Towards initial mass functions for asteroids and Kuiper Belt Objects

Abstract

Our goal is to understand primary accretion of the first planetesimals. Some examples are seen today in the asteroid belt, providing the parent bodies for the primitive meteorites. The primitive meteorite record suggests that sizeable planetesimals formed over a period longer than a million years, each of which being composed entirely of an unusual, but homogeneous, mixture of mm-size particles. We sketch a scenario that might help explain how this occurred, in which primary accretion of 10-100km size planetesimals proceeds directly, if sporadically, from aerodynamically-sorted mm-size particles (generically "chondrules"). These planetesimal sizes are in general agreement with the currently observed asteroid mass peak near 100km diameter, which has been identified as a "fossil" property of the pre-erosion, pre-depletion population. We extend our primary accretion theory to make predictions for outer solar system planetesimals, which may also have a preferred size in the 100km diameter range. We estimate formation rates of planetesimals and explore parameter space to assess the conditions needed to match estimates of both asteroid and Kuiper Belt Object (KBO) formation rates. For parameters that satisfy observed mass accretion rates of Myr-old protoplanetary nebulae, the scenario is roughly consistent with not only the "fossil" sizes of the asteroids, and their estimated production rates, but also with the observed spread in formation ages of chondrules in a given chondrite, and with a tolerably small radial diffusive mixing during this time between formation and accretion. As previously noted, the model naturally helps explain the peculiar size distribution of chondrules within such objects. The optimum range of parameters, however, represents a higher gas density and fractional abundance of solids, and a smaller difference between keplerian and pressure-supported orbital velocities, than "canonical" models of the solar nebula. We discuss several potential explanations for these differences. The scenario also produces 10-100km diameter primary KBOs, and also requires an enhanced abundance of solids to match the mass production rate estimates for KBOs (and presumably the planetesimal precursors of the ice giants themselves). We discuss the advantages and plausibility of the scenario, outstanding issues, and future directions of research.

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

“…We next argue that the cascade model used in the quantitative calculations of Chambers (2010) and Cuzzi et al (2010) may considerably overestimate the probability of finding large and dense particle clumps for planetesimal formation. In their Appendix A, C08 preformed a 24 level cascade for St = 1 particles, and found a significant probability (10 −5 -10 −6 ) for the existence of clumps with C = 1000 (see Figure 5 in C08).…”

“…These persistent clumps would form "sandpile" planetesimals of 10-100 km, once the particle sedimentation toward the clump center is complete. Cuzzi et al (2010) and Chambers (2010) further developed this idea and gave quantitative predictions for the planetesimal formation rate and the initial mass function of asteroids (Cuzzi et al 2010). The key element in these studies is the prediction of the probability of finding clumps of sufficient size ( 10 4 km) and intensity (with local Φ ∼ 100).…”

“…Therefore the prediction of the probability requires understanding of turbulent clustering at inertial-range scales, which, however, has not been well explored. In their quantitative predictions for that probability, Chambers (2010) and Cuzzi et al (2010) made use of the cascade mode for the joint PDF of the particle concentration and the flow enstrophy developed by Hogan & Cuzzi (2007).…”

The effect of gas drag on the growth of protoplanets

“…The latter three are all functions of the particle's stopping time, a measure of how well particles couple to the gas. With increasing size (or, more correctly, increasing mass-to-surface area) particles couple less well to the gas and relative velocities increase, culminating in the so called metersize barrier, which, at our current level of understanding, can best be overcome by the combined efforts of turbulent concentration and gravitational collapse (Johansen et al , 2009Cuzzi et al 2010). …”

The Emerging Paradigm of Pebble Accretion

“…Clearly, geometric and Safronov accretion are not effective in growing planetesimals large; and the initiation of pebble accretion relies on the presence of a massive-enough seed that is produced by a process other than sweep up of small particles. Such a seed may result from classical self-coagulation mechanisms (i.e., runaway growth of planetesimals) or, more directly, from the high-mass tail of the planetesimal formation mechanism, e.g., by streaming or gravitational instabilities (Cuzzi et al 2010;Johansen et al 2015;Simon et al 2016;Schäfer et al 2017).…”