The Impact Environment of the Hadean Earth

Chemie der Erde 73 (2013) 227–248

Contents lists available at ScienceDirect

Chemie der Erde

jou rnal homepage: www.elsevier.de/chemer

Invited review

The impact environment of the Hadean Earth

a b c,d,e,∗

Oleg Abramov , David A. Kring , Stephen J. Mojzsis

United States Geological Survey, Astrogeology Science Center, 2255 North Gemini Drive, Flagstaff, AZ 86001, USA

USRA – Lunar and Planetary Institute, Center for Lunar Science & Exploration, 3600 Bay Area Boulevard, Houston, TX 77058-1113, USA

University of Colorado, Department of Geological Sciences, NASA Lunar Science Institute, Center for Lunar Origin and Evolution (CLOE), 2200 Colorado

Avenue, UCB 399, Boulder, CO 80309-0399, USA

Ecole Normale Supérieure de Lyon and Université Claude Bernard Lyon 1, Laboratoire de Géologie de Lyon, CNRS UMR 5276, 2 rue Raphael Dubois,

Villeurbanne 69622, France

Hungarian Academy of Sciences, Research Center for Astronomy and Earth Sciences, Institute for Geological and Geochemical Research, 45 Budaörsi ut,

H-1112 Budapest, Hungary

a r t i c l e i n f o a b s t r a c t

Article history: Impact bombardment in the ﬁrst billion years of solar system history determined in large part the initial

Received 1 July 2013

physical and chemical states of the inner planets and their potential to host biospheres. The range of

Accepted 13 August 2013

physical states and thermal consequences of the impact epoch, however, are not well quantiﬁed. Here, we

assess these effects on the young Earth’s crust as well as the likelihood that a record of such effects could be

Keywords:

preserved in the oldest terrestrial minerals and rocks. We place special emphasis on modeling the thermal

Hadean

effects of the late heavy bombardment (LHB) – a putative spike in the number of impacts at about 3.9 Gyr

Zircon

ago – using several different numerical modeling and analytical techniques. A comprehensive array of

Late heavy bombardment

impact-produced heat sources was evaluated which includes shock heating, impact melt generation,

Origin of life

uplift, and ejecta heating. Results indicate that ∼1.5–2.5 vol.% of the upper 20 km of Earth’s crust was

Thermal modeling

∼

Cratering processes melted in the LHB, with only 0.3–1.5 vol.% in a molten state at any given time. The model predicts

that approximately 5–10% of the planet’s surface area was covered by >1 km deep impact melt sheets. A

global average of ∼600–800 m of ejecta and ∼800–1000 m of condensed rock vapor is predicted to have

been 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-dimensional

models 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 would

be of Hadean zircons on a global scale. Zircons entrained in ejecta are projected to have the following

average global distribution after the end of the LHB: ∼59% with no impact-induced Pb*-loss, ∼26% with

partial Pb*-loss and ∼15% with complete Pb*-loss or destruction of the grain. In addition to the relatively

high erodibility of ejecta, our results show that if discordant ca. 3.9 Gyr old zones in the Jack Hills zircons

Contents

1. Introduction ...... 228

1.1. The late heavy bombardment hypothesis...... 228

1.2. Effects of the late heavy bombardment on Earth ...... 228

2. Thermal models for global bombardments ...... 230

2.1. Model construction ...... 230

2.2. Crater cooling ...... 234

2.3. Ejecta cooling ...... 235

2.4. Global bombardment models ...... 236

2.5. Diffusion models for zircons ...... 236

∗

Corresponding author at: University of Colorado, Department of Geological Sciences, Center for Lunar Origin and Evolution (CLOE), 2200 Colorado Avenue, UCB 399,

Boulder, CO 80309-0399, USA. Tel.: +1 303 492 5014; fax: +1 303 492 2606.

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

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

3. Results and analysis ...... 238

3.1. Global bombardment models ...... 238

3.2. Thermal ﬁelds within individual impact craters ...... 238

3.3. Thermal ﬁelds from globally emplaced impact ejecta ...... 240

4. Discussion ...... 242

4.1. LHB-induced ages to undamaged vs. damaged zircons in the Hadean crust ...... 242

4.2. Effects of zircon grain size...... 242

4.3. Effects of target lithotype ...... 242

4.4. Predictions for the Hadean terrestrial zircon record...... 242

5. Conclusions ...... 244

Acknowledgements ...... 245

References ...... 245

1. Introduction extend for long after (e.g., Bogard, 1995; Ash et al., 1996; Turner

et al., 1997; Kring and Cohen, 2002; Bogard, 2011; Cohen, 2013; see

Impacts fundamentally contribute to several key physical and Bottke et al., 2012). The most intense epoch of this solar-system-

chemical aspects of the evolution of the terrestrial (a.k.a. silicate wide bombardment is now commonly referred to as the “late heavy

or “rocky”) planets, the largest of the asteroids, as well as icy bombardment” (LHB), a term we use in this review. Thermal events

objects of the outer solar system. The planetary-scale effects of recorded in pre-4.0 Ga terrestrial zircons which cluster at ca. 3.9 Ga

bombardments range from profound to subtle, and include (i) mod- may also be suggestive of this bombardment (Trail et al., 2007;

iﬁcations in surface morphology expressed as cratered terrains; (ii) Abbott et al., 2012; Bell and Harrison, 2013), but aside from this

compositional changes via delivery of exogenous materials to the evidence there is little reliable conﬁrmation of the LHB from the ter-

crust or deep interior, melt mixing and differentiation of meteoritic restrial rock record (e.g., Anbar et al., 2001; Schoenberg et al., 2002;

and crustal components; (iii) alterations to primordial atmosphere cf. Frei and Rosing, 2005). We discuss the nature of the Hadean zir-

compositions and atmospheric densities, and thus strong forcing con evidence for an LHB in more detail later. Finally, the population

on paleoclimate; and (iv) deﬁning the initial conditions that helped structure of the main asteroid belt appears to preserve a record of

to determine the overall thermal structures of the affected worlds. giant planet migration that has been implicated in triggering the

Impacts on Earth have also had important biological consequences LHB (Minton and Malhotra, 2009). A self-consistent mechanism for

over geologic time. its origin has been proposed (Gomes et al., 2005; Morbidelli, 2010;

The effect of major bolide impacts on the habitability of rocky Morbidelli et al., 2012) which involved a rapid migration of giant

worlds is a two-edged sword. Impacts may be conducive to ancient planets which strongly perturbed both the asteroid belt and the icy

biospheres via the formation of new habitats such as hydrothermal planetessimal disk outside their initial orbits. Much remains to be

systems (e.g., Kring, 2000, 2003). Studies of preserved remains of done, however, to further constrain the timing, duration and inten-

post-impact hydrothermal systems (e.g., Versh et al., 2006) lend sity of the LHB, and to understand its physical effects on planetary

credence to the idea that the consequences of an impact could be surfaces.

benign for microbial life, or even advantageous to it (Cockell and It is important to note that although the LHB hypothesis pro-

Lee, 2002). They may also be deleterious to biomes through steril- vides a compelling explanation of the various observations cited

ization events of the surface zone by collision with catastrophically above, other interpretations of the ancient lunar record are also

large impactors and/or ﬁery rain from such impactors’ debris (e.g., possible. Some workers invoke a smooth post-accretionary decline

Chyba, 1993; Ryder, 2002). Analysis has shown that the largest to account for the cratered surface of the Moon, in which the ages of

impacts have the potential to sterilize the surface zone (e.g., photic lunar rocks older than ca. 3.9 Ga have been overprinted by the con-

zone of the oceans, shallow sub-surface of land). As such, the vio- tinuous effects of impact cratering over the last 4 Gyr (e.g., Baldwin,

lent environments for the origin of life on the Hadean Earth would 1974; Hartmann, 1975; Neukum and Ivanov, 1994; Hartmann et al.,

appear to have conﬁned the long-term continuity of the ﬁrst biomes 2000). Although we adopt the LHB scenario in our analysis, all of

to the deep subsurface (Abramov and Mojzsis, 2009a). the modeling techniques described herein are as applicable to a uni-

form post-accretionary decline as they are to a spike in the number

of impacts.

1.1. The late heavy bombardment hypothesis

The foundations of our current understanding of the timing and 1.2. Effects of the late heavy bombardment on Earth

intensity of impact metamorphism in the inner solar system are

derived from the study of lunar samples. Analyses of the lunar crust Several lines of evidence suggest that the bolide populations

(e.g., Turner et al., 1973; Tera et al., 1974) and impact melts (e.g., of the inner solar system LHB, at least in its later stages, were

Dalrymple and Ryder, 1993, 1996) returned by the Apollo and Luna dominated by main belt asteroids: (i) there is a statistically sig-

missions, as well as lunar meteorites (e.g., Cohen et al., 2000), indi- niﬁcant correlation between the size-frequency distribution of the

cate that rocks in the Moon’s crust were shock-metamorphosed or lunar highland craters and the present-day asteroid belt (Strom

brought to melting in events that typically group around and/or et al., 2005; Richardson, 2009; Marchi et al., 2012); (ii) trace ele-

seldom exceed in age approximately 3.9 Ga. These observations ment compositions of lunar impact melts point to asteroidal-type

have been interpreted in the context of a dramatic increase in the signatures (Kring and Cohen, 2002); (iii) fragments of projectiles

number of impacts over a relatively brief time span of 20–200 Myr recovered from ancient (>3.4 Ga) lunar regolith breccias imply that

(e.g., Ryder et al., 2000) originally termed the “lunar cataclysm” primitive chondritic asteroids dominated the latter stages of the

(Tera et al., 1974). Evidence for this epoch of bombardment is not basin-forming epoch (Joy et al., 2012); and (iv) recent dynamical

limited to the Earth–Moon system, as meteorites from multiple modeling studies by Bottke et al. (2012) indicates that comets were

parent bodies in the asteroid belt also appear to show the effects a minor player in the bombardment of the Earth and Moon during

of impact-induced metamorphism that extended at ca. 3.9 Ga, and the LHB based on the excellent match between the asteroid-only

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 229

model results and lunar crater counts (Marchi et al., 2012). Further- of impact melt sheets (e.g., Wielicki et al., 2012), and the latter

more, the Bottke et al. (2012) study points to the so-called “E belt”, results from partial or complete Pb* diffusion from the outermost

an extended and now largely extinct (cf. Hungarias) portion of the parts of a mineral grain, recrystallization, or the formation of a man-

asteroid belt between 1.7 and 2.1 AU from Earth, as the main source tle or overgrowth on pre-existing crystals. A large number of lunar

of the LHB impactors. The current state of knowledge, which now zircons have been dated by the U–Pb* method and most of these

advocates a “soft cataclysm” scenario for the LHB (Morbidelli et al., were done by spot analysis on high-resolution ion microprobes

2012), points to the start of this bombardment epoch at around (SHRIMP or Cameca ims1270/1280). These analyses have yielded

4.1–4.2 Ga. Under this hypothesis, basins continued to be produced a multitude of zircon core U–Pb* ages, with most recorded to be

albeit at a declining rate well after the conventional end of the LHB older than about 3.9 Ga. Based on this outcome, it was previously

at about 3.81 Ga, the proposed age of Orientale Basin. asserted that “lunar zircons did not record the cataclysm” (Meyer

Dynamical models (e.g., Gomes et al., 2005; Bottke et al., 2012) et al., 2008). Partial resetting of zircon grains by impacts, however,

and analytical estimates (e.g., Minton and Malhotra, 2010) show remains a distinct possibility, as is complete age-resetting of zir-

that the median impact velocity on Earth for the LHB bolides was cons within melt sheets generated by large basin-forming impacts

