Differences between the impact regimes of the terrestrial planets: Implications for primordial D:H ratios
Introduction
The nature of impacts in our Solar System is something that is of great interest to astronomers, geologists, and the general public alike. Which objects pose the greatest threat to the Earth? Where did the terrestrial planets acquire their water? What killed the dinosaurs?
Over the years, our understanding of the impact regime on the Earth has evolved in fits and starts – in fact, it is only really in the last fifty or sixty years that the idea that impacts are anything of a threat has been accepted! Traditionally, the Earth was viewed as a peaceful, tranquil place, unchanging, and unthreatening. Over the early 1900s, this view slowly shifted, with the acceptance of processes such as plate tectonics and mass extinctions replacing the paradigm of constant peace and safely. Finally, thanks to the work of a few scientists (such as Gene Shoemaker), the craters on the Earth's surface were accepted as being impact features, and impacts were confirmed as being both a current concern and an important part of the history of our planet. Since this realisation, many authors have carried out studies of the impact flux on the Earth, attempting to determine which groups of objects pose the greatest threat, and trying to explain peculiarities of the impact history constructed for the Earth from the study of craters here and on the Moon. Less work, however, has been carried out to examine the differences in impact regimes experienced by the different terrestrial planets, with a common assumption being that Venus and Mars have experienced the same general impact history as the Earth. In this work, we attempt to address this question, and to see what similarities, and what differences, there are between the impact fluxes raining down on these three worlds.
A tool which can tell us many things about the formation of the inner Solar System is the study of the ratio between deuterium and hydrogen in water. Recent modelling work (Drouart et al., 1999; Mousis et al., 2000; Mousis, 2004; Horner et al., 2007, Horner et al., 2008) suggests that the D:H ratio in the water within icy bodies will vary as a function of their formation distance from the Sun. In brief, because water falling into the solar nebula from beyond was highly enriched in deuterium when compared with the infalling molecular hydrogen,1 a reversible gas-phase reaction between these two nebula components leads to a slow but steady reduction in the deuteration of the water. Once the temperature of the nebula drops, the water freezes out, halting the reaction and fixing the D:H value. As the nebula cools over time, the areas furthest from the Sun, which are initially the coldest, are the first to experience water freezing out in this way, fixing the D:H value acquired in the gas phase, with the “ice-line” moving inward over time. In other words, this means that the closer to the Sun a body formed, the lower the D:H ratio within its water would be. Across the Solar System, the resulting value changes dramatically, as one moves through the regions in which asteroidal and cometary bodies would have formed.
A field in which knowledge of the D:H ratio in water is particularly important is the study of the atmospheres of the terrestrial planets, Venus, the Earth, and Mars. In that work, examination of the current D:H is used to study a variety of planetary properties, from the hydration history of Venus (Donahue, 1999; Lécuyer et al., 2000), to the structure of the early Martian atmosphere (Solomon et al., 2005). However, all these studies require knowledge of the original D:H ratios on these planets – values that are currently unknown. Despite this, a large amount of work has been done on the deuterium budgets of these worlds, often involving complicated models of atmospheric physics. The fact that different escape rates would be expected from the atmospheres of the planets for hydrogen and deuterium complicates the matter, as do isotope-sensitive processes on the surfaces of the planets in question. In fact, it is strikingly obvious that the deuteration on each planet at the current day is quite different to the native value. The bulk of authors who study the behaviour of deuterium on these worlds make the simplifying assumption that the original values were the same for the three worlds (so, for example, assuming that the initial level of deuteration in Martian water was identical to that of the Earth) (Krasnopolsky et al., 1998; Lécuyer et al., 2000; Gurwell, 1995). Such assumptions allow the authors to use the modern values as a tool to aid their understanding of the various physical processes through which the values can be changed.
