The Origin of Heavy Element Content Trend in Giant Planets via Core Accretion

TL;DR

This paper investigates the origin of the observed heavy element content trend in giant exoplanets, proposing a simplified model that links planet formation stages to the power-law relation between heavy elements and planetary mass.

Contribution

It introduces a physically motivated analysis demonstrating how the heavy element trend can be produced during the final stages of planet formation, emphasizing the role of planetesimal dynamics.

Findings

The heavy element mass follows a power-law relation with planetary mass, $M_Z \,\propto \, M_p^{3/5}$.

Planetary heavy element content is primarily set during the final accretion stage involving gapped planetesimal disks.

Dust accretion does not significantly contribute to heavy elements for planets with mass less than 1000 Earth masses.

Abstract

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.