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Zahnle, Kevin

Publications and source records attributed to Zahnle, Kevin.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Earth's Early Reduced Atmospheres

Earth’s early atmosphere evolved in response to cosmic impacts, photochemistry generated by the copious extreme ultraviolet radiation emitted by the young Sun, hydrogen escape, mineral redox buffering, the evolution of iron in the mantle, and the character of crustal weathering and subduction. No single chemical composition, surface pressure, or temperature was typical. After the biggest impacts the temperature likely rose above 3000 K and the atmosphere held rock vapor. As the atmosphere cooled its constituents rained out: first the silicates, then the geochemical volatiles (such as salt), and last the water. Depending on the size of the impact, cooling took thousands to millions of years. Between impacts the atmosphere was thick with gases like CO2, H2, and CH4 that do not condense at Earth but provide greenhouse warming that could easily have maintained surface temperatures in excess of 500 K. At some point the early atmosphere must have been conducive to the evolution of organic chemistry and the origin of life. It was therefore --- at times --- dominated by reduced gases like hydrogen and methane. Hydrogen-methane atmospheres are easily formed thermochemically after major impacts if H2O and CO2 were present on Earth in quantities consistent with their inventories on Earth today – the key is high pressure. Hydrogen-methane atmospheres slowly break down over millions of years by hydrogen escape and photochemistry. At first methane decomposes into tars and nitriles that precipitate, but later as the atmosphere grows more oxidized from hydrogen escape the methane oxidizes to CO and CO2, with a small fraction going to HCN. Impacts can also produce NH3 directly from N2 and H2O, which is expected to rain out with the H2O. As impacts grew infrequent the climate cooled in response to the fixing of CO2 as carbonate and carbonate subduction. Eventually the CO2 was mostly removed to the mantle and the surface mostly frozen.

Zahnle, Kevin↗
NASA NTRS2017

Limits to Creation of Oxygen-Rich Atmospheres on Planets in the Outer Reaches of the Conventional Habitable Zone

Abundant free oxygen appears to be a requirement for macroflora and macrofauna. To the best of our knowledge, a general discussion of which habitable planets are conducive to oxygen has not taken place. Theories for the rise of oxygen fall into 4 categories: (i) It is governed by an intrinsic rate of biological innovation, independent of environmental factors. (ii) It is caused by mantle evolution, probably consequent to secular cooling. (iii) It is caused by hydrogen escape, which irreversibly oxidizes the Earth. (iv) It is Gaia's response to the brightening Sun, its rise prevented until reduced greenhouse gases were no longer needed to maintain a clement climate. All but the first of these make implicit astronomical predictions that can be quantified and made explicit. Here we address the third hypothesis. In this hypothesis hydrogen escape acts like an hourglass that continues until all relevant reduced mineral buffers have been oxidized (titrated, as it were) and the surface made safe for O2. The hypothesis predicts that abundant free O2 will be absent from habitable planets that have not experienced significant hydrogen escape. Where hydrogen escape is modest or insignificant, the atmosphere can be approximated as hydrostatic, which makes assessing radiative cooling by embedded molecules, atoms, and ions such as CO2 and H3+ straightforward. In particular, H2 is efficient at exciting non-LTE CO2 15 micron emission, which makes radiative cooling very effective when H2 is abundant. We can therefore map out the region of phase space in which habitable planets do not lose hydrogen, and therefore do not develop O2 atmospheres. A related matter is the power of radiative cooling by embedded molecules to enforce the diffusion limit to hydrogen escape. This matter in particular is relevant to addressing the empirical observation that rocky planets with thin or negligible atmospheres are rarely or never bigger than approx.1.6 Earth radii.

Zahnle, Kevin↗
NASA NTRS2016

Lucifer's Planet: Photolytic Hazes in the Atmosphere of 51 Eri b

We use a 1D model to address photochemistry and possible haze formation in the irradiated atmosphere of 51 Eri b (2016arXiv160407388Z). The intended focus was to have been on carbon and organic hazes, but sulfur photochemistry turns out to be interesting and possibly more important. The case for organic photochemical hazes is intriguing but falls short of being compelling. If organic hazes form abundantly, they are likeliest to do so if vertical mixing in 51 Eri b is weaker than in Jupiter, and they would be found below the altitudes where methane and water are photolyzed. The more novel result is that photochemistry turns H2S into elemental sulfur, here treated as S8. In the cooler models, S8 is predicted to condense in optically significant clouds of solid sulfur particles, whilst in the warmer models S8 remains a vapor along with several other sulfur allotropes that are both visually striking and potentially observable. For 51 Eri b, the division between models with and without condensed sulfur is at an effective temperature of 700 K, which is within error its actual effective temperature; the local temperature where sulfur condenses is between 280 and 320 K. The sulfur photochemistry we discuss is quite general and ought to be found in a wide variety of worlds over a broad temperature range, both colder and hotter than the 650-750 K range studied here, and we show that products of sulfur photochemistry will be nearly as abundant on planets where the UV irradiation is orders of magnitude weaker than it is on 51 Eri b.

