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

One possible mechanism for giant planet formation is disk instability in which the planet is formed as a result of gravitational instability in the protoplanetary disk surrounding the young star. The final composition and core mass of the planet will depend on the planet’s mass, environment and the planetesimal accretion efficiency. 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 (σ) functions σ = σ0a −α with α < 2, the accretion timescale is significantly longer at larger radial distances. Efficient accretion is limited to the first ∼ 10 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 with α = 1/2, 1, and 3/2. We show that a Jupiter-mass protoplanet can accrete 1 to 110 M⊕ of heavy elements, depending on the disk properties. Due to the limitation on the accretion timescale, our results provide lower bounds on heavy element enrichment. Our results can 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