Linking planetary embryo formation to planetesimal formation: I. The effect of the planetesimal surface density in the terrestrial planet zone

Context. The growth-timescales of planetary embryos and their formation process are imperative for our understanding on how planetary systems form and develop. They determine the subsequent growth mechanisms during the life stages of a circumstellar disk.Aims. We quantify the timescales and spatial distribution of planetary embryos through collisional growth and fragmentation of dynamically forming 100 km sized planetesimals. In our study, the formation timescales of viscous disk evolution and planetesimal formation are linked to the formation of planetary embryos in the terrestrial planet zone.Methods. We connected a one-dimensional model for viscous gas evolution, dust and pebble dynamics, and pebble flux-regulated planetesimal formation to the N-body code LIPAD. Our framework enabled us to study the formation, growth, fragmentation, and evolution of planetesimals with an initial size of 100 km in diameter for the first million years of a viscous disk.Results. Our study shows the effect of the planetesimal surface density evolution on the preferential location and timescales of planetary embryo formation. Only the innermost embryos (<2 au) in our study form well within the lifetime of an active pebble flux for any disk studied. Higher planetesimal disk masses and steeper planetesimal surface density profiles result in more massive embryos within a larger area, rather than in a higher number of embryos. A one-dimensional analytically derived model for embryo formation based on the local planetesimal surface density evolution is presented. This model can reproduce the spatial distribution, formation rate, and total number of planetary embryos at a fraction of the computational cost of the N-body simulations.Conclusions. The formation of planetary embryos in the terrestrial planet zone occurs simultaneously with the formation of planetesimals. The local planetesimal surface density evolution and the orbital spacing of planetary embryos in the oligarchic regime are good constraints for modeling planetary embryo formation analytically. Our embryo formation model is a valuable asset in future studies of planet formation.