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Register a new userThe Heavy-element Content Trend of Planets: A Tracer of their Formation Sites
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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.
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We explore the origin of the trend of heavy elements in observed massive exoplanets. Coupling of better measurements of mass ($M_p$) and radius of exoplanets with planet structure models enables estimating the total heavy element mass ($M_Z$) in these planets. The corresponding relation is characterized by a power-law profile, $M_Z propto M_p^{3/5}$. We develop a simplified, but physically motivated analysis to investigate how the power-law profile can be produced under the current picture of planet formation. Making use of the existing semi-analytical formulae of accretion rates of pebbles and planetesimals, our analysis shows that the relation can be reproduced well if it traces the final stage of planet formation. In the stage, planets accrete solids from gapped planetesimal disks and gas accretion is limited by disk evolution. We also find that dust accretion accompanying with gas accretion does not contribute to $M_Z$ for planets with $M_p < 10^3 M_{oplus}$. Our findings are broadly consistent with that of previous studies, yet we explicitly demonstrate how planetesimal dynamics is crucial for better understanding the relation. While our approach is simple, we can also reproduce the trend of a correlation between planet metallicity and $M_p$ that is obtained by detailed population synthesis calculations, when the same assumption is adopted. Our analysis suggests that pebble accretion would not play a direct role at the final stage of planet formation, whereas radial drift of pebbles might be important indirectly for metal enrichment of planets. Detailed numerical simulations and more observational data are required for confirming our analysis.
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