Chemie der Erdeabramovo/papers/Abramov_Kring...Abramov et al. / Chemie der Erde 73 (2013) 227–248...

I

T

Oa

b

c

Ad

Ve

H

a

ARA

KHZLOTC

C

B

0h

Chemie der Erde 73 (2013) 227– 248

Contents lists available at ScienceDirect

Chemie der Erde

jou rn al homepage: www.elsev ier .de /chemer

nvited review

he impact environment of the Hadean Earth

leg Abramova, David A. Kringb, Stephen J. Mojzsisc,d,e,∗

United States Geological Survey, Astrogeology Science Center, 2255 North Gemini Drive, Flagstaff, AZ 86001, USAUSRA – Lunar and Planetary Institute, Center for Lunar Science & Exploration, 3600 Bay Area Boulevard, Houston, TX 77058-1113, USAUniversity of Colorado, Department of Geological Sciences, NASA Lunar Science Institute, Center for Lunar Origin and Evolution (CLOE), 2200 Coloradovenue, UCB 399, Boulder, CO 80309-0399, USAEcole Normale Supérieure de Lyon and Université Claude Bernard Lyon 1, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 2 rue Raphael Dubois,illeurbanne 69622, FranceHungarian Academy of Sciences, Research Center for Astronomy and Earth Sciences, Institute for Geological and Geochemical Research, 45 Budaörsi ut,-1112 Budapest, Hungary

r t i c l e i n f o

rticle history:eceived 1 July 2013ccepted 13 August 2013

eywords:adeanirconate heavy bombardmentrigin of lifehermal modelingratering processes

a b s t r a c t

Impact bombardment in the first billion years of solar system history determined in large part the initialphysical and chemical states of the inner planets and their potential to host biospheres. The range ofphysical states and thermal consequences of the impact epoch, however, are not well quantified. Here, weassess these effects on the young Earth’s crust as well as the likelihood that a record of such effects could bepreserved in the oldest terrestrial minerals and rocks. We place special emphasis on modeling the thermaleffects of the late heavy bombardment (LHB) – a putative spike in the number of impacts at about 3.9 Gyrago – using several different numerical modeling and analytical techniques. A comprehensive array ofimpact-produced heat sources was evaluated which includes shock heating, impact melt generation,uplift, and ejecta heating. Results indicate that ∼1.5–2.5 vol.% of the upper 20 km of Earth’s crust wasmelted in the LHB, with only ∼0.3–1.5 vol.% in a molten state at any given time. The model predictsthat approximately 5–10% of the planet’s surface area was covered by >1 km deep impact melt sheets. Aglobal average of ∼600–800 m of ejecta and ∼800–1000 m of condensed rock vapor is predicted to havebeen deposited in the LHB, with most of the condensed rock vapor produced by the largest (>100-km)projectiles. To explore for a record of such catastrophic events, we created two- and three-dimensionalmodels of post-impact cooling of ejecta and craters, coupled to diffusion models of radiogenic Pb*-loss in

zircons. We used this to estimate what the cumulative effects of putative LHB-induced age resetting wouldbe of Hadean zircons on a global scale. Zircons entrained in ejecta are projected to have the followingaverage global distribution after the end of the LHB: ∼59% with no impact-induced Pb*-loss, ∼26% withpartial Pb*-loss and ∼15% with complete Pb*-loss or destruction of the grain. In addition to the relativelyhigh erodibility of ejecta, our results show that if discordant ca. 3.9 Gyr old zones in the Jack Hills zirconsare a signature of the LHB, they were most likely sourced from impact ejecta.

© 2013 Elsevier GmbH. All rights reserved.

ontents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2281.1. The late heavy bombardment hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2281.2. Effects of the late heavy bombardment on Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228

2. Thermal models for global bombardments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2302.1. Model construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2302.2. Crater cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234

2.3. Ejecta cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Global bombardment models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Diffusion models for zircons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

∗ Corresponding author at: University of Colorado, Department of Geological Sciencesoulder, CO 80309-0399, USA. Tel.: +1 303 492 5014; fax: +1 303 492 2606.

E-mail address: [email protected] (S.J. Mojzsis).

009-2819/$ – see front matter © 2013 Elsevier GmbH. All rights reserved.ttp://dx.doi.org/10.1016/j.chemer.2013.08.004

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236

, Center for Lunar Origin and Evolution (CLOE), 2200 Colorado Avenue, UCB 399,

dx.doi.org/10.1016/j.chemer.2013.08.004http://www.sciencedirect.com/science/journal/00092819http://www.elsevier.de/chemerhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.chemer.2013.08.004&domain=pdfmailto:[email protected]/10.1016/j.chemer.2013.08.004

228 O. Abramov et al. / Chemie der Erde 73 (2013) 227– 248

3. Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2383.1. Global bombardment models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2383.2. Thermal fields within individual impact craters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2383.3. Thermal fields from globally emplaced impact ejecta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

4. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2424.1. LHB-induced ages to undamaged vs. damaged zircons in the Hadean crust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2424.2. Effects of zircon grain size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2424.3. Effects of target lithotype . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2424.4. Predictions for the Hadean terrestrial zircon record. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

5. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

. . . . . .

1

coobiccacotIo

wbspcbLilCizlat

1

id(Dmcbshn((lpo

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. Introduction

Impacts fundamentally contribute to several key physical andhemical aspects of the evolution of the terrestrial (a.k.a. silicater “rocky”) planets, the largest of the asteroids, as well as icybjects of the outer solar system. The planetary-scale effects ofombardments range from profound to subtle, and include (i) mod-

fications in surface morphology expressed as cratered terrains; (ii)ompositional changes via delivery of exogenous materials to therust or deep interior, melt mixing and differentiation of meteoriticnd crustal components; (iii) alterations to primordial atmosphereompositions and atmospheric densities, and thus strong forcingn paleoclimate; and (iv) defining the initial conditions that helpedo determine the overall thermal structures of the affected worlds.mpacts on Earth have also had important biological consequencesver geologic time.

The effect of major bolide impacts on the habitability of rockyorlds is a two-edged sword. Impacts may be conducive to ancient

iospheres via the formation of new habitats such as hydrothermalystems (e.g., Kring, 2000, 2003). Studies of preserved remains ofost-impact hydrothermal systems (e.g., Versh et al., 2006) lendredence to the idea that the consequences of an impact could beenign for microbial life, or even advantageous to it (Cockell andee, 2002). They may also be deleterious to biomes through steril-zation events of the surface zone by collision with catastrophicallyarge impactors and/or fiery rain from such impactors’ debris (e.g.,hyba, 1993; Ryder, 2002). Analysis has shown that the largest

mpacts have the potential to sterilize the surface zone (e.g., photicone of the oceans, shallow sub-surface of land). As such, the vio-ent environments for the origin of life on the Hadean Earth wouldppear to have confined the long-term continuity of the first biomeso the deep subsurface (Abramov and Mojzsis, 2009a).

.1. The late heavy bombardment hypothesis

The foundations of our current understanding of the timing andntensity of impact metamorphism in the inner solar system areerived from the study of lunar samples. Analyses of the lunar cruste.g., Turner et al., 1973; Tera et al., 1974) and impact melts (e.g.,alrymple and Ryder, 1993, 1996) returned by the Apollo and Lunaissions, as well as lunar meteorites (e.g., Cohen et al., 2000), indi-

ate that rocks in the Moon’s crust were shock-metamorphosed orrought to melting in events that typically group around and/oreldom exceed in age approximately 3.9 Ga. These observationsave been interpreted in the context of a dramatic increase in theumber of impacts over a relatively brief time span of 20–200 Myre.g., Ryder et al., 2000) originally termed the “lunar cataclysm”

Tera et al., 1974). Evidence for this epoch of bombardment is notimited to the Earth–Moon system, as meteorites from multiplearent bodies in the asteroid belt also appear to show the effectsf impact-induced metamorphism that extended at ca. 3.9 Ga, and

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

extend for long after (e.g., Bogard, 1995; Ash et al., 1996; Turneret al., 1997; Kring and Cohen, 2002; Bogard, 2011; Cohen, 2013; seeBottke et al., 2012). The most intense epoch of this solar-system-wide bombardment is now commonly referred to as the “late heavybombardment” (LHB), a term we use in this review. Thermal eventsrecorded in pre-4.0 Ga terrestrial zircons which cluster at ca. 3.9 Gamay also be suggestive of this bombardment (Trail et al., 2007;Abbott et al., 2012; Bell and Harrison, 2013), but aside from thisevidence there is little reliable confirmation of the LHB from the ter-restrial rock record (e.g., Anbar et al., 2001; Schoenberg et al., 2002;cf. Frei and Rosing, 2005). We discuss the nature of the Hadean zir-con evidence for an LHB in more detail later. Finally, the populationstructure of the main asteroid belt appears to preserve a record ofgiant planet migration that has been implicated in triggering theLHB (Minton and Malhotra, 2009). A self-consistent mechanism forits origin has been proposed (Gomes et al., 2005; Morbidelli, 2010;Morbidelli et al., 2012) which involved a rapid migration of giantplanets which strongly perturbed both the asteroid belt and the icyplanetessimal disk outside their initial orbits. Much remains to bedone, however, to further constrain the timing, duration and inten-sity of the LHB, and to understand its physical effects on planetarysurfaces.