−1

approximately 20 km s . Estimates of material accreted by Earth (Nemchin et al., 2012). Of note is a study by Nemchin et al. (2009),

during the impact cataclysm, scaled from lunar crater counts (e.g., which examined four Apollo 14 breccias and reported that the

Hartmann et al., 2000; Ryder, 2002) and derived from dynam- U–Pb* system was completely reset at ca. 3.9 Ga (LHB age) in lunar

ical modeling (Levison et al., 2001; Gomes et al., 2005) range apatite, but was undisturbed in zircons from the same sample. A

20 20 20

∼

from 1.3 × 10 kg to ∼2.2 × 10 kg, with a mean of ∼2 × 10 kg. similar study of an Apollo 17 melt breccia by Grange et al. (2009)

Although this constitutes a mere 0.015% of Earth’s mass, it has been also reported resetting of the U–Pb* system in apatite at about

estimated that the number of impact-generated hydrothermal sys- 3.9 Ga, but noted that although zircon grains within the sample

tems on Earth exceeded those generated by volcanic activity at the showed older ca. 4.3 Ga ages, a zircon aggregate that occurred as a

time (Kring, 2000; see discussion in Ivanov and Melosh, 2003). Dur- rim around a baddeleyite (ZrO2) grain had an “LHB age” (ca. 3.9 Ga).

ing the LHB at least 1700 craters greater than ∼20 km in diameter This important result provides good constraints on the thermal his-

were produced on the Moon (e.g., Wilhelms, 1987). This value scales tory of the samples because the differential Pb*-isotope retentivity

by a factor of about 20 for the Earth depending on factors such as of zircon and apatite (e.g., Cherniak et al., 1991) coupled with pet-

impact velocity and size distribution (e.g., Zahnle and Sleep, 2002). rographic context can be used to more precisely resolve the impact

Simple extrapolation would indicate that at least ∼34,000 large history of the Moon.

impact events affected the Hadean Earth. We consider this to be a Data from terrestrial craters provide readily testable insights

conservative (low) estimate due to the fact that lunar crater erasure into the complete and partial resetting of radiogenic systems by

suppresses crater count statistics, and the higher average impact impacts (Deutsch and Shärer, 1994). Krogh et al. (1993) performed

velocities onto the Earth lead to generation of larger craters than on U–Pb* dating of zircons from the Cretaceous–Paleogene (K–Pg) dis-

the Moon. The stochastic cratering model of Abramov and Mojzsis tal ejecta from a site in the Raton Basin of southern Colorado; results

(2009a) used total mass delivered and size-frequency distribu- show that both the extent of displacement from the 544 ± 5 Ma pri-

tions of the impacting population as constraints to estimate that mary age of zircons toward the time of impact at 65.5 ± 3.0 Ma,

∼

100,000 craters > 20 km in diameter, or ∼3000 craters > 100 km, as well as the degree of discordance (attributable to diffusional

were formed on Earth in the LHB. This output agrees well with the Pb*-loss in the hot ejecta) correlates closely with the extent to

2500–3000 craters > 100 km in diameter earlier proposed by Grieve which the zircon grain was shocked. They concluded that Pb*-loss

(1980). resulted from a post-impact thermal pulse while the zircon was

A great deal of our current understanding of impact-produced aloft in the ﬁreball cloud. The simplest explanation for the results

shock metamorphism and age-resetting of radiogenic systems in of Krogh et al. (1993) is that the zircons they analyzed contained

minerals derives from studies of lunar materials (e.g., Heisinger two components: a concordant, 544 ± 5 Ma core, and a discordant,

and Head, 2006). Speciﬁcally, it has been hypothesized that the 65.5 ± 3.0 Ma outer rim, with the relative proportions of the two

metamorphism of the lunar crust by the LHB led to widespread components dependent on the degree of shock (see Leroux et al.,

radiogenic argon (Ar*) and (to a lesser extent) radiogenic lead (Pb*)- 1999) and/or thermal diffusive loss of lead. Similar conclusions

loss – correlated to disturbances in the Rb–Sr system – as measured were reached by Kalleson et al. (2009) for zircons from the ∼5-

in returned lunar rocks (Turner et al., 1973; Tera et al., 1974). Sub- km Gardnos impact structure in Norway. The Onaping Formation

40 39

sequent high-precision Ar– Ar analyses of Apollo 14, 15 and 17, of Sudbury crater (southern Ontario, Canada), contains zircons that

207 206

Luna 24, and highlands meteorite impact-melt rocks show a range appear to have two components based on Pb*/ Pb* ages: one

of ages (Cadogan and Turner, 1977; Swindle et al., 1991; Dalrymple with the age of target lithologies, and another corresponding to the

and Ryder, 1993; Cohen et al., 2000; Culler et al., 2000; Fernandes time of impact, with the relative proportion of the latter increasing

et al., 2000; Levine et al., 2004; Cohen et al., 2005; Norman et al., with the degree of impact shock (Krogh et al., 1996). Complete and

2006; Zellner et al., 2009a,b; Norman et al., 2010; Fernandes et al., partial U–Pb* age-resetting has also been observed in zircons from

2013), but few that are older than approximately 4.0 Ga. The Ar*- the Vredefort impact structure in South Africa (Kamo et al., 1996;

loss is attributable to impact heating, whereby high temperatures Moser et al., 2011) and the Haughton impact structure in Canada

lead to argon diffusion and outgassing (McDougall and Harrison, (Schärer and Deutsch, 1990).

1988). Both Pb*- and Sr-loss in whole rock samples cited above The oldest terrestrial zircons so far identiﬁed are about 4.37 Gyr

require at least partial melting of the target material to mobilize old and are the only known datable materials that formed prior to

these elements. the LHB on Earth. As such, these minerals have been intensively

Along with age-resetting in whole rocks, isotopic disturbances used to probe early Earth conditions (e.g., Harrison, 2009). The

within individual minerals that preserve Pb*/U ratios, particularly U–Th–Pb* zircon ion microprobe depth-proﬁling technique was

zircon (Zr(SiO4)), apatite (Ca5(PO4)3(OH, F, Cl)), and to a lesser developed by Mojzsis and Harrison (2002) to resolve the age and

extent whitlockite (Ca9MgH(PO4)7), have been increasingly used chemical compositions of discrete (micrometer to sub-␮m) zones

as indicators of impacts (e.g., Pidgeon et al., 2010; Liu et al., in individual zircon crystals that correspond to distinct thermal

2012). These indicators generally fall into either of two cate- and/or chemical events to have affected the grain. A study by Trail

gories: complete or partial age-resetting. The former category et al. (2007) used this method to explore for evidence of the LHB in

includes neoform mineral growth within the para-igneous regimes a small collection of pre-4.0 Ga zircons from the Jack Hills and Mt.

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

Narryer localities of the Narryer Gneiss Complex (NGC) in Western 1990; Ahrens, 1993), or their densiﬁcation and subsequent tipping

Australia. These workers reported the results of their depth pro- into runaway greenhouse regimes (e.g., Segura et al., 2012).

ﬁles through 2- to 4 ␮m-wide discordant ca. 3.95 Ga mantles over

older original igneous cores in 3 of the 4 zircons they analyzed.

2. Thermal models for global bombardments

While it was argued that these overgrowths may represent thermal

events endogenous to the crust that pre-date the geologic record,

We now evaluate an assortment of impact-produced heat

the ages also happen to coincide well with independent estimates

sources that affect silicate crusts: post-impact temperature distri-

of peak bombardment from the lunar record cited above. More-

butions associated with a wide range of impact events that account

over, these thin mantles showed Pb*-loss (up to 90% discordance)

for heat deposited by shock into the crust and include the formation

over narrow domains that could be interpreted to be the result of

of melt, uplift of hot deep crustal material by impacts, and heat from

impact-induced heating (Trail et al., 2007). If the data indeed rep-

ejecta blankets deposited by impacts. The results include crustal

resent thermal events of the impact cataclysm recorded as zircon

melting as a function of time, fractions of crust melted by impactors

overgrowths, it would be the ﬁrst time such a signal has been found

within a given size bin, percentage of the surface covered by impact

on Earth. Subsequent work by Abbott et al. (2012) showed that 8 of

melt, temperatures and thicknesses of ejecta blankets associated

22 Hadean zircons preserved overgrowths with ages between ca.

with impacts of a given size, and the characteristics of the global

3.85–3.95 Ga and characterized by temperatures obtained from Ti-

xln surface ejecta cover following the bombardment. Furthermore, this

in-zircon thermometry (Ti ; Watson and Harrison, 2005; Watson

study aims to evaluate the thermal effects of impacts on the crust

et al., 2006) that are consistently higher than “normal” igneous core

that may be preserved in the chemistry of Hadean zircon grains that

values. A probabilistic analysis of the data of Abbott et al. (2012)

are known to pre-date the LHB. Laboratory-derived element diffu-

shows that there is an overall ∼13% probability of obtaining ages

sion equations require the input parameters of both temperature

in between 3.85 Ga and 3.95 Ga in Hadean Jack Hills zircons. This

and time spent at that temperature to evaluate impact-induced age

comports remarkably well with our model predictions that approx-

resetting, Pb*-, Ti-, and REE-loss in zircons. The models reported

imately 15% of the zircons should show ages for this time span (see

herein can evaluate such conditions on a global scale as well as

Section 4.4). Recent work by Bell and Harrison (2013) has added

within individual impact craters and ejecta blankets, and create

to the growing dataset of LHB-era ages in the Hadean zircons from

output that can be tested against the Hadean zircon record.

Western Australia; an interpretable record of the late heavy bom-

bardment on Earth may have ﬁnally been found.

Recent work by Wielicki et al. (2012) reported U–Pb* ages, 2.1. Model construction

xln

rare earth element (REE) abundances and Ti thermometry for

111 zircon grains from impact melts of the terrestrial craters The stochastic cratering model we used is a Perl program based

Manicouagan, Morokweng, Sudbury, and Vredefort. These workers in part on the work of Richardson et al. (2005). It has the following

performed a statistical comparison of data from these impact melt inputs: (i) size-frequency distribution (SFD) of the impactor popu-

−1

zircons to 69 Hadean (>4 Ga) zircon grains from the NGC outcrops in lation; (ii) mass delivered per year (kg yr ); (iii) LHB duration (in

xln

Western Australia. The results of their Ti thermometry compar- Myr); (iv) total model run time (if less than the LHB duration); (v)

ison indicate that crystallization temperatures of Hadean zircons output frequency; and (iv) model area (in km ). The default output

◦

formed in magmas were, on the average, ∼100 C lower than of frequency of our Baseline stochastic model is 1/1000 the duration

those produced by impacts. Wielicki et al. (2012) conclude that of our chosen LHB timescale, or 0.1 Myr. The model area is typi-

8 2

impact-generated melts were not a dominant mechanism of pro- cally the surface area of the Earth, 5.1 × 10 km , although smaller

ducing the bulk of the pre-4 Ga Hadean igneous zircon record, even areas can be speciﬁed in the model to examine the localized thermal

if the mantle overgrowths reported in Trail et al. (2007) and Abbott effects of smaller impactors.

et al. (2012) may have been formed by impact-induced thermal Using these inputs, the stochastic cratering model calculates

events. Wielicki et al. (2012) further showed that REE abundance the number of impactors of a given diameter striking a speciﬁed

patterns in impact-produced zircons are indistinguishable from area within a speciﬁed time period. The density of the impactors

