Exploring the conditions for forming cold gas giants through planetesimal accretion

Abstract

The formation of cold gas giants similar to Jupiter and Saturn in orbit and mass is a great challenge for planetesimal-driven core accretion models because the core growth rates far from the star are low. Here we model the growth and migration of single protoplanets that accrete planetesimals and gas. We integrated the core growth rate using fits in the literature to N-body simulations, which provide the efficiency of accreting the planetesimals that a protoplanet migrates through. We take into account three constraints from the solar system and from protoplanetary discs: (1) the masses of the terrestrial planets and the comet reservoirs in Neptune's scattered disc and the Oort cloud are consistent with a primordial planetesimal population of a few Earth masses per AU, (2) evidence from the asteroid belt and the Kuiper belt indicates that the characteristic planetesimal diameter is 100 km, and (3) observations of protoplanetary discs indicate that the dust is stirred by weak turbulence; this gas turbulence also excites the inclinations of planetesimals. Our nominal model built on these constraints results in maximum protoplanet masses of 0.1 Earth masses. Ignoring constraint (1) above, we show that even a planetesimal population of 1,000 Earth masses, corresponding to 50 Earth masses per AU, fails to produce cold gas giants (although it successfully forms hot and warm gas giants). We conclude that a massive planetesimal reservoir is in itself insufficient to produce cold gas giants. The formation of cold gas giants by planetesimal accretion additionally requires that planetesimals are small and that the turbulent stirring is very weak, thereby violating all three above constraints.

A pebble accretion model for the formation of the terrestrial planets in the Solar System

“…After the successful application of the analytical growth tracks to Venus and Mars, we now turn to numerical integration of the masses and orbits of protoplanets undergoing pebble accretion, planetesimal accretion, and inward type I migration, using the code developed and presented in ( 5 , 2 ). The protoplanetary disc model is described in Materials and Methods.…”

“…The long formation time scale of gas giants and ice giants in the outer regions of protoplanetary discs by traditional planetesimal accretion (1,2) instigated the development of the pebble accretion theory in which the pebbles drifting through the protoplanetary disc are accreted rapidly by the growing protoplanets (3,4). While pebble accretion clearly aids the formation of gas giants (5), the formation of terrestrial planets has so far, with a few exceptions (6)(7)(8)(9), mainly been explored in classical N-body simulations where terrestrial planets grow by successive impacts between increasingly massive protoplanets (10).…”

Linking planetary embryo formation to planetesimal formation

“…Forming massive planetary cores of 10 M ⊕ at larger distances to the star within the lifetime of a gaseous disk is currently a challenge for planetesimal accretion models (Johansen & Bitsch 2019). A solution to this conundrum has appeared in the form of pebble accretion onto distant planetary embryos (Klahr & Bodenheimer 2006;Ormel & Klahr 2010;Lambrechts & Johansen 2012;Bitsch et al 2015;Ndugu et al 2017).…”

Effect of pebble flux-regulated planetesimal formation on giant planet formation

“…The formation of planetesimals is such a process, and the one-dimensional formation model by Lenz et al (2019) is such an attempt. Previous work on the accretion of planetesimals for planetary growth such as Johansen & Bitsch (2019), Mordasini (2018), or Ida & Lin (2004) used initial distributions of planetesimals and initially placed planetary embryos, while neglecting the presence of pebbles. Other formation models such as those of Bitsch et al (2015) or Brügger et al (2018) modeled planetary growth by the accretion of pebbles and initially set planetary embryos, while neglecting the formation, or accretion, of planetesimals.…”