Long-term evolution of models with planet formation processes. Panela: a schematic illustration of the evolution of a model with a variable Z_accretion and an opacity increase of A₂ = 0.12. In the early phase, the metallicity of the proto-Sun increases with time due to the high-Z accretion, which results from the dust drift and selective removal of hydrogen and helium by disk winds (see text). Once protoplanets are formed or dust grains in the protosolar disk are exhausted, the disk metallicity decreases, and consequently, the solar surface metallicity, Z_surf, decreases. The signature of this variable Z_accretion remains in the solar core until the solar age. The circles (not to scale) show the solar metallicity profile at times t_A = 1.73 Myr, t_B = 10 Myr, and t_⊙ = 4.567 Gyr. Panelsb–d: the evolution of Z_accretion, Z_surf, and Z_center of the models with a variable Z_accretion (solid blue lines) and a constant Z_accretion (dotted gray lines), respectively. Panele: the internal structure evolution (the so-called Kippenhahn diagram). The cloudy and white regions show the convective and radiative regions, respectively. The two lines (blue and gray) are almost the same. A radiative core emerges at time t_A. The solid black line indicates the stellar mass. Panelf: the metallicity profile of the present-day Sun. Animations that show the metallicity profile in the solar interior of these models are available online and at Zenodo. (See “K2-MZvar-A2-12” and “K2-A2-12” in Table A.1 and the CDS table for more details regarding the models with and without planet formation processes, respectively.)