−3

those of contemporary igneous or Hadean grains, but make the is assumed to be 2700 kg m , which approximates the average

point that REE partition modeling could be useful in discriminating density of main belt asteroids (Birlan, 2002). The impactors are

between newly formed and age-reset zircon grains. It is clear that randomly distributed in space and time, but the mass and SFD con-

the Hadean zircons are powerful tools for discerning events coinci- straints are rigorously enforced. The output of the model includes

dent with the early evolution of life, but that they are still difﬁcult time and coordinates of impact, impactor diameter, and the rim-

to interpret. To provide a better interpretive frame work for the to-rim diameter of the ﬁnal crater calculated using Pi-group scaling

zircons, we investigate in detail the thermal environment created laws and the Abramov and Kring (2005) expression for converting

by impact bombardment during the LHB with an eye toward how transient to ﬁnal crater diameters.

this could have affected the early biosphere. The stochastic cratering model was used to generate the

That the biological effects of impact bombardments may be both four LHB scenarios: (i) “Baseline”, with a total delivered mass of

20 −1

lethal and benevolent has been explored previously by, among oth- 2 × 10 kg, impact velocity of 20 km s , and a duration of 100 Myr;

−1

ers, Oberbeck and Fogleman (1989) and Chyba and Sagan (1992). A (ii) “40 km s ”, with the impact velocity doubled; (iii) “10×”,

consensus view is that impacts can fundamentally affect the hab- which increased the total mass delivered by a factor of ten; and (iv)

itability of a planet in a variety of ways, including: (i) sterilization “10 Myr”, which reduced the duration by factor of ten. These values

of the surface by thermal radiation from ejecta re-entry and depo- were purposefully chosen to express end-member scenarios in the

−1

sition of global layers of hot ejecta (e.g., Sleep et al., 1989; Segura bombardment. The 40 km s impact velocity is meant to approx-

et al., 2002); (ii) vaporization of oceans (e.g., Chyba, 1990; Zahnle imate cometary impacts: Although, as described in Section 1.2,

and Sleep, 1998); (iii) creation of long-lived hydrothermal systems, there are several indications that the inner solar system LHB was

which can serve as sites of the origin of life or provide refuges dominated by main belt asteroids, it is also possible that this con-

for existing life (e.g., Kring, 2000; Abramov and Mojzsis, 2009a,b); dition applied only to its later stages, which may have overprinted

(iv) modulation of mantle convection, core dynamos, and magnetic an initial cometary signature (e.g., Gomes et al., 2005). A summary

ﬁelds (e.g., Roberts et al., 2009; Watters et al., 2009); and (v) ero- of input parameters used in the stochastic cratering model is

sion of atmospheres (Arrhenius et al., 1974; Vickery and Melosh, given in Table 1. The size-frequency distribution of the impacting

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

1e+06 1e+06 Baseline 10X delivered mass 100000 100000

10000 10000

1000 1000

100 100

10 10 Number of impacts Number of impacts 1 1

0.1 0.1

a. 1 10 100 1000 b. 1 10 100 1000 Impactor diameter (km) Impactor diameter (km)

1e+21 1e+21 Baseline 10X delivered mass

1e+20 1e+20

1e+19 1e+19

1e+18 1e+18 Mass contribution (kg) Mass contribution (kg)

1e+17 1e+17

c. 1 10 100 1000 d. 1 10 100 1000

Impactor diameter (km) Impactor diameter (km)

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 contribution

to the LHB by impactors within each size bin. (d) Total mass contribution to the LHB by impactors within each size bin, 10× delivered mass. The bin width increases by a

factor of 1.25. Only impactors larger than 1 km in diameter are included.

Table 1

is produced, it pools in the topographically lowest regions of the

Summary of impact bombardment properties. References and/or justiﬁcations for

crater basin and forms a melt sheet. The ﬁnal major heat source is

these values are provided in the text (Section 2.1). Model abbreviations are as

the central uplift, which is material that has been uplifted from

follows: IH, impact heating (includes both subsurface and ejecta heating); SC,

stochastic cratering. lower, warmer regions of the crust during the formation of the

crater. The relative importance of the melt sheet and the cen-

Parameter Value(s) Units Models used in

tral uplift increases with crater size: small, simple craters, such as

−1 a

Impact velocity 20, 40 km s IH, SC

the ∼1-km Meteor Crater in northern Arizona, produce negligible

◦ a

Impact angle 45 IH, SC

−3 amounts of melt and uplift, but the melt sheet and central uplift

Impactor density 2700 kg m IH, SC

form a progressively larger fraction of the thermal budget with

LHB duration 10, 100 Myr SC

20 21

Total mass delivered 2 × 10 , 2 × 10 kg SC increasing crater diameter. Melt sheets generally contain signiﬁ-

Size-frequency distribution Asteroid belt – SC

cantly more energy than central uplifts (Daubar and Kring, 2001;

Used by stochastic cratering model only for calculating ﬁnal rim-to-rim crater Thorsos et al., 2001). A fraction of shocked target material leaves

diameters. the crater as vapor or ejecta, with the ratio of heat retained to heat

removed increasing with increasing crater diameter. Thus, large

population is modeled after the present-day asteroid belt (Bottke basins retain proportionally more hot material than smaller craters.

et al., 2005; Section 1.2), and is illustrated in Fig. 1 for both A temperature distribution associated with a given impact

Baseline and 10× scenarios. Although the number of impactors must take into account the heat sources described above (shock-

declines quickly with increasing diameter, the delivered mass emplaced heat, central uplift, impact melt) as well as properly

increases steeply, implying that most of the energy would have account for material ejected from the crater. Temperature distribu-

been delivered by relatively few very large (≥100 km in diameter) tions can be generated by hydrocode simulations (e.g., Ivanov and

impact events. Deutsch, 1999; Ivanov, 2004; Turtle et al., 2003). The advantage of

A key starting condition for modeling the thermal effects of using hydrocodes is that they allow tracking of movements of hot

impact bombardment is the distribution of subsurface tempera- material during the crater’s modiﬁcation stage, which is difﬁcult

tures immediately after the impact. Three signiﬁcant long-term to model analytically. Severe computational constraints, however,

heat sources are created by a large impact event: shock-deposited preclude the use of a hydrocode simulation for tens of thousands of

heat, a melt sheet, and a central uplift. The shock wave compresses individual impacts that are needed to account for planetary-scale

∼

the target material, depositing large amounts of energy, and the thermal models. For this project 60,000 post-impact temperature

subsequent decompression yields waste heat, which increases the distributions were required. Hence, we made use of the analytical

ﬁnal temperature of the target (e.g., Ahrens and O’Keefe, 1972). For methods (e.g., Abramov and Kring, 2005; Abramov and Mojzsis,

large impacts, sufﬁcient heat is deposited to induce phase changes 2009a,b) described below, which have the advantage of rapidly

and the melting and vaporization of target rocks. If enough melt generating temperature distributions for a crater of any arbitrary

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

diameter. Tens- to hundreds of thousands of thermal ﬁelds of temperature and geothermal gradients that were tested are listed

impacts in the crust can be analyzed in this manner. in Table 2.

The initial temperature distribution, representing shock- Once the initial subsurface temperature distribution is calcu-

heating only, is analytically calculated using an expression for lated, the volume of the transient crater (which approximately

speciﬁc waste heat (Ew) derived from the Murnaghan equation represents material vaporized, ejected, or displaced by the impact)

of state by Kieffer and Simonds (1980): is removed from the model. The transient crater diameter, as mea-

− sured at the pre-impact surface, is calculated using the Pi-group

1 2K V Pn 1/n

0 0 scaling laws (e.g., Holsapple and Schmidt, 1982; Housen et al., 1983)

E = PV − 1 − + 1

w 2 0 n K

0 and corrected for the impact angle using the approximation of

Pierazzo and Melosh (1999): 1−(1/n)

K0V0 Pn

+ − +

1 1 (1) 0.78 0.44 −0.22 1/3

− = n(1 n) K

0 Dtc 1.16d vi g sin (5)

where P is the peak shock pressure, K0 is the adiabatic bulk modulus where d is the impactor diameter and g is the terrestrial acceleration

at zero pressure, n is the pressure derivative of the bulk modulus, of gravity. The above expression is valid only if the impactor and

and V0 is the speciﬁc uncompressed target volume (1/t). For a target density are assumed to be equivalent (here, 2700 kg/m ).

granite target chosen here (see Section 4.3) to represent the pres- The depth of the transient crater is estimated by multiplying the

ence of some fraction of felsic type crust in the Hadean (Mojzsis rim-to-rim diameter of the transient crater by 0.25 (Melosh, 1989).

et al., 2001), the uncompressed density t is 2700 kg/m , K0 is Several analytical expressions have been developed to estimate

35.7 GPa, and n is 3.94 (McQueen et al., 1967). the volume of melt produced during the formation of an impact

Hydrocode simulations suggest that the center of the impact, crater of a given diameter. Perhaps the simplest and most com-

from which the shock originates, is at a depth equal to approxi- monly used expression is that by Grieve and Cintala (1992, 1995,

mately the radius of the impactor (Pierazzo et al., 1997; Pierazzo 1997), derived using an analytical model (Cintala, 1992) based on

and Melosh, 2000), although a small variation with impact velocity a modiﬁed Murnaghan equation of state and veriﬁed with obser-

is observed. Surrounding the impact center is the isobaric core, a vations at terrestrial impact structures (Grieve and Cintala, 1992).

region where shock pressure is constant or slowly decaying (e.g., In that expression, melt volume is deﬁned as cDtc, where c is a

Croft, 1982). The ratio of isobaric core radius to impactor radius material-, velocity-, and gravity-dependent constant, and d is a con-

shows only a small dependence on impact velocity and projectile stant deﬁned as 3.85 for all materials, impact velocities, and surface

and target compositions in hydrocode simulations and is approxi- gravities.

mately unity (Pierazzo and Melosh, 2000). Shock pressure P drops A new melt scaling model by Abramov et al. (2012) agrees well

off with distance r according to the power law: with the earlier results of Grieve and Cintala (1992, 1995, 1997)

in terms of absolute melt volumes predicted, and validates, builds

−k

= r upon, and implements several improvements to that expression.

P A (2)

Rp Where the new study differs, however, with the Grieve and Cintala

model is that melt volumes for both a given crater and a given

where R is the radius of the projectile, k is the decay exponent, and

p projectile were derived, with the latter being:

A is pressure at r = Rp (e.g., Pierazzo and Melosh, 2000). The decay

−0.85 p 3 1.7 1.3

exponent k varies with impact velocity: = Vmelt 0.22Em Dp vi sin (6)

≈ +

k 0.625 log(vi) 1.25 (3)

where Em is the speciﬁc internal energy of the target at shock pres-

with vi being in kilometers per second (Ahrens and O’Keefe, 1987). sure that results in melting upon release (please refer to Bjorkman

Additional validation of this expression can be found in Pierazzo and Holsapple (1987) for a full deﬁnition), and has a value of

6 −1

∼ ×

and Melosh (2000), who concluded, based on CTH hydrocode sim- 5.2 10 J kg for granite (Pierazzo et al., 1997), p is projective

ulations, that the volumetric pressure decay exponent nV (nV = k/3) density, and Dp is projectile diameter.

◦ ◦

can be considered constant for impacts between 30 and 90 and The Abramov et al. (2012) expression provides additional ver-

has a weighted average value of 0.671. This corresponds to a k of iﬁcation of the analytical shock-heating model used in this work.

2.01, and agrees well with the Ahrens and O’Keefe (1987) predic- For the purposes of this comparison, melt volumes were derived

−1

tion of 2.06 for the 20 km s impact investigated by Pierazzo and from the temperature increase (T) in the target predicted by the

Melosh (2000). shock-heating model. To keep the comparison general, a target with

The term A depends on target and impactor properties, and is no geothermal gradient and a homogeneous initial temperature of

◦

based here on an estimate by Collins et al. (2002), corrected for the 0 C was assumed. This allows a straightforward comparison to the

impact angle based on the results of Pierazzo and Melosh (2000): Baseline expression (Eq. (6)) which does not include effects of tar-

get temperature; a correction for pre-existing target temperature

= i is also given in Abramov et al. (2012).