It is important to note that although the LHB hypothesis pro-vides a compelling explanation of the various observations citedabove, other interpretations of the ancient lunar record are alsopossible. Some workers invoke a smooth post-accretionary declineto account for the cratered surface of the Moon, in which the ages oflunar rocks older than ca. 3.9 Ga have been overprinted by the con-tinuous effects of impact cratering over the last 4 Gyr (e.g., Baldwin,1974; Hartmann, 1975; Neukum and Ivanov, 1994; Hartmann et al.,2000). Although we adopt the LHB scenario in our analysis, all ofthe modeling techniques described herein are as applicable to a uni-form post-accretionary decline as they are to a spike in the numberof impacts.

1.2. Effects of the late heavy bombardment on Earth

Several lines of evidence suggest that the bolide populationsof the inner solar system LHB, at least in its later stages, weredominated by main belt asteroids: (i) there is a statistically sig-nificant correlation between the size-frequency distribution of thelunar highland craters and the present-day asteroid belt (Stromet al., 2005; Richardson, 2009; Marchi et al., 2012); (ii) trace ele-ment compositions of lunar impact melts point to asteroidal-typesignatures (Kring and Cohen, 2002); (iii) fragments of projectilesrecovered from ancient (>3.4 Ga) lunar regolith breccias imply thatprimitive chondritic asteroids dominated the latter stages of the

basin-forming epoch (Joy et al., 2012); and (iv) recent dynamicalmodeling studies by Bottke et al. (2012) indicates that comets werea minor player in the bombardment of the Earth and Moon duringthe LHB based on the excellent match between the asteroid-only

ie der

mmaaoa24aa

atadHifAettiwbiSicsvt(t∼w2(

smamrlisLoae22ll1rt

wzea2gi

O. Abramov et al. / Chem

odel results and lunar crater counts (Marchi et al., 2012). Further-ore, the Bottke et al. (2012) study points to the so-called “E belt”,

n extended and now largely extinct (cf. Hungarias) portion of thesteroid belt between 1.7 and 2.1 AU from Earth, as the main sourcef the LHB impactors. The current state of knowledge, which nowdvocates a “soft cataclysm” scenario for the LHB (Morbidelli et al.,012), points to the start of this bombardment epoch at around.1–4.2 Ga. Under this hypothesis, basins continued to be producedlbeit at a declining rate well after the conventional end of the LHBt about 3.81 Ga, the proposed age of Orientale Basin.

Dynamical models (e.g., Gomes et al., 2005; Bottke et al., 2012)nd analytical estimates (e.g., Minton and Malhotra, 2010) showhat the median impact velocity on Earth for the LHB bolides waspproximately 20 km s−1. Estimates of material accreted by Earthuring the impact cataclysm, scaled from lunar crater counts (e.g.,artmann et al., 2000; Ryder, 2002) and derived from dynam-

cal modeling (Levison et al., 2001; Gomes et al., 2005) rangerom ∼1.3 × 1020 kg to ∼2.2 × 1020 kg, with a mean of ∼2 × 1020 kg.lthough this constitutes a mere 0.015% of Earth’s mass, it has beenstimated that the number of impact-generated hydrothermal sys-ems on Earth exceeded those generated by volcanic activity at theime (Kring, 2000; see discussion in Ivanov and Melosh, 2003). Dur-ng the LHB at least 1700 craters greater than ∼20 km in diameter

ere produced on the Moon (e.g., Wilhelms, 1987). This value scalesy a factor of about 20 for the Earth depending on factors such as

mpact velocity and size distribution (e.g., Zahnle and Sleep, 2002).imple extrapolation would indicate that at least ∼34,000 largempact events affected the Hadean Earth. We consider this to be aonservative (low) estimate due to the fact that lunar crater erasureuppresses crater count statistics, and the higher average impactelocities onto the Earth lead to generation of larger craters than onhe Moon. The stochastic cratering model of Abramov and Mojzsis2009a) used total mass delivered and size-frequency distribu-ions of the impacting population as constraints to estimate that100,000 craters > 20 km in diameter, or ∼3000 craters > 100 km,ere formed on Earth in the LHB. This output agrees well with the

500–3000 craters > 100 km in diameter earlier proposed by Grieve1980).

A great deal of our current understanding of impact-producedhock metamorphism and age-resetting of radiogenic systems ininerals derives from studies of lunar materials (e.g., Heisinger

nd Head, 2006). Specifically, it has been hypothesized that theetamorphism of the lunar crust by the LHB led to widespread

adiogenic argon (Ar*) and (to a lesser extent) radiogenic lead (Pb*)-oss – correlated to disturbances in the Rb–Sr system – as measuredn returned lunar rocks (Turner et al., 1973; Tera et al., 1974). Sub-equent high-precision 40Ar–39Ar analyses of Apollo 14, 15 and 17,una 24, and highlands meteorite impact-melt rocks show a rangef ages (Cadogan and Turner, 1977; Swindle et al., 1991; Dalrymplend Ryder, 1993; Cohen et al., 2000; Culler et al., 2000; Fernandest al., 2000; Levine et al., 2004; Cohen et al., 2005; Norman et al.,006; Zellner et al., 2009a,b; Norman et al., 2010; Fernandes et al.,013), but few that are older than approximately 4.0 Ga. The Ar*-

oss is attributable to impact heating, whereby high temperaturesead to argon diffusion and outgassing (McDougall and Harrison,988). Both Pb*- and Sr-loss in whole rock samples cited aboveequire at least partial melting of the target material to mobilizehese elements.

Along with age-resetting in whole rocks, isotopic disturbancesithin individual minerals that preserve Pb*/U ratios, particularly

ircon (Zr(SiO4)), apatite (Ca5(PO4)3(OH, F, Cl)), and to a lesserxtent whitlockite (Ca9MgH(PO4)7), have been increasingly used

s indicators of impacts (e.g., Pidgeon et al., 2010; Liu et al.,012). These indicators generally fall into either of two cate-ories: complete or partial age-resetting. The former categoryncludes neoform mineral growth within the para-igneous regimes

Erde 73 (2013) 227– 248 229

of impact melt sheets (e.g., Wielicki et al., 2012), and the latterresults from partial or complete Pb* diffusion from the outermostparts of a mineral grain, recrystallization, or the formation of a man-tle or overgrowth on pre-existing crystals. A large number of lunarzircons have been dated by the U–Pb* method and most of thesewere done by spot analysis on high-resolution ion microprobes(SHRIMP or Cameca ims1270/1280). These analyses have yieldeda multitude of zircon core U–Pb* ages, with most recorded to beolder than about 3.9 Ga. Based on this outcome, it was previouslyasserted that “lunar zircons did not record the cataclysm” (Meyeret al., 2008). Partial resetting of zircon grains by impacts, however,remains a distinct possibility, as is complete age-resetting of zir-cons within melt sheets generated by large basin-forming impacts(Nemchin et al., 2012). Of note is a study by Nemchin et al. (2009),which examined four Apollo 14 breccias and reported that theU–Pb* system was completely reset at ca. 3.9 Ga (LHB age) in lunarapatite, but was undisturbed in zircons from the same sample. Asimilar study of an Apollo 17 melt breccia by Grange et al. (2009)also reported resetting of the U–Pb* system in apatite at about3.9 Ga, but noted that although zircon grains within the sampleshowed older ca. 4.3 Ga ages, a zircon aggregate that occurred as arim around a baddeleyite (ZrO2) grain had an “LHB age” (ca. 3.9 Ga).This important result provides good constraints on the thermal his-tory of the samples because the differential Pb*-isotope retentivityof zircon and apatite (e.g., Cherniak et al., 1991) coupled with pet-rographic context can be used to more precisely resolve the impacthistory of the Moon.

Data from terrestrial craters provide readily testable insightsinto the complete and partial resetting of radiogenic systems byimpacts (Deutsch and Shärer, 1994). Krogh et al. (1993) performedU–Pb* dating of zircons from the Cretaceous–Paleogene (K–Pg) dis-tal ejecta from a site in the Raton Basin of southern Colorado; resultsshow that both the extent of displacement from the 544 ± 5 Ma pri-mary age of zircons toward the time of impact at 65.5 ± 3.0 Ma,as well as the degree of discordance (attributable to diffusionalPb*-loss in the hot ejecta) correlates closely with the extent towhich the zircon grain was shocked. They concluded that Pb*-lossresulted from a post-impact thermal pulse while the zircon wasaloft in the fireball cloud. The simplest explanation for the resultsof Krogh et al. (1993) is that the zircons they analyzed containedtwo components: a concordant, 544 ± 5 Ma core, and a discordant,65.5 ± 3.0 Ma outer rim, with the relative proportions of the twocomponents dependent on the degree of shock (see Leroux et al.,1999) and/or thermal diffusive loss of lead. Similar conclusionswere reached by Kalleson et al. (2009) for zircons from the ∼5-km Gardnos impact structure in Norway. The Onaping Formationof Sudbury crater (southern Ontario, Canada), contains zircons thatappear to have two components based on 207Pb*/206Pb* ages: onewith the age of target lithologies, and another corresponding to thetime of impact, with the relative proportion of the latter increasingwith the degree of impact shock (Krogh et al., 1996). Complete andpartial U–Pb* age-resetting has also been observed in zircons fromthe Vredefort impact structure in South Africa (Kamo et al., 1996;Moser et al., 2011) and the Haughton impact structure in Canada(Schärer and Deutsch, 1990).

