Towards initial mass functions for asteroids and Kuiper Belt Objects

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 millimeter-size particles. We sketch a scenario that might help explain how this occurred, in which primary accretion of 10-100 km size planetesimals proceeds directly, if sporadically, from aerodynamically-sorted millimeter-size particles (generically “chondrules”). These planetesimal sizes are in general agreement with the currently observed asteroid mass peak near 100 km 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 100 km 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 10-100 km 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.     

Planetary growth with collisional fragmentation and gas drag

As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 10⁷ years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System.     

On oligarchic growth of planets in protoplanetary disks

In this paper we present a new semianalytical model of oligarchic growth of planets considering a distribution of planetesimal sizes, fragmentation of planetesimals in mutual collisions, sublimation of ices through the snow line, random velocities out of equilibrium and merging of planetary embryos. We show that the presence of several planetary embryos growing simultaneously at different locations in the protoplanetary disk affects the whole accretion history, specially for the innermost planets. The results presented here clearly indicate the relevance of considering a distribution of planetesimal sizes. Fragmentation occurring during planetesimal-planetesimal collisions represent only a marginal effect in shaping the surface density of solid material in the protoplanetary disc.     

The effects of ablation on the cross section of planetary envelopes at capturing planetesimals

We explore the cross section of giant planet envelopes at capturing planetesimals of different sizes. For this purpose we employ two sets of realistic planetary envelope models (computed assuming for the protoplanetary nebula masses of 10 and 5 times the mass of the minimum mass solar nebula), account for drag and ablation effects and study the trajectories along which planetesimals move. The core accretion of these models has been computed in the oligarchic growth regime [Fortier, A., Benvenuto, O.G., Brunini, A., 2007. Astron. Astrophys. 473, 311-322], which has also been considered for the velocities of the incoming planetesimals. This regime predicts velocities larger that those used in previous studies of this problem. As the rate of ablation is dependent on the third power of velocity, ablation is more important in the oligarchic growth regime. We compute energy and mass deposition, fractional ablated masses and the total cross section of planets for a wide range of values of the critical parameter of ablation. In computing the total cross section of the planet we have included the contributions due to mass deposited by planetesimals moving along unbound orbits. Our results indicate that, for the case of small planetary cores and low velocities for the incoming planetesimals, ablation has a negligible impact on the capture cross section in agreement with the results presented in Inaba and Ikoma [Inaba, S., Ikoma, M., 2003. Astron. Astrophys. 410, 711-723]. However for the case of larger cores and high velocities of the incoming planetesimals as predicted by the oligarchic growth regime, we find that ablation is important in determining the planetary cross section, being several times larger than the value corresponding ignoring ablation. This is so regardless of the size of the incoming planetesimals.