A sin (4)

4 Following Abramov and Kring (2007), the latent heat of fusion

in the shock-heating model was modeled using the approximation

where is impactor and target density, both of which are assumed

−3 of Jaeger (1968), following Onorato et al. (1978) in a study of the

to be 2700 kg m , consistent with a rocky asteroid striking a plane-

Manicouagan (Quebec, Canada) impact melt sheet, by replacing the

tary crust, vi is impact velocity, and is the impact angle. An impact

◦ heat capacity Cp in the temperature range between the liquidus (TL)

angle of 45 is used in the present investigation because it is the

and the solidus (TS) with

most probable impact trajectory (Gilbert, 1893; Shoemaker, 1962).

To obtain the temperature increase T, the speciﬁc waste heat L

C = C + (7)

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

−1 ◦ −1 L S

837 J kg C for granite (Section 4.3), as listed in the HEATING

−1

materials library (Childs, 1993). The subsurface temperature distri- where L is the latent heat of fusion (418 J kg for granite as reported

bution due to shock-heating is then obtained by adding geothermal in Birch et al., 1942 and Jaeger et al., 1959), and TS and TL are solidus

◦

temperatures to the impact-deposited heat. The values for surface and liquidus temperatures, set to 997 and 1177 C, respectively.

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 233

Table 2

Summary 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 IH

Adiabatic bulk modulus at zero pressure 35.7 × 10 Pa IH

−1 ◦ −1

Heat capacity 837 J kg C IH, CC, ECC, ECH

−3

Density 2700 kg m IH, CC, ECC, ECH

−1

Latent heat of fusion 418 J kg IH, CC, ECC, ECH

◦

Liquidus temperature 1177 C IH, CC, ECC, ECH

◦

Solidus temperature 997 C IH, CC, ECC, ECH

◦

Surface temperature 20 C IH, CC, ECH

◦ −1

Geothermal gradient 12, 70 C km IH, CC, ECH

−1 ◦ −1

Thermal conductivity 2.51 W m C CC, ECC, ECH

Porosity (ejecta) f(z), 40% at the surface Unitless ECH

Porosity (basement) f(z), 20% at pre-impact surface Unitless ECH

−2

Permeability (ejecta) f(z,T), 10 at the surface Darcies ECH

−3

Permeability (basement) f(z,T), 10 at pre-impact surface Darcies ECH

Melt was deﬁned as material heated above the average granite which presents melt volumes as a function of impactor diame-

◦

melting temperature of 1087 C. ter with impact angle and velocity held constant. Fig. 2b shows

Results of the melt volume comparisons are presented in Fig. 2. melt volumes as a function of impact velocity, which differ from

−1

Melt volumes predicted by the shock-heating method used in this Abramov et al. (2012) by almost a factor of two for 10 km s

work and Abramov et al. (2012) differ by less than 20% in Fig. 2a, impacts; however, this difference decreases with increasing veloc-

−1

ity, becoming less than 20% for 20 km s impacts. Fig. 2c shows

melt volumes as a function of impact angle with comparisons to

109

Abramov et al. (2012) and Pierazzo and Melosh (2000), who derived a. Impact angle = 45°, v = 20 km s-1

108 i

melt volumes from shock pressures predicted by CTH hydrocode 7

) 10

3 calculations. Melt volume decreases as a function of impact angle

106

at the same rate as in Abramov et al. (2012), and the absolute dif-

10 ference between the two approaches is again under 20%. It should

10 be noted, however, that Abramov et al. (2012) and Pierazzo and

3 −3

10 Melosh (2000) assumed a density of ∼3300 kg m for the pro-

Melt Volume (km 2 −3

10 jectile and ∼2700 kg m for the target, whereas this particular

1 Earth (granite), this work

10 simulation assumes approximately equivalent densities. If melt Earth (granite), Abramov et al. (2012)

10 volumes are adjusted by a factor of ∼1.22 to account for these den-

1 2 5 10 20 50 100 300

sity differences (∼3300/∼2700, see Abramov et al., 2012), the ∼20%

Projectile Diameter (km)

difference described above vanishes and results in a near-perfect

b. match to Abramov et al. (2012) and a close match to Pierazzo and 5 Impact angle = 45°, Dp = 10 km

10 Melosh (2000). )

With the above validation, the amount of melt can be estimated

for every impact in the model using the shock-heating method

(Eq. (1)), and corrected for the effects of target temperature using

104

the surface temperature and geothermal gradient speciﬁed in the

model. To accomplish this, the calculated temperature increase T

Melt Volume (km

Earth (granite), this work due to shock is added to the pre-existing temperature at a given

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

3 depth, and, if appropriate, adjusted for latent heat of fusion using

10 ◦

10 20 50 100 Eq. (7). Material heated to a ﬁnal temperature of 1087 C or above

-1

Impact velocity (km s ) is considered herein to be melt.

During the formation of complex craters, warm material from

c. D = 10 km, v = 20 km s-1

p i depth is uplifted in the central regions of the crater, forming another

heat source (e.g., Daubar and Kring, 2001). The heat contributed )

104 by the central uplift can be estimated from the vertical distance

traversed by the uplifted material and the pre-impact temperature

as a function of depth, calculated from surface temperature and

geothermal gradient. The maximum vertical displacement due to

the stratigraphic uplift, based on observations at terrestrial craters, Melt Volume (km

Earth (granite), this work

is estimated by: Earth (granite), Abramov et al. (2012) Earth (granite), Pierazzo and Melosh (2000)

103 1.1 = 30 45 60 75 90 hsu 0.06D (8)

Impact Angle (degrees)

where D is the ﬁnal crater diameter in kilometers (Grieve et al.,

Fig. 2. Melt volume comparisons for model validation. Effects of target temperature 1981). The structure and diameter of the uplift is modeled based on

are not included here. (a) Melt volume as a function of projectile diameter. (b) Melt

SALE-B hydrocode simulations of Ivanov and Deutsch (1999). The

volume as a function of impact velocity. (c) Melt volume as a function of impact

vertical displacement decreases linearly with depth, and reaches

angle. Melt volumes in this work would be ∼22% higher if adjusted for projectile

zero at 1.25 times the depth of the transient crater. The verti-

and target densities assumed in Pierazzo and Melosh (2000) and Abramov et al.

(2012), resulting in a near-perfect match. 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 of

distance from impact center, and material within the transient crater is removed from the model. This vaporized/ejected/displaced material is treated separately in the ejecta

model. (ii) Topography is eliminated and the temperature distribution is moved up to the surface, approximating uplift. (iii) Geothermal and central uplift temperatures are

added, yielding the ﬁnal model temperature distribution.

the crater x as (x − Rcp) , reaching zero at x = Rcp, where Rcp is the to yield T distributions. The T distributions in the library are

lateral extent of the uplift, approximately 0.22 of the ﬁnal crater two-dimensional, axially symmetric, have a resolution of 75 33

◦

radius, which is derived from the morphometry of lunar craters elements, and include all parts of the crater where T exceeds 1 C.

(Pike, 1985) and is entirely consistent with hydrocode simulations Variables include impactor diameter, varied in increments of 1 km,

−1

of Ivanov and Deutsch (1999). A typical temperature distribution impactor velocity, varied in increments of 1 km s , as well as sur-

associated with a central uplift is shown in the lower left panel of face temperature and geothermal gradient, for which several values

Fig. 3. are tested as described below.

A ﬁnal diameter is calculated for every crater predicted by the For the purposes of this work, the initial temperature of ejecta

stochastic cratering model for the purposes of estimating uplift produced by a given impact was calculated by volumetrically aver-

geometries, ejecta blanket thicknesses, and the degree of global aging the temperatures to which non-vaporized material ejected

resurfacing. The rim-to-rim diameter of the ﬁnal crater is calcu- from the transient crater was heated. It is also recognized that con-

lated using the following relationship (Abramov and Kring, 2005): densed rock vapor would deliver a signiﬁcant thermal component

for very large craters, and the volume of vapor produced by each

1.125 particular impact was calculated. Temperature distributions and

Dtr

D = 0.91 (9) dimensions of the transient crater are calculated as described ear-

D0.09

Q lier in this section. For this calculation, it was assumed that material

above the excavation depth, computed as 1/2 of the transient crater

where Dtr is the rim-to-rim diameter of the transient crater, which

depth, was ejected, whereas material below the excavation depth

is measured above the pre-impact surface and is ∼1.2 times larger

was displaced, compacted and distributed along the crater ﬂoor

than Dtc (Melosh, 1989), and DQ is the simple-to-complex transition

and walls (Melosh, 1989). Temperature of the asthenosphere was

∼

diameter, which is 3000 m for Earth, based on observations at ter- ◦

set to a constant of 1700 C. Melt volumes are calculated using the

restrial craters (Grieve, 1987) and gravity-scaling of observed lunar

Murnaghan EOS-based shock-heating method, with full account-

morphometries (Holsapple, 1993). All values are in meters, and

ing for latent heat of fusion. Vapor volumes are estimated based

Eq. (9) is applicable only to complex craters (those with diameters ◦

on a vaporization temperature of 3327 C for granite, as estimated

greater than ∼3 km).

by Pierazzo et al. (1997) using a weighted average of the available

For most thermal models presented in this work, and with the

vaporization temperatures of its components (Ahrens and O’Keefe,

exception of individual crater models, ﬁnal crater topography is

1972). The process for calculating impact ejecta temperatures is

omitted because large terrestrial craters (>100 km in diameter)

shown schematically in Fig. 4.

have very shallow depth-to-diameter ratios. Grieve and Pesonen

(1992) estimate based on data from terrestrial craters that the

0.43

apparent (rim-to-ﬂoor) depth varies as 0.15D for crystalline 2.2. Crater cooling

targets, which yields a depth of ∼1.1 km for a 100-km crater. For

the purposes of the thermal models, this can be considered ﬂat. A Conductive post-impact cooling of impact craters is a reason-

graphical illustration of how ﬁnal post-impact temperature distri- ably well-understood process and has been modeled by a number of

butions are calculated, taking into account shock-deposited heat, workers, with the cooling timescales of craters 20–200 km in diam-

3 6

geothermal temperatures, and uplift, is presented in Fig. 3. eter estimated at 10 –10 years (e.g., Onorato et al., 1978; Daubar

A library of post-impact T distributions, which include the and Kring, 2001; Turtle et al., 2003; Ivanov, 2004; Abramov and

combined effects of shock heating and uplift, is generated using Kring, 2004, 2005, 2007). For this problem we employed HEATING

the methods described above. Background temperatures are sub- 7.3, a multi-dimensional, ﬁnite-difference heat transfer code sys-

tracted from ﬁnal temperature distributions (Fig. 3, bottom right) tem developed by Oak Ridge National Laboratories (Childs, 1993).

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 235

to that in the ejecta blanket, whereas the lower 100 nodes have a

resolution coarser by a factor of 10. Thickness and initial tempera-

ture of the ejecta are speciﬁed as inputs. Temperatures in the range

◦

of 1000–1500 C, chosen by radiogenic Pb* mobility estimates in

◦

zircon and tested in 100 C increments, and ejecta thicknesses

of 100 and 350 m were also tested. The model is run until the

entire ejecta blanket cools to temperatures at which no further

age-resetting is possible, which can range from less than a year to

over 10 years, depending on the initial thickness and temperature

of the blanket.