The oldest terrestrial zircons so far identified are about 4.37 Gyrold and are the only known datable materials that formed prior tothe LHB on Earth. As such, these minerals have been intensivelyused to probe early Earth conditions (e.g., Harrison, 2009). TheU–Th–Pb* zircon ion microprobe depth-profiling technique wasdeveloped by Mojzsis and Harrison (2002) to resolve the age andchemical compositions of discrete (micrometer to sub-�m) zones

in individual zircon crystals that correspond to distinct thermaland/or chemical events to have affected the grain. A study by Trailet al. (2007) used this method to explore for evidence of the LHB ina small collection of pre-4.0 Ga zircons from the Jack Hills and Mt.

2 ie der

NAfioWetoooiroo23ievsiciStWb

r1MpzWiftidieeptpbtdtzbt

lecioseawf(fis

30 O. Abramov et al. / Chem

arryer localities of the Narryer Gneiss Complex (NGC) in Westernustralia. These workers reported the results of their depth pro-les through 2- to 4 �m-wide discordant ca. 3.95 Ga mantles overlder original igneous cores in 3 of the 4 zircons they analyzed.hile it was argued that these overgrowths may represent thermal

vents endogenous to the crust that pre-date the geologic record,he ages also happen to coincide well with independent estimatesf peak bombardment from the lunar record cited above. More-ver, these thin mantles showed Pb*-loss (up to 90% discordance)ver narrow domains that could be interpreted to be the result ofmpact-induced heating (Trail et al., 2007). If the data indeed rep-esent thermal events of the impact cataclysm recorded as zirconvergrowths, it would be the first time such a signal has been foundn Earth. Subsequent work by Abbott et al. (2012) showed that 8 of2 Hadean zircons preserved overgrowths with ages between ca..85–3.95 Ga and characterized by temperatures obtained from Ti-

n-zircon thermometry (Tixln; Watson and Harrison, 2005; Watsont al., 2006) that are consistently higher than “normal” igneous corealues. A probabilistic analysis of the data of Abbott et al. (2012)hows that there is an overall ∼13% probability of obtaining agesn between 3.85 Ga and 3.95 Ga in Hadean Jack Hills zircons. Thisomports remarkably well with our model predictions that approx-mately 15% of the zircons should show ages for this time span (seeection 4.4). Recent work by Bell and Harrison (2013) has addedo the growing dataset of LHB-era ages in the Hadean zircons from

estern Australia; an interpretable record of the late heavy bom-ardment on Earth may have finally been found.

Recent work by Wielicki et al. (2012) reported U–Pb* ages,are earth element (REE) abundances and Tixln thermometry for11 zircon grains from impact melts of the terrestrial cratersanicouagan, Morokweng, Sudbury, and Vredefort. These workers

erformed a statistical comparison of data from these impact meltircons to 69 Hadean (>4 Ga) zircon grains from the NGC outcrops in

estern Australia. The results of their Tixln thermometry compar-son indicate that crystallization temperatures of Hadean zirconsormed in magmas were, on the average, ∼100 ◦C lower than ofhose produced by impacts. Wielicki et al. (2012) conclude thatmpact-generated melts were not a dominant mechanism of pro-ucing the bulk of the pre-4 Ga Hadean igneous zircon record, even

f the mantle overgrowths reported in Trail et al. (2007) and Abbottt al. (2012) may have been formed by impact-induced thermalvents. Wielicki et al. (2012) further showed that REE abundanceatterns in impact-produced zircons are indistinguishable fromhose of contemporary igneous or Hadean grains, but make theoint that REE partition modeling could be useful in discriminatingetween newly formed and age-reset zircon grains. It is clear thathe Hadean zircons are powerful tools for discerning events coinci-ent with the early evolution of life, but that they are still difficulto interpret. To provide a better interpretive frame work for theircons, we investigate in detail the thermal environment createdy impact bombardment during the LHB with an eye toward howhis could have affected the early biosphere.

That the biological effects of impact bombardments may be bothethal and benevolent has been explored previously by, among oth-rs, Oberbeck and Fogleman (1989) and Chyba and Sagan (1992). Aonsensus view is that impacts can fundamentally affect the hab-tability of a planet in a variety of ways, including: (i) sterilizationf the surface by thermal radiation from ejecta re-entry and depo-ition of global layers of hot ejecta (e.g., Sleep et al., 1989; Segurat al., 2002); (ii) vaporization of oceans (e.g., Chyba, 1990; Zahnlend Sleep, 1998); (iii) creation of long-lived hydrothermal systems,hich can serve as sites of the origin of life or provide refuges

or existing life (e.g., Kring, 2000; Abramov and Mojzsis, 2009a,b);iv) modulation of mantle convection, core dynamos, and magneticelds (e.g., Roberts et al., 2009; Watters et al., 2009); and (v) ero-ion of atmospheres (Arrhenius et al., 1974; Vickery and Melosh,

Erde 73 (2013) 227– 248

1990; Ahrens, 1993), or their densification and subsequent tippinginto runaway greenhouse regimes (e.g., Segura et al., 2012).

2. Thermal models for global bombardments

We now evaluate an assortment of impact-produced heatsources that affect silicate crusts: post-impact temperature distri-butions associated with a wide range of impact events that accountfor heat deposited by shock into the crust and include the formationof melt, uplift of hot deep crustal material by impacts, and heat fromejecta blankets deposited by impacts. The results include crustalmelting as a function of time, fractions of crust melted by impactorswithin a given size bin, percentage of the surface covered by impactmelt, temperatures and thicknesses of ejecta blankets associatedwith impacts of a given size, and the characteristics of the globalsurface ejecta cover following the bombardment. Furthermore, thisstudy aims to evaluate the thermal effects of impacts on the crustthat may be preserved in the chemistry of Hadean zircon grains thatare known to pre-date the LHB. Laboratory-derived element diffu-sion equations require the input parameters of both temperatureand time spent at that temperature to evaluate impact-induced ageresetting, Pb*-, Ti-, and REE-loss in zircons. The models reportedherein can evaluate such conditions on a global scale as well aswithin individual impact craters and ejecta blankets, and createoutput that can be tested against the Hadean zircon record.

2.1. Model construction

The stochastic cratering model we used is a Perl program basedin part on the work of Richardson et al. (2005). It has the followinginputs: (i) size-frequency distribution (SFD) of the impactor popu-lation; (ii) mass delivered per year (kg yr−1); (iii) LHB duration (inMyr); (iv) total model run time (if less than the LHB duration); (v)output frequency; and (iv) model area (in km2). The default outputfrequency of our Baseline stochastic model is 1/1000 the durationof our chosen LHB timescale, or 0.1 Myr. The model area is typi-cally the surface area of the Earth, 5.1 × 108 km2, although smallerareas can be specified in the model to examine the localized thermaleffects of smaller impactors.

Using these inputs, the stochastic cratering model calculatesthe number of impactors of a given diameter striking a specifiedarea within a specified time period. The density of the impactorsis assumed to be 2700 kg m−3, which approximates the averagedensity of main belt asteroids (Birlan, 2002). The impactors arerandomly distributed in space and time, but the mass and SFD con-straints are rigorously enforced. The output of the model includestime and coordinates of impact, impactor diameter, and the rim-to-rim diameter of the final crater calculated using Pi-group scalinglaws and the Abramov and Kring (2005) expression for convertingtransient to final crater diameters.

The stochastic cratering model was used to generate thefour LHB scenarios: (i) “Baseline”, with a total delivered mass of2 × 1020 kg, impact velocity of 20 km s−1, and a duration of 100 Myr;(ii) “40 km s−1”, with the impact velocity doubled; (iii) “10×”,which increased the total mass delivered by a factor of ten; and (iv)“10 Myr”, which reduced the duration by factor of ten. These valueswere purposefully chosen to express end-member scenarios in thebombardment. The 40 km s−1 impact velocity is meant to approx-imate cometary impacts: Although, as described in Section 1.2,there are several indications that the inner solar system LHB wasdominated by main belt asteroids, it is also possible that this con-

dition applied only to its later stages, which may have overprintedan initial cometary signature (e.g., Gomes et al., 2005). A summaryof input parameters used in the stochastic cratering model isgiven in Table 1. The size-frequency distribution of the impacting

O. Abramov et al. / Chemie der Erde 73 (2013) 227– 248 231

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

Num

ber

of im

pact

s

Impactor diameter (km)

0.1

1

10

100

1000

10000

100000

1e+06

1 10 100 1000

Num

ber

of im

pact

s


1e+17

1e+18

1e+19

1e+20

1e+21

1 10 100 1000

Mas

s co

ntrib

utio

n (k

g)


1e+17

1e+18

1e+19

1e+20

1e+21

1 10 100 1000

Mas

s co

ntrib

utio

n (k

g)


a. b.

c. d.

Baseline 10X delivered mass

Baseline 10X delivered mass

Fig. 1. (a) Baseline size-frequency distribution of LHB impactors. (b) Size-frequency distribution of LHB impactors with 10 times delivered mass. (c) Total mass contributionto the LHB by impactors within each size bin. (d) Total mass contribution to the LHB by factor of 1.25. Only impactors larger than 1 km in diameter are included.

Table 1Summary of impact bombardment properties. References and/or justifications forthese values are provided in the text (Section 2.1). Model abbreviations are asfollows: IH, impact heating (includes both subsurface and ejecta heating); SC,stochastic cratering.

