The Origin of the Outer Edge of the Kuiper Belt

The existence of an outer edge of the Kuiper belt is very intriguing. Several mechanisms for its origin have been proposed, none of which have resulted in a general consensus between the experts in the field. These mechanisms can be grouped in three classes.

Class I: Destroying the Distant Planetesimal Disk

It has been shown, with numerical simulations in [19], that a Martian mass body residing for 1 Gy on an orbit with a ~ 60 AU and e ~ 0.15-0.2 could have scattered most of the Kuiper belt bodies originally in the 50-70 AU range into Neptune-crossing orbits, leaving this region strongly depleted and dynamically excited. As shown in Fig. 6, the apparent edge at 50 AU might simply be the inner edge of such a gap in the distribution of Kuiper belt bodies. A problem with this scenario is that there are no evident dynamical mechanisms that would ensure the later removal of the massive body from the system. In other words, the massive body should still be present, somewhere in the ~50-70AU region. A Mars-size body with 4% albedo at 70 AU would have apparent magnitude brighter than 20. In addition its inclination should be small, both in the scenario where it was originally a Scattered disk object whose eccentricity (and inclination) were damped by dynamical friction [19], and in that where the body reached its required heliocentric distance by migrating through the primordially massive Kuiper belt [62]. Thus, in view of its brightness and small inclination, it is unlikely that the putative Mars-size body could escape detection in the numerous wide field ecliptic surveys that have been performed up to now, and in particular in that led by Trujillo and Brown [171].

A second possibility is that the planetesimal disk was truncated by a close stellar encounter. The eccentricities and inclinations of the planetesimals resulting from a stellar encounter depend critically on a/D, where a is their semi-major axis of the planetesimal and D is the heliocentric distance of the stellar encounter [85,99]. A stellar encounter at —200 AU would make most of the bodies beyond 50 AU so eccentric that they intersect the orbit of Neptune, which would eventually produce the observed edge [123]. An interesting constraint on the time at which such an encounter occurred is set by the existence of the Oort cloud. It was shown in [113] that the encounter had to occur much earlier than —10 My after the formation of Uranus and Neptune; otherwise most of the existing Oort cloud would have been ejected to interstellar space. Moreover, many of the planetesimals in the Scattered disk at that time would have had their perihelion distance lifted beyond Neptune, decoupling them from the planet. As a consequence, the Extended Scattered disk population, with a > 50 AU and 40 < q < 50 AU, would have had a mass comparable or larger than that of the resulting Oort cloud, hardly compatible with the few detections of Extended Scattered disk objects achieved up to now. As discussed in Sect. 3.2, a close encounter with a star during the first million years of planetary formation is a possible event if the Sun formed in a stellar cluster. However, at such an early time, the Kuiper belt objects were presumably not yet fully formed [92,153] (unless they accreted very rapidly by gravitational instability). In this case, the edge of the belt would be at a heliocentric distance corresponding to a post-encounter eccentricity excitation of —0.05, a threshold value below which collisional damping is efficient and accretion can recover and beyond which the objects rapidly grind down to dust [95].

An edge-forming stellar encounter could not be responsible for the origin of the peculiar orbit of Sedna, unlike the scenario proposed in [96]. In fact, such a close encounter would also produce a relative overabundance of bodies with perihelion distance similar to that of Sedna but with semi-major axes in the 50-200 AU range [129]. These bodies have never been discovered, although they would be favored by observational biases.

Class II: Forming a Bound Planetesimal Disk from an Extended Gas-dust Disk

In [176], it was suggested that the outer edge of the Kuiper belt is the result of two facts: i) accretion takes longer with increasing heliocentric distance and ii) small planetesimals drift inward because of gas drag. This leads to a steepening of the radial surface density gradient of solids. The edge effect is augmented because, at whatever distance large bodies can form, they capture the approximately metre-sized bodies spiraling inward from farther out. The net result of the process, as shown by numerical modeling in [176], is the production of an effective edge, where both the surface density of solid matter and the mean size of planetesimals decrease sharply with distance.

A variant of this scenario has been proposed in [187]. In their model, planetesimals could form by gravitational instability in the regions where the local solid/gas ratio was 2-10 times that corresponding to cosmic abundances. According to the authors, this large ratio could be achieved because of a radial variations of orbital drift speeds of millimeter-sized particles induced by gas drag. However, this mechanism would have worked only within some threshold distance from the Sun, so that the resulting planetesimal disk would have had a natural edge.

A third possibility is that planetesimals formed only within a limited heliocentric distance, because of the effect of turbulence. If turbulence in proto-planetary disks is driven by magneto-rotational instability (MRI), one can expect that it was particularly strong in the vicinity of the Sun and at large distances (where solar and stellar radiation could more easily ionize the gas), while it was weaker in the central, optically thick region of the nebula, known as the "dead zone" [158]. The accretion of planetesimals should have been inhibited by strong turbulence, because the latter enhanced the relative velocities of the grains. Consequently, the planetesimals could have formed only in the dead zone, with well-defined outer (and inner) edge(s).

Class III: Truncating the Original Gas Disk

The detailed observational investigation of star formation regions has revealed the existence of many proplyds (anomalously small proto-planetary disks). It is believed that these disks were originally much larger, but in their distant regions, the gas was photo-evaporated by highly energetic radiation emitted by the massive stars of the cluster [1]. Thus, it has been proposed that the outer edge of the Kuiper belt reflects the size of the original Solar System proplyd [81].

A Remark on the Location of the Kuiper Belt Edge

In all the scenarios discussed above, the location of the edge can be adjusted by tuning the relevant parameters of the corresponding model. In all cases, however, Neptune plays no direct role in the edge formation. In this context, it is particularly important to remark (as seen in Fig. 3) that the edge of the Kuiper belt appears to coincide precisely with the location of the 1:2 mean-motion resonance with Neptune. This strongly suggests that, whatever mechanism formed the edge, the planet was able to adjust the final location of the outer boundary through gravitational interactions. I will return to this in Sect. 4.5.

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