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We calculate the minimum mass of heavy elements required in the envelopes ofJupiter and Saturn to match the observed oversolar abundances of volatiles.Because the clathration efficiency remains unknown in the solar nebula, we haveconsidered a set of sequences of ice formation in which the fraction of wateravailable for clathration is varied between 0 and 100 %. In all the casesconsidered, we assume that the water abundance remains homogeneous whatever theheliocentric distance in the nebula and directly derives from a gas phase ofsolar composition. Planetesimals then form in the feeding zones of Jupiter andSaturn from the agglomeration of clathrates and pure condensates in proportionsfixed by the clathration efficiency. A fraction of Kr and Xe may have beensequestrated by the H3+ ion in the form of stable XeH3+ and KrH3+ complexes inthe solar nebula gas phase, thus implying the formation of at least partly Xe-and Kr-impoverished planetesimals in the feeding zones of Jupiter and Saturn.These planetesimals were subsequently accreted and vaporized into the hydrogenenvelopes of Jupiter and Saturn, thus engendering volatiles enrichments intheir atmospheres, with respect to hydrogen. Taking into account bothrefractory and volatile components, and assuming plausible molecular mixingratios in the gas phase of the outer solar nebula, we show that it is possibleto match the observed enrichments in Jupiter and Saturn, whatever theclathration efficiency. Our calculations predict that the O/H enrichmentdecreases from 6.7 to 5.6 times solar (O/H) in the envelope of Jupiter and from18.1 to 15.4 times solar (O/H) in the envelope of Saturn with the growingclathration efficiency in the solar nebula.

Determination of the minimum masses of heavy elements in the envelopes of Jupiter and Saturn