Calculation of the enrichment of the giant planet envelopes during the late heavy bombardment

The giant planets of our solar system possess envelopes consisting mainly of hydrogen and helium but are also significantly enriched in heavier elements relatively to our Sun. In order to better constrain how these heavy elements have been delivered, we quantify the amount accreted during the so-called late heavy bombardment, at a time when planets were fully formed and planetesimals could not sink deep into the planets. On the basis of the Nice model, we obtain accreted masses (in terrestrial units) equal to 0.15 +/- 0.04 M-circle plus for Jupiter, and 0.08 +/- 0.01 M-circle plus for Saturn. For the two other giant planets, the results are found to depend mostly on whether they switched position during the instability phase. For Uranus, the accreted mass is 0.051 +/- 0.003M(circle plus) with an inversion and 0.030 +/- 0.001 M-circle plus without an inversion. Neptune accretes 0.048 +/- 0.015 M-circle plus in models in which it is initially closer to the Sun than Uranus, and 0.066 +/- 0.006M(circle plus) otherwise. With well-mixed envelopes, this corresponds to an increase in the enrichment over the solar value of 0.033 +/- 0.001 and 0.074 +/- 0.007 for Jupiter and Saturn, respectively. For the two other planets, we find the enrichments to be 2.1 +/- 1.4 (w/ inversion) or 1.2 +/- 0.7 (w/o inversion) for Uranus, and 2.0 +/- 1.2 (w/ inversion) or 2.7 +/- 1.6 (w/o inversion) for Neptune. This is clearly insufficient to explain the inferred enrichments of similar to 4 for Jupiter, similar to 7 for Saturn and similar to 45 for Uranus and Neptune. (C) 2009 Elsevier Ltd. All rights reserved.