The model described above only includes thermal conduc-

tion and radiation, however, the rate of ejecta cooling as well as

the degree of subsurface heating would be different in a “wet”

environment characterized by the presence of groundwater and

atmospheric precipitation. In particular, higher heat capacities and

the latent heat of vaporization of water would result in lower tem-

Fig. 4. Graphical illustration of how ejecta temperatures are calculated. Transient

peratures, and the venting of steam would effectively and rapidly

crater (white line), with dimensions derived from Pi-group scaling laws, is superim-

posed on a post-impact temperature distribution. Temperatures within the transient remove heat from the system. To quantify these effects, a com-

cavity above the excavation depth (dashed line) are volumetrically averaged. parison model that included the presence and vaporization of

water, as well as hydrothermal venting, was assembled for a 350-m

◦

thick, 1200 C ejecta blanket based on HYDROTHERM 2.2, a ﬁnite-

A two-dimensional (r − z) cylindrical coordinate system is used to

difference computer code developed by the U.S. Geological Survey

take advantage of the model crater’s radial symmetry. Post-impact

to simulate water and heat transport in porous media (Hayba and

temperature distribution is computed as described elsewhere (Sec-

Ingebritsen, 1994). The model is laid out on a two-dimensional grid

tion 2.1). The bottom boundary has a prescribed heat ﬂux needed

of 75 × 75 elements, with the ejecta layer at a resolution of 7 m

to maintain the speciﬁed geothermal gradient. Heat is lost by radi-

and the basement rocks at a resolution of 70 m. The model’s upper

ation through the surface-to-environment upper boundary, which

boundary is held at a constant pressure of 1 atm and functions as

is assumed to be a blackbody and has an equilibrium temperature

an inﬁnite source or sink of the ﬂuid, donating or accepting water

speciﬁed in Table 2. Several different ﬁnite-difference techniques

and steam depending on underlying hydrologic conditions.

available in the HEATING code were evaluated: Classical Explicit

A pressure of 1 atm was chosen because it is unclear what (if

Procedure (CEP), Levy explicit method, and the implicit technique,

any) substantial differences existed between surface (air) pressure

which can range from the Crank–Nicolson method to the Clas-

in the Hadean/Archean (e.g., Som et al., 2012). Nevertheless, argu-

sical Implicit Procedure (CIP), depending on model conditions. It

ments based, for example, on limits to mass-independent sulfur

was found that the three techniques produced nearly identical

isotopes from Rayleigh scattering in dense CO2 atmospheres show

results, but the implicit technique is signiﬁcantly computationally

that air pressure could not have greatly exceeded ∼1 bar since the

faster than the other two. Therefore, an implicit transient solu-

Eoarchean (Mojzsis, 2007).

tion technique is used, in which a system of equations is solved by ◦ −1

A geothermal gradient of 40 C km was included, but it has

point-successive over-relaxation iteration. The initial time step is

a negligible effect on model results, but the porosity and perme-

calculated by the code based on Classical Explicit Procedure (CEP)

ability of rocks to ﬂuids could be important to the cooling times of

conductive stability criteria, and each current time step is multi-

bombarded crusts. Rock porosity decays exponentially with depth

plied by a factor of 1.1 to determine the new time step. It was found

to account for the pore space closing by lithostatic pressure (Binder

through trial-and-error that using a time step multiplication factor

and Lange, 1980):

of 1.1 signiﬁcantly speeds up solution time without affecting the −z

ﬁnal result.

˚(z) = ˚0 exp (10)

The additional effects of heat transport by water and steam K

as a result of post-impact hydrothermal activity have also been

where K is a gravity-dependent constant (1.07 km for Earth;

evaluated in recent years (Rathbun and Squyres, 2002; Abramov

Clifford, 1993), z is depth below the original surface, and ˚0 is initial

and Kring, 2004, 2005, 2007; Jõeleht et al., 2005; Sanford, 2005;

porosity, assumed to be 40% at the top of the ejecta blanket, based

Barnhart et al., 2010). The net result of these studies is that,

on the upper limits for polymict breccias recovered from the Yax-1

although hydrothermal activity can remove heat from the crater

borehole at Chicxulub crater (Mayr et al., 2008a) and 20% at the

signiﬁcantly faster than conduction alone, it does not take place

top of the original pre-impact basement, based on typical crustal

in the hottest (molten or ductile) parts of the crater, and it deliv-

porosities. Permeability decays in a similar way with depth, and is

ers heat from the deep interior up to the near-surface. As a

also a function of temperature T:

result, hydrothermal crater cooling times are roughly compara-

−z

ble to conduction-only cases. This is particularly important when ◦

k(z) = k0 exp T < 360 C

considering how minerals that preserve radiogenic systems are K

affected, where element diffusion is dependent on temperature

log k(z) 11 ◦

and time. log k(z, T) = (500 − T) − 11 360 ≤ T ≤ 500 C

500 − 360

−11 ◦

k = 10 darcies T > 500 C

2.3. Ejecta cooling (11)

Conductive models of cooling impact ejecta blankets were based

−2

on HEATING 7.3. The model consists of hot ejecta overburden, mod- Initial permeability k0 is set to 10 darcies at the top of the

eled on a 100-node grid with a radiative upper boundary, overlying ejecta blanket, based on the upper limits from recovered Chicxulub

◦ −3

a 200-node original surface with an initial temperature of 0 C. The suevite breccias (Mayr et al., 2008b) and 10 darcies at the top of

resolution of the upper 100 nodes in the basement is equivalent the basement rocks, based on mid-range permeability of the Earth’s

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

crust (Brace, 1980, 1984). This rate at which permeability decreases 2.5. Diffusion models for zircons

with depth is similar to that described by Manning and Ingebritsen

(1999) based on geothermal data and metamorphic systems. Per- With the global thermal model of the LHB to Earth’s crust

meability is a function of temperature due to the brittle/ductile established, we now turn our attention to the potential for a

◦

transition at about 360 C in silicic rocks (Fournier, 1991), which is record of the bombardment in the oldest terrestrial minerals. We

modeled by log-linearly decreasing permeability between 360 and investigate whether partial age-resetting in zircon grains recorded

◦

500 C (Hayba and Ingebritsen, 1997). thermal perturbations of the Hadean crust using diffusion equa-

tions derived for both unshocked (Cherniak and Watson, 2001) and

shock-damaged zircons (Cherniak et al., 1991) coupled to the con-

ductive and hydrothermal impact ejecta cooling models described

2.4. Global bombardment models

above. Our output was also tested against a previously published

simulations of the post-impact cooling of the ∼180-km Sudbury

A three-dimensional model representing the upper 140 km

crater (Ontario, Canada) (Abramov and Kring, 2004).

of the Earth’s crust and lithospheric mantle was used to track

Cherniak and Watson (2001) characterized diffusion of Pb* in

impact-induced melting as the bombardment progresses. Inputs

both natural and synthetic zircon under a wide range of conditions.

were provided by the stochastic cratering model, which gener-

In-diffusion and out-diffusion experiments were conducted, using

ates impactor diameter and impact coordinates, the temperature

both synthetic Pb*-doped and natural zircon with relatively high

distribution library, which provides an appropriate subsurface

Pb* concentrations. Results for diffusion in natural and synthetic

temperature distribution for a given impact, calculated by the

zircon were similar, as were those for in- and out-diffusion, and

shock-heating model, and a subroutine that calculates the ﬁnal

are described by the following Arrhenius relation:

crater diameter for each impact. Only impactors 10 km in diam-

−1

− ±

eter and larger are included in this model. Other input parameters −1 550 30 kJ mol 2 −1

D = 1.1 × 10 exp m s (12)

are listed in Table 1. RT

The bottom boundary of the model is insulating, and heat

is lost by radiation through the upper boundary, which has an where D is the diffusion coefﬁcient, R is the universal gas constant,

◦

equilibrium temperature of 20 C. The lateral boundaries have peri- and T is absolute temperature. In their work, a mean activation

−1

odic boundary conditions (continuous wrap-arounds), so that all energy value of 550 kJ mol was used. This result can be used to

deposited heat is preserved in the system. The geothermal gradi- calculate the diffusive length scale X, which provides a measure

◦ −1

ent is 12 C km , based on the arguments that the average global of how far the diffusant has propagated in one direction during

heat ﬂow was lower in the Hadean as a result of a thicker litho- time t:

√

sphere (e.g., Korenaga, 2006), that consequently subdued plume

X ≈ Dt (13)

activity and slowed plate tectonics (if it was even operative at that

time). However, because the paradigm embraced by most work-

In these calculations, zircon is assumed to be an isotropic sphere,

ers is that Hadean heat ﬂow was substantially higher compared to

which is adequate for the purposes of our study in lieu of models for

◦ −1

present, a geothermal gradient of 70 C km was also tested in this

anisotropic diffusion in cylindrical geometries (e.g., Watson et al.,

study.

2010). Eqs. (12) and (13) are easily coupled to any thermal sim-

The horizontal dimensions of the model were 22,500 km ×

ulation that has discrete time steps. For every model element, a

22,500 km, corresponding to the Earth’s surface area of

diffusion constant D is calculated based on its temperature T, and

8 2

5.1 × 10 km , and the model depth is 140 km, equivalent to

then multiplied by the duration of the time step. Assuming isotropic

maximum lithospheric thickness. The model is represented on a

diffusion, taking the square root of the result then yields distance

grid of 76 × 76 × 34 nodes, with a corresponding inter-nodal dis-

diffused during the time step. The diffusion distance, shown in

tance of 300 km in the horizontal and 4.2 km in the vertical. These

Fig. 5 as a function of temperature and time, is summed for every

resolutions were chosen by trial-and-error to provide the best

model element to estimate the total average distance diffused by

balance between model accuracy and computational efﬁciency;

Pb* during the course of the simulation.

the resolution was iteratively increased until the model results no

longer changed.

As the model run progresses, output is written out every t/1000

years, where t is the total duration of the run (typically, the LHB

duration of the model set at 100 Myr). The resulting output ﬁles

record the temperatures of every node in the model, which are then

used to assess the thermal state of the lithosphere as a function of

time.

As an additional check of the transient heating model, a high-

resolution approach was employed to estimate the degree of crustal

heating during an impact bombardment. Here, the temperature

distribution library is used to calculate the volume raised above a

speciﬁed temperature for every crater predicted by the stochas-

tic cratering model. Additional inputs are surface temperature,

geothermal gradient and crustal thickness. This simple model

assumes that impacts do not overlap and neglects any post-impact

conductive heating. The tradeoff is a much higher overall reso-

lution, whereby a temperature distribution associated with each

individual impact is represented on a 75 × 33 grid, which allows

the inclusion of impactors as small as 1 km in diameter. Thus, this

Fig. 5. Pb* diffusion in undamaged zircon, based on equations of Cherniak and

model allows an assessment of the relative contribution of small

Watson (2001). Solid line indicates diffusion distance of 3 ␮m, a typical zone width

vs. large impactors to crustal melting.

observed during ion microprobe depth-proﬁling (Trail et al., 2007).

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 237

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.

−1 ◦ −1 −1

(a–d) Baseline, 40 km s , 10×, and 10 Myr LHB scenarios, respectively, with a geothermal gradient of 12 C km . (e–h) Baseline, 40 km s , 10×, and 10 Myr LHB scenarios,

◦ −1

respectively, with a geothermal gradient of 70 C km .

