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Context: Planetary embryos can continue to grow by pebble accretion untilthey become giant planet cores. Simultaneously, these embryos mutually interactand also migrate due to torques arising from the protoplanetary disk.  Aims: Our aim is to investigate how pebble accretion alters the orbitalevolution of embryos undergoing the Type-I migration. In particular, we studywhether they establish resonant chains, whether these chains are prone toinstabilities and if giant planet cores form through embryo merging, thusoccurring more rapidly than by pebble accretion alone.  Methods: For the first time, we perform self-consistent global-scaleradiative hydrodynamic simulations of a two-fluid protoplanetary diskconsisting of gas and pebbles, the latter being accreted by embedded embryos.Accretion heating, along with other radiative processes, is accounted for tocorrectly model the Type-I migration.  Results: We track the evolution of four super-Earth-like embryos, initiallylocated in a region where the disk structure allows for a convergent migration.Generally, embryo merging is facilitated by rapidly increasing embryo massesand breaks the otherwise oligarchic growth. Moreover, we find that the orbitaleccentricity of each embryo is considerably excited ($\simeq0.03$) due to thepresence of an asymmetric underdense lobe of gas, a so-called `hot trail',produced by accretion heating of the embryo's vicinity. Eccentric orbits leadthe embryos to frequent close encounters and make resonant locking moredifficult.  Conclusions: Embryo merging typically produces one massive core ($\gtrsim10\,\mathrm{M_{E}}$) in our simulations, orbiting near $10\,\mathrm{AU}$.Pebble accretion is naturally accompanied by occurrence of eccentric orbitswhich should be considered in future efforts to explain the structure ofexoplanetary systems.

Eccentricity excitation and merging of planetary embryos heated by pebble accretion