kbar) -- (2.7 + 338 st - 900 st2) •1oud ' i'• "-'"'""•'""• • *•---D,sc Source x (1 - E/E,,,) (12) Fig. 4. Particlevelocity flow field at r -- 2.35 for 0.1 g/cm3 ice projectileimpacting a gabbroicanorthosite surface at 5 km/s. where E,, is the specificinternal energy required for melting [O'Keefeand Ahrens,1977a]. The finite difference grid was constructedwith some COMETARY CRATERING 154 Eulerian zones to define the projectile and, initially, some 900 zones to define a planetary half space. As the The particle velocity field induced at early times as the impact induced flows were numerically generated,radial and resultof the impactof a 1 g/cm3 solidice sphereon a gab- axial particle velocities, specific internal energy, mass, and broic anorthositeplanetary is shown for impact velocitiesof the principal stressesin each cell were stored. As the initial 5 and 15 km/s in Figures 2 and 3. The apparent source computation mesh was consumed by the propagation of (indicated) for the flow is slightly above the initial free sur- shock waves and the ensuing large particle motions associ- face for the 5 km/s impactcase and slightlybelow the sur- ated with cratering flow, the initial grid was enlarged face, but within the boundariesof the vaporized ice projec- geometrically,approximately 5 times in the courseof calcu- tile, for the 15 km/s impact case. As in the case of rock lations. In some casesthe physical dimensionof each zone impactors, the source point moves downward below the ini- was increasedby a factor of 40 in the courseof the calcula- tial free surfacewith increasingimpact velocity [Thomsen et tions. As a result, the computationyields accurate estimates al., 1980], and a bowl-shapedcrater is expected. Notably, of the amount of planetary surfacemelted and vaporizedand the subsurfaceflow is nearly completelyradial, and the flow the quantity of high speed ejecta only at early times when field is similar to that observed at r --- 0.3 in the earlier cal- the grid spacing is small enough to resolvevariation in the culations of anorthosite impacting anorthosite by O'Keefe entropy density generated by irreversible processes(and and Ahrens [1977a, Figure lc] in what they namedtheir hencethe massof melt and/or vapor produced)in various cavitation regime. regionsof the impactedsurface [Ahrens and O'Keefe,1972, In the 5 km/s impact case, the peak pressurein the 1977]. The icy projectileis vaporizedin virtually all the flow, 42 kbar, occursalong the center line of the flow in the flows considered. The growth and chemistry of volatiles in 'detachedshock' region [O'Keefeand Ahrens, 1977a] some planetary regoliths(M. A. Lange and T. J. Ahrens, private two projectile diametersbelow the original free surface. The communication, 1981) are a problem which has not been icy projectile at low pressureis vaporized but has not yet addressedin this study. expanded,although it clearly has the highestparticle velocity in the flow. The resulting impact crater flow field is more developedat earlier times for the same impact cratering geometryat 15 km/s (Figure 3). In this case,the peak pressure of 850 kbar occursat a depth of 1.8 projectilediame- I0KM/s •,, i•_[.I.mdlometer--7•pactor ters within the downward driven shock wave, whereas the pressurein the ice projectile is nearly completely relieved below 100 kbar. It appears that the impact of solid ice is similar to that of a solid silicateobject. Bowl-shapedcraters are expected from the impact-inducedflows we have calculated for craters in the diameter range smaller than 1 to 10 km where gravity effectsjust beginto appear [O'Keefeand Ahrens, 1978]. The particle velocity field inducedat early times for the impactof a porousice spherehaving a densityof 0.1 g/cm2 is shownin Figures 4 and 5 for impact velocitiesof 5 and 15 km/s. The flow field geometryhas aspectsnot seenin the case of the impact of denseprojectiles. The most obviousis the large plume generatedby.the vaporization of the porous ice projectile. In addition, the flow field 'source' is not a sin- projectileFig.3.Particleimpacting velocitya gabbroicflow fieldanorthosite at r --surface 1.50 forat 151.0 km/s. g/cm 3ice I glekm/s). point Thisbut broadeningis shaped likeof theadisc source (5pointkm/s) resultsandain ring a shal-(15 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES 6673

I0 KM/s V = 15KM/s Impactor H20 --*- AN p=0.t g/cm 3 :Ejecta Cloud

...... ' ', ' ' ' ' ' ' ...... Source ...... ,,•½•,,• ...... ET

,,,;;: ;,,:; , , , ,, ...... ,,, ,,,, , ,, --J PROJECTILEDIAMETER Fig. 5. Particlevelocity flow field at r - 1.95 for 0.1 g/cm3 ice Fig. 7. Particlevelocity flow field at r - 5.10 for 0.01 g/cm3 ice projectileimpacting a gabbroicanorthosite surface at 15 km/s. projectileimpacting a gabbroicanorthosite surface at 15 km/s. lower bowl-shapedcrater at relatively early times. The that the diameter/depthratio for impact at 15.8 km/s is effective source, as in the case of dense impactors, moves similar to that at 5 km/s. We note the depth • decreases downward below the initial free surface with increasing with porosityand scalesapproximately as impact velocity(total impact energy). The particle velocity field changessignificantly for the (13) impactof highlyporous (0.01 g/cm3) ice objects(Figures 6 and 7). The bifurcation of the apparent sourceof the flow observedfor densitiesof 0.1 g/cm3 is moreapparent for pro- where pt is the densityof the impactingprojectile. For projectile densitiesof 0.01 g/cm3 In this casethe sourcehas jectiledensities less than 0.1 g/cm3, the craterdepth is less moved below the free surface into the planetary material; than the projectilediameter. Moreover,for very low density this has a profoundeffect on the geometryof the projectile- impactors, the mean of the excavation depth is near zero, target interface. Toroidal flow fields are produced that and what is shown is the maximum depth of the surface could give rise to central peaks. An example of the apparent undulationsin Figure 8. disc source is indicated in Figure 5. The crater depth to The cratering phenomenologyexhibited by solid and diameter ratios in this regime are in a range of 1:20, and porous volatile projectilesdemonstrates a surprisingvariety accordingto the trend demonstratedby Schultz et al. [1981] of physical processes. To understand better the source of this ratio increases with time. Thus a flat-floored crater with toroidal flow field and the surface undulations sometimes a central peak might be expected. observed,we computed the cratering due to the impact of In order to gain somejudgment as to how close to the porous refractory projectiles. We sought to examine the final crater depth the present calculations can describe the hypothesisthat the interface-instabilityphenomenology could flow, we have examined (Figure 8) the crater depth versus be associatedwith vaporization processes. Another motiva- normalizedtime. We concludethat the depthsof craters are establishedbetween •- -- 10 and 100 (for 5 km/s impacts). Moreover, the work of Schultz et al. [1981] demonstrates I0 i i

