The evolution of protoplanetary discs embedded in stellar clusters depends on the age and the stellar density in which they are embedded .
Stellar clusters of young age and high stellar surface density destroy protoplanetary discs by external photoevaporation and stellar encounters .
Here we consider the effect of background heating from newly formed stellar clusters on the structure of protoplanetary discs and how it affects the formation of planets in these discs .
Our planet formation model is build on the core accretion scenario , where we take the reduction of the core growth time-scale due to pebble accretion into account .
We synthesize planet populations that we compare to observations obtained by radial velocity measurements .
The giant planets in our simulations migrate over large distances due to the fast type-II migration regime induced by a high disc viscosity ( \alpha = 5.4 \times 10 ^ { -3 } ) .
Cold Jupiters ( r _ { p } > 1 AU ) originate preferably from the outer disc , due to the large scale planetary migration , while hot Jupiters ( r _ { p } < 0.1 AU ) preferably form in the inner disc .
We find that the formation of gas giants via pebble accretion is in agreement with the metallicity correlation , meaning that more gas giants are formed at larger metallicity .
However , our synthetic population of isolated stars host a significant amount of giant planets even at low metallicity , in contradiction to observations where giant planets are preferably found around high metallicity stars , indicating that pebble accretion is very efficient in the standard pebble accretion framework .
On the other hand , discs around stars embedded in cluster environments hardly form any giant planets at low metallicity in agreement with observations , where these changes originate from the increased temperature in the outer parts of the disc , which prolongs the core accretion time-scale of the planet .
We therefore conclude that the outer disc structure and the planet ’ s formation location determines the giant planet occurrence rate and the formation efficiency of cold and hot Jupiters .