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

In addition, Pb*-loss in shock-damaged zircons was modeled. two geothermal temperature gradients described above. For the

◦ −1

Wittmann et al. (2006) described granular textures within a vari- 12 C km geothermal gradient case, sharp peaks and the long time

ety of shocked zircon grains from several impact structures, which between them indicate that most melting is caused by a few large

exhibit Raman characteristics that overall follow the trend of nat- impacts. Following a basin-forming impact, the amount of melt

ural radiation damage. As a ﬁrst-order approximation of this, decreases substantially due to long cooling times before another

we used the diffusion equation for radiation-damaged zircons basin is formed. In the Baseline scenario, a maximum of 0.3% of the

(Cherniak et al., 1991), which have a signiﬁcantly faster rate of upper crust is molten at any time, and even in the 10× scenario, the

◦ −1

Pb*-loss: maximum molten fraction is under 2%. For the 70 C km geother-

− −1 mal gradient, smaller impacts are proportionally more important,

−12 142 kJ mol 2 −1

D = 2 × 10 exp m s (14) 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 this

ﬁgure increases to over 11% for the 10× scenario.

here variables have the same deﬁnitions as in Eq. (12), and this

The melting results described above were derived from a rela-

equation is coupled to thermal simulations in the same way as for

tively low resolution transient heating model, which only included

undamaged zircons.

impactors larger than 10 km. In order to test these results and assess

the relative importance of smaller impactors, a high-resolution

3. Results and analysis

static model (Section 2.4) was employed to calculate cumulative

crustal heating. The results, presented in Table 3, are in excellent

3.1. Global bombardment models

agreement with those in Fig. 7, validating the model and imply-

ing the relative unimportance of small (<10-km) albeit abundant

A graphical overview of the cumulative thermal effects of sev-

impactors. Indeed, the percentage of the crust melted is at least

eral LHB scenarios modeled in this work is shown in Fig. 6. These

an order of magnitude smaller for impactors <10-km compared

results are from the three-dimensional transient heating model

to impactors in the other two size categories (10–100 km and

(Section 2.4) and provide a visual starting point for the analysis

100+ km).

of our results and application to diffusion models of Pb*-loss in zir-

cons. For our Baseline model, note the deﬂection of the isotherms

at the lateral boundaries of the model due to impacts, and that, 3.2. Thermal ﬁelds within individual impact craters

although a relatively large number of craters have formed, most

◦

have cooled below 100 C at the upper boundary of the model To set up our model to explore age-resetting of zircons emplaced

−1

(4 km depth into the crust). In the high impact velocity, 40 km s within individual impact structures that covered Earth’s surface in

scenario, a larger number of hot craters is present and tempera- the LHB, we used a previously published simulation of the post-

tures within each crater are noticeably higher due to each impact impact cooling of the ∼180-km Sudbury crater (Ontario, Canada)

depositing three to four times more thermal energy relative to the (Abramov and Kring, 2004). Rock properties appropriate for the

Baseline setting. In the 10× bombardment scenario, with ten times Sudbury site are used. The initial temperature distribution of

delivered mass, craters formed by impactors > 10 km in diameter in the Sudbury crater was previously calculated using the SALEB

this model essentially saturate the surface and a substantial frac- hydrocode (Ivanov and Deutsch, 1999).

◦

tion of the near-subsurface is above 100 C. A few percent of the The individual crater cooling simulations were coupled to equa-

upper ∼20 km of the crust is molten in this simulation. The results tions of diffusion models for both undamaged and shock-damaged

−1

for the 10 Myr bombardment scenario are similar to the 40 km s (Section 2.5) zircons, and the distance diffused by Pb* was calcu-

bombardment, with a larger number of active hotspots compared lated numerically at each model time step. For both normal (Fig. 8a)

to the Baseline model due to a higher frequency of impacts. Com- and damaged (Fig. 8b) zircons, there is a rather strong dichotomy

◦ −1

parisons of the models that use a 70 C km geothermal gradient – either 100% Pb*-loss occurs within a zircon grain or none at all,

◦ −1

to those with 12 C km , along with much thinner lithosphere and with very few areas of partial Pb*-loss. We ﬁnd that this result is

higher average temperatures of impact-induced hotspots, yields an independent of grain diameter. For normal zircons (Fig. 8a), the

even higher percentage of melting within the crust. model predicts that areas of the crater that have 100% Pb*-loss are

◦

The degree of melting in the upper 20 km of the crust during the central uplift (initial temperature of ∼1000 C) the central melt

the LHB is shown in Fig. 7 for the four bombardment scenarios and sheet, as well as the small melt sheet in the annular trough (initial

-1 -1

Crustal melting during LHB. dT/dz = 12 °C km Crustal melting during LHB. dT/dz = 70 °C km 0.02 0.12 Baseline Baseline -1 -1 40 km s 0.1 40 km s 0.015 10X 10X 10 My 10 My 0.08

0.01 0.06

0.04 0.005 0.02 Fraction of crust molten Fraction of crust molten 0 0 a. 0 20 40 60 80 100 b. 0 20 40 60 80 100

Time (My) Time (My)

Fig. 7. The degree of melting in the upper 20 km of the crust as the LHB progresses. Derived from a three-dimensional transient thermal model. Only impactors larger than

−1

10 km in diameter are included. Melt deposited in ejecta blankets is not included. (a) The effects of Baseline, 40 km s , 10×, and 10 Myr LHB scenarios with a geothermal

◦ −1 −1 ◦ −1

gradient of 12 C km . (a) The effects of Baseline, 40 km s , 10×, and 10 Myr LHB scenarios with a geothermal gradient of 70 C km .

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 239

Table 3

Maximum 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 (Section

2.4). 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

◦ −1

12 C km Baseline 100+ km 32 1.1

◦ −1

12 C km Baseline 10–100 km 1496 0.39

◦ −1

12 C km Baseline 1–10 km 173,667 0.037

◦ −1 −1

12 C km 40 km s 100+ km 32 3.2

◦ −1 −1

12 C km 40 km s 10–100 km 1496 1.6

◦ −1 −1

12 C km 40 km s 1–10 km 173,667 0.14

◦ −1 ×

12 C km 10 100+ km 296 9.7

◦ −1

12 C km 10× 10–100 km 14,969 3.9

◦ −1

12 C km 10× 1–10 km 1,736,677 0.38

◦ −1

70 C km Baseline 100+ km 32 1.5

◦ −1

70 C km Baseline 10–100 km 1496 0.82

◦ −1

70 C km Baseline 1–10 km 173,667 0.12

◦ −1 −1

70 C km 40 km s 100+ km 32 4.2

◦ −1 −1

70 C km 40 km s 10–100 km 1496 2.8

◦ −1 −1

70 C km 40 km s 1–10 km 173,667 0.45

◦ −1

70 C km 10× 100+ km 296 14

◦ −1 ×

70 C km 10 10–100 km 14,969 8.3

◦ −1

70 C km 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 zircon

grain. (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).

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

◦

temperature of ∼1700 C). In addition, since the thermal decompo- Final Crater Diameter (km)

◦

sition temperature of zircon is 1673 C (Kaiser and Lobert, 2008), 20 100 1000 4000

complete loss of grains emplaced within the melt is also likely (see 10

-1

Wielicki et al., 2012). Impact angle = 45°, vi = 20 km s

The results for damaged zircons, illustrated in Fig. 8b, show that 10

12 °C km-1

a signiﬁcantly larger rock volume within the crater contains zircons -1

101 70 °C km

that suffer complete Pb*-loss, as well as a somewhat wider band

which experience partial Pb*-loss in zircons. The Pb*-loss results 10

in zircons we modeled were compared to ﬁeld observations at the

-1

somewhat larger (∼280 km) Vredefort crater (South Africa). Moser 10

et al. (2011) documented that complete and partial age-resetting in

10-2

zircon is limited to ∼27 km from the center of the impact (Fig. 8c).

-3

These results are in agreement with our models for normal zircon 10

(Fig. 8a), but not for shock-damaged zircon (Fig. 8b). It should be

-4

noted, however, that the onset of deformation in zircons at Vre- Mean Global Ejecta Thickness (m) 10

1 10 100 500

defort is at ∼29 km from center, and is offset by only ∼2 km from

the observed age-resetting. In other words, the most severely dam- a. Projectile Diameter (km)

aged zircons would be expected to occur close to the center of the

structure, where they would be age-reset in either scenario.

Final Crater Diameter (km) 20 100 1000 4000

103

3.3. Thermal ﬁelds from globally emplaced impact ejecta -1 Impact angle = 45°, vi = 20 km s 102

-1

Hot impact ejecta generated by the LHB draped the Hadean 12 °C km

1 -1

Earth’s surface. The amount of material ejected or vaporized by 10 70 °C km

an impact of a given magnitude is estimated using the model

100

described in Section 2.1. This volume can then be normalized

by the Earth’s surface area to calculate the mean global ejecta

10-1

(Fig. 9a) and condensed vapor thickness (Fig. 9b) for each indi-

-2

vidual impact. The fraction of material ejected at escape velocity 10

or higher is expected to be signiﬁcantly smaller than the mass of

10-3

the impactor (e.g., O’Keefe and Ahrens, 1977a) and is not included

in the model. The volume of both ejecta and rock vapor produced

10-4

increase with impactor diameter in an expected way: ejecta scales 1 10 100 500

2.34 Mean Global Rock Vapor Thickness (m)

∼ as Dp in proportion to transient crater volume (Pierazzo and b. Projectile Diameter (km)

∼

Melosh, 2000), and vaporized volume scales as Dp (e.g., O’Keefe

and Ahrens, 1977b). The ratio of vaporized to ejected material

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

0.66

increases as ∼D , which results in deposition of signiﬁcantly

p a function of binned projectile and ﬁnal rim-to-rim crater diameters. The bin width

more condensed vapor than ejecta for very large impactors. For increases by a factor of 1.25. Ejecta includes impact melt, but not rock vapor.

a 500-km diameter impactor, the largest possible in the 10× sce-

nario, the estimated global rock vapor thickness is ∼400 m, and the

global ejecta thickness varies from ∼10 to ∼40 m, depending on the ejecta by the expected number of impacts in that size bin (Fig. 10a).

assumed geothermal gradient. This is in excellent agreement with The same technique is used to calculate the cumulative thickness

the estimate of Sleep and Zahnle (1998) of ∼300 m of condensed of condensed rock vapor as a function of binned impactor diam-

rock vapor and ∼50 m of ejecta, considering that earlier work used eter (Fig. 10b). The model does not include ejecta redistribution

−1

a lower impact velocity of 17 km s (which would decrease vapor- by subsequent impacts, which is an acceptable assumption for the

∼

ized volume), and did not include the geothermal gradient (which Baseline model, in which only 25% of the surface is covered by

would result in an over-estimate of ejecta volume). impact craters and typical ejecta thicknesses are small compared

Both ejected and vaporized volumes exhibit some dependence to excavation depths of craters that produce most of the ejecta. The

on the geothermal gradient, but that dependence is signiﬁcant dependence of cumulative ejecta and condensed rock vapor vol-

only for particular ranges in crater diameter. For impactors over umes on the geothermal gradient is identical to Fig. 9, an expected

∼

50 km in diameter, ejecta volumes become increasingly larger result. The shape of the cumulative ejecta volume distribution,

◦ −1

with increasing impactor diameter for a colder (12 C km ) tar- however, is remarkably ﬂat, indicating that smaller impacts gen-

◦ −1

get compared to a warmer (70 C km ) target (Fig. 9a). This is due erated roughly the same total volume of ejecta as larger impacts.

to a lower fraction of material within the excavation zone becom- The cumulative condensed rock vapor distribution, on the other

ing vaporized if the target is colder. Conversely, more rock vapor hand, increases with impactor size up to projectiles ∼100-km in

is produced if the target is warmer, as can be seen in Fig. 9b. This diameter, at which point it ﬂattens out as well. Thus, in contrast

effect is most signiﬁcant for impactor diameters between ∼50 and to the ejecta, most condensed rock vapor is produced by impacts