AN(p= 2.96) 5 KM/s Impactor diameter

EjectaCloud .,,•X "'"Ix

x/ H20(•o:0.1) 0.1 x•X- H20(•o: O.Ol) /x 0.01 x I I I0 I00 IOOO vt Disc Source --• Gabbro•cAnorthos•te NONDIMENSIONALTIME, r-- D Fig. 8. Normalized crater depth versusnondimensional time for the Fig. 6. Particlevelocity flow field at r - 2.80 for 0.01 g/cm3 ice impact of variousdensity impacts at 5 km/s on an anorthositic projectileimpacting a gabbroicanorthosite surface at 5 km/s. planetary surface. 6674 O'KEEFEAND AHRENS:COMETARY IMPACT ON PLANETARYSURFACES

2K M/s Porous, i•._Llmpactor Project dinmeter

orthos•e e - ;; '-''-'-' ...... -'.' , .... • x

• ..- ,......

.- ....-...... • • .., ......

' ..Ill

Fig. 9. Particlevelocity, flow field at r = 0.90 for porous,but Fig. 11. Particlevelocity flow field at r = 2.80 for porous,but refractory (Ecv-- I0z Mbar - cm3/g), 0.1 g/cm3 projectile refractory(E,,-' 102 Mbar- cm3/g), 0.1 g/cm3 projectile impactinga gabbroicanorthosite surface at 5 km/s. impactinga gabbroicanorthosite surface at 5 km/s.

tion for studyingsuch impact flows is the possibilitythat the cal flow fields are shownin Figures11 and 12. The source impactof porousrefractory projectiles might representthe geometryfor the 5 km/s is a ring whoseposition is within interactionof Apolloobjects with terrestrialplanetary sur- the planetarysurface, whereas for the 15 km/s casethe faces. Anothermodel which we mightbe testinghere is that sourceis in the projectile. Again the trend observedis that of a disaggregated(fragmented) object or cloudof silicate with increasingvelocity from 5 km/s to greater than objects. 15 km/s the crater morphologyevolves from that with a The earlytime particlevelocity flow fieldsfor an impact centralmound to a shallowbowl-shaped crater. of refractoryprojectiles having a densityof 0.1 g/cm3 are The impact of porousvolatile objects on solid silicate shownin Figures9 and 10. The sourcegeometry for the 5 surfacesgives rise to all the necessaryconditions for the clas- km/s caseflow is a ring, and the flow geometryis also sicalKelvin-Helmholtz [Lamb, 1932, p. 374] and Rayleigh- toroidal.Note the lack of a vaporplume. The ring sourceis Taylor [Taylor, 1950] surfaceinstabilities. belowthe initial free surfaceand withinthe planetarysur- The conditionfor the Kelvin-Helmholtzinstability is face. At an impactvelocity of 15 km/s, the apparentflow that thereis a tangentialvelocity and density difference, sourceis near the projectile-planetarysurface boundary. The depth of the sourcepoint doesnot changemuch with increasingimpact velocity, but the boundary of the projectile-planetarysurface boundary moves below the source 2a' P•P2 (14) point. The particlevelocity fields for the impact of highly whereu is the tangentialvelocity, O the density,g the gravi- porous or highly disaggregatedrefractory (density of tationalacceleration, h the characteristicwavelength of a 0.01 g/cm3) projectileshas many characteristics of the flow disturbance,and the subscripts1 and 2 refer to planetary fieldsof thosefrom impactor densities of 0.1 g/cm3. Typi- surfaceand projectile,respectively. In the caseunder con-

.5KM/s= • Impacto_[•.• dinmeter Project•1•,--• D•scSource

.... ::: ,,,: ,-.,'..- ...... " ,•I• ......

