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Migration and Growth of Protoplanetary Embryos I: Convergence of Embryos in Protoplanetary Disks

According to the core-accretion scenario, planets form in protostellar disks through the condensation of dust, coagulation of planetesimals, and emergence of protoplanetary embryos. At a few AU in a minimum mass nebula, embryos' growth is quenched by dynamical isolation due to the depletion of planetesimals in their feeding zone. However, embryos with masses ($M_p$) in the range of a few Earth masses ($M_\oplus$) migrate toward a transition radius between the inner viscously heated and outer irradiated regions of their natal disk. Their limiting isolation mass increases with the planetesimals surface density. When $M_p > 10 M_\oplus$, embryos efficiently accrete gas and evolve into cores of gas giants. We use numerical simulation to show that, despite streamline interference, convergent embryos essentially retain the strength of non-interacting embryos' Lindblad and corotation torque by their natal disks. In disks with modest surface density (or equivalently accretion rates), embryos capture each other in their mutual mean motion resonances and form a convoy of super Earths. In more massive disks, they could overcome these resonant barriers to undergo repeated close encounters including cohesive collisions which enable the formation of massive cores.