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 ( \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 \sim 10 ^ { 5 } 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 _ { \odot } with \alpha = 1/2 , 1 , and 3/2 .
We show that a Jupiter-mass protoplanet can accrete 1 to 110 M _ { \oplus } 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 disk instability or core accretion .