∼

100 km; for impactors with diameters larger than ∼100 km, most larger than ∼100 km.

of the vaporization takes place in the isothermal asthenosphere Fig. 11 illustrates the predicted mean temperatures and melt

and the lithospheric geothermal gradient becomes progressively content of ejecta produced by impactors of various diameters,

less relevant with increasing diameter. calculating using the volume-averaging method (Section 2.1 and

The volume of ejecta produced by each impact can be coupled to Fig. 4). In general, ejecta temperature increases with increas-

◦

the LHB size-frequency distribution (Section 2.1 and Fig. 1), and the ing projectile diameter, from ∼300 C for a 1-km impactor to

∼ ◦

cumulative thickness of deposited ejecta is calculated as a function 2500 C for a 500-km impactor (Fig. 11a). The dependence on the

of impactor diameter by multiplying the mean global thickness of geothermal gradient is most pronounced for mid-size impactors

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 241

Final Crater Diameter (km) Final Crater Diameter (km) 20 100 1000 4000 20 100 1000 4000

103 2500

-1 -1 Impact angle = 45°, vi = 20 km s Impact angle = 45°, vi = 20 km s

12 °C km-1 2000 70 °C km-1 102 1500

1000 101 500 12 °C km-1 70 °C km-1 100 Mean Ejecta Temperature (°C) 0 1 10 100 500 1 10 100 500 a. Mean Cumulative Global Ejecta Thickness (m) Projectile Diameter (km) a. Projectile Diameter (km)

Final Crater Diameter (km) Final Crater Diameter (km) 20 100 1000 4000 20 100 1000 4000

-1 10 -1 Impact angle = 45°, vi = 20 km s Impact angle = 45°, vi = 20 km s 1

12 °C km-1 70 °C km-1 0.8 102 0.6

0.4 101

0.2 -1

Fraction of melt in ejecta 12 °C km 70 °C km-1 100 0 1 10 100 500 1 10 100 500 Projectile Diameter (km) b. Projectile Diameter (km)

b. Mean Cumulative Global Rock Vapor Thickness (m)

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

Fig. 10. Mean cumulative global thickness expected during the Baseline LHB for (a)

crater diameters. (b) Mean fraction of melt in ejecta as a function of projectile and

impact ejecta and (b) condensed rock vapor, as a function of binned projectile and

ﬁnal rim-to-rim crater diameters. Ejecta includes impact melt, but not rock vapor.

ﬁnal rim-to-rim crater diameters. The bin width increases by a factor of 1.25. Ejecta

includes impact melt, but not rock vapor.

for the hydrothermal model, despite the presence of a geothermal

∼ gradient. Also, maximum temperatures are lower at 5000 years

( 10–100 km): small impacts excavate from the shallow subsur-

compared to the conductive model. However, the initial phases of

face, whereas very large impacts excavate from the periphery of the

cooling for both models are nearly identical, due to the latent heat

transient crater, and the geothermal gradient becomes less impor-

of fusion and the lack of water circulation through the hot and par-

tant in either case. The initial melt content of the ejecta (Fig. 11b)

tially molten ejecta. This is noteworthy for age-resetting in zircon,

increases gradually with projectile diameter from a few percent to

◦

∼ which generally takes place at temperatures above 1000 C (see

20% for ∼1–10 km impacts, and then increases steeply up to ∼300-

below).

km impacts, at which point the ejecta is composed of 100% melt. As

Results for Pb*-loss and consequent age-resetting within ejecta

before, the geothermal gradient dependence is most pronounced

blankets, derived from the coupling of ejecta cooling models to

for mid-size impactors (∼10–100 km).

diffusion equations of Pb* in zircon (Section 2.5) are presented

Representative results of ejecta cooling models in purely con-

in Fig. 13. For a 350-m thick ejecta (Fig. 13a), partial Pb*-loss

ductive and hydrothermal environments are presented in Fig. 12a

throughout a substantial (& 25%) portion of the blanket takes

and b, respectively. Here, a 350-m thick ejecta blanket with an ini-

◦ ◦ ◦

place for initial temperatures between ∼1000 C and ∼1300 C. If

tial mean temperature of 1200 C, typical for impactors ∼25 km in

◦

the initial temperature is under ∼1000 C, essentially no zircon

diameter, is emplaced over an initially cold surface and allowed to

◦

age-resetting occurs, whereas initial temperatures above ∼1300 C

cool. The differences between the two models are most noticeable

result in nearly complete open system behavior and age-resetting.

in the later stages of cooling: at 500 years, maximum temperatures

◦

The range of initial temperatures resulting in partial resetting in a

in the hydrothermal model are ∼300 C lower than in the purely

◦

100-m ejecta blanket (Fig. 13b) is fairly similar, at ∼1100–1400 C,

conductive model, and the shape of the temperature vs. depth

though some partial resetting (within ∼15% of the blanket) takes

curve is noticeably deformed due to the formation of water vapor

◦

place at temperatures as high as ∼1500 C. In the case of shock-

and consequent heat loss at the peripheries of the ejecta blanket.

◦

damaged zircons (Fig. 13c), initial temperatures of 1200 C and

We did not model the local explosive nature of the groundwater-

◦

900 C resulted in nearly complete Pb*-loss throughout most of the

impact ejecta interface, but note that the generation of lahars from

◦ ◦

ejecta blanket, 300 C resulted in partial Pb*-loss, and only 600 C

such a process is expected. We ﬁnd that the thermal pulse from

resulted in partial Pb**-loss.

the hot ejecta does not penetrate nearly as far into the subsurface

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

° ° 350-m Ejecta, Tinitial =1200 C, Conductive only 350-m Ejecta, Tinitial =1200 C, Hydrothermal 0 0

-500 -500

-1000 -1000 Depth (m) Depth (m) 0 years 0 years -1500 100 years -1500 100 years 500 years 500 years 5000 years 5000 years

-2000 -2000

0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200 a. b.

Temperature (°C) Temperature (°C)

Fig. 12. Comparison of two models of impact ejecta cooling. (a) A purely conductive case. (b) A hydrothermal model with up to 40% water. Both models represent a 350-m

◦ ◦ −1

layer of melt-rich ejecta initially at 1200 C. The hydrothermal model includes a 40 C km geothermal gradient.

4. Discussion Blichert-Toft and Albarède, 2008). The largest impacts tested in

this work would have excavated well into the mantle, however,

4.1. LHB-induced ages to undamaged vs. damaged zircons in the introducing a maﬁc component as well. Therefore, both granitic and

Hadean crust basaltic end members were tested during the course of this study.

Granite and basalt have a nearly identical speciﬁc heat capacity, as

The results for Pb*-loss in undamaged zircons within an impact well similar thermal conductivity and other thermal and physical

crater (Section 3.2) provide better agreement with ﬁeld obser- parameters. Trial global bombardment model runs were conducted

vations than those for damaged zircons. However, as mentioned to assess the differences between these two lithologies (Abramov

previously, this may be explained by the most damaged zircons and Mojzsis, 2009b), and a comparison between of ejecta temper-

being near the center of the crater, where temperatures are sufﬁ- atures for granite and basalt is presented in Abramov and Mojzsis

ciently high to age-reset the grain whether it is damaged or not. (2012). The difference is under 10% for most of the impactor diam-

Of greater concern are the results for age-resetting of damaged zir- eter range, and the agreement is particularly good for very large

◦

cons within impact ejecta, where initial temperatures of 600 C and (100+ km) impactors which would have excavated a signiﬁcant

◦

900 C result in partial and complete resetting, respectively. This mantle component. Given the minor differences in model outcomes

appears contradictory to observations in the Apollo samples, where and evidence for granitoids and perhaps signiﬁcant continental

zircons from ejecta associated with large impact basins, often with crust (Harrison et al., 2005) in the Hadean, thermal and physical

substantial melt content and initial equilibrium temperatures of parameters for granite were used in all other models presented in

◦

1100–1400 C (Simonds et al., 1976) do not always record age- this work.

resetting at ∼3.9 Ga (e.g., Nemchin et al., 2009; Grange et al., 2009;

Grange et al., 2013). This may indicate that shock damage does not

signiﬁcantly increase the rate of Pb* diffusion from zircon, and/or 4.4. Predictions for the Hadean terrestrial zircon record

that radiation damage is a poor approximation for shock deforma-

tion. In any case, results for Pb*-loss in undamaged zircons are more Results indicate that most of the terrestrial crust would not have

consistent with observations (Moser et al., 2011), and will be used been destroyed by the LHB (Table 3 and Fig. 7): for the Baseline sce-

∼

exclusively in further discussion. nario, only 2% of the upper crust is melted, and even in the 10×

scenario with a high geothermal gradient, melting of the upper

4.2. Effects of zircon grain size crust is under ∼25%. Signiﬁcantly, impact melt tends to pool in

the near-surface and the degree of melting is higher when only

Results presented in Figs. 8 and 13 assume a typical zircon grain the upper few km of the crust are considered in these analyses.

∼ ␮

with a mean radius of 50 m. Other zircon sizes were tested As an end member scenario for the Baseline model, ∼5–10% of the

within the model, however, and it was found that the results do not Earth’s surface would be covered by (generally crystallized) impact

depend strongly on the size of the grain. For example, decreasing melt sheets > 1 km deep at the end of the LHB, whereas for the 10×

␮ ␮

the zircon radius from 50 m to 10 m is comparable to raising the model, this value may exceed ∼50%. Taking to ﬁrst order crustal

◦

∼

initial temperature of the ejecta blanket by 100 C in terms of the melting as a condition needed to age-reset zircons, it would suggest

obtained result. Thus, results presented here are broadly applica- that the vast majority of the Hadean zircons in the upper crust and

∼ ␮

ble to zircon grains with common sizes of 20–200 m in diameter even the near-surface would not have been completely age-reset by

that are found within the Jack Hills sedimentary record. the Baseline LHB, and certainly no signiﬁcant spike of dominantly

∼3.9 Ga zircon core ages would be expected in the Hadean Jack Hills

4.3. Effects of target lithotype zircon collection.

The modeling presented in this work shows that zircons within

A granitic lithology was assumed throughout this paper, mainly melt sheets and central uplifts associated with impact craters are

due to the results reported for the crystal chemistry of the oldest expected to show relatively minor amounts of partial age-resetting

Jack Hills zircons, most of which likely crystallized from a granitic (Fig. 8); it tends to be an all-or-none situation. This result is in good

melt (e.g., Maas et al., 1992; Hopkins et al., 2008, 2010). Although agreement with Wielicki et al. (2012), who determined U–Pb* ages

the petrological composition of the Hadean crust is not well con- of grains from impact melt sheets of numerous terrestrial craters

strained, evidence continues to accumulate for the presence of and reported a high degree of concordance of grains age-reset by,

a signiﬁcant fraction of granitic crustal rocks at that time (e.g., or formed as a result of, impact.

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 243

∼

Pb-loss in normal zircon - 350 m ejecta blanket form. In contrast, 75% of ejecta is produced by smaller (<100 km)

0 impactors that consists predominantly of crustal lithologies and is

deposited, on the average, in much thicker layers.