photochemistry↗
NASA NTRS2016

The Stability of Hydrogen-Rich Atmospheres of Earth-Like Planets

Understanding hydrogen escape is essential to understanding the limits to habitability, both for liquid water where the Sun is bright, but also to assess the true potential of H2 as a greenhouse gas where the Sun is faint. Hydrogen-rich primary atmospheres of Earth-like planets can result either from gravitational capture of solar nebular gases (with helium), or from impact shock processing of a wide variety of volatile-rich planetesimals (typically accompanied by H2O, CO2, and under the right circumstances, CH4). Most studies of hydrogen escape from planets focus on determining how fast the hydrogen escapes. In general this requires solving hydro- dynamic equations that take into account the acceleration of hydrogen through a critical transonic point and an energy budget that should include radiative heating and cooling, thermal conduction, the work done in lifting the hydrogen against gravity, and the residual heat carried by the hydrogen as it leaves. But for planets from which hydrogen escape is modest or insignificant, the atmosphere can be approximated as hydrostatic, which is much simpler, and for which a relatively full-featured treatment of radiative cooling by embedded molecules, atoms, and ions such as CO2 and H3+ is straightforward. Previous work has overlooked the fact that the H2 molecule is extremely efficient at exciting non-LTE CO2 15 micron emission, and thus that radiative cooling can be markedly more efficient when H2 is abundant. We map out the region of phase space in which terrestrial planets keep hydrogen-rich atmospheres, which is what we actually want to know for habitability. We will use this framework to reassess Tian et al's hypothesis that H2-rich atmospheres may have been rather long-lived on Earth itself. Finally, we will address the empirical observation that rocky planets with thin or negligible atmospheres are rarely or never bigger than 1.6 Earth radii.

Earth-like planets↗
NASA NTRS2016

Ancient Air Caught by Shooting Stars

It is a truth almost universally acknowledged that Earth’s atmosphere before about 2.5 billion years ago had little or no free oxygen. The classic argument for anoxia on ancient Earth is that a distinct change occurred in the oxidation state of many surface rocks and minerals around the end of the Archaean eon (which lasted from 4 billion to 2.5 billion years ago). A more recent argument is that a sudden, permanent change in the relative abundances of rare sulfur isotopes preserved in sediments also occurred at that time — a change that can be linked to differences in sulfur’s atmospheric chemistry in the presence or absence of oxygen. These arguments are strong. It therefore comes as a surprise that melted meteor fragments recovered from Archaean limestone indicate that the contemporaneous atmosphere above 75 kilometres was highly oxidized, as reported by Tomkins et al. on page 235.

ancient Earth's atmosphere↗
NASA NTRS2015

Environmental Consequences of Big Nasty Impacts on the Early Earth

The geological record of the Archean Earth is spattered with impact spherules from a dozen or so major cosmic collisions involving Earth and asteroids or comets (Lowe, Byerly 1986, 2015). Extrapolation of the documented deposits suggests that most of these impacts were as big or bigger than the Chicxulub event that famously ended the reign of the thunder lizards. As the Archean impacts were greater, the environmental effects were also greater. The number and magnitude of the impacts is bounded by the lunar record. There are no lunar craters bigger than Chicxulub that date to Earth's mid-to-late Archean. Chance dictates that Earth experienced no more than approximately 10 impacts bigger than Chicxulub between 2.5 billion years and 3.5 2.5 billion years, the biggest of which were approximately30-100 times more energetic, comparable to the Orientale impact on the Moon (1x10 (sup 26) joules). To quantify the thermal consequences of big impacts on old Earth, we model the global flow of energy from the impact into the environment. The model presumes that a significant fraction of the impact energy goes into ejecta that interact with the atmosphere. Much of this energy is initially in rock vapor, melt, and high speed particles. (i) The upper atmosphere is heated by ejecta as they reenter the atmosphere. The mix of hot air, rock vapor, and hot silicates cools by thermal radiation. Rock raindrops fall out as the upper atmosphere cools. (ii) The energy balance of the lower atmosphere is set by radiative exchange with the upper atmosphere and with the surface, and by evaporation of seawater. Susequent cooling is governed by condensation of water vapor. (iii) The oceans are heated by thermal radiation and rock rain and cooled by evaporation. Surface waters become hot and salty; if a deep ocean remains it is relatively cool. Subsequently water vapor condenses to replenish the oceans with hot fresh water (how fresh depending on continental weathering, which might be rather rapid under the circumstances). (iv) The surface temperature of dry land is presumed to be the same as the lower atmosphere. A thermal wave propagates into the land at a rate set by conduction. Impacts not greatly larger than Chicxulub can raise the surface temperature by tens, hundreds, or even thousands of degrees, and evaporate meters to hundreds of meters of water. The biggest should have vitrified exposed dry land. More results are for the talk, as here we have run out of space.