..•1• •, ...... , ..... ,••,, . ,•,,• ...... ,,,, •;,,• •',,, t',• ,,

Fig. 10. Particlevelocity flow field at r = 2.25 for porous,but Fig. 12. Particlevelocity flow field at r • 7.05 for porous,but refractory(E,.,,-- 102Mbar- cm3/g), 0.1 g/cm3 projectilerefractory (E• = 102 Mbar- cm3/g),0.01 g/cm 3 projectile impactinga gabbroic anorthosite surface at 15 km/s. impactinga gabbroic anorthosite surface at 15 km/s. O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES 6675

The instabilities occur near the periphery of the crater lip ...... - .... 'r = 0.65 and may be one sourceof multiple rings. I-L•I 0.1•- • • • • • • (a)• • • • • • • • SPACINGMESH The condition of the Rayleigh-Taylor type is also satisfied during the earlier portion of the impact inducedflow. If we consider the cometary projectile-planetary surface inter- • -0.•5 .... , .... •-= 1.06 w 005 '• • • • , , • • • • • • • • • • • • • • • • • • • • • • , • • DOUBLED face, the impact-induced acceleration of the interface is .-J (b) MESH -- S PAC I NG downward from material 2 (impactor) toward material l (planet). Accordingto the analysisof Taylor [1950], if ini- L•J -0.1 • T =1.•1 tial perturbation, amplitude of the interface is •to, the inter- 0 0 • 0.1 face undulationwill grow with time t exponentiallyas % (c)

• -0.1 • 0 • .... • = 2.8 •t = •to exp 2a-a A) •/-• 0.1 • (15) (d) I I I I I I I I i i 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 RADIAL DISTANCE/PROJECTILE RADIUS Here 7, is the wavelengthof the initial displacementpertur- Fig. 13. Con[i•uration o[ marker particles at inter[ace between the bation, a is the downward acceleration of the interface, and vaporizedice and planetsurface [or impacto[ 0.01 g/cm• ice pro- A is the Atwood number, jectile onto gabbroicanorthosite at • km/s. Figures 13•, 13c, and 13g are the sur[ace inter[ace at the time r [or calculation with the mesh spacing indicated. Shown in Fi•ur• I]g is the same case in ,• = (p, - p_,)/(p, + p_,) (16) which the initial computational mesh spacing was decreased by a [actor o[ 2. Dependingon the rheologyof the materials, both the depen- dence of instability velocity and dominant wavelengthof the sideration this condition is readily satisfied since there are instability can be cast in terms of the characteristic dimen- several orders of magnitude difference in the densities and sions,viscosity, and/or effective strengthof the materials on nearly an order of magnitude difference in tangential veloci- either side of the interface[e.g., Ramberg,1967; Barneset ties. An example of a surface instability that might be attri- al., 1974;Menikoff et al., 1977, 1978;Drucker, 1980]. buted to the Kelvin-Helmholtz type is shown in Figure 5. Rayleigh-Taylor type instabilities have not been previ-

TABLE 2. Summary of Crater Morphologiesfor Various Impact Condi- tions for Impact into a Silicate Planetary Surface

Case

Projectile Impact Expected Surface Densityg/cm3Velocit¾ km/sVolatilit¾Crater Shape Instabilities

1.0 5 high bowl no 1.0 15 high bowl no 1.0 45 high bowl no 0.1 5 high shallow bowl no 0.1 15 high shallowbowl yes 0.1 5 low flat-floored no central peak 0.1 15 low shallow bowl no possiblecentral peak 0.01 5 high flat-floored yes central peak 0.01 15 high flat-floored yes central peak 0.01 45 high flat-floored yes central peak 0.01 5 low flat-floored no central peak 0.01 15 low shallow bowl no possiblecentral peak 6676 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES

73KBAR 2.8 KBAR 0.4KBAR 0.4 KBAR Taylor type instabilitiesare expectedto occur for low-density impactors and that these instabilities are a function of the effective planetary viscosity,structure, and projectile dimen- 0.8 KE,P ,.otI.i i i sion and require further analyses. The impact of porous volatile projectiles exhibits a 0.4 variety of crater morphologiesnot previously describedfor flows producedby the impact of denseprojectile. The range (Z•O.2 of observedbehavior varies from bowl-shapedcraters to flat- floored, multiple ringed central peaked craters with features LI_ 5 15 25 35 45 55 attributable to surface instabilities. The conditions for each 'r AFTER IMPACT of these morphologiesdepend upon the impact velocity,pro- Fig. 14. Energy partitioning versus nondimensionalizedtime for jectile density,and volatility and are summarizedin Table 2. 1 g/cm3 icy cometarynucleus impacting gabbroic anorthosite planet at 5 km/s. IE,C is internal energy of comet; IE,P is internal Density is the primarily variable that determineswhether or energy of planet; KE,C is kinetic energy of comet; and KE,P is not a bowl-shapedcrater will occur. For impactor densities kinetic energy of planetary surface material. Pressuresshown along •0.1 g/cm3 bowl-shapedcraters are formedindependent of upper edge of figure indicate the peak pressure in the impact- projectile velocity or volatility. The exception is for low- induced flow at that time. velocity impacts(--5 km/s) of refractory projectileswhere central mounds were observedto occur. For densities >•0.01, ously observedand were not calculated to occur in a large complex crater morphologiesare observedearly in the flow number of numericalcalculations in which the projectileden- characterizedby flat-floors, multiple rings, and central peaks sity was comparable to or greater than the target density except for high-velocity(>•15 km/s) refractory projectiles. (e.g., Figures 3 and 4). However, in the casesof the impact In addition to volatility, we examinedthe effects of material of a volatile low-density projectile, surface instabilities, that strength and equation of state on crater morphology. The might be attributable to a Rayleigh-Taylor type, have been material strength was varied for anorthositefrom zero to the observedand an exampleis shownin Figure 6. valuesgiven in (12). This did not changethe transitionfrom In order to gain some insight into the questionof how bowl-shapedto flat-floored craters with decreasingimpactor the zone spacingof our calculationsaffects the wavelength density. The equation of state was changed from that of and growth characteristicsof Rayleigh-Taylor instabilitieswe anorthositewith a high-pressurephase change model (Table have examined (Figure 13) the evolution of the surface 1) to that of andesite(Table 1) with a single phase model; between the vaporized ice and planet surface. As can be again this also did not change the above generalizations seenin Figure 13a, the planetary surface is slightly depressed (Table 2). (•- -- 0.65) when the projectile has penetratedthe surface. Subsequently, the expanding water vapor drives surface ENERGY PARTITIONING instabilities at the interface which grow with time. The wavelengthof the fastestgrowing or dominant wavelengthis The variation of energy partitioning with time and probably a function of the planet viscosity,internal structure impactvelocity for 1 g/cm3 ice objectsimpacting a gabbroic and projectile dimensions. The viscosity in the numerical anorthosite half-space planet is depicted in Figures 14 and calculationsis a function of the mesh spacing. As the mesh 15. The variation with time of impact energy is qualitatively spacing decreases,the viscosity increases,and the fastest similar for impacts at speedsvarying from 5 to 45 km/s. growing wavelengthdecreases. A calculation was performed Similar energy partitioningis observedfor impact onto a fin- in which the mesh spacingwas doubled. This had the effect ite strength gabbroic anorthositematerial (equation (12)) of decreasingthe one of dominant,wavelengths in the inter- and a material describedby the andesite equation of state face. This is shown in Figure 13b. Becauseof the mesh (Table 1). In all cases,the cometary projectile initially con- spacingdependence on the wavelength,the direct scaling to tains all the impactor energy,i.e., KE,C -- 1.0. planetary conditionsfrom the present calculationswould be Upon shockinteraction within one normalized time unit, difficult. We concludefrom the presentwork that Rayleigh- •- • 1, the internal energy of the comet (IE,C) increases