In the absence of data, the assumption that the original D:H ratios within the water on Venus and Mars were the same as the original terrestrial value is an obvious simplification to make, particularly since it allows various studies of these bodies to be carried out. However, while such studies are doubtlessly valuable, it is far from obvious that the three planets would have had identical initial levels of deuteration. Indeed, given our growing understanding of the chaotic nature of planetary accretion, together with the effects of late giant impacts and the late heavy bombardment (LHB), it seems more likely that the planets would obtain their volatiles from a variety of different reservoirs, and would therefore have acquired water with a wide variety of D:H values. Such variation between the amounts of water delivered to the terrestrial planets from various sources has, in fact, been identified before. Levison et al. (2001) carried out dynamical simulations to examine the idea that Uranus and Neptune's formation led to the proposed cataclysm known as the late heavy bombardment. Their results, highlighted in figure 4 of that work, suggest that Mars would have experienced more impacts from objects in the Uranus–Neptune region, per asteroidal impactor, than any of the other terrestrial planets. Although that work was based on a very small sample of potential impactors (600 bodies in total, spread between the asteroid belt, the Jovian Trojan family, and in the Uranus–Neptune region, with collision rates on the terrestrial planets estimated using Öpik's equation (Öpik, 1951)), and despite the fact that it examined just one possible scenario for Solar System evolution, it provides a strong indication that the terrestrial worlds would have experienced greatly disparate hydration regimes, at least for that component of their water sourced from beyond the orbit of Mars. This conclusion is supported by the work of Lunine et al. (2003), who examine the question of the origin of Martian water. The authors consider the scenario in which the bulk of the water provided to the Earth is sourced by a small number of collisions between the Earth and planet-sized embryos, rich in water, sourced from the asteroid belt (Morbidelli et al., 2000). To explain the current mass of Mars, the authors propose that the planet must have experienced no such giant collisions, and so would be expected to form solely through the accretion of smaller bodies. Essentially, the authors propose that the rare and stochastic nature of such collisions during the late stages of planet formation could lead to proto-Mars experiencing no such event during its evolution, whilst the larger Earth experienced at least one, or even a few. Mars’ volatiles, then, would have been contributed by the ongoing background flux of asteroidal and cometary impacts during its formation, while the contribution of those reservoirs to the Earth's hydration would have been swamped by the bulk of material delivered in collision with such embryos. This would clearly lead to a greatly different origin for the bulk of that planet's hydration when compared to the Earth. Although recent work (Andrews-Hanna et al., 2008) has provided evidence that Mars has experienced at least one giant impact over the course of its evolution, the work of Lunine et al. once again highlights the fact that caution must be taken when attempting to equate the primordial levels of deuteration on the other terrestrial planets to that of the Earth.
In this work, we aim to build upon these earlier studies, which examined very specific scenarios of terrestrial planet hydration. A series of more general simulations involving a variety of simple, but plausible, populations of potential impactors covering a wide range of possible formation scenarios were carried out in order to examine the similarities and the differences between the impact flux upon the terrestrial worlds. This allowed us, in turn, to examine the effect such differences would have on the degree of deuteration experienced by those planets. In Section 2, we introduce the various scenarios which are currently used to explain the volatilisation of the terrestrial planets, before detailing the dynamical simulations carried out to assess the impact regimes in Section 3. In Section 4, we present a detailed discussion of how the differences between the impact rates on the terrestrial worlds would affect their volatilisation history, with a particular focus on the D:H values in their water, while in Section 5, we state our main conclusions.
Section snippets
Scenarios for planetary hydration
Two main models exist for the hydration of the terrestrial planets: in the endogeneous water scenario, the water originates from the region of the solar nebula in which the planet is forming; whilst in the exogeneous water scenario, it originates from regions beyond that planet's feeding zone. In the endogeneous case, the source of water was therefore local, coming from the same feeding zone as the rocky material making up the terrestrial planet in question, and was concomitantly accreted to
Simulating the impact flux
Our simulations, conducted in order to study the differences between the asteroidal and cometary contributions to the terrestrial planet impact flux, were carried out using the hybrid integrator within the MERCURY package (Chambers, 1999). Test populations of massless particles were created representing asteroidal and cometary material, and followed for a period of 10 Myr under the gravitational influence of Venus, the Earth, Mars, Jupiter, Saturn, Uranus, and Neptune, in their current orbits.
Discussion
The values of Nf in Table 1 imply that the number of asteroids hitting a planet per comet varies drastically through the inner Solar System. What does this mean? If we look at the formation of the planets, and their acquisition of volatiles, these results must be considered in terms of the three main competing theories outlined above.
First, we have the endogenous accretion model, which requires that volatiles were acquired by the planets during their formation. As stated earlier, this theory is
Conclusions
Through a number of detailed n-body simulations, we have studied the way in which the impact rates on Venus, the Earth and Mars vary as a function of the source population of impactors. As a result of different delivery mechanisms, we found that, for our simple source populations, Mars is far more likely to be impacted by asteroidal material than either the Earth or Venus, even in situations where the asteroid belt has been hugely stirred and destabilised (as has been suggested occurred to
Acknowledgements
We would like to thank our reviewers, Dr. Alessandro Morbidelli and an anonymous Referee for their highly detailed and beneficial comments on our original manuscript. In addition, JAH appreciates the ongoing financial support of STFC.
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