asteroids↗
NASA NTRS2015

Understanding the Atmosphere of 51 Eri b: Do Photochemical Hazes Cloud the Planets Spectrum?

The first young giant planet to be discovered by the Gemini Planet Imager was the (is) approximately 2MJ planet 51 Eri b. This approximately 20 Myr old young Jupiter is the first directly imaged planet to show unmistakable methane in H band. To constrain the planet's mass, atmospheric temperature, and composition, the GPI J and H band spectra as well as some limited photometric points were compared to the predictions of substellar atmosphere models. The best fitting models reported in the discovery paper (Macintosh et al. 2015) relied upon a combination of clear and cloudy atmospheric columns to reproduce the data. However for an object as cool as 700 K, the origin of the cloud coverage is somewhat puzzling, as the global silicate and iron clouds would be expected to have sunk well below the photosphere by this effective temperature. While strong vertical mixing in these low gravity atmospheres remains a plausible explanation, we have explored whether atmospheric photochemistry, driven by the UV flux from the primary star, may yield hazes that also influence the observed spectrum of the planet. To explore this possibility we have modeled the atmospheric photochemistry of 51 Eri b using two state-of-the-art photochemical models, both capable of predicting yields of complex hydrocarbons under various atmospheric conditions. In our presentation we will summarize the modeling approach employed to characterize 51 Eri b, explaining constraints on the planet's effective temperature, gravity, and atmospheric composition and also present results of our studies of atmospheric photochemistry. We will discuss whether photochemical hazes could indeed be responsible for the particulate opacity that apparently sculpts the spectrum of the planet.

GPI - Gemini Planet Imager↗
NASA NTRS2015

Environmental Consequences of Big Nasty Impacts on the Early Earth

The geological record of the Archean Earth is spattered with impact spherules from a dozen or so major cosmic collisions involving Earth and asteroids or comets (Lowe, Byerly 1986, 2015). Extrapolation of the documented deposits suggests that most of these impacts were as big or bigger than the Chicxulub event that famously ended the reign of the thunder lizards. As the Archean impacts were greater, the environmental effects were also greater. The number and magnitude of the impacts is bounded by the lunar record. There are no lunar craters bigger than Chicxulub that date to Earth's mid-to-late Archean. Chance dictates that Earth experienced no more than approximately 10 impacts bigger than Chicxulub between 2.5 billion years and 3.5 billion years, the biggest of which were approximately 30-100 times more energetic, comparable to the Orientale impact on the Moon (1x10 (sup 26) joules). To quantify the thermal consequences of big impacts on old Earth, we model the global flow of energy from the impact into the environment. The model presumes that a significant fraction of the impact energy goes into ejecta that interact with the atmosphere. Much of this energy is initially in rock vapor, melt, and high speed particles. (i) The upper atmosphere is heated by ejecta as they reenter the atmosphere. The mix of hot air, rock vapor, and hot silicates cools by thermal radiation. Rock raindrops fall out as the upper atmosphere cools. (ii) The energy balance of the lower atmosphere is set by radiative exchange with the upper atmosphere and with the surface, and by evaporation of seawater. Susequent cooling is governed by condensation of water vapor. (iii) The oceans are heated by thermal radiation and rock rain and cooled by evaporation. Surface waters become hot and salty; if a deep ocean remains it is relatively cool. Subsequently water vapor condenses to replenish the oceans with hot fresh water (how fresh depending on continental weathering, which might be rather rapid under the circumstances). (iv) The surface temperature of dry land is presumed to be the same as the lower atmosphere. A thermal wave propagates into the land at a rate set by conduction. Impacts not greatly larger than Chicxulub can raise the surface temperature by tens, hundreds, or even thousands of degrees, and evaporate meters to hundreds of meters of water. The biggest should have vitrified exposed dry land. More results are for the talk, as here we have run out of space.