435KBAR 3 KBAR KM/SEC r zøz 5 I0 15 30 50 >-- 1.0 (.9 'ok KE,P i,I KE, P Z 0.8 i;i•!!::•::•:.,...'"'z•..:,..,,•. i,I '•'•::'::::•:::..":•i•iKE,C::::•:::.:.:•:.:....:.•.....•....:....:•....,-•...... '-,,• :'•':':4:: :.:":•ii •."::• i::•:::::..:. :•½.:'::...:•: •!:.:•::• ::.:...:•::.::. :•..: :.....:• •:::....:•:: :.,:•: •: :.:. :•::.,., :•:::...,• :...... ,•.....:: :...... •..:...•..... (O 0.6

IE,P -- 0.4

0 F-- 0.2 ½½•:•:•:•:•:•:•:•:•:•:•:•:h::...:..,•.::.:.•,. iiiiiiiiiiIE,C ii!i!!!iiiiii!iiiii!i•:::::5•:::::•..:.:..,•...... ,•..

0.7 0.8 0.9 1.0 I.I 1.2 I.;.'.'5 1.4 1.5 1.6 1.7 30 90 150 210 270 LOGic(IMPACT VELOCITY, KM/SEO) T AFTER IMPACT Fig. 15. Finalenergy partitioning versus impact velocity for 1 g/cm3 Fig. 16. Energy partitioning versus nondimensionalizedtime for icy cometary nucleusimpacting gabbroic anorthositeplanet. Notes 0.1 g/cm3 icy cometarynucleus impacting gabbroic anorthosite in caption to Figure 14 apply. planetat 15 km/s. Notes in captionto Figure 14 apply. O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES 6677

0.087 KBAR

SILICATE IMPACTOR (P:2.9 g/cm3) a 5 km/s o 7.5 "15 ß :30 ß 45 COMET(P:O.01 g/cm3) 5O v 15 km/s

Fig. 17. Energypartitioning versus time for 0.01 g/cm3 icy come- 14 15 16 ' tary nucleusimpacting gabbroic anorthositeplanet at 5 km/s. PLANETARY ESCAPE VELOCITY (cm/s) Notes in captionto Figure 14 apply. Fig. 19. Energyescaped in ejectaafter impact,normalized by kinetic en.ergyof meteorite,for 2.9 g/cm3 silicateobjects impacting sharply. This energy is then, in part, delivered into the 2.9 g/cm3 silicateplanetary surface, versus planetary escape velocity. The relativelylarge fraction of energythat a 0.01 g/cm3 icy kinetic energy of the planetarysurface material (KE,P) in 15 km/s impactor loses upon impact on planetary surfaceswith immediate contact with it within about two normalized time escapevelocity > 104cm/s is shown by theupper curve. units. After this interaction the kinetic energy of the comet (KE,C) and IE,C remain nearly constant. The cometary material is effectivelydetached from the flow, as water vapor 18 and the flow fields of Figures 6 and 7, little cometary escapesthe cratering region. During the time that the peak projectile energy becomes locally coupled into the silicate pressurein the subsurfaceflow decreases from --102 kbarto planetarysurface by impactof very porous(0.01 g/cm3) nearly zero, the internal energyof the planet (IE,P) steadily projectiles. This is dramatically illustrated in Figure 19, increasesat the expenseof KE,P within the cratered region. whichdemonstrates that 0.8 of the energyof a 0.01 g/cm3 Most of the KE,P is tied-up in the motion of the ejecta, water 15 km/s impactor escapesa planet that has an escape which in turn, on the average is only very lightly shocked, velocityof 105 km/s as comparedto only 0.2 for a silicate and movesat relatively low velocity in comparisonto the ini- impactor at the same speed. In the case of a planetary tial projectilevelocity. Most of this material will impact the escapevelocity of 11 km/s (e.g., the earth), --0.5 of the planet as secondary ejecta, and thus, eventually, all the energyof the 0.01 g/cm3 impactorescapes, whereas for a energy containedin it will becomeplanetary internal energy silicate15 km/s impactor,only --10 -4 of the impactenergy except that it will be distributedover a wide area surround- is lost to space. ing the impact. Figure 15 demonstrateshow, quite surpris- In Figure 20, we compare the energy delivered to a ingly,low velocityimpacts of 1 g/cm3 ice resultin a higher planetary surfacevia cometaryimpacts at 15 km/s for dif- IE,C, whereas KE,C representsabout 5% of total energy ferent initial density cometsto that calculated for gabbroic and is virtually independentof projectile velocity. The inter- anorthosite and iron projectiles striking a gabbroic anortho- nal energydelivered to the planetary material IE,P increases site planet. Clearly, the internal energy deposited into the from ---48% of the total energy at 5 km/s to 58% of the comet (IE,C) decreasesmarkedly with increasingcometary total at 45 km/s. density. Significantly, the fraction of internal energy As is demonstratedin Figure 16, the peak in projec- retainedby the planetfor a 1 g/cm3 cometis about0.6, tile internal energy at one normalizedtime unit becomesvery marked with increasedvelocity for 0.1 g/cm3 projectiles, whereas this phenomenonwas not resolved by the present calculationfor 0.01 g/cm3 projectileimpacts depicted in Figures 17 and 18. As is evident from both Figures 17 and 1.0H20 H20 H20t) A•e

