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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.