Heavy Element Enrichment of a Jupiter-mass Protoplanet as a Function of Orbital Location

We calculate heavy element enrichment in a Jupiter-mass protoplanet formed by disk instability at various radial distances from the star, considering different disk masses and surface density distributions. Although the available mass for accretion increases with radial distance (a) for disk solid surface density (sigma) functions sigma=sigma_0*a^(-alpha) with alpha < 2, the accretion timescale is significantly longer at larger radial distances. Efficient accretion is limited to the first ~ 1E5 years of planetary evolution, when the planet is extended and before gap opening and type II migration take place. The accreted mass is calculated for disk masses of 0.01, 0.05 and 0.1 M_sun with alpha = 1/2, 1, and 3/2. We show that a Jupiter-mass protoplanet can accrete 1 to 110 M_earth of heavy elements, depending on the disk properties. Our results explain the large variation in heavy element enrichment found in extra-solar giant planets. Since higher disk surface density is found to lead to larger heavy element enrichment, our model results are consistent with the correlation between heavy element enrichment and stellar metallicity. Our calculations also suggest that Jupiter could have formed at a larger radial distance than its current location while still accreting the mass of heavy elements predicted by interior models. We conclude that in the disk instability model the final composition of a giant planet is strongly determined by its formation environment. The heavy element abundance of a giant planet does not discriminate between its origin by either disk instability or core accretion.

💡 Research Summary

This paper investigates how much heavy‑element material a Jupiter‑mass protoplanet can accrete when it forms by disk‑instability (DI) at different orbital distances, under a variety of protoplanetary‑disk conditions. The authors adopt a simple power‑law for the solid surface density, σ_s = σ₀ a⁻ᵅ, and explore three values of the exponent (α = 0.5, 1, 1.5) together with three total disk masses (0.01, 0.05, 0.1 M☉). The protoplanet is assumed to be in its early, highly extended phase for the first 10⁵ yr after collapse, when its radius is tens of Jupiter radii and its cross‑section for solid capture is maximized. During this window the planet can sweep up planetesimals and dust before gap opening and Type II migration reduce the inflow of material.

The accretion model combines the local solid inventory (set by σ_s and the annular area at a given distance a) with a capture probability that depends on the relative velocity between the planet and the solids, the orbital period of the solids, and the planet’s expanding radius. Because the orbital period and relative speed increase with a, the capture efficiency declines at larger distances, even though the total amount of solids available grows as a² for α < 2. By integrating the capture rate over the 10⁵‑yr window, the authors obtain the cumulative heavy‑element mass that can be incorporated into the planet.

Results show a wide range of possible enrichments. In the lowest‑mass disks (0.01 M☉) the protoplanet can acquire only a few Earth masses of heavy elements, regardless of α. In the most massive disks (0.1 M☉) the enrichment can reach 80–110 M⊕ for α = 1.5 at 30 AU, while for α = 0.5 the enrichment is strongest at smaller radii (≈10–20 AU) but still exceeds 30 M⊕. Generally, steeper surface‑density profiles (larger α) concentrate solids toward the star, boosting enrichment at small a, whereas flatter profiles allow substantial accretion even at large a because the total solid mass in the feeding zone is larger.

These findings naturally explain the observed diversity of heavy‑element contents among extrasolar giant planets, which span roughly 10–100 M⊕. The positive correlation between stellar metallicity and planetary heavy‑element mass is reproduced: higher metallicity stars are expected to host higher‑σ₀ disks, leading to larger enrichments in the DI scenario. Moreover, the authors argue that Jupiter itself could have formed farther out (10–20 AU) and still accreted the 20–30 M⊕ of heavy elements required by interior structure models, before migrating inward to its present orbit.

The paper concludes that, within the DI framework, the final composition of a giant planet is dictated primarily by the local disk environment—its mass, surface‑density gradient, and the planet’s formation radius. Consequently, heavy‑element abundance alone cannot discriminate between DI and core‑accretion origins; additional diagnostics (e.g., atmospheric composition, disk observations) are needed. This work reinforces the view that planet formation is a highly stochastic process, with the protoplanetary disk’s initial conditions playing a decisive role in shaping the diversity of giant‑planet compositions observed today.