n.- 0.8 Z .•.0..:.:.:.:.:.:...... :v...... 9-,.•. 0.45KBAR 0.25 KBAR 0.13 KBAR F •o • • . i - X-KE, M ß • ii?......

o.o• o.i i.o io LOG•o(IMPACTOR DENSITY, G/CM 3) LL 15 45 75 105 135 165 Fig. 20. Energy partitioning versus initial density for 15 km/s •- AFTER IMPACT impacts into a gabbroic anorthositeplanet by cometary objects and Fig. 18. Energypartitioning versus time for 0.0! g/cm3 icy come- anorthositeand iron meteorites. (Energy fraction in IE,P is less tary nucleusimpacting gabbroic anorthositeplanet at 15 km/s. than from O'Keefeand Ahrens [1977a], sincethe planetarysurface Notes in caption to Figure 14 apply. was assumedto be strengthless.) 6678 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES

IO3 . • 5 IMPACTMETEORITE DENSITY (g/cm 3) / o Fe-- An 7.8 MELT,/ •= H20--AnAn--An2.9;561.0 / / •/%,V2 IO2 =h20--An O.I /7,3' / ß H20--An 0.01 / • ,.•/ /•/VAPOR

O• IOI

_o-I- • 5 KM/SEC o ß 15KM/SEC 5• KM/SEC o • IG/CM 3-COMET \ ••5 o \ J I I I \ \ - 2102 IO3 IO4 IO5 IO 6 PLANETARYESCAPE VELOCITY, CM/SEC Fig. 23. Logarithm of normalized cjccta mass versus planetary escapevelocity for 0.01 g/cm3 icy objectsimpactin8 anorthositc planctcsimalsat 5 and 15 km/s. Dashedcurves are for anorthositc I• iO io• iO• impactors[after O'Keefe•nd Ahrenx,1977b].

Figure 21 in terms of the similarity variable developed by Fig. 21. Volume of melt or vapor(upon cooli,g to STP) of planetary material normalizedby meteorite volume versussimilarity parame- O'Keefeand Ahrens[1977a]. Notably,S may be considered ter, S = (p2/pl)(•/Ce)•. HereP2 and Pl, as in equation(16), are a normalizedstagnation pressure p2V 2, and the representa- the meteorite (projectile) and planetary density, respectively,• is tion of Figure 21 may be consideredas indicating that stag- impactvelocity and Ce is the soundspeed of the high-pressurephase nation pressuresof --70 GPa (700 kbar) and 100 GPa (1000 of the planetarysurface material [e.g., O'Keefe and Ahrens,1977a]. Here An indicatesanorthosite, and Fe and H20 have their usual kbar) are required for the onsetof melting and vaporization. meaning. At high speedsthe melt and vapor productioncurves are pro- portionalto kineticenergy V 2. Finally, we addressthe questionof the efficiency with slightly lessthan the 0.6 and 0.7 valuesappropriate for the which planets with silicate surfacescan accrete cometary and anorthositeand the iron meteorite impact case. presumably volatile objects. A number of authors have sug- On the other hand, the physical reason for the max- gested [Smith, 1977; Ringwood,1979; Anders and Owen, imum defined for the kinetic energy of the comet (IE,C) at 1977] that much of the volatileinventory of the terrestrial --0.1 g/cm3 initial densitydemonstrated by Figure20 is not planets was accreted late. Thus objectsthe size of Mercury, understood. This maximum is, however, based on adequate the Moon, and, to a lesser degree, Mars were too small to time dependentresults of Figure 16. collect hydrocarbonsand H,_O in appreciable quantities at The amount of silicate impact melt produced by the the time that the solar systemcooled off to the point that the impact of icy objectsis relatively small as comparedto sili- volatileswould accrete. In Figures 22 and 23 the logarithms cate and iron impactorsat the same speeds. This is shownin of the ratio of the ejecta mass to cometary mass versus planetary escape velocities are plotted for the hypothetical impactof 1.0 and 0.01 g/cm3 H20 bearingcomets onto terrestrial surfaces. First, we note that a factor of--2 to --5 more ejecta is producedupon impact of 15 km/s than upon impact of 5 km/s projectiles. This is true for water impactors havinginitial densitiesof 0.01 or 1 g/cm3. The zero horizontal line has specialsignificance in Figures 22 and 23, since the crossingof the various velocity curves represents the locusof impact and escapevelocities for which the ejecta lossesto the planet are just equal to the gain or net mass accreted.In the caseof 1 g/cm3 cometsthis critical escape velocity is 1.2 and 2.5 km/s for 5 and 15 km/s impactors, respectively. This implies that for planets with escapevelo- O_O.OI oG/CM 5 KM/SEC3-COMET EROSIONACCRETION *' 15 KM/SEC city less than this value, more material is lost than accreted at theseencounter speeds. For 0.01 g/cm3 comets,the criti- -I 5•\ \15KIVVSEC cal escapevelocities for 5 and 15 km/s impactorsare 1.4 and 2.75 km/s, respectively. In both casesfor cometarymedia, O2 iO$ iO4 iO5 106 the critical escape velocity for parity (no loss, no gain of PLANETARYESCAPE VELOCITY, CM/SEC masson impact) are at higher escapevelocities than the 0.83 Fig. 22. Logarithm of normalized ejecta mass versus planetary and 1.51 km/s values previouslyobtained by O'Keefe and escapevelocity for I g/cm3 icy objectsimpacting anorthosite planetesimalsat 5 and 15 km/s. Dashedcurves are resultsfor simi- /lhrens [1977b]for anorthositestriking an anorthositeplanet lar calculationsfor anorthositeimpactors [after O'Keefeand Ahrcns, at 5 and 15 km/s, respectively. Therefore for escapeveloci- 1977b]. ties of objects in the size range of the Moon, Mercury, and O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES 6679

