Evolution of the gas accretion history. For the MTG (Eq. (7)), 1D disk accretion into the gap (Eq. (1)), and the 3D gap accretion as prescribed by Morbidelli et al. (2014; Eq. (2)). We increased the rate of the 1D disk accretion by a an order of magnitude to account for the possibility that gas accretion into the gap is increased by the generation of gravitational instabilities near the gap edge. For the 1D and 3D accretion rates, we assumed static efficiencies of 0.8 and 0.5, respectively. In each of the subfigures, the black dashed line denotes the point where the planet opens a gap.
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