Parameter Value(s) Units Models used in

Impact velocity 20, 40 km s−1 IH, SCa

Impact angle 45 ◦ IH, SCa

Impactor density 2700 kg m−3 IH, SCLHB duration 10, 100 Myr SCTotal mass delivered 2 × 1020, 2 × 1021 kg SC

d

peBdibi

ithhtsfila

Size-frequency distribution Asteroid belt – SC

a Used by stochastic cratering model only for calculating final rim-to-rim crateriameters.

opulation is modeled after the present-day asteroid belt (Bottket al., 2005; Section 1.2), and is illustrated in Fig. 1 for bothaseline and 10× scenarios. Although the number of impactorseclines quickly with increasing diameter, the delivered mass

ncreases steeply, implying that most of the energy would haveeen delivered by relatively few very large (≥100 km in diameter)

mpact events.A key starting condition for modeling the thermal effects of

mpact bombardment is the distribution of subsurface tempera-ures immediately after the impact. Three significant long-termeat sources are created by a large impact event: shock-depositedeat, a melt sheet, and a central uplift. The shock wave compresseshe target material, depositing large amounts of energy, and the

ubsequent decompression yields waste heat, which increases thenal temperature of the target (e.g., Ahrens and O’Keefe, 1972). For

arge impacts, sufficient heat is deposited to induce phase changesnd the melting and vaporization of target rocks. If enough melt

impactors within each size bin, 10× delivered mass. The bin width increases by a

is produced, it pools in the topographically lowest regions of thecrater basin and forms a melt sheet. The final major heat source isthe central uplift, which is material that has been uplifted fromlower, warmer regions of the crust during the formation of thecrater. The relative importance of the melt sheet and the cen-tral uplift increases with crater size: small, simple craters, such asthe ∼1-km Meteor Crater in northern Arizona, produce negligibleamounts of melt and uplift, but the melt sheet and central upliftform a progressively larger fraction of the thermal budget withincreasing crater diameter. Melt sheets generally contain signifi-cantly more energy than central uplifts (Daubar and Kring, 2001;Thorsos et al., 2001). A fraction of shocked target material leavesthe crater as vapor or ejecta, with the ratio of heat retained to heatremoved increasing with increasing crater diameter. Thus, largebasins retain proportionally more hot material than smaller craters.

A temperature distribution associated with a given impactmust take into account the heat sources described above (shock-emplaced heat, central uplift, impact melt) as well as properlyaccount for material ejected from the crater. Temperature distribu-tions can be generated by hydrocode simulations (e.g., Ivanov andDeutsch, 1999; Ivanov, 2004; Turtle et al., 2003). The advantage ofusing hydrocodes is that they allow tracking of movements of hotmaterial during the crater’s modification stage, which is difficultto model analytically. Severe computational constraints, however,preclude the use of a hydrocode simulation for tens of thousands ofindividual impacts that are needed to account for planetary-scalethermal models. For this project ∼60,000 post-impact temperature

distributions were required. Hence, we made use of the analyticalmethods (e.g., Abramov and Kring, 2005; Abramov and Mojzsis,2009a,b) described below, which have the advantage of rapidlygenerating temperature distributions for a crater of any arbitrary

2 ie der

di

hso

�

waagee3

fmairCsamo

P

wAe

k

wAauch2tM

bi

A

wttam

�8mbt


iameter. Tens- to hundreds of thousands of thermal fields ofmpacts in the crust can be analyzed in this manner.

The initial temperature distribution, representing shock-eating only, is analytically calculated using an expression forpecific waste heat (�Ew) derived from the Murnaghan equationf state by Kieffer and Simonds (1980):

Ew = 12[

PV0 −2K0V0

n

][1 −

(Pn

K0+ 1

)−1/n]

+ K0V0n(1 − n)

[1 −

(Pn

K0+ 1

)1−(1/n)](1)

here P is the peak shock pressure, K0 is the adiabatic bulk modulust zero pressure, n is the pressure derivative of the bulk modulus,nd V0 is the specific uncompressed target volume (1/�t). For aranite target chosen here (see Section 4.3) to represent the pres-nce of some fraction of felsic type crust in the Hadean (Mojzsist al., 2001), the uncompressed density �t is 2700 kg/m3, K0 is5.7 GPa, and n is 3.94 (McQueen et al., 1967).

Hydrocode simulations suggest that the center of the impact,rom which the shock originates, is at a depth equal to approxi-

ately the radius of the impactor (Pierazzo et al., 1997; Pierazzond Melosh, 2000), although a small variation with impact velocitys observed. Surrounding the impact center is the isobaric core, aegion where shock pressure is constant or slowly decaying (e.g.,roft, 1982). The ratio of isobaric core radius to impactor radiushows only a small dependence on impact velocity and projectilend target compositions in hydrocode simulations and is approxi-ately unity (Pierazzo and Melosh, 2000). Shock pressure P drops

ff with distance r according to the power law:

= A(

r

Rp

)−k(2)

here Rp is the radius of the projectile, k is the decay exponent, and is pressure at r = Rp (e.g., Pierazzo and Melosh, 2000). The decayxponent k varies with impact velocity:

≈ 0.625 log(vi) + 1.25 (3)

ith vi being in kilometers per second (Ahrens and O’Keefe, 1987).dditional validation of this expression can be found in Pierazzond Melosh (2000), who concluded, based on CTH hydrocode sim-lations, that the volumetric pressure decay exponent nV (nV = k/3)an be considered constant for impacts between 30◦ and 90◦ andas a weighted average value of 0.671. This corresponds to a k of.01, and agrees well with the Ahrens and O’Keefe (1987) predic-ion of 2.06 for the 20 km s−1 impact investigated by Pierazzo and

elosh (2000).The term A depends on target and impactor properties, and is

ased here on an estimate by Collins et al. (2002), corrected for thempact angle based on the results of Pierazzo and Melosh (2000):

= �v2i

4sin � (4)

here � is impactor and target density, both of which are assumedo be 2700 kg m−3, consistent with a rocky asteroid striking a plane-ary crust, vi is impact velocity, and � is the impact angle. An impactngle of 45◦ is used in the present investigation because it is theost probable impact trajectory (Gilbert, 1893; Shoemaker, 1962).To obtain the temperature increase �T, the specific waste heat

Ew is divided by the heat capacity of the target rock, which is

37 J kg−1 ◦C−1 for granite (Section 4.3), as listed in the HEATINGaterials library (Childs, 1993). The subsurface temperature distri-

ution due to shock-heating is then obtained by adding geothermalemperatures to the impact-deposited heat. The values for surface

Erde 73 (2013) 227– 248

temperature and geothermal gradients that were tested are listedin Table 2.

Once the initial subsurface temperature distribution is calcu-lated, the volume of the transient crater (which approximatelyrepresents material vaporized, ejected, or displaced by the impact)is removed from the model. The transient crater diameter, as mea-sured at the pre-impact surface, is calculated using the Pi-groupscaling laws (e.g., Holsapple and Schmidt, 1982; Housen et al., 1983)and corrected for the impact angle using the approximation ofPierazzo and Melosh (1999):

Dtc = 1.16d0.78v0.44i g−0.22 sin1/3 � (5)

where d is the impactor diameter and g is the terrestrial accelerationof gravity. The above expression is valid only if the impactor andtarget density are assumed to be equivalent (here, 2700 kg/m3).The depth of the transient crater is estimated by multiplying therim-to-rim diameter of the transient crater by 0.25 (Melosh, 1989).

Several analytical expressions have been developed to estimatethe volume of melt produced during the formation of an impactcrater of a given diameter. Perhaps the simplest and most com-monly used expression is that by Grieve and Cintala (1992, 1995,1997), derived using an analytical model (Cintala, 1992) based ona modified Murnaghan equation of state and verified with obser-vations at terrestrial impact structures (Grieve and Cintala, 1992).In that expression, melt volume is defined as cDdtc , where c is amaterial-, velocity-, and gravity-dependent constant, and d is a con-stant defined as 3.85 for all materials, impact velocities, and surfacegravities.

A new melt scaling model by Abramov et al. (2012) agrees wellwith the earlier results of Grieve and Cintala (1992, 1995, 1997)in terms of absolute melt volumes predicted, and validates, buildsupon, and implements several improvements to that expression.Where the new study differs, however, with the Grieve and Cintalamodel is that melt volumes for both a given crater and a givenprojectile were derived, with the latter being:

Vmelt = 0.22Em−0.85�p�t

Dp3v1.7i sin

1.3 � (6)

where Em is the specific internal energy of the target at shock pres-sure that results in melting upon release (please refer to Bjorkmanand Holsapple (1987) for a full definition), and has a value of∼5.2 × 106 J kg−1 for granite (Pierazzo et al., 1997), �p is projectivedensity, and Dp is projectile diameter.

The Abramov et al. (2012) expression provides additional ver-ification of the analytical shock-heating model used in this work.For the purposes of this comparison, melt volumes were derivedfrom the temperature increase (�T) in the target predicted by theshock-heating model. To keep the comparison general, a target withno geothermal gradient and a homogeneous initial temperature of0 ◦C was assumed. This allows a straightforward comparison to theBaseline expression (Eq. (6)) which does not include effects of tar-get temperature; a correction for pre-existing target temperatureis also given in Abramov et al. (2012).

Following Abramov and Kring (2007), the latent heat of fusionin the shock-heating model was modeled using the approximationof Jaeger (1968), following Onorato et al. (1978) in a study of theManicouagan (Quebec, Canada) impact melt sheet, by replacing theheat capacity Cp in the temperature range between the liquidus (TL)and the solidus (TS) with

C ′p = Cp +L

T − T (7)

L Swhere L is the latent heat of fusion (418 J kg−1 for granite as reportedin Birch et al., 1942 and Jaeger et al., 1959), and TS and TL are solidusand liquidus temperatures, set to 997 and 1177 ◦C, respectively.