Archean Earth↗
NASA NTRS2015

The Atmospheres of the Terrestrial Planets:Clues to the Origins and Early Evolution of Venus, Earth, and Mars

We review the current state of knowledge of the origin and early evolution of the three largest terrestrial planets - Venus, Earth, and Mars - setting the stage for the chapters on comparative climatological processes to follow. We summarize current models of planetary formation, as revealed by studies of solid materials from Earth and meteorites from Mars. For Venus, we emphasize the known differences and similarities in planetary bulk properties and composition with Earth and Mars, focusing on key properties indicative of planetary formation and early evolution, particularly of the atmospheres of all three planets. We review the need for future in situ measurements for improving our understanding of the origin and evolution of the atmospheres of our planetary neighbors and Earth, and suggest the accuracies required of such new in situ data. Finally, we discuss the role new measurements of Mars and Venus have in understanding the state and evolution of planets found in the habitable zones of other stars.

origin of mars↗
NASA NTRS2014

The Atmospheres of Directly Imaged Planets: Where Has All the Methane Gone?

Methane and ammonia both first appear at lower effective temperatures in brown dwarf atmospheres than equilibrium chemistry models would suggest. This has traditionally been understood as a consequence of vertical mixing timescales being shorter than chemical equilibration timescales in brown dwarf photospheres. Indeed the eddy diffusivity, a variable accounting for the vigor of vertical mixing, has become a standard part of the description of brown dwarf atmosphere models, along with Teff and log g. While some models have suggested that methane is less favored at lower gravity, the almost complete absence of methane in the atmospheres of directly imaged planets, such as those orbiting HR 8799, even at effective temperatures where methane is readily apparent in brown dwarf spectra, has been puzzling. To better understand the paucity of methane in low gravity atmospheres we have revisited the problem of methane chemistry and mixing. We employed a 1-D atmospheric chemistry code augmented with an updated and complete network of the chemical reactions that link CO to CH4. We find the methane abundance at altitudes at or above the effective photosphere is a strong function of surface gravity because higher g shifts the p-T structure to higher pressures (i.e., a given optical depth is proportional to p/g, a relation mitigated somewhat by pressure broadening). Thus quenching in more massive brown dwarfs occurs at a lower temperature and higher pressure, both favoring CH4. We predict that in the lowest mass young giant planets, methane will appear very late, at effective temperatures as low as 600 K rather than the 1200 K seen among field brown dwarfs. This methane deficiency has important implications for the interpretation of spectra as well as methane-based planetary companion searches, such as the NICI survey. The GPI and SPHERE surveys will test these ideas and probe atmospheric chemistry and composition in an entire new range of parameter space. A caveat is that these calculations presume that the C to O ratio is comfortably less than one; the behavior is quite different if C and O are equally abundant, and of course CH4 is always present if C exceeds O.

young giant planets↗
NASA NTRS2014

The Tethered Moon

A reasonable initial condition on Earth after the Moonforming impact is that it begins as a hot global magma ocean1,2. We therefore begin our study with the mantle as a liquid ocean with a surface temperature on the order of 3000- 4000 K at a time some 100-1000 years after the impact, by which point we can hope that early transients have settled down. A 2nd initial condition is a substantial atmosphere, 100-1000 bars of H2O and CO2, supplemented by smaller amounts of CO, H2, N2, various sulfur-containing gases, and a suite of geochemical volatiles evaporated from the magma. Third, we start the Moon with its current mass at the relevant Roche limit. The 4th initial condition is the angular momentum of the Earth-Moon system. Canonical models hold this constant, whilst some recent models begin with considerably more angular momentum than is present today. Here we present a ruthlessly simplified model of Earth's cooling magmasphere based on a full-featured atmosphere and including tidal heating by the newborn Moon. Thermal blanketing by H2O-CO2 atmospheres slows cooling of a magma ocean. Geochemical volatiles - chiefly S, Na, and Cl - raise the opacity of the magma ocean's atmosphere and slow cooling still more. We assume a uniform mantle with a single internal (potential) temperature and a global viscosity. The important "freezing point" is the sharp rheological transition between a fluid carrying suspended crystals and a solid matrix through which fluids percolate. Most tidal heating takes place at this "freezing point" in a gel that is both pliable and viscous. Parameterized convection links the cooling rate to the temperature and heat generation inside the Earth. Tidal heating is a major effect. Tidal dissipation in the magma ocean is described by viscosity. The Moon is entwined with Earth by the negative feedback between thermal blanketing and tidal heating that comes from the temperature-dependent viscosity of the magma ocean. Because of this feedback, the rate that the Moon's orbit evolves is limited by the modest radiative cooling rate of Earth's atmosphere, which in effect tethers the Moon to the Earth. Consequently the Moon's orbit evolves orders of magnitude more slowly than in conventional models. Slow orbital evolution promotes capture by orbital resonances that may have been important in the Earth-Moon system

