The Heavy-element Content Trend of Planets: A Tracer of their Formation Sites

Identification of the main planet formation site is fundamental to understanding how planets form and migrate to the current locations. We consider the heavy-element content trend of observed exoplanets derived from improved measurements of mass and radius, and explore how this trend can be used as a tracer of their formation sites. Using gas accretion recipes obtained from detailed hydrodynamical simulations, we confirm that the disk-limited gas accretion regime is most important for reproducing the heavy-element content trend. Given that such a regime is specified by two characteristic masses of planets, we compute these masses as a function of the distance ($r$) from the central star, and then examine how the regime appears in the mass-semimajor axis diagram. Our results show that a plausible solid accretion region emerges at $r \simeq 0.6$ au and expands with increasing $r$, using the conventional disk model. Given that exoplanets that possess the heavy-element content trend distribute currently near their central stars, our results imply the importance of planetary migration that would occur after solid accretion onto planets might be nearly completed at $r \geq 0.6$ au. Self-consistent simulations would be needed to verify the predictions herein.