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Most super-Earths formed by dry pebble accretion are less massive than 5 Earth masses

We study the formation of rocky planets by dry pebble accretion from self-consistent dust-growth models. In particular, we aim at computing the maximum core mass of a rocky planet that can sustain a thin H-He atmosphere to account for the second peak of the Kepler's size distribution. We simulate planetary growth by pebble accretion inside the ice line. The pebble flux is computed self-consistently from dust growth by solving the advection-diffusion equation for a representative dust size. Dust coagulation, drift, fragmentation and sublimation at the water iceline are included. The disc evolution is computed for $α$-discs with photoevaporation from the central star. The planets grow from a moon-mass embryo by silicate pebble accretion and gas accretion. We analyse the effect of a different initial disc mass, $α$-viscosity, disc metallicity and embryo location. Finally, we compute atmospheric mass-loss due to evaporation. We find that inside the ice line, the fragmentation barrier determines the size of pebbles, which leads to different planetary growth patterns for different disc viscosities. Within the iceline the pebble isolation mass typically decays to values below 5 M$_{\oplus}$ within the first million years of disc evolution, limiting the core masses to that value. After computing atmospheric-mass loss, we find that planets with cores below $\sim$4 M$_{\oplus}$ get their atmospheres completely stripped, and a few 4-5 M$_{\oplus}$ cores retain a thin atmosphere that places them in the gap/second peak of the Kepler size distribution. Overall, we find that rocky planets form only in low-viscosity discs ($α\lesssim 10^{-4}$). When $α\geq 10^{-3}$, rocky objects do not grow beyond Mars-mass. The most typical outcome of dry pebble accretion is terrestrial planets with masses spanning from Mars to $\sim$4 M$_{\oplus}$.