Earth-Moon system↗
NASA NTRS2013

The Rise of Oxygen and the Hydrogen Hourglass

Oxygenic photosynthesis appears to be necessary for an oxygen-rich atmosphere like Earth's. But available geological and geochemical evidence suggest that at least 200 Myr, and possibly more than 700 Myr, elapsed between the advent of oxygenic photosynthesis and the establishment of an oxygen atmosphere. The interregnum implies that at least one other necessary condition for O2 needed to be met. Here we argue that the second condition was the oxidation of the surface and crust to the point where O2 became more stable than competing reduced gases such as CH4. The cause of Earth's surface oxidation would be the same cause as it is for other planets with oxidized surfaces: hydrogen escape to space. The duration of the interregnum would have been determined by the rate of hydrogen escape and by the size of the reduced reservoir that needed to be oxidized before O2 became favored. We suggest that continental growth has been influenced by hydrogen escape, and we speculate that, if there must be an external bias to biological evolution, hydrogen escape can be that bias.

atmospheric evolution↗
NASA NTRS2012

Impact-Induced Climate Change on Titan

Titan's thick atmosphere and volatile surface cause it to respond to big impacts like the one that produced the prominent Menrva impact basin in a somewhat Earth-like manner. Menrva was big enough to raise the surface temperature by 100 K. If methane in the regolith is generally as abundant as it was at the Huygens landing site, Menrva would have been big enough to double the amount of methane in the atmosphere. The extra methane would have drizzled out of the atmosphere over hundreds of years. Conditions may have been favorable for clathrating volatiles such as ethane. Impacts can also create local crater lakes set in warm ice but these quickly sink below the warm ice; whether the cryptic waters quickly freeze by mixing with the ice crust or whether they long endure under the ice remains a open question. Bigger impacts can create shallow liquid water oceans at the surface. If Titan's crust is made of water ice, the putative Hotei impact (a possible 800-1200 km diameter basin, Soderblom et al 2009) would have raised the average surface temperature to 350-400 K. Water rain would have fallen and global meltwaters would have averaged 50 m to as much as 500 m deep. The meltwaters may not have lasted more than a few decades or centuries at most, but are interesting to consider given Titan's organic wealth.

Zahnle, Kevin↗
NASA NTRS2006

Sulfur during the Transition from Anoxic to Oxic Atmospheres

The invention of oxygenic photosynthesis was likely accompanied by the introduction of large amounts of O2 and complementary reduced gases (chiefly CH4) into the atmosphere. To first approximation the venting of O2 and CH4 are stochiometrically linked. We therefore present a suite of numerical photochemical models that address the anoxic-oxic transition in an atmosphere driven by large linked inputs of biogenic 02 and CH4. We find in general that, in steady state, there are two solutions, one oxic and the other anoxic. The anoxic solution appears to be linearly stable. If volcanic SO2 fluxes are large, S disproportionates into oxidized (H2S04) and reduced (S8) exit channels. As elemental sulfur is insoluble it provides a means of preserving photochemical mass-independent fractionation (MIF). On the other hand, if the source of volcanic SO2 is smaller than today, all S can leave the atmosphere as S8. Under these conditions there would be no MIF signal. The oxic solution appears to be linearly unstable. In the oxic solutions S is invariably oxidized to sulfate, and the MIF signal would be absent. The transitional atmosphere is relatively unstable and is also the most photochemically active. Consequently it is the transitional atmosphere, not the oxic or anoxic atmospheres, that has the lowest CH4 levels and weakest greenhouse warming. As a practical matter we expect the transitional atmospheres to vary strongly in response to diurnal and seasonal biological forcing.