Mars, Figures 22 and 23 indicate that these planets accrete have escape velocities similar to the Moon, Mercury, and anorthositesome 10 • to 10-'times more efficiently than they Mars than it is to accrete silicate materials. In contrast, in can accrete cometary water at infall velocitiesof 5 and 15 the lower(104 cm/s) escapevelocity range, the accretional km/s. At lower escapevelocity in the l04 to 10s km/s efficienciesfor anorthositeand variousporosity ices are simi- range the anorthosite and cometary ejecta curves coincide, lar. implying that planetesimalscomposed of rock and ice of widely varying porosity accrete with low, but similar, effi- ,4cknowledgments.We appreciate the assistanceof J. Peter ciencies. Watt in constructingan equation of state of water and the contribution of David Jewitt in suggestingbounds on cometary properties Finally, we note that as demonstratedby Figure 19, the and helpful commentsduring the course of this work and on the impact energywhich porous(e.g., 0.01 g/cm•) icy objects final manuscript proferred by David Stevenson. Reviews of the can contribute to accreting planets is comparable to that of paper by Peter H. Schultz and William B. McKinnon were most silicate planetesimalswhen the growing planet has a low helpful. The continuedcomputational assistance of M. Lainhart and the support of NASA (NSG 7129) is appreciated. Contribution (----10-• km/s) escapevelocity. However,for largerplanets 3491, Division of Geological and Planetary Sciences, California with escapevelocities of ----10•' km the impact energydue to Institute of Technology,Pasadena, Calit'ornia 91125. volatile impactors retained by the planet declines to < 10% of that initially delivered by the impactor. REFERENCES CONCLUSIONS Ahrens,T. J., and J. D. O'Keefe, Shockmelting and vaporizationof There are significantqualitative and quantitativediffer- lunar rocks and minerals, Moon, 4, 214-249, 1972. Ahrens, T. J., and J. D. O'Keefe, Equationsof state and impact- ences in the form of craters produced by porous cometary induced shock-waveattenuation on the moon, in Impact and impactors relative to solid silicate and iron objects on silicate Explosion Cratering,edited by D. J. Roddy, R. O. Pepin, and R. planetary surfaces. The cratering flows induced by both B. Merrill, pp. 639-656, Pergamon,New York, 1977. volatile and involatile but porous low-density objects tend to Anders, E., and T. Owen, Mars and the earth: Origin and abun- have toroidal streamlinesin which the apparent sourceof the dance of volatiles, Science, 198, 453-465, 1977. Anderson,G. D., The equationof state of ice and compositefrozen flow is not a point as in an explosionor impact of solid sili- soil material, Res. Rep. 257, U.S. Army Cold Reg. Res. and Eng. cate or iron objectsbut is a ring or disc, which, dependingon Lab., Hanover, New Hampshire, 1968. projectiledensity or velocity,can be aboveor below the ini- Barnes,J. F., P. J. Blewett, R. G. McQueen, K. A. Meyer, and D. tial planetary surface. During the cratering flow from Venable, Taylor instability in solids,J. Appl. Phys., 45, 727-732, 1974. porousimpactors, the central portionsof the cratersin many Bjork, R. L., Analysis of the formation of Meteor Crater, Arizona: cases have motions upward, whereas the outsides of the A preliminary report, J. Geophys.Res., 66, 3379-3388, 1961. craters move downward. Brin, D. G., Three models of dust layers on cometary nuclei, We proposethat upon interaction of planetary surfaces Astrophys.J., 237, 265-279, 1980. with volatile low-density impactors such as cometary nuclei, Bryan, J. B., D. E. Burton, M. E. Cunningham, and L. A. Lettis, Jr., A two-dimensionalcomputer simulation of hypervelocityimpact undulationsof the projectile-planetsurface can be produced cratering: Some preliminary results for Meteor Crater, Arizona, by the mechanismsof the Rayleigh-Taylor and Kelvin- Proc. Lunar Sci. Conf., 9th, 3931-3964, 1978. Helmholtz instabilities. The growth rate of the undulations Campbell, D. B., B. A. Burns, and V. Boriakoff, Venus: Further evi- of the Rayleigh-Taylor instability are determined by the denceof impact cratering and tectonicactivity from radar observa- tions, Science,204, 1424-1427, 1979. ratio of the difference in density, initial perturbation height Drucker, D.C., Taylor instabilityof the surfaceof an elastic-plastic and wavelength. The wavelength perturbations are, in turn, plate, Mech. Today, 5, 37-47, 1980. presumablycontrolled by contrast in effective rheology of Gaffney, E. S., and T. J. Ahrens, Identification of ice ¾I on the planetary surface and projectilematerials. Kelvin-Helmholtz Hugoniotof iceIn, Geophys.Res. Lett., 7, 407-409, 1980. instabilitiesform along the transient crater rim on accountof Glass, B. P., Silicate spherulesfrom Tunguska impact area: Electron microprobeanalysis, Science, 164, 547-549, 1969. the markedly lower density and higher particle velocity of Hageman, L. J., and J. M. Walsh, Help, a multimaterial eulerian the vaporized projectile versusthat of the planetary surface program for compressiblefluid and elastic-plasticflows in two acrosswhich the projectile flows. Both instabilitiesmay con- spacedimensions and time, Rep. 3SR-350, vol. 1, Systems,Science tribute to concentric rings in the inner region of the craters and Software, La Jolla, Calif., 1970. Henderson-Sellers,A., A. Benlow, and A. J. Meadows, The early which are frequently observedon planetary surfaceson many atmospheresof the terrestrial planets, Q. J. R. Astron. Soc., 21, size scales and geological terranes. We recognize, however, 74-81, 1980. thatother mechafilSms may produce these features. Krinov, E. L., Giant Meteorites, 397 pp., Pergamon, New York, The final partitioning of energy from cometary impac- 1966. Lamb, H., Hydrodynamics,6th ed., 738 pp., Dover, New York, tors is such that much more of the initial kinetic energy of 1932. the projectile residesin the cometary and planetary material Larsen, D. G., G. D. Bearson,and J. R. Taylor, Shock wave studies ejecta and the internal energy of the cometary material than of ice and two frozen soils, in Permafrost, 2nd International in the case of impact onto silicate surfaces. Conference,North American Contribution,pp. 318-325, National The critical escapevelocity at which as much material is Academyof Science,Washington, D.C., 1973. Liu, V. C., A test of the comethypothesis of the TunguskaMeteor ejected from a planet as accreted, for a given impact velo- Fall: Nature of the meteor 'thermal' explosionparadox, Geophys. city, is 1.2 to 2.5 and 1.4 and 2.75 km/s for 5 to 15 km/s Res. Lett., 5, 309-311, 1978. cometary impactors having initial densities of 1.0 to Maxwell, D. E., Simple Z model of cratering,ejection, and the over- 0.01 g/cm'. Theseare considerablyhigher than the critical turned flap, in Impact and Explosion Cratering, edited by D. J. Roddy, R. O. Pepin, and R. B. Merrill, pp. 1003-1008, Pergamon, accretionescape velocities of 0.83 and 1.5 km/s for normal New York, 1977. density silicates at similar encountervelocities. This implies McCaulley, J. F., M. H. Carr, J. A. Cutts, W. K. Hartmann, H. that it is more difficult to accrete volatiles for planets which Masursky, D. J. Milton, R. P. Sharp, and D. E. Wilhelms, Prelim- 6680 O'KEEFE AND AHRENS: COMETARY IMPACT ON PLANETARY SURFACES

