Origin of the Late Heavy Bombardment of the Terrestrial Planets

The models proposed in the previous sections for the formation of the Oort cloud and the sculpting of the Kuiper belt seem to offer a quite complete view of the formation and evolution of the Solar System. But they are not entirely satisfactory, because they ignore an important fact in the history of the Solar System: the late heavy bombardment (LHB) of the terrestrial planets.

Below, I review the observational constraints on the LHB, then describe the models proposed in the past to explain a spike in the bombardment rate. Finally, I will focus on an emerging view of what happened ^650 My after the formation of the planets. In Sect. 6, I will discuss how our understanding of Oort cloud and Kuiper belt formation needs to be modified in light of the LHB evidence and will point to open problems and prospects for future research.

Evidence for a Late Cataclysmic Bombardment

The crust of the Moon crystallized around 4.44 Gy ago, and the morphology of its highlands records a dense concentration of impact craters, excavated before the emplacement - around 3.8 Gy ago - of the first volcanic flows in the mare plains [184]. Thus, a period of intense bombardment - the LHB - occurred in the first 600-700 My of the Moon's history. However, the magnitude and the chronology of the collisions between 4.5 and 4 Gy remain a topic of controversy.

Two explanations have been proposed. According to [74, 184], the frequency of impacts declined slowly and progressively after the end of the accretion period, up to 3.9 Gy ago. In this view, the LBH is not an exceptional event. Rather, it is a 600 My tail of the collisional process that built the terrestrial planets.

Another view advocates a rapid decline in the frequency of impacts after the formation of the Moon, down to a value comparable to the current one. This was followed by a cataclysmic period between ^4.0 and ~3.8Gy ago, marked by an extraordinarily high rate of collisions [27,147-149,164].

Today, the majority of authors favor the cataclysmic scenario of the LHB. This theory is supported by a series of arguments:

i) 600 million years of continual impacts should have left an obvious trace on the Moon. So far, no such trace has been found. The isotopic dating of the samples returned by the various Apollo and Luna missions revealed no impact melt-rock older than 3.92 Gy [147,148]. The lunar meteorites confirm this age limit. The meteorites provide a particularly strong argument because they likely originated from random locations on the Moon [27], unlike the lunar samples collected directly on its surface. A complete resetting of all ages all over the Moon is possible [67] but highly unlikely, considering the difficulties of completely resetting isotopic ages at the scale of a full planet [31]. The U-PB and Rb-Sr isochrones of lunar highland samples indicate a single metamorphic event at 3.9 Gy ago, and between 3.85 and 4 Gy, ago respectively [164]. There is no evidence for these isotopic systems being reset by intense collisions between 4.4 and 3.9 Gy.

ii) The old upper crustal lithologies of the Moon do not show the expected enrichment in siderophile elements (in particular the Platinum Group Elements) implied by an extended period of intense collisions [148].

iii) If the elevated mass accretion documented in the period around 3.9 Gy is considered to be the tail end of an extended period of collisions, the whole Moon should have accreted at about 4.1 Gy ago instead of 4.5 Gy [100,149].

iv) The 15 largest impact structures on the Moon, the so-called basins, with diameters between 300 and 1200 km, have been dated to have formed between 4.0 and 3.9 Gy ago. If the bombardment had declined monotonically since 4.5 Gy ago, it appears strange that the largest impacts all occurred at the end of the period.

v) On Earth, the oxygen isotopic signature of the oldest known zircons (age: 4.4 Gy) indicates formation temperatures compatible with the existence of liquid water [173]. This argument seems contradictory with an extended period of intense collisions, which would have raised the Earth's temperature to exceed the water evaporation threshold.

vi) These same zircons retain secondary overgrowths developed after primary core crystallization during their 4.4 Gy long crystal residence times. The rim overgrowths can record discrete thermal events subsequent to zircon formation and provide a unique window in crustal processes before the beginning of the terrestrial rock record. In [167], all these rim overgrowths have been dated to be ~3.9Gy old. No (preserved) older rim overgrowths, associated to more primoridal events, have been found. This suggests that the thermal events were associated to impacts and that these impacts were concentrated in time about 3.9 Gy ago.

Therefore, it can be concluded that there is strong evidence for a cataclysmic Late Heavy Bombardment event around 3.9 Gy ago. This cataclysm did not just affect the Moon, but has now been clearly established throughout the inner Solar System [102]. The exact duration of the cataclysm is difficult to estimate, however. On the basis of the cratering record of the Moon, it lasted between 20 and 200 My, depending on the mass flux estimate used in the calculation.

Early Models of LHB Origin

The occurrence of a cataclysmic LHB challenges our naive view of a Solar System gradually evolving from chaos to order. Several ideas have been proposed to examine what could have abruptly changed the evolution of the system, causing a spike in the bombardment rate.

The possibility of a stochastic break-up of an asteroid close to a resonance in the main belt has been investigated in [188]. The flux of projectiles inferred from the crater density would require the break-up of an object larger than Ceres. This event is very implausible and would have left a huge asteroid family in the main belt, of which we see no trace.

