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Fig. 12

image

Total metallicity (solid lines) and envelope metallicity (dashed lines) as a function of the planet mass for different models of planet formation with envelope enrichment. The different colours indicate different choices of opacities and accretion rates of solids. Violet corresponds to our nominal model (opacity of Mordasini and Freedman, and Z = 10-6M/yr). Orange shows opacities of Semenov and Ferguson, and Z = 3 × 10-6M/yr. The green curves were computed using the nominal opacities, but the dust opacities of Mordasini are enhanced by a factor of 400. The accretion rate of solids is Z = 4 × 10-6M/yr. Mthresh was chosen such that the corresponding envelope is massive enough to destroy icy planetesimals of 1–10 km. The thick lines show the formation results, and they all end at times of ~4–5 Myr (the choice of the accretion rates was to compute similar formation times). The thin lines are an extrapolation and are shown to see what we should expect in terms of metallicities up to Jovian masses. The total metallicities predicted for the giant planets of the solar system are overplotted for reference (data taken from Helled et al. 2011, for Uranus and Neptune; and from Baraffe et al. 2014, for Jupiter and Saturn). The circular points indicate the onset of the runaway of gas. This means that masses at the right of these points, especially after the simulations stop, are unlikely (the expected elapsed time between the end of the simulations and the time required for MP 100 M is ~105 yr). This figure suggests that a combination of high opacities is preferred for the solar system with respect to the low opacities adopted in the nominal model.

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