inary Mariner 9 report on the geology of Mars, Icarus, 17, Roddy, D. J., K. Kreyenhagen,S. Schuster,and D. Orphal, Theoret- 289-327, 1972. ical and observationalsupport for formation of flat-floored central Melosh,H. J., and W. B. McKinnon,The mechanicsof ringedbasin uplift craters by low-densityimpacting bodies (abstract), Lunar formation, Geophys.Res. Lett., 5, 985-988, 1978. Planet. Sci., XI, 943-945, 1980. Menikoff, R., R. C. Mjolsness, D. H. Sharp, and C. Zemach, Schultz, P. H., D. L. Orphal, B. Miller, W. F. Borden, and S. A. Unstable normal mode for Rayleigh-Taylor instability in viscous Larson, Impact crater growth and ejecta characteristics:Results fluids, Phys. Fluids, 20, 2000-2004, 1977. from computer simulations (abstract), Lunar Planet. Sci., XII, Menikoff, R., R. J. Mjolsness,D. H. Sharp, C. Zemach, and B. J. 949-951, 1981. Doyle, Initial value problem for Rayleigh-Taylor instability of Shoemaker,E. M., Astronomicallyobservable crater-forming projec- viscousfluids, Phys. Fluids, 21, 1674-1687, 1978. tiles, in Impact and ExplosionCratering, edited by D. J. Roddy,R. Mitchell, A. C., and W. J. Nellis, Water Hugoniot measurementsin O. Pepin, and R. B. Merrill, pp. 617-628, Pergamon,New York, the range 30 to 220 GPa, High PressureScience and Technology, 1977. vol. 1, edited by K. D. Timmerhaus and M. S. Barber, pp. Shoemaker, E. M., M. H. Hait, G. A. Swann, D. L. Schleicher,G. 428-434, Plenum, New York, 1979. G. Schaber,R. L. Sutton, and D. H. Dahlem, Origin of the lunar Murray, B.C., M. J. S. Belton, G. E. Danielson, M. E. Davies, B. regolithof Tranquility Base,Proc. Apollo I I Lunar Sci. Conf., 3, Hapke, B. T. O'Leary, R. G. Strom, V. E. Suomi, and N.J. 2399-2412, 1970. Trask, Mariner 10 picturesof Mercury: First results,Science, 184, Smith, B. A., L. A. Soderbloom,T. V. Johnson,A. P. Ingersoll,S. 459, 1974. A. Collins, E. M. Shoemaker,G. E. Hunt, H. Masursky, M. H. O'Keefe, J. D. and T. J. Ahrens, Shock effects from a large impact Carr, M. E. Davies, A. F. Cook II, J. Boyce, G. E. Danielson,T. on the moon, Proc. Lunar Planet. Sci. Conf., 6th, 2831-2844, Owen,C. Sager,R. F. Beebe,J. Veverka,R. G. Strom,J. F. 1975. McCauley, D. Morrison, G. A. Briggs, and V. E. Suomi, The O'Keefe, J. D., and T. J. Ahrens, Impact-inducedenergy partition- Jupiter system through the eyes of Voyager l, Science, 204, ing meltingand vaporizationon terrestrialplanets, Proc. Lunar Sci. 945-972, 1979. Conf., 8th 3357-3374, 1977a. Smith, J. V., Possiblecontrols on the bulk compositionof the earth: O'Keefe, J. D., and T. J. Ahrens, Meteorite impact ejecta: Depen- Implicationsfor the origin of the earth and moon, Proc. Lunar Sci. dence of mass and energy lost on planetary escape velocity, Conf., 8th, 333-370, 1977. Science, 198, 1249-1251, 1977b. Taylor, G., The instability of liquid surfaceswhen acceleratedin a O'Keefe, J. D., and T. J. Ahrens, Impact flows and crater scaling on direction perpendicularto their planes, I, Proc. R. Soc. London, the moon,Phys. Earth Planet. Inter., 16, 341-351, 1978. Ser. A, 201, 192-196, 1950. O'Keefe, J. D., and T. J. Ahrens, The effect of gravity on impact Thomsen,J. M., M. G. Austin, and P. H. Schultz, The development crater excavation time and maximum depth; comparison with of the ejecta plume