If a stochastic break-up is ruled out, then the remaining possibility is that a reservoir of small bodies, which remained stable up to the time of the LHB, suddenly became unstable, with most of its objects achieving planet crossing orbits.

A comet shower from the Oort cloud, possibly triggered by a stellar encounter, is a first possibility. However, a new LPC has a probability to collide with the Earth of about 10~9. Because the mass hitting the Earth during the LHB is estimated to be [75], this would require an Oort cloud initially containing 104 Earth masses, which - as discussed in Sect. 3 - is impossible.

In [21], it was proposed that a fifth terrestrial planet, with a mass comparable to that of Mars, became unstable after ^600 My of evolution, and crossed the asteroid belt before being dynamically removed. Invaded by this new perturber, the asteroid belt became unstable and most of its objects acquired planet crossing eccentricities. The simulations presented in [21] show that a late instability of a 5-planet terrestrial system is indeed possible, but it requires that the rogue planet was initially at about 1.9 AU, with an inclination of ~15°. Whether this initial configuration is consistent with terrestrial planet formation models was not discussed. Similarly, the resulting orbital distribution in the asteroid belt, after the removal of the rogue planet, was not investigated. Moreover, in most simulations, the rogue planet was removed by a collision with Mars, and the red planet does not show any sign of such a gigantic strike.

In [114], it was proposed that the LHB was associated with the "late appearance" of Uranus and Neptune in the planetesimal disk. That paper showed that the planetesimals scattered away from the neighborhoods of the ice giants would have been sufficient to cause a bombardment on the Moon with a magnitude comparable to that of the LHB. Moreover, the dynamical removal of these planetesimals would have caused a radial migration of Jupiter and Saturn, which in turn would have forced the v6 secular resonance to sweep across the main asteroid belt [58]. Their eccentricities being excited by the resonance passage, most asteroids would have acquired planet-crossing orbits. Consequently, they would have contributed to - or even dominated -the terrestrial planets cratering process. The problem in this work was that the "late appearance" of Uranus and Neptune was postulated, rather than explained. The authors argued that these planets might have formed very slowly, although this seems implausible given that they accreted hydrogen atmospheres of 1-2 Earth masses from the proto-solar nebula [66], which should have dissipated within ~10My [72]. Later, in [110], it was proposed that Uranus and Neptune formed in between Jupiter and Saturn. The system remained stable for 600 My, until an instability was produced by the gradual evolution of the planetary orbits. Consequently, Uranus and Neptune were scattered outward by Jupiter and Saturn. After this, interactions with the disk eventually damped their eccentricities and parked them on stable orbits. As a by-product of this process, the planetesimal disk was destroyed as in [114]. The simulations in [110] showed that a late instability of a Jupiter-Uranus-Neptune-Saturn system is indeed possible. However, the instability time depends critically on the initial conditions, and it is unclear if those adopted in the successful simulations could be consistent with giant planet formation models. More importantly, the scattering of Uranus and Neptune by Jupiter and Saturn would have destabilized the regular satellite systems of all the planets. Finally, the massive planetesimal disk required to stabilize the orbits of Uranus and Neptune would have forced the latter to migrate well beyond its current position. Thus, as admitted by the authors themselves, this scenario has to be considered as a "fairy tale."

The Great Comet-A steroid Alliance: An Emerging View of the Origin of the LHB

Starting from two key considerations:

i) giant planet migration through the planetesimal disk induces a bombardment of the terrestrial planets of sufficient magnitude to explain the LHB (from [114]), ii) at the end of the migration phase, the Solar System is essentially identical to the current one (namely there are no more reservoirs of planetesimals to destabilize), it was realized in [130] that solving the problem of the LHB origin required a plausible mechanism to be found that would trigger planet migration at a late time.

Pursuing this goal, in [64] the authors remarked that, in all previous simulations, planet migration started immediately because planetesimals were placed close enough to the planets to be violently unstable. While this type of initial condition was reasonable for the goals of those works, it is unlikely to have been the case in reality. In fact, planetesimal-driven migration is probably not important for planetary dynamics as long as the gaseous massive nebula exists (the nebula accounts for about 100 times more mass than the planetesimals). The initial conditions in simulations of the planetesimal-driven migration should therefore represent the system that existed at the time the nebula dissipated. Thus, the planetesimal disk should contain only those particles that had dynamical lifetimes longer than the lifetime of the solar nebula (a few million years), because the planetesimals initially on orbits with shorter dynamical lifetimes should have been eliminated earlier, during the nebula era. If this constraint on the initial conditions is fulfilled, then the resulting migration is necessarily slow, because it depends on the rate at which disk particles evolve onto planet-crossing orbits, which is long by definition. If the planetary system, in the absence of planetesimals, is stable, this slow migration can continue for a long time, slightly accelerating or damping depending on the disk's surface density [62]. Conversely, if the planet system is - or becomes - unstable, then the planets tend to increase their orbital separation. The outermost planet penetrates into the disk, and this starts a fast migration, similar to that obtained in previous simulations, where the planets are embedded in the disk from the very beginning. Thus, the problem of triggering the LHB is reduced to the problem of understanding how the giant planets, during their slow migration, could pass from a stable configuration to an unstable one.

