Making giant planet cores: convergent migration and growth of planetary embryos in non-isothermal discs

Context. Rapid gas accretion onto gas giants requires the prior formation of ~ 10 M_⊕ cores, and this presents a continuing challenge to planet formation models. Recent studies of oligarchic growth indicate that in the region around 5 AU growth stalls at ~ 2 M_⊕. Earth-mass bodies are expected to undergo Type I migration directed either inward or outward depending on the thermodynamical state of the protoplanetary disc. Zones of convergent migration exist where the Type I torque cancels out. These "convergence zones" may represent ideal sites for the growth of giant planet cores by giant impacts between Earth-mass embryos.
Aims: We study the evolution of multiple protoplanets of a few Earth masses embedded in a non-isothermal protoplanetary disc. The protoplanets are located in the vicinity of a convergence zone located at the transition between two different opacity regimes. Inside the convergence zone, Type I migration is directed outward and outside the zone migration is directed inward.
Methods: We used a grid-based hydrodynamical code that includes radiative effects. We performed simulations varying the initial number of embryos and tested the effect of including stochastic forces to mimic the effects resulting from disc turbulence. We also performed N-body runs calibrated on hydrodynamical calculations to follow the evolution on Myr timescales.
Results: For a small number of initial embryos (N = 5-7) and in the absence of stochastic forcing, the population of protoplanets migrates convergently toward the zero-torque radius and forms a stable resonant chain that protects embryos from close encounters. In systems with a larger initial number of embryos, or in which stochastic forces were included, these resonant configurations are disrupted. This in turn leads to the growth of larger cores via a phase of giant impacts between protoplanets, after which the system settles to a new stable resonant configuration. Giant planets cores with masses ≥ 10 M_⊕ formed in about half of the simulations with initial protoplanet masses of m_p = 3 M_⊕ but in only 15% of simulations with m_p = 1 M_⊕, even with the same total solid mass.
Conclusions: If 2 - 3 M_⊕ protoplanets can form in less than ~1 Myr, convergent migration and giant collisions can grow giant planet cores at Type I migration convergence zones. This process can happen fast enough to allow for a subsequent phase of rapid gas accretion during the disc's lifetime.