Table 2Summary of target properties. A granitic lithology is assumed (see Sections 2.1 and 4.3). Thermal conductivity is given in the HEATING materials library (Childs, 1993);references and/or justifications for other values are given in the text. Model abbreviations are as follows: IH: impact heating (includes both subsurface and ejecta heating);CC: crater cooling (as used on the global bombardment model); ECC: ejecta cooling, conductive; ECH: ejecta cooling, hydrothermal.

Parameter Value(s) Units Models used in

Pressure derivative of the bulk modulus 3.94 Unitless IHAdiabatic bulk modulus at zero pressure 35.7 × 109 Pa IHHeat capacity 837 J kg−1 ◦C−1 IH, CC, ECC, ECHDensity 2700 kg m−3 IH, CC, ECC, ECHLatent heat of fusion 418 J kg−1 IH, CC, ECC, ECHLiquidus temperature 1177 ◦C IH, CC, ECC, ECHSolidus temperature 997 ◦C IH, CC, ECC, ECHSurface temperature 20 ◦C IH, CC, ECHGeothermal gradient 12, 70 ◦C km−1 IH, CC, ECHThermal conductivity 2.51 W m−1 ◦C−1 CC, ECC, ECHPorosity (ejecta) f(z), 40% at the surface Unitless ECH

pact suurfacempac

Mm

Mw

Favaa(

Porosity (basement) f(z), 20% at pre-imPermeability (ejecta) f(z,T), 10−2 at the sPermeability (basement) f(z,T), 10−3 at pre-i

elt was defined as material heated above the average granite◦
elting temperature of 1087 C.
Results of the melt volume comparisons are presented in Fig. 2.elt volumes predicted by the shock-heating method used in thisork and Abramov et al. (2012) differ by less than 20% in Fig. 2a,

100101102103104105106107108109

1 2 5 10 20 50 100 300

Mel

t Vol

ume

(km

3 )

Projectile Diameter (km)

Impact angle = 45°, vi = 20 km s-1

Earth (granite), this workEarth (granite), Abramov et al. (2012)

103

104

105

10 20 50 100

Mel

t Vol

ume

(km

3 )

Impact velocity (km s-1)

Impact angle = 45°, Dp = 10 km


103

104

30 45 60 75 90

Mel

t Vol

ume

(km

3 )

Impact Angle (degrees)

Dp = 10 km, vi = 20 km s-1


Earth (granite), Pierazzo and Melosh (2000)

a.

b.

c.

ig. 2. Melt volume comparisons for model validation. Effects of target temperaturere not included here. (a) Melt volume as a function of projectile diameter. (b) Meltolume as a function of impact velocity. (c) Melt volume as a function of impactngle. Melt volumes in this work would be ∼22% higher if adjusted for projectilend target densities assumed in Pierazzo and Melosh (2000) and Abramov et al.2012), resulting in a near-perfect match.

rface Unitless ECH Darcies ECH

t surface Darcies ECH

which presents melt volumes as a function of impactor diame-ter with impact angle and velocity held constant. Fig. 2b showsmelt volumes as a function of impact velocity, which differ fromAbramov et al. (2012) by almost a factor of two for 10 km s−1

impacts; however, this difference decreases with increasing veloc-ity, becoming less than 20% for 20 km s−1 impacts. Fig. 2c showsmelt volumes as a function of impact angle with comparisons toAbramov et al. (2012) and Pierazzo and Melosh (2000), who derivedmelt volumes from shock pressures predicted by CTH hydrocodecalculations. Melt volume decreases as a function of impact angleat the same rate as in Abramov et al. (2012), and the absolute dif-ference between the two approaches is again under 20%. It shouldbe noted, however, that Abramov et al. (2012) and Pierazzo andMelosh (2000) assumed a density of ∼3300 kg m−3 for the pro-jectile and ∼2700 kg m−3 for the target, whereas this particularsimulation assumes approximately equivalent densities. If meltvolumes are adjusted by a factor of ∼1.22 to account for these den-sity differences (∼3300/∼2700, see Abramov et al., 2012), the ∼20%difference described above vanishes and results in a near-perfectmatch to Abramov et al. (2012) and a close match to Pierazzo andMelosh (2000).

With the above validation, the amount of melt can be estimatedfor every impact in the model using the shock-heating method(Eq. (1)), and corrected for the effects of target temperature usingthe surface temperature and geothermal gradient specified in themodel. To accomplish this, the calculated temperature increase �Tdue to shock is added to the pre-existing temperature at a givendepth, and, if appropriate, adjusted for latent heat of fusion usingEq. (7). Material heated to a final temperature of 1087 ◦C or aboveis considered herein to be melt.

During the formation of complex craters, warm material fromdepth is uplifted in the central regions of the crater, forming anotherheat source (e.g., Daubar and Kring, 2001). The heat contributedby the central uplift can be estimated from the vertical distancetraversed by the uplifted material and the pre-impact temperatureas a function of depth, calculated from surface temperature andgeothermal gradient. The maximum vertical displacement due tothe stratigraphic uplift, based on observations at terrestrial craters,is estimated by:

hsu = 0.06D1.1 (8)

where D is the final crater diameter in kilometers (Grieve et al.,1981). The structure and diameter of the uplift is modeled based on

SALE-B hydrocode simulations of Ivanov and Deutsch (1999). Thevertical displacement decreases linearly with depth, and reacheszero at 1.25 times the depth of the transient crater. The verti-cal displacement also decreases with distance from the center of

234 O. Abramov et al. / Chemie der Erde 73 (2013) 227– 248

Fig. 3. Graphical illustration of the process used to generate post-impact temperature distributions. (i) The initial shock-emplaced waste heat is calculated as a function ofd m them to thea

tlr(oaF

sgrl

D

witdrmEg

eoh(attgbg

ctt

istance from impact center, and material within the transient crater is removed froodel. (ii) Topography is eliminated and the temperature distribution is moved up

dded, yielding the final model temperature distribution.

he crater x as (x − Rcp)2, reaching zero at x = Rcp, where Rcp is theateral extent of the uplift, approximately 0.22 of the final crateradius, which is derived from the morphometry of lunar cratersPike, 1985) and is entirely consistent with hydrocode simulationsf Ivanov and Deutsch (1999). A typical temperature distributionssociated with a central uplift is shown in the lower left panel ofig. 3.

A final diameter is calculated for every crater predicted by thetochastic cratering model for the purposes of estimating uplifteometries, ejecta blanket thicknesses, and the degree of globalesurfacing. The rim-to-rim diameter of the final crater is calcu-ated using the following relationship (Abramov and Kring, 2005):

= 0.91 D1.125tr

D0.09Q(9)

here Dtr is the rim-to-rim diameter of the transient crater, whichs measured above the pre-impact surface and is ∼1.2 times largerhan Dtc (Melosh, 1989), and DQ is the simple-to-complex transitioniameter, which is ∼3000 m for Earth, based on observations at ter-estrial craters (Grieve, 1987) and gravity-scaling of observed lunarorphometries (Holsapple, 1993). All values are in meters, and

q. (9) is applicable only to complex craters (those with diametersreater than ∼3 km).

For most thermal models presented in this work, and with thexception of individual crater models, final crater topography ismitted because large terrestrial craters (>100 km in diameter)ave very shallow depth-to-diameter ratios. Grieve and Pesonen1992) estimate based on data from terrestrial craters that thepparent (rim-to-floor) depth varies as 0.15D0.43 for crystallineargets, which yields a depth of ∼1.1 km for a 100-km crater. Forhe purposes of the thermal models, this can be considered flat. Araphical illustration of how final post-impact temperature distri-utions are calculated, taking into account shock-deposited heat,eothermal temperatures, and uplift, is presented in Fig. 3.

A library of post-impact �T distributions, which include theombined effects of shock heating and uplift, is generated usinghe methods described above. Background temperatures are sub-racted from final temperature distributions (Fig. 3, bottom right)

model. This vaporized/ejected/displaced material is treated separately in the ejecta surface, approximating uplift. (iii) Geothermal and central uplift temperatures are

to yield �T distributions. The �T distributions in the library aretwo-dimensional, axially symmetric, have a resolution of 75 × 33elements, and include all parts of the crater where �T exceeds 1 ◦C.Variables include impactor diameter, varied in increments of 1 km,impactor velocity, varied in increments of 1 km s−1, as well as sur-face temperature and geothermal gradient, for which several valuesare tested as described below.

For the purposes of this work, the initial temperature of ejectaproduced by a given impact was calculated by volumetrically aver-aging the temperatures to which non-vaporized material ejectedfrom the transient crater was heated. It is also recognized that con-densed rock vapor would deliver a significant thermal componentfor very large craters, and the volume of vapor produced by eachparticular impact was calculated. Temperature distributions anddimensions of the transient crater are calculated as described ear-lier in this section. For this calculation, it was assumed that materialabove the excavation depth, computed as 1/2 of the transient craterdepth, was ejected, whereas material below the excavation depthwas displaced, compacted and distributed along the crater floorand walls (Melosh, 1989). Temperature of the asthenosphere wasset to a constant of 1700 ◦C. Melt volumes are calculated using theMurnaghan EOS-based shock-heating method, with full account-ing for latent heat of fusion. Vapor volumes are estimated basedon a vaporization temperature of 3327 ◦C for granite, as estimatedby Pierazzo et al. (1997) using a weighted average of the availablevaporization temperatures of its components (Ahrens and O’Keefe,1972). The process for calculating impact ejecta temperatures isshown schematically in Fig. 4.

