Accretion in the Early Kuiper Belt. II. Fragmentation

Abstract

We describe new planetesimal accretion calculations in the Kuiper Belt that include fragmentation and velocity evolution. All models produce two power law cumulative size distributions, N C ∝ r −2.5 for radii ∼ < 0.3-3 km and N C ∝ r −3 for radii ∼ > 1-3 km. The power law indices are nearly independent of the initial mass in the annulus, M 0 ; the initial eccentricity of the planetesimal swarm, e 0 ; and the initial size distribution of the planetesimal swarm. The transition between the two power laws moves to larger radii as e 0 increases. The maximum size of objects depends on their intrinsic tensile strength, S 0 ; Pluto formation requires S 0 ∼ > 300 erg g −1 . The timescale to produce Pluto-sized objects, τ P , is roughly proportional to M −1 0 and e 0 , and is less sensitive to other input parameters. Our models yield τ P ≈ 30-40 Myr for planetesimals with e 0 = 10 −3 in a Minimum Mass Solar Nebula. The production of several 'Plutos' and ∼ 10 5 50 km radius Kuiper Belt objects leaves most of the initial mass in 0.1-10 km radius objects that can be collisionally depleted over the age of the solar system. These results resolve the puzzle of large Kuiper Belt objects in a small mass Kuiper Belt.

Evolution of Jovian planets in a self-gravitating planetesimal disk

“…Most of them have diameters (D) larger than 100 km, while there are roughly a dozen giant objects with diameters of about 1000 km or more, such as Pluto 1 MPCs: http://www.cfa.harvard.edu/iau/lists/TNOs.html (D ≈ 2320 km) and 2003 UB313 (D ≈ 2400 km). Previous studies show that the current belt mass between 30 and 50 AU of less than 0.1 M ⊕ could not produce the KBOs in situ (Stern 1996;Stern & Colwell 1997;Kenyon & Luu 1998;Kenyon & Luu 1999). Thus, the KBOs should form in a denser region much closer to the Sun and were subsequently transported outwards to their present locations (Levison & Morbidelli 2003;Gomes 2003).…”

Planet Formation by Coagulation: A Focus on Uranus and Neptune

“…In Sections 9 and 10, we provide appropriate expressions for during oligarchy, an important stage of planet formation. However, at earlier times, must be obtained by solving an integro-differential equation ( Kenyon & Luu (1999) have proposed, it is a frozen image of the formation epoch. In the following, we treat as a free function.…”

Planetesimals in Debris Disks of Sun-Like Stars

“…There are at least two reasons to question this assumption. First, conglomeration models (Kenyon & Luu 1999;Kenyon & Bromley 2001) typically require a few 10 7 years to produce Pluto-like bodies in a Kuiper-belt-like environment, with the timescale increasing as one moves away from the star. 7 This will delay the onset of the debris phase.…”

“…The value of q is then reduced to ≈4 (Morishima et al 2008). Using particles-in-a-box simulations and later hybrid simulations, Kenyon & Luu (1999) and Kenyon & Bromley (2004b followed the growth of planetesimals. They also found that q decreases with time after the runaway phase, finishing up with 3.75 q 4.5 for planetesimals of sizes between 10 and 1000 km.…”