Orbital migration of interacting low-mass planets in evolutionary radiative turbulent models

The torques exerted by a locally isothermal disk on an embedded planet lead to rapid inward migration. Recent work has shown that modeling the thermodynamics without the assumption of local isothermality reveals regions where the net torque on an embedded planet is positive, leading to outward migration of the planet. When a region with negative torque lies directly exterior to this, planets in the inner region migrate outwards and planets in the outer region migrate inwards, converging where the torque is zero. We incorporate the torques from an evolving non-isothermal disk into an N-body simulation to examine the behavior of planets or planetary embryos interacting in the convergence zone. We find that mutual interactions do not eject objects from the convergence zone. Small numbers of objects in a laminar disk settle into near resonant orbits that remain stable over the 10 Myr periods that we examine. However, either or both increasing the number of planets or including a correlated, stochastic force to represent turbulence drives orbit crossings and mergers in the convergence zone. These processes can build gas giant cores with masses of order ten Earth masses from sub-Earth mass embryos in 2-3 Myr.