Protoplanets of Super-Earth sizes may get trapped in convergence zones for planetary migration and form gas giants there .
These growing planets undergo accretion heating , which triggers a hot-trail effect that can reverse migration directions , increase planetary eccentricities and prevent resonant captures of migrating planets ( Chrenko et al .
2017 ) .
In this work , we study populations of embryos accreting pebbles , under different conditions , by changing the surface density , viscosity , pebble flux , mass , and the number of protoplanets .
For modelling we use Fargo-Thorin 2D hydrocode which incorporates a pebble disk as a 2nd pressure-less fluid , the coupling between the gas and pebbles and the flux-limited diffusion approximation for radiative transfer .

We find that massive embryos embedded in a disk with high surface density ( \Sigma = 990 { g } { cm } ^ { -2 } at 5.2 { au } ) undergo numerous ‘ unsuccessful ’ two-body encounters which do not lead to a merger .
Only when a 3rd protoplanet arrives to the convergence zone , three-body encounters lead to mergers .
For a low-viscosity disk ( \nu = 5 \times 10 ^ { 13 } { cm } ^ { 2 } { s } ^ { -1 } ) a massive coorbital is a possible outcome , for which a pebble isolation develops and the coorbital is further stabilised .
For more massive protoplanets ( 5 M _ { \oplus } ) , the convergence radius is located further out , in the ice-giant zone .
After a series of encounters , there is an evolution driven by a dynamical torque of a tadpole region , which is systematically repeated several times , until the coorbital configuration is disrupted and planets merge .
This may be a pathway how to solve the problem that coorbitals often form in simulations but they are not observed in nature .

In contrast , the joint evolution of 120 low-mass protoplanets ( 0.1 M _ { \oplus } ) reveals completely different dynamics .
The evolution is no longer smooth , but rather a random walk .
This is because the spiral arms , developed in the gas disk due to Lindblad resonances , overlap with each other and affect not only a single protoplanet but several in the surroundings .
Our hydrodynamical simulations may have important implications for N-body simulations of planetary migration that use simplified torque prescriptions and are thus unable to capture protoplanet dynamics in its full glory .