2.2. Crater cooling

Conductive post-impact cooling of impact craters is a reason-ably well-understood process and has been modeled by a number ofworkers, with the cooling timescales of craters 20–200 km in diam-eter estimated at 103–106 years (e.g., Onorato et al., 1978; Daubar

and Kring, 2001; Turtle et al., 2003; Ivanov, 2004; Abramov andKring, 2004, 2005, 2007). For this problem we employed HEATING7.3, a multi-dimensional, finite-difference heat transfer code sys-tem developed by Oak Ridge National Laboratories (Childs, 1993).

O. Abramov et al. / Chemie der

Fig. 4. Graphical illustration of how ejecta temperatures are calculated. Transientcrater (white line), with dimensions derived from Pi-group scaling laws, is superim-pc

AttttaisaPwswrftpccptofi

aeaBasierbcaa

2

oear

−2

osed on a post-impact temperature distribution. Temperatures within the transientavity above the excavation depth (dashed line) are volumetrically averaged.

two-dimensional (r − z) cylindrical coordinate system is used toake advantage of the model crater’s radial symmetry. Post-impactemperature distribution is computed as described elsewhere (Sec-ion 2.1). The bottom boundary has a prescribed heat flux neededo maintain the specified geothermal gradient. Heat is lost by radi-tion through the surface-to-environment upper boundary, whichs assumed to be a blackbody and has an equilibrium temperaturepecified in Table 2. Several different finite-difference techniquesvailable in the HEATING code were evaluated: Classical Explicitrocedure (CEP), Levy explicit method, and the implicit technique,hich can range from the Crank–Nicolson method to the Clas-

ical Implicit Procedure (CIP), depending on model conditions. Itas found that the three techniques produced nearly identical

esults, but the implicit technique is significantly computationallyaster than the other two. Therefore, an implicit transient solu-ion technique is used, in which a system of equations is solved byoint-successive over-relaxation iteration. The initial time step isalculated by the code based on Classical Explicit Procedure (CEP)onductive stability criteria, and each current time step is multi-lied by a factor of 1.1 to determine the new time step. It was foundhrough trial-and-error that using a time step multiplication factorf 1.1 significantly speeds up solution time without affecting thenal result.

The additional effects of heat transport by water and steams a result of post-impact hydrothermal activity have also beenvaluated in recent years (Rathbun and Squyres, 2002; Abramovnd Kring, 2004, 2005, 2007; Jõeleht et al., 2005; Sanford, 2005;arnhart et al., 2010). The net result of these studies is that,lthough hydrothermal activity can remove heat from the craterignificantly faster than conduction alone, it does not take placen the hottest (molten or ductile) parts of the crater, and it deliv-rs heat from the deep interior up to the near-surface. As aesult, hydrothermal crater cooling times are roughly compara-le to conduction-only cases. This is particularly important whenonsidering how minerals that preserve radiogenic systems areffected, where element diffusion is dependent on temperaturend time.

.3. Ejecta cooling

Conductive models of cooling impact ejecta blankets were based

n HEATING 7.3. The model consists of hot ejecta overburden, mod-led on a 100-node grid with a radiative upper boundary, overlying

200-node original surface with an initial temperature of 0 ◦C. Theesolution of the upper 100 nodes in the basement is equivalent

Erde 73 (2013) 227– 248 235

to that in the ejecta blanket, whereas the lower 100 nodes have aresolution coarser by a factor of 10. Thickness and initial tempera-ture of the ejecta are specified as inputs. Temperatures in the rangeof 1000–1500 ◦C, chosen by radiogenic Pb* mobility estimates inzircon and tested in 100 ◦C increments, and ejecta thicknessesof 100 and 350 m were also tested. The model is run until theentire ejecta blanket cools to temperatures at which no furtherage-resetting is possible, which can range from less than a year toover 104 years, depending on the initial thickness and temperatureof the blanket.

The model described above only includes thermal conduc-tion and radiation, however, the rate of ejecta cooling as well asthe degree of subsurface heating would be different in a “wet”environment characterized by the presence of groundwater andatmospheric precipitation. In particular, higher heat capacities andthe latent heat of vaporization of water would result in lower tem-peratures, and the venting of steam would effectively and rapidlyremove heat from the system. To quantify these effects, a com-parison model that included the presence and vaporization ofwater, as well as hydrothermal venting, was assembled for a 350-mthick, 1200 ◦C ejecta blanket based on HYDROTHERM 2.2, a finite-difference computer code developed by the U.S. Geological Surveyto simulate water and heat transport in porous media (Hayba andIngebritsen, 1994). The model is laid out on a two-dimensional gridof 75 × 75 elements, with the ejecta layer at a resolution of 7 mand the basement rocks at a resolution of 70 m. The model’s upperboundary is held at a constant pressure of 1 atm and functions asan infinite source or sink of the fluid, donating or accepting waterand steam depending on underlying hydrologic conditions.

A pressure of 1 atm was chosen because it is unclear what (ifany) substantial differences existed between surface (air) pressurein the Hadean/Archean (e.g., Som et al., 2012). Nevertheless, argu-ments based, for example, on limits to mass-independent sulfurisotopes from Rayleigh scattering in dense CO2 atmospheres showthat air pressure could not have greatly exceeded ∼1 bar since theEoarchean (Mojzsis, 2007).

A geothermal gradient of 40 ◦C km−1 was included, but it hasa negligible effect on model results, but the porosity and perme-ability of rocks to fluids could be important to the cooling times ofbombarded crusts. Rock porosity decays exponentially with depthto account for the pore space closing by lithostatic pressure (Binderand Lange, 1980):

˚(z) = ˚0 exp(−z

K

)(10)

where K is a gravity-dependent constant (1.07 km for Earth;Clifford, 1993), z is depth below the original surface, and ˚0 is initialporosity, assumed to be 40% at the top of the ejecta blanket, basedon the upper limits for polymict breccias recovered from the Yax-1borehole at Chicxulub crater (Mayr et al., 2008a) and 20% at thetop of the original pre-impact basement, based on typical crustalporosities. Permeability decays in a similar way with depth, and isalso a function of temperature T:

k(z) = k0 exp(−z

K

)T < 360 ◦C

log k(z, T) = log k(z) + 11500 − 360 (500 − T) − 11 360 ≤ T ≤ 500

◦C

k = 10−11 darcies T > 500 ◦C(11)

Initial permeability k0 is set to 10 darcies at the top of theejecta blanket, based on the upper limits from recovered Chicxulubsuevite breccias (Mayr et al., 2008b) and 10−3 darcies at the top ofthe basement rocks, based on mid-range permeability of the Earth’s

2 ie der

cw(mtm5

2

oiwadtscea

ieodehsateps

25mgtrbtl

ydrut

rhdstgaclitmv

diffused during the time step. The diffusion distance, shown inFig. 5 as a function of temperature and time, is summed for everymodel element to estimate the total average distance diffused byPb* during the course of the simulation.


rust (Brace, 1980, 1984). This rate at which permeability decreasesith depth is similar to that described by Manning and Ingebritsen

1999) based on geothermal data and metamorphic systems. Per-eability is a function of temperature due to the brittle/ductile

ransition at about 360 ◦C in silicic rocks (Fournier, 1991), which isodeled by log-linearly decreasing permeability between 360 and

00 ◦C (Hayba and Ingebritsen, 1997).

.4. Global bombardment models

A three-dimensional model representing the upper 140 kmf the Earth’s crust and lithospheric mantle was used to trackmpact-induced melting as the bombardment progresses. Inputs

ere provided by the stochastic cratering model, which gener-tes impactor diameter and impact coordinates, the temperatureistribution library, which provides an appropriate subsurfaceemperature distribution for a given impact, calculated by thehock-heating model, and a subroutine that calculates the finalrater diameter for each impact. Only impactors 10 km in diam-ter and larger are included in this model. Other input parametersre listed in Table 1.

The bottom boundary of the model is insulating, and heats lost by radiation through the upper boundary, which has anquilibrium temperature of 20 ◦C. The lateral boundaries have peri-dic boundary conditions (continuous wrap-arounds), so that alleposited heat is preserved in the system. The geothermal gradi-nt is 12 ◦C km−1, based on the arguments that the average globaleat flow was lower in the Hadean as a result of a thicker litho-phere (e.g., Korenaga, 2006), that consequently subdued plumectivity and slowed plate tectonics (if it was even operative at thatime). However, because the paradigm embraced by most work-rs is that Hadean heat flow was substantially higher compared toresent, a geothermal gradient of 70 ◦C km−1 was also tested in thistudy.

The horizontal dimensions of the model were 22,500 km ×2,500 km, corresponding to the Earth’s surface area of.1 × 108 km2, and the model depth is 140 km, equivalent toaximum lithospheric thickness. The model is represented on a

rid of 76 × 76 × 34 nodes, with a corresponding inter-nodal dis-ance of 300 km in the horizontal and 4.2 km in the vertical. Theseesolutions were chosen by trial-and-error to provide the bestalance between model accuracy and computational efficiency;he resolution was iteratively increased until the model results noonger changed.

As the model run progresses, output is written out every t/1000ears, where t is the total duration of the run (typically, the LHBuration of the model set at 100 Myr). The resulting output filesecord the temperatures of every node in the model, which are thensed to assess the thermal state of the lithosphere as a function ofime.

