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The growth time scales of planetary embryos and their formation process areimperative for our understanding on how planetary systems form and develop.They determine the subsequent growth mechanisms during the life stages of acircumstellar disk. We quantify the timescales and spatial distribution ofplanetary embryos via collisional growth and fragmentation of dynamicallyforming 100km sized planetesimals. In our study, the formation timescales ofviscous disk evolution and planetesimal formation are linked to the formationof planetary embryos in the terrestrial planet zone. We connect a onedimensional model for viscous gas evolution, dust and pebble dynamics andpebble flux regulated planetesimal formation to the N-body code LIPAD. Ourframework enables us to study the formation, growth, fragmentation andevolution of planetesimals with an initial size of 100km in diameter for thefirst million years of a viscous disk. Our study shows the effect of theplanetesimal surface density evolution on the preferential location andtimescales of planetary embryo formation. A one dimensional analyticallyderived model for embryo formation based on the local planetesimal surfacedensity evolution is presented. This model manages to reproduce the spatialdistribution, formation rate and total number of planetary embryos at afraction of the computational cost of the N-body simulations. The formation ofplanetary embryos in the terrestrial planet zone occurs simultaneously to theformation of planetesimals. The local planetesimal surface density evolutionand the orbital spacing of planetary embryos in the oligarchic regime servewell as constraints to model planetary embryo formation analytically. Ourembryo formation model will be a valuable asset in future studies regardingplanet formation.

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