In situ accretion of gaseous envelopes on to planetary cores embedded in evolving protoplanetary discs

Abstract: The core accretion hypothesis posits that planets with significant gaseous envelopes accreted them from their protoplanetary discs after the formation of rocky/icy cores. Observations indicate that such exoplanets exist at a broad range of orbital radii, but it is not known whether they accreted their envelopes in situ, or originated elsewhere and migrated to their current locations. We consider the evolution of solid cores embedded in evolving viscous discs that undergo gaseous envelope accretion in situ with orbital radii in the range $0.1-10\rm au$. Additionally, we determine the long-term evolution of the planets that had no runaway gas accretion phase after disc dispersal. We find: (i) Planets with $5 \rm M_{\oplus}$ cores never undergo runaway accretion. The most massive envelope contained $2.8 \rm M_{\oplus}$ with the planet orbiting at $10 \rm au$. (ii) Accretion is more efficient onto $10 \rm M_{\oplus}$ and $15 \rm M_{\oplus}$ cores. For orbital radii $a_{\rm p} \ge 0.5 \rm au$, $15 \rm M_{\oplus}$ cores always experienced runaway gas accretion. For $a_{\rm p} \ge 5 \rm au$, all but one of the $10 \rm M_{\oplus}$ cores experienced runaway gas accretion. No planets experienced runaway growth at $a_{\rm p} = 0.1 \rm au$. (iii) We find that, after disc dispersal, planets with significant gaseous envelopes cool and contract on Gyr time-scales, the contraction time being sensitive to the opacity assumed. Our results indicate that Hot Jupiters with core masses $\lesssim 15 \rm M_{\oplus}$ at $\lesssim 0.1 \rm au$ likely accreted their gaseous envelopes at larger distances and migrated inwards. Consistently with the known exoplanet population, Super-Earths and mini-Neptunes at small radii during the disc lifetime, accrete only modest gaseous envelopes.