  During their formation, planets form large, hot atmospheres due to the
ongoing accretion of solids. It has been customary to assume that all solids
end up at the center constituting a "core" of refractory materials, whereas the
envelope remains metal-free. Recent work, as well as observations by the JUNO
mission, indicate however that the distinction may not be so clear cut. Indeed,
small silicate, pebble-sized particles will sublimate in the atmosphere when
they hit the sublimation temperature (T ~ 2,000 K). In this paper we extend
previous analytical work to compute the properties of planets under such a
pebble accretion scenario. We conduct 1D numerical calculations of the
atmosphere of an accreting planet, solving the stellar structure equations,
augmented by a non-ideal equation of state that describes a
hydrogen/helium-silicate vapor mixture. Calculations terminate at the point
where the total mass in metal equals that of the H/He gas, which we numerically
confirm as the onset of runaway gas accretion. When pebbles sublimate before
reaching the core, insufficient (accretion) energy is available to mix dense,
vapor-rich lower layers with the higher layers of lower metallicity. A gradual
structure in which Z decreases with radius is therefore a natural outcome of
planet formation by pebble accretion. We highlight, furthermore, that (small)
pebbles can act as the dominant source of opacity, preventing rapid cooling and
presenting a channel for (mini-)Neptunes to survive in gas-rich disks.
Nevertheless, once pebble accretion subsides, the atmosphere rapidly clears
followed by runaway gas accretion. We consider atmospheric recycling to be the
more probable mechanisms that have stalled the growth of these planets'
envelopes.