As an additional check of the transient heating model, a high-esolution approach was employed to estimate the degree of crustaleating during an impact bombardment. Here, the temperatureistribution library is used to calculate the volume raised above apecified temperature for every crater predicted by the stochas-ic cratering model. Additional inputs are surface temperature,eothermal gradient and crustal thickness. This simple modelssumes that impacts do not overlap and neglects any post-impactonductive heating. The tradeoff is a much higher overall reso-ution, whereby a temperature distribution associated with each

ndividual impact is represented on a 75 × 33 grid, which allowshe inclusion of impactors as small as 1 km in diameter. Thus, this

odel allows an assessment of the relative contribution of smalls. large impactors to crustal melting.

Erde 73 (2013) 227– 248

2.5. Diffusion models for zircons

With the global thermal model of the LHB to Earth’s crustestablished, we now turn our attention to the potential for arecord of the bombardment in the oldest terrestrial minerals. Weinvestigate whether partial age-resetting in zircon grains recordedthermal perturbations of the Hadean crust using diffusion equa-tions derived for both unshocked (Cherniak and Watson, 2001) andshock-damaged zircons (Cherniak et al., 1991) coupled to the con-ductive and hydrothermal impact ejecta cooling models describedabove. Our output was also tested against a previously publishedsimulations of the post-impact cooling of the ∼180-km Sudburycrater (Ontario, Canada) (Abramov and Kring, 2004).

Cherniak and Watson (2001) characterized diffusion of Pb* inboth natural and synthetic zircon under a wide range of conditions.In-diffusion and out-diffusion experiments were conducted, usingboth synthetic Pb*-doped and natural zircon with relatively highPb* concentrations. Results for diffusion in natural and syntheticzircon were similar, as were those for in- and out-diffusion, andare described by the following Arrhenius relation:

D = 1.1 × 10−1 exp(

−550 ± 30 kJ mol−1RT

)m2 s−1 (12)

where D is the diffusion coefficient, R is the universal gas constant,and T is absolute temperature. In their work, a mean activationenergy value of 550 kJ mol−1 was used. This result can be used tocalculate the diffusive length scale X, which provides a measureof how far the diffusant has propagated in one direction duringtime t:

X ≈√

Dt (13)

In these calculations, zircon is assumed to be an isotropic sphere,which is adequate for the purposes of our study in lieu of models foranisotropic diffusion in cylindrical geometries (e.g., Watson et al.,2010). Eqs. (12) and (13) are easily coupled to any thermal sim-ulation that has discrete time steps. For every model element, adiffusion constant D is calculated based on its temperature T, andthen multiplied by the duration of the time step. Assuming isotropicdiffusion, taking the square root of the result then yields distance

Fig. 5. Pb* diffusion in undamaged zircon, based on equations of Cherniak andWatson (2001). Solid line indicates diffusion distance of 3 �m, a typical zone widthobserved during ion microprobe depth-profiling (Trail et al., 2007).


Fig. 6. A three-dimensional thermal model representing the upper 140 km of the Earth at the end of the LHB. Only impactors larger than 10 km in diameter are included.Dark circles indicate crater locations, and blue areas indicate the extent of the subsurface habitable zone. The upper boundary shows temperatures at a depth of 4 km.(a–d) Baseline, 40 km s−1, 10×, and 10 Myr LHB scenarios, respectively, with a geothermal gradient of 12 ◦C km−1. (e–h) Baseline, 40 km s−1, 10×, and 10 Myr LHB scenarios,respectively, with a geothermal gradient of 70 ◦C km−1.

2 ie der

Weeuw(P

D

heu

3

3

er(ocaah(stdBdttufbtpthe

t

F1g


In addition, Pb*-loss in shock-damaged zircons was modeled.ittmann et al. (2006) described granular textures within a vari-

ty of shocked zircon grains from several impact structures, whichxhibit Raman characteristics that overall follow the trend of nat-ral radiation damage. As a first-order approximation of this,e used the diffusion equation for radiation-damaged zircons

Cherniak et al., 1991), which have a significantly faster rate ofb*-loss:

= 2 × 10−12 exp(

−142 kJ mol−1RT

)m2 s−1 (14)

ere variables have the same definitions as in Eq. (12), and thisquation is coupled to thermal simulations in the same way as forndamaged zircons.

. Results and analysis

.1. Global bombardment models

A graphical overview of the cumulative thermal effects of sev-ral LHB scenarios modeled in this work is shown in Fig. 6. Theseesults are from the three-dimensional transient heating modelSection 2.4) and provide a visual starting point for the analysisf our results and application to diffusion models of Pb*-loss in zir-ons. For our Baseline model, note the deflection of the isothermst the lateral boundaries of the model due to impacts, and that,lthough a relatively large number of craters have formed, mostave cooled below 100 ◦C at the upper boundary of the model4 km depth into the crust). In the high impact velocity, 40 km s−1

cenario, a larger number of hot craters is present and tempera-ures within each crater are noticeably higher due to each impactepositing three to four times more thermal energy relative to theaseline setting. In the 10× bombardment scenario, with ten timeselivered mass, craters formed by impactors > 10 km in diameter inhis model essentially saturate the surface and a substantial frac-ion of the near-subsurface is above 100 ◦C. A few percent of thepper ∼20 km of the crust is molten in this simulation. The resultsor the 10 Myr bombardment scenario are similar to the 40 km s−1

ombardment, with a larger number of active hotspots comparedo the Baseline model due to a higher frequency of impacts. Com-arisons of the models that use a 70 ◦C km−1 geothermal gradiento those with 12 ◦C km−1, along with much thinner lithosphere and

igher average temperatures of impact-induced hotspots, yields anven higher percentage of melting within the crust.

The degree of melting in the upper 20 km of the crust duringhe LHB is shown in Fig. 7 for the four bombardment scenarios and

0

0.005

0.01

0.015

0.02

0 20 40 60 80 100

Fra

ctio

n of

cru

st m

olte

n

Time (My)

Crustal melting during LHB. dT/dz = 12 °C km-1

Baseline40 km s-1

10X10 My

a.

ig. 7. The degree of melting in the upper 20 km of the crust as the LHB progresses. Deriv0 km in diameter are included. Melt deposited in ejecta blankets is not included. (a) Thradient of 12 ◦C km−1. (a) The effects of Baseline, 40 km s−1, 10×, and 10 Myr LHB scenar

Erde 73 (2013) 227– 248

two geothermal temperature gradients described above. For the12 ◦C km−1 geothermal gradient case, sharp peaks and the long timebetween them indicate that most melting is caused by a few largeimpacts. Following a basin-forming impact, the amount of meltdecreases substantially due to long cooling times before anotherbasin is formed. In the Baseline scenario, a maximum of 0.3% of theupper crust is molten at any time, and even in the 10× scenario, themaximum molten fraction is under 2%. For the 70 ◦C km−1 geother-mal gradient, smaller impacts are proportionally more important,and a higher percentage of the crust is molten: in the Baseline sce-nario, up to 1.5% of the crust is molten at any one time, and thisfigure increases to over 11% for the 10× scenario.

The melting results described above were derived from a rela-tively low resolution transient heating model, which only includedimpactors larger than 10 km. In order to test these results and assessthe relative importance of smaller impactors, a high-resolutionstatic model (Section 2.4) was employed to calculate cumulativecrustal heating. The results, presented in Table 3, are in excellentagreement with those in Fig. 7, validating the model and imply-ing the relative unimportance of small (


Table 3Maximum melting in the upper 20 km of the crust for three impactor diameter ranges in several LHB scenarios. Calculated using the high-resolution delta T model (Section2.4). Melt deposited in ejecta blankets is not included. Results for a 10 Myr LHB would be identical to the Baseline model.

Geothermal gradient LHB model Impactor diameter range Number of impacts % of crust melted

12 ◦C km−1 Baseline 100+ km 32 1.112 ◦C km−1 Baseline 10–100 km 1496 0.3912 ◦C km−1 Baseline 1–10 km 173,667 0.03712 ◦C km−1 40 km s−1 100+ km 32 3.212 ◦C km−1 40 km s−1 10–100 km 1496 1.612 ◦C km−1 40 km s−1 1–10 km 173,667 0.1412 ◦C km−1 10× 100+ km 296 9.712 ◦C km−1 10× 10–100 km 14,969 3.912 ◦C km−1 10× 1–10 km 1,736,677 0.3870 ◦C km−1 Baseline 100+ km 32 1.570 ◦C km−1 Baseline 10–100 km 1496 0.8270 ◦C km−1 Baseline 1–10 km 173,667 0.1270 ◦C km−1 40 km s−1 100+ km 32 4.270 ◦C km−1 40 km s−1 10–100 km 1496 2.870 ◦C km−1 40 km s−1 1–10 km 173,667 0.4570 ◦C km−1 10× 100+ km 296 1470 ◦C km−1 10× 10–100 km 14,969 8.370 ◦C km−1 10× 1–10 km 1,736,677 1.2

Fig. 8. Percentage of Pb*-loss in 100-�m zircon grains within a 180-km terrestrial impact crater. Pb*-loss within the ejecta is not included in this model. (a) Normal zircongrain. (b) Damaged zircon grain. (c) Estimate of the extent of age-resetting within the ∼280 km (Therriault et al., 1997) Vredefort crater constrained by field observations(from Moser et al., 2011).

2 ie der Erde 73 (2013) 227– 248

tscW

atwisezT(ndtas

3

Eadb(votiiaMaimangatraiw

oo∼wgtiie∼oal

tco

a.

b.

