  Observations of protoplanetary discs have revealed dust rings which are
likely due to the presence of pressure bumps in the disc. Because these
structures tend to trap drifting pebbles, it has been proposed that pressure
bumps may play an important role in the planet formation process. In this
paper, we investigate the orbital evolution of a $0.1$ $M_\oplus$ protoplanet
embedded in a pressure bump using 2-dimensional hydrodynamical simulations of
protoplanetary discs consisting of gas and pebbles. We examine the role of
thermal forces generated by the pebble accretion-induced heat release, taking
into account the feedback between luminosity and eccentricity. We also study
the effect of the pebble-scattered flow on the planet's orbital evolution. Due
to accumulation of pebbles at the pressure bump, the planet's accretion
luminosity is high enough to induce significant eccentricity growth through
thermal forces. Accretion luminosity is also responsible for vortex formation
at the planet position through baroclinic effects, which cause the planet
escape from the dust ring if dust feedback onto the gas is neglected. Including
the effect of the dust back-reaction leads to weaker vortices, which enable the
planet to remain close to the pressure maximum on an eccentric orbit.
Simulations in which the planet mass is allowed to increase as a consequence of
pebble accretion resulted in the formation of giant planet cores with mass in
the range $5-20$ $M_\oplus$ over $\sim 2\times 10^4$ yrs. This occurs for
moderate values of the Stokes number $St \approx 0.01$ such that the pebble
drift velocity is not too high and the dust ring mass not too small. Our
results suggest that pressure bumps mays be preferred locations for the
formation of giant planets, but this requires a moderate level of grain growth
within the disc.
