Recently performed nested-grid, high-resolution hydrodynamic and radiation-hydrodynamics simulations of gas and particle dynamics in the vicinity of Mars- to Earth-mass planetary embryos (Popovas et al 2018MNRAS.479.5136P and 2019MNRAS.482L.107P) have provided quantitatively robust estimates of accretion rates for planet embryos formed inside a pressure trap. The simulations extended from the resolved surfaces of the embryos to several vertical disk scale heights, with a vertical dynamic range exceeding 1e5. Heating due to the accretion of solids caused vigorous convective motions, however even convection driven by a nominal accretion rate one Earth mass per Myr did not significantly alter the pebble accretion rate. Ray-tracing radiative transfer showed that rocky planet embryos embedded in protoplanetary disks can retain hot and light atmospheres throughout much of the evolution of the disks.
Importantly, the results showed that particles larger than the chondrules ubiquitously observed in meteorites are not required to explain the accretion of rocky planets such as Earth and Mars within the lifetime of the disk. Due to cancellation effects, accretion rates of a given size particles are nearly independent of disk surface density, while proportional to the dust-to-gas ratio. As a result, accurate growth times for specified particle sizes may be estimated. For 0.3-1 mm size particles, and assuming a dust-to-gas ratio of 1:100, the growth time from a small seed is ~1.5 million years for an Earth mass planet at 1 AU and ~1 million years for a Mars mass planet at 1.5 AU.
The magnitude and robustness of the accretion rate estimates hinges on the assumption of the embryo residing in a pressure trap. A vertically projected dust to gas ratio of 1:100 is thus a lower limit, with continued trapping of mm-size particles expected to accelerate accretion. This mechanism is therefore a prime candidate to explain rapid formation of rocky planets, leaving open only the question of by which mechanism the accretion is quenched, thus determining the final mass.
I will discuss provocative scenarios where this question is resolved, including implications for the formation of gas dwarfs and gas giants.