Mea

n G

loba

l Eje

cta

Thi

ckne

ss (

m)



Final Crater Diameter (km)

12 °C km-1

70 °C km-1

10-4

10-3

10-2

10-1

100

101

102

103

500 1 10 100

20 4000 100 1000

Mea

n G

loba

l Roc

k V

apor

Thi

ckne

ss (

m)




12 °C km-1

70 °C km-1

10-4

10-3

10-2

10-1

100

101

102

103

500 1 10 100

20 4000 100 1000

Fig. 9. Mean global thickness of (a) impact ejecta and (b) condensed rock vapor as


emperature of ∼1700 ◦C). In addition, since the thermal decompo-ition temperature of zircon is 1673 ◦C (Kaiser and Lobert, 2008),omplete loss of grains emplaced within the melt is also likely (see

ielicki et al., 2012).The results for damaged zircons, illustrated in Fig. 8b, show that

significantly larger rock volume within the crater contains zirconshat suffer complete Pb*-loss, as well as a somewhat wider bandhich experience partial Pb*-loss in zircons. The Pb*-loss results

n zircons we modeled were compared to field observations at theomewhat larger (∼280 km) Vredefort crater (South Africa). Mosert al. (2011) documented that complete and partial age-resetting inircon is limited to ∼27 km from the center of the impact (Fig. 8c).hese results are in agreement with our models for normal zirconFig. 8a), but not for shock-damaged zircon (Fig. 8b). It should beoted, however, that the onset of deformation in zircons at Vre-efort is at ∼29 km from center, and is offset by only ∼2 km fromhe observed age-resetting. In other words, the most severely dam-ged zircons would be expected to occur close to the center of thetructure, where they would be age-reset in either scenario.

.3. Thermal fields from globally emplaced impact ejecta

Hot impact ejecta generated by the LHB draped the Hadeanarth’s surface. The amount of material ejected or vaporized byn impact of a given magnitude is estimated using the modelescribed in Section 2.1. This volume can then be normalizedy the Earth’s surface area to calculate the mean global ejectaFig. 9a) and condensed vapor thickness (Fig. 9b) for each indi-idual impact. The fraction of material ejected at escape velocityr higher is expected to be significantly smaller than the mass ofhe impactor (e.g., O’Keefe and Ahrens, 1977a) and is not includedn the model. The volume of both ejecta and rock vapor producedncrease with impactor diameter in an expected way: ejecta scaless ∼D2.34p in proportion to transient crater volume (Pierazzo andelosh, 2000), and vaporized volume scales as ∼D3p (e.g., O’Keefe

nd Ahrens, 1977b). The ratio of vaporized to ejected materialncreases as ∼D0.66p , which results in deposition of significantly

ore condensed vapor than ejecta for very large impactors. For 500-km diameter impactor, the largest possible in the 10× sce-ario, the estimated global rock vapor thickness is ∼400 m, and thelobal ejecta thickness varies from ∼10 to ∼40 m, depending on thessumed geothermal gradient. This is in excellent agreement withhe estimate of Sleep and Zahnle (1998) of ∼300 m of condensedock vapor and ∼50 m of ejecta, considering that earlier work used

lower impact velocity of 17 km s−1 (which would decrease vapor-zed volume), and did not include the geothermal gradient (which

ould result in an over-estimate of ejecta volume).Both ejected and vaporized volumes exhibit some dependence

n the geothermal gradient, but that dependence is significantnly for particular ranges in crater diameter. For impactors over50 km in diameter, ejecta volumes become increasingly largerith increasing impactor diameter for a colder (12 ◦C km−1) tar-

et compared to a warmer (70 ◦C km−1) target (Fig. 9a). This is dueo a lower fraction of material within the excavation zone becom-ng vaporized if the target is colder. Conversely, more rock vapors produced if the target is warmer, as can be seen in Fig. 9b. Thisffect is most significant for impactor diameters between ∼50 and100 km; for impactors with diameters larger than ∼100 km, mostf the vaporization takes place in the isothermal asthenospherend the lithospheric geothermal gradient becomes progressivelyess relevant with increasing diameter.

The volume of ejecta produced by each impact can be coupled tohe LHB size-frequency distribution (Section 2.1 and Fig. 1), and theumulative thickness of deposited ejecta is calculated as a functionf impactor diameter by multiplying the mean global thickness of

a function of binned projectile and final rim-to-rim crater diameters. The bin widthincreases by a factor of 1.25. Ejecta includes impact melt, but not rock vapor.

ejecta by the expected number of impacts in that size bin (Fig. 10a).The same technique is used to calculate the cumulative thicknessof condensed rock vapor as a function of binned impactor diam-eter (Fig. 10b). The model does not include ejecta redistributionby subsequent impacts, which is an acceptable assumption for theBaseline model, in which only ∼25% of the surface is covered byimpact craters and typical ejecta thicknesses are small comparedto excavation depths of craters that produce most of the ejecta. Thedependence of cumulative ejecta and condensed rock vapor vol-umes on the geothermal gradient is identical to Fig. 9, an expectedresult. The shape of the cumulative ejecta volume distribution,however, is remarkably flat, indicating that smaller impacts gen-erated roughly the same total volume of ejecta as larger impacts.The cumulative condensed rock vapor distribution, on the otherhand, increases with impactor size up to projectiles ∼100-km indiameter, at which point it flattens out as well. Thus, in contrastto the ejecta, most condensed rock vapor is produced by impactslarger than ∼100 km.

Fig. 11 illustrates the predicted mean temperatures and meltcontent of ejecta produced by impactors of various diameters,calculating using the volume-averaging method (Section 2.1 andFig. 4). In general, ejecta temperature increases with increas-

ing projectile diameter, from ∼300 ◦C for a 1-km impactor to∼2500 ◦C for a 500-km impactor (Fig. 11a). The dependence on thegeothermal gradient is most pronounced for mid-size impactors


.a

.b

Mea

n C

umul

ativ

e G

loba

l Eje

cta

Thi

ckne

ss (

m)




12 °C km-1

70 °C km-1

100

101

102

103

500 1 10 100

20 4000 100 1000M

ean

Cum

ulat

ive

Glo

bal R

ock

Vap

or T

hick

ness

(m

)




12 °C km-1

70 °C km-1

100

101

102

103

500 1 10 100

20 4000 100 1000

Fig. 10. Mean cumulative global thickness expected during the Baseline LHB for (a)impact ejecta and (b) condensed rock vapor, as a function of binned projectile andfii

(ftti∼kbf

datdciiccaWist

a.

b.

0

500

1000

1500

2000

2500

500 1 10 100

20 4000 100 1000

Mea

n E

ject

a T

empe

ratu

re (

°C)




12 °C km-1

70 °C km-1

0

0.2

0.4

0.6

0.8

1

500 1 10 100

20 4000 100 1000

Fra

ctio

n of

mel

t in

ejec

ta




12 °C km-1

70 °C km-1

Fig. 11. (a) Mean ejecta temperature as a function of projectile and final rim-to-rim

nal rim-to-rim crater diameters. The bin width increases by a factor of 1.25. Ejectancludes impact melt, but not rock vapor.

∼10–100 km): small impacts excavate from the shallow subsur-ace, whereas very large impacts excavate from the periphery of theransient crater, and the geothermal gradient becomes less impor-ant in either case. The initial melt content of the ejecta (Fig. 11b)ncreases gradually with projectile diameter from a few percent to20% for ∼1–10 km impacts, and then increases steeply up to ∼300-m impacts, at which point the ejecta is composed of 100% melt. Asefore, the geothermal gradient dependence is most pronouncedor mid-size impactors (∼10–100 km).

Representative results of ejecta cooling models in purely con-uctive and hydrothermal environments are presented in Fig. 12and b, respectively. Here, a 350-m thick ejecta blanket with an ini-ial mean temperature of 1200 ◦C, typical for impactors ∼25 km iniameter, is emplaced over an initially cold surface and allowed toool. The differences between the two models are most noticeablen the later stages of cooling: at 500 years, maximum temperaturesn the hydrothermal model are ∼300 ◦C lower than in the purelyonductive model, and the shape of the temperature vs. depthurve is noticeably deformed due to the formation of water vapornd consequent heat loss at the peripheries of the ejecta blanket.e did not model the local explosive nature of the groundwater-

mpact ejecta interface, but note that the generation of lahars fromuch a process is expected. We find that the thermal pulse fromhe hot ejecta does not penetrate nearly as far into the subsurface

crater diameters. (b) Mean fraction of melt in ejecta as a function of projectile andfinal rim-to-rim crater diameters. Ejecta includes impact melt, but not rock vapor.

for the hydrothermal model, despite the presence of a geothermalgradient. Also, maximum temperatures are lower at 5000 yearscompared to the conductive model. However, the initial phases ofcooling for both models are nearly identical, due to the latent heatof fusion and the lack of water circulation through the hot and par-tially molten ejecta. This is noteworthy for age-resetting in zircon,which generally takes place at temperatures above 1000 ◦C (seebelow).

Results for Pb*-loss and consequent age-resetting within ejectablankets, derived from the coupling of ejecta cooling models todiffusion equations of Pb* in zircon (Section 2.5) are presentedin Fig. 13. For a 350-m th

Chemie der Erdeabramovo/papers/Abramov_Kring...Abramov et al. / Chemie der Erde 73 (2013) 227–248...

Documents

Transcript of Chemie der Erdeabramovo/papers/Abramov_Kring...Abramov et al. / Chemie der Erde 73 (2013) 227–248...