  Super-Earths are found in tighter orbits than the Earth's around more than
one third of main sequence stars. It has been proposed that super-Earths are
scaled-up terrestrial planets that formed similarly, through mutual accretion
of planetary embryos, but in discs much denser than the solar protoplanetary
disc. We argue instead that terrestrial planets and super-Earths have two
distinct formation pathways that are regulated by the disc's pebble reservoir.
Through numerical integrations, which combine pebble accretion and N-body
gravity between embryos, we show that a difference of a factor of two in the
pebble mass-flux is enough to change the evolution from the terrestrial to the
super-Earth growth mode. If the pebble mass-flux is small, then the initial
embryos within the ice line grow slowly and do not migrate substantially,
resulting in a widely spaced population of Mars-mass embryos when the gas disc
dissipates. Without gas being present, the embryos become unstable and a small
number of terrestrial planets are formed by mutual collisions. The final
terrestrial planets are at most 5 Earth masses. Instead, if the pebble
mass-flux is high, then the initial embryos within the ice line rapidly become
sufficiently massive to migrate through the gas disc. Embryos concentrate at
the inner edge of the disc and growth accelerates through mutual merging. This
leads to the formation of a system of closely spaced super-Earths in the 5 to
20 Earth-mass range, bounded by the pebble isolation mass. Generally,
instabilities of these super-Earth systems after the disappearance of the gas
disc trigger additional merging events and dislodge the system from resonant
chains. The pebble flux - which controls the transition between the two growth
modes - may be regulated by the initial reservoir of solids in the disc or the
presence of more distant giant planets that can halt the radial flow of
pebbles.