-50

Combining data from Figs. 10 and 11, and assuming partial

◦

-100 age-resetting at temperatures between 1000 and 1300 C (Fig. 13),

1500 °C we can estimate the degree of global age-resetting in the zircons

1400 °C

-150 entrained in ejecta. Based purely on ejecta temperatures and vol-

1300 °C

umes, ∼36% of the ejecta deposited during the Baseline LHB are

-200 1200 °C

1100 °C predicted to have no Pb*-loss in zircons, ∼16% are predicted to have

Depth (m)

∼

-250 1000 °C partial Pb*-loss, and 48% are predicted to have complete Pb*-loss

or destruction of the zircon grain. This result is not dependent on

-300 the geothermal gradient. However, because the hottest ejecta is

excavated by the largest impacts, a majority of it would be of man-

-350

tle origin, and thus the actual percentage of observable complete

0 20 40 60 80 100

age resetting would be signiﬁcantly lower. Compensating for this

a. Pb loss (%)

effect requires an assumption of mean crustal thickness; thicker

crusts would result in a higher percentage of fully age-reset zir-

Pb-loss in normal zircon - 100 m ejecta blanket

0 cons in ejecta, whereas for thinner crusts that percentage would be

◦ −1

lower. If a 35-km crust is assumed for the 12 C km model, and

◦ −1

a 20-km crust is assumed for the 70 C km model, the percent-

-20

ages for observable age-resetting in ejecta-entrained zircons are

∼ ∼

1500 °C predicted to be: 59% with no Pb*-loss, 26% with partial Pb*-loss,

-40 1400 °C and ∼15% with complete Pb*-loss or destruction of the grain. These

1300 °C numbers are global averages; speciﬁc regions of the Earth were

1200 °C

likely dominated by ejecta from one or more individual impacts. -60 1100 °C

Depth (m)

1000 °C Ejecta emplaced on the surface of the Earth would have been

subject to fairly rapid erosion, particularly during the LHB, when

-80

impacts repeatedly vaporized hundreds of meters of water from the

global ocean (e.g., Sleep and Zahnle, 1998). This may also provide

-100 an explanation for why the source rock(s) for pre-∼3.8 Ga Jack Hills

0 20 40 60 80 100 zircons have not been located: they may have been derived from

Pb loss (%)

b. readily erodible impact ejecta that was long ago lost to subduc-

tion. Ejecta from smaller impacts (<10 km) contain less than 20%

Pb-loss in damaged zircon - 100 m ejecta blanket melt (Fig. 11b) and likely eroded faster than ejecta from larger

craters welded by a higher melt content. If these had similar rhe-

ological properties to contemporary terrestrial ejecta blankets,

-20 they would have been rapidly weathered and preferentially lost

to the ocean. Interestingly, the original crustal formation depth

of the Jack Hills zircons was estimated to be ∼20 km (Hopkins

-40 120 0 °C

900 °C et al., 2008), and excavation depths for impacts needed to produce

600 °C ejecta with a mean temperature conducive to partial age reset-

-60 ◦

∼ ∼

Depth (m) 300 °C ting ( 1000–1300 C) range from 11 km for a 10-km impactor

to ∼38 km for a 50-km impactor: a substantial overlap with the

-80 conclusions of Hopkins et al. (2010).

Impact ejecta covered the entire surface of the LHB-era Earth to

-100 a depth close to 1 km in the Baseline scenario, whereas impact melt

0 20 40 60 80 100 sheets would have covered only 5–10% of the surface, though often

c. Pb loss (%) to signiﬁcantly greater depths. As outlined below, impact ejecta

appears signiﬁcantly more likely to contain zircons that have expe-

rienced partial Pb*-loss similar to that observed in some ∼3.9 Ga

Fig. 13. Percentage of Pb*-loss in 100-␮m zircon grains within impact ejecta blan-

◦

kets of various initial temperatures and thicknesses. (a) Normal zircon grain, 350-m Jack Hills data. Even ejecta temperatures below 1000 C can poten-

ejecta blanket. (b) Normal zircon grain, 100-m ejecta blanket. (c) Damaged zircon

tially result in the LHB-age zones observed over Hadean cores in

grain, 100-m ejecta blanket.

some Jack Hills zircons: Abbott et al. (2012) estimated crystal-

◦

lization temperatures of 840–875 C associated with the ∼3.9 Ga

The story becomes more complicated when the effects of impact overgrowths. Other mechanisms for partial age-resetting of zircon

ejecta and condensed rock vapor are taken into account. The Base- grains associated with impact ejecta blankets have also been sug-

∼

line LHB would have deposited a global average of 600–800 m of gested (e.g., Krogh et al., 1993). All these factors imply that, if the

∼ ∼

ejecta and 800–1000 m of condensed rock vapor (Fig. 10), depend- 3.9 Ga zones in the Jack Hills zircons are indeed a signature of the

ing on assumed geothermal gradient. For the purposes of this LHB, then they were likely sourced from impact ejecta.

discussion, condensed rock vapor is less important, as the majority Evaluating the discordance (i.e., Pb*-loss) vs. U–Pb age rela-

∼

of it ( 80%) is produced by very large (>100 km) impactors and is tionships in ancient zircons that survived the LHB requires a large

derived primarily from the ultramaﬁc (and therefore, zirconium- sample set of depth proﬁle analyses be available that could poten-

∼

poor) mantle. The other 20% of rock vapor is associated with tially sample age-resetting events manifest as overgrowths within

smaller impactors and relatively small volumes that condense into the detrital population (Trail et al., 2007; Abbott et al., 2012).

thin sheets of a few meters at most (Fig. 9); we consider these To quantitatively analyze this possibility, we constructed a 2-D

as unlikely to provide sufﬁcient time for new zircon grains to probability density function plot that graphically represents the

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

the near surface; in the Baseline model, ∼5–10% of the Earth’s sur-

face would have been covered by >1 km deep impact melt sheets;

and in the 10× model, this percentage may have exceeded 50%.

The largest impactor in the Baseline model, at ∼300 km, may have

◦

raised the temperature of the global ocean by as much as 100 C.

The modeling presented in this work predicts that a global aver-

age of ∼600–800 m of ejecta and ∼800–1000 m of condensed rock

vapor would have been deposited by the Baseline LHB. Smaller

impacts generate roughly the same cumulative volume of ejecta as

larger impacts, but most of the condensed rock vapor is produced

by the very largest (>100-km) projectiles. Mean ejecta temperature

◦

increases with increasing projectile diameter, from ∼300 C for a 1-

◦

km impactor to ∼2500 C for a 500-km impactor, and melt content

in the ejecta increases from a few percent to 100% for the same

range.

Once deposited, ejecta blankets cool conductively and likely via

hydrothermal interactions depending on the availability of water.

Hydrothermal cooling signiﬁcantly accelerates heat removal and

reduces the penetration depth of the thermal pulse from hot ejecta

into the subsurface. However, the initial stages of cooling, when

most age-resetting takes place, are nearly identical in the two

models, due to the latent heat of fusion and the lack of water and

steam circulation through the majority of the partially molten

ejecta blanket.

The temperature range for partial Pb*-loss in zircons within

◦

ejecta blankets is estimated at ∼1000–1300 C, varying weakly with

ejecta thickness. After accounting for excavation from the mantle

by the largest impacts, ejecta-entrained zircons are predicted to

have the following distribution in the Baseline LHB scenario: ∼59%

with no Pb*-loss, ∼26% with partial Pb*-loss, and ∼15% with com-

plete Pb*-loss or destruction of the grain. In contrast, model zircons

within individual impact craters, particularly in the melt sheets,

generally exhibit all-or-none age-resetting in the Pb* system, and

partial resetting is relatively uncommon. The prediction from these

207 206

Fig. 14. (Top panel) Plot of Pb/ Pb age (in Ma) vs. % discordance for individual models that ∼15% of the Hadean zircon population experienced age

spots taken during U–Th–Pb ion microprobe depth proﬁles from a sample suite of 22

resetting from the LHB agrees well with the observations of Abbott

pre-LHB aged Hadean zircons from the Narryer Gneiss Complex, Western Australia.

et al. (2012), who computed that ∼13% of the Jack Hills zircons

(Bottom panel) 2D probability density function plot of the data. The colors shown

preserved ca. 3.9 Ga “LHB-era” domains.

are, from the top to the bottom in the key, of increasing constant probability density.

There is a distinct trajectory in the data from a concordant (zero Pb*-loss) population The ubiquitous surface presence of ejecta during impact

at ca. 4 Ga to increasing discordance of the population (up to 85%) at 3930–3975 Ma

bombardments, its propensity to cause partial Pb*-loss and/or over-

and and later (ca. 3825 Ma). This age range corresponds well to the timing of the

growths in zircons, and its relatively high erodibility suggest that,

LHB.

if some Jack Hills zircons contain a signature of the LHB in the form

of ∼3.9 Ga zones, these were most likely entrained in impact ejecta.

complete data output of 22 published and unpublished U–Th–Pb

Most previous efforts that have sought to quantify the effects of

207 206

depth-proﬁle data for Hadean zircons in terms of Pb/ Pb age

impact bombardments on the habitability of early Earth focused

207 235

vs. degree of Pb*-loss represented by discordance in the Pb/ U

on surface sterilization and vaporization of oceans. Maher and

206 238

vs. Pb/ U systems (Fig. 14). Dark purple and blue through red

Stevenson (1988) speculated that based on the lunar cratering

colors in the plot represent the least probably density level; sub-

record, the surface of the Earth became hospitable to life sometime

sequent levels show a density accession to highest probability of a

between about 4.0 and 3.7 Ga, whereas they also pointed out that

particular age at a particular degree of discordance. It is apparent

the deep ocean remained consistently habitable beginning as far

here – as it was in Abbott et al. (2012) – that the highest density of

back as 4.2 Ga. We are unclear how the ca. 4.2 Ga limit was derived.

concordant ages is found in those domains with ages as old or older

Moreover, despite the fact that their calculations did not explic-

than about 4.0 Ga. There is a trend, however, from the core region

itly take the LHB into account, these estimates are consistent with

of ≥4.0 Ga ages to younger ages with increasing discordance (30%

the work of Sleep and Zahnle (1998), which showed that a 500-

and 80%) centered at about 3920–3960 Ma.

km impactor was required to evaporate the ocean. Abramov and

Mojzsis (2009a) calculated that the largest impactor that was likely

5. Conclusions to have struck the Earth during the LHB was on the order of ∼300 km

in diameter. As shown here, there exists a strong dependence on

Global bombardment models indicate that only a relatively energy partitioning so that even a 300 km impactor can potentially

small portion of the crust was melted by the LHB. In the Base- raise the mean temperature of the entire volume of the world ocean

◦

∼

line scenario, a total of 1.5–2.5% of the upper 20 km of the crust to over 100 C.

was melted, depending on the geothermal gradient, and only up to Hydrocode simulations of the formation of marine craters

∼

0.3–1.5% was molten at any given time. In the most “extreme” sce- on Earth (e.g., Shuvalov and Trubetskaya, 2002; Shuvalov et al.,

◦ −1

nario, a 10 bombardment with a 70 C km geothermal gradient, 2005) suggest that crater formation is relatively unaffected when

∼

the total fraction of the upper crust that was melted is under 25%. water depth is on the order of projectile diameter. Assuming

One caveat is that impact melt tends to pool in crater depressions in that the Hadean Earth had a mean ocean depth roughly similar

O. Abramov et al. / Chemie der Erde 73 (2013) 227–248 245

to present-day (∼3.8 km), the ocean would have affected only visits to the islands where this work was discussed in its early

the smallest impactors in our models (∼1–4 km), which were stages. We express our sincere gratitude to Associate Editor Klaus

responsible for only a minor fraction of ejecta deposition (Fig. 10) Keil for inviting us to prepare review and for his patience during

and a negligible amount of crustal heating (Table 3). As mentioned this manuscript’s unusually long gestation time. Mahalo Klaus!

above, the largest impactor in our Baseline LHB scenario is only

∼

300 km in diameter (Fig. 1a); a 500-km impactor is only possible

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