A solution to this problem has been proposed in [172]. This work postulated that, at the time of the dissipation of the gas disk, the four giant planets were in a compact configuration, with quasi-circular, quasi-coplanar orbits with radii ranging from 5.5 to 13-17 AU. Saturn and Jupiter were close enough to have a ratio of orbital periods less than 2. This choice of the initial conditions for the two giant planets is supported by simulations of their evolution during the gas-disk phase [122] [132]. The assumption of initial small eccentricities and inclinations is consistent with planet formation models. The small eccentricities ensure the stability of such a compact planet configuration. In the scenario of [172], during their migration in divergent directions, Jupiter and Saturn eventually crossed their mutual 1:2 mean-motion resonance. This resonance crossing excited their eccentricities to values comparable to those currently observed (for eccentricity excitation because of resonance crossing, see also [24]). The acquired eccentricities of Jupiter and Saturn destabilized the planetary system as a whole. The planetary orbits became chaotic and started to approach each other. Thus, a short phase of encounters followed the resonance-crossing event. Consequently, both ice giants were scattered outward, deep into the disk. As discussed above, this abruptly increased the migration rates of the planets. During this fast migration phase, the eccentricities and inclinations of the planets decreased as a result of the dynamical friction exerted by the planetesimals and the planetary system was finally stabilized.

With a planetesimal disk of about 35 M0, the simulations in [172] reproduced the current architecture of the orbits of the giant planets remarkably well, in terms of semi-major axes, eccentricities, and inclinations. In particular, this happened in the simulations where at least one of the ice giants encountered Saturn (see Fig. 31). Conversely, in the simulations where encounters with Saturn never occurred, Uranus typically ended its evolution on an orbit too close to the Sun, and the final eccentricities and inclinations of all the planets involved were too small.

With this result, [64] could put all the elements together in a coherent scenario for the LHB origin. Assuming an initial planetary system like that described in [172], the planetesimal disk fulfilled the lifetime constraint discussed above only if its inner edge was located about 1 AU beyond the position of the last planet. With this kind of disk, the 1:2 resonance crossing event that destabilized the planetary system occurred at a time ranging from 192 to 875 My (see Fig. 32). Modifying the planetary orbits also led to changes in the resonance-crossing time, pushing it up to 1.1 Gy after the beginning of the simulation. This range of instability times well brackets the estimated date of the LHB from lunar data.

The top panel of Fig. 33 shows the giant planets' evolution in a representative simulation of [64]. Initially, the giant planets migrated slowly because of the leakage of particles from the disk. This phase lasted 875 My, at which point Jupiter and Saturn crossed their 1:2 resonance. At the resonance crossing event, as in [172], the orbits of the ice giants became unstable, and they were scattered into the disk by Saturn. They disrupted the disk and scattered objects all over the Solar System, including the inner regions. Eventually,

15 20 25 Semi-major axis (AU)

15 20 25 Semi-major axis (AU)

Fig. 31. Comparison of the synthetic final planetary systems obtained in [172] with the real outer Solar System. Top: Proper eccentricity vs. semi-major axis. Bottom: Proper inclination vs. semi-major axis. Here, proper eccentricities and inclinations are defined as the maximum values acquired over a 2 My time-span and were computed from numerical integrations. The inclinations are measured relative to Jupiter's orbital plane. The values for the real planets are presented as filled black dots. The gray squares mark the mean of the proper values for the runs with no planetary encounters involving Saturn, while the black triangles mark the same quantities for the runs where at least one ice giant encountered the ringed planet (about 15 runs in each case). The error bars represent one standard deviation of the measurements. From [172]

15 20 25 Semi-major axis (AU)

Fig. 31. Comparison of the synthetic final planetary systems obtained in [172] with the real outer Solar System. Top: Proper eccentricity vs. semi-major axis. Bottom: Proper inclination vs. semi-major axis. Here, proper eccentricities and inclinations are defined as the maximum values acquired over a 2 My time-span and were computed from numerical integrations. The inclinations are measured relative to Jupiter's orbital plane. The values for the real planets are presented as filled black dots. The gray squares mark the mean of the proper values for the runs with no planetary encounters involving Saturn, while the black triangles mark the same quantities for the runs where at least one ice giant encountered the ringed planet (about 15 runs in each case). The error bars represent one standard deviation of the measurements. From [172]

they stabilized on orbits very similar to the current ones, at ^20 and ^30 AU respectively. The solid curve in the bottom panel shows the amount of material that struck the Moon as a function of time. As predicted in [114], the amount of material hitting the Moon after resonance crossing is consistent

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