Zahnle, Kevin↗
NASA NTRS2006

Earth After the Moon Forming Impact

The Hadean Earth is widely and enduringly pictured as a world of exuberant volcanism, exploding meteors, huge craters, infernal heat, and billowing sulfurous steams; i.e., a world of fire and brimstone punctuated with blows to the head. In the background the Moon looms gigantic in the sky. The popular image has given it a name that celebrates our mythic roots. A hot early Earth is an inevitable consequence of accretion. The Moon-forming impact ensured that Earth as we know it emerged from a fog of silicate vapor. The impact separated the volatiles from the silicates. It took -100 years to condense and rain out the bulk of the vaporized silicates, although relatively volatile elements may have remained present in the atmosphere throughout the magma ocena stage. The magma ocean lasted approx. 2 Myr, its lifetime prolonged by tidal heating and thermal blanketing by a thick (CO2-rich steam atmosphere. Water oceans condensed quickly after the mantle solidified, but for some 10-100 Myr the surface would have stayed warm (approx. 500 K) until the CO2 was removed into the mantle. Thereafter the faint young Sun suggests that a lifeless Earth would always have been evolving toward a bitterly cold ice world, but the cooling trend was frequently interrupted by volcanic or impact induced thaws.

Zahnle, Kevin↗
NASA NTRS2003

Cratering Rates in the Outer Solar System

We have constructed a self-consistent study of cratering rates in the outer solar system. Two papers were written, one on cratering asymmetries on synchronously rotating satellites and the other on the cratering rates themselves. The first addresses the well-founded expectation that the leading hemisphere of a synchronously rotating satellite should be more heavily cratered than the trailing hemisphere, and how our solar system has avoided showing much sign of this. We conclude that Ganymede has in the past rotated nonsynchronously, which may imply that it once harboured a thicker inner ocean than it does now. The other study began as an attempt to determine the age of the surface of Europa at a time when Europa was regarded as a major Exobiological target. In keeping with changing times the study expanded to the point that it now recommends cratering rates for worlds as diverse as Charon and Pluto, and includes the contributions of several invaluable co-authors, none of whom would agree with all of my conclusions. The nexus of the work is the size-frequency distribution of comets striking Jupiter (Figure). This was determined using the historically observed record of comets striking or nearly striking Jupiter; the size-frequency distributions of craters on lightly cratered surfaces of Europa, Ganymede, and Triton; and the size-frequncy distribution of Kuiper Belt objects. Extreme reductionists will be happy to know that the surface of Europa probably has an age of around 50 million years. Perhaps more intriguing is that Neptune's moon Triton, by origin a giant comet and by capture and orbital evolution a once fully melted giant comet, has a surface that is probably no older than Europa's.

Zahnle, Kevin↗
NASA NTRS2002

Differential Cratering of Synchronously Rotating Satellites by Ecliptic Comets

We use Monte Carlo methods to simulate impacts of ecliptic comets on the synchronously rotating satellites of giant planets. We reconfirm the long-standing prediction that the cratering rate should be much higher on the leading hemispheres than on the trailing hemisphere; indeed we find that previously published analytical formulations modestly underestimate the degree of apex-antapex asymmetry to be expected. We then compare our results to new mapping of impact craters on Ganymede, Callisto, and Triton. Ganymede reveals a pronounced apex-antapex asymmetry that is nonetheless much less than predicted. All of Triton's confirmed impact craters are clustered toward the apex of motion, far exceeding the predicted asymmetry. No asymmetry is observed on Callisto. In each case at least one of our basic assumptions must be wrong. Likely candidates include the following: (i) the surfaces of all but the most sparsely cratered satellites are saturated or nearly saturated with impact craters; (ii) these satellites have rotated nonsynchronously over geological time; (iii) most of the craters are made not by heliocentric (Sun-orbiting) comets and asteroids but rather by planetocentric (planet-orbiting) debris of indeterminate origin; or (iv) pathological endogenic resurfacing has created illusions of structure. Callisto's surface is readily classified as nearly saturated. Ganymede's bright terrains, although less heavily cratered than those of Callisto, can also be explained by crater densities approaching saturation on a world where endogenic processes were active. The leading alternative is nonsynchronous rotation, an explanation supported by the distribution of catenae (crater chains produced by impact of tidally disrupted comets). Triton's craters can be explained by planetocentric debris or by capricious resurfacing, but both hypotheses are inherently improbable.

Zahnle, Kevin↗