  The omnipresence of super-Earths suggests that they are able to be retained
in natal disks around low-mass stars, whereas exoplanets' mass distribution
indicates that some cores have transformed into gas giants through runaway gas
accretion at 1AU from solar-type stars. In this paper, we show that transition
to runaway gas accretion by cores may be self-impeded by an increase of the
grain opacity in their envelope after they have acquired sufficient mass
(typically 10Mearth) to enter a pebble-isolation phase. The accumulation of
mm-m size pebbles in their migration barriers enhances their local
fragmentation rates. The freshly produced sub-mm grains pass through the
barrier, elevate the effective dust opacity and reduce the radiative flux in
the cores envelope. These effects alone are adequate to suppress the transition
to runaway accretion and preserve super-Earths in the stellar proximity (0.1
AU), albeit entropy advection between the envelope and the disk can further
reduce the accretion rate. At intermediate distance (1AU) from their host
stars, the escalation in the dust opacity dominates over entropy advection in
stalling the transition to runaway accretion for marginally pebble-isolated
cores. Beyond a few AU, the transformation of more massive cores to gas giants
is reachable before severe depletion of disk gas. This requirement can be
satisfied either in extended disks with large scale height via orderly
accretion of migrating pebbles or through the mergers of oligarchic
protoplanetary embryos, and can account for the correlated occurrence of
long-period gas giants and close-in super-Earths.