in a laboratory-scaleimpact crateringevent experiment(abstract), Lunar Planet. Sci., X, 934-936, 1979. (abstract), Lunar Planet. Sci., XI, 1146-1148, 1980. O'Keefe, J. D., and T. J. Ahrens, Impact cratering: The effect of Tillotson,J. H., Metallic equationsof state for hypervelocityimpact, crustal strengthand planetary gravity, Rev. Geophys.Space Phys., Gener. At. Rep. GA 3216, General Dynamics Corp., San Diego, 19, 1-12, 1981. Calif., 1962. Palme, H., E. Gobel, and R. A. F. Grieve, The distribution of vola- Ullrich, G. W., D. J. Roddy, and G. Simmons, Numerical simula- tile and siderophileelements in the impact melt of East Clearwater tionsof a 20-ton TNT detonationon the earth'ssurface and impli- (Quebec), Proc. Lunar Planet. Sci. Conf., I0, 2465-2492, 1979. cations concerningthe mechanicsof central uplift formation, in Passey,Q. R., and H. J. Melosh, Effects of atmosphericbreakup on Impact and Explosion Cratering, edited by D. J. Roddy, R. O. crater field formation, icarus, 42, 211-233, 1980. Pepin, and R. B. Merrill, pp. 959-982, Pergamon, New York, Petrov, G.I., and V. P. Stulov, Motion of large bodiesin the atmo- 1977. spheresof planets,Cosmic Res., 13, 525-531, 1976. Veverka, J., and T. C. Duxbury, Viking observationsof Phobosand Pettengill, G. H., P. G. Ford, W. E. Brown, W. M. Kaula, H. Deimos: Preliminary results, J. Geophys. Res., 82, 4213-4233, Masursky, E. Eliason and G. E. McGill, Venus:Preliminary topo- 1977. graphic and surface imaging results from the Pioneer orbiter, Veverka, J., P. Thomas, M. Davies, and D. Morrison, Amalthea, J. Science, 205, 91-93, 1979. Geophys.Res., 86, 8675-8692, 1981. Quaide, W. L., and V. R. Oberbeck, Thicknessdetermination of the Wetherill, G. W., Where do the meteorites come from? A reevalua- lunar surfacelayer from lunar impact craters,J. Geophys.Res., 73, tion of the earth-crossingApollo objectsas sourcesof stonemeteor- 5247-5270, 1968. ites, Geochim. Cosmochim.Acta, 40, 1297-1317, 1976. Ramberg, H., Gravity, Deformation and the Earth's Crust, 214 pp., Wetherill, G. W., The nature of the presentinterplanetary crater- Academic, New York, 1967. forming projectiles,in Impact and Explosion Cratering,edited by Ringwood, A. E., Origin of the Earth and the Moon, 295 pp., D. J. Roddy, R. O. Pepin, and R. B. Merrill, pp. 613-616, Per- Springer-Verlag,New York, 1979. gamon, New York, 1977. Robie, R. A., B. S. Hemingway,and J. R. Fisher, Thermodynamic Whipple, F. L., The constitution of cometary nuclei, in Comets, pro[•ertiesof mineralsand related substances at 298.15K and I bar Asteroids,Meteorites: Interrelations, Evolution and Origins,edited (10> pascals)pressure and at highertemperatures, Bull. U.S. Geol. by A. H. Delsemme, pp. 25-35, University of Toledo Press, Surv., 1452, 1978. Toledo, Ohio, 1977. Roddy, D. J., The Flynn Creek Crater, Tennessee,in Shock Metamorphismof Natural Materials, edited by B. M. French and N.M. Short, pp. 291-322, Mono, Baltimore, Maryland, 1968. Roddy, D. J., Large-scaleimpact and explosioncraters: Comparison of morphologicaland structural analogs,in Impact and Explosion (Received October 25, 1980; Cratering, edited by D. J. Roddy, R. O. Pepin, and R. B. Merrill, revised June 2, 1981; pp. 185-246, Pergamon,New York, 1977. acceptedJuly 31, 1981.)