In protoplanetary disks, the growth and inward drift of dust lead to the generation of a temporal ``pebble wave'' of increased metallicity. This phase must be followed by a phase in which the exhaustion of the pebbles in the disk and the formation of planets lead to the accretion of metal-poor gas. At the same time, disk winds may lead to the selective removal of hydrogen and helium from the disk. Hence, stars grow by accreting gas that has an evolving composition. In this work, we investigated how the formation of the Solar System may have affected the composition and structure of the Sun, and whether it plays any role in solving the so-called solar-abundance problem, that is, the fact that standard models with up-to-date lower-metallicity abundances reproduce helioseismic constraints significantly more poorly than those with old higher-metallicity abundances. We simulated the evolution of the Sun from the protostellar phase to the present age and attempted to reproduce spectroscopic and helioseismic constraints. We performed chi-squared tests to optimize our input parameters, which we extended by adding secondary parameters. These additional parameters accounted for the variations in the composition of the accreted material and an increase in the opacities. We confirmed that, for realistic models, planet formation occurs when the solar convective zone is still massive; thus, the overall changes due to planet formation are too small to significantly improve the chi-square fits. We found that solar models with up-to-date abundances require an opacity increase of 12% to 18% centered at T = 10^6.4 K to reproduce the available observational constraints. This is slightly higher than, but is qualitatively in good agreement with, recent measurements of higher Fe opacities. These models result in better fits to the observations than those using old abundances; therefore, they are a promising solution to the solar abundance problem. Using these improved models, we found that planet formation processes leave a small imprint in the solar core, whose metallicity is enhanced by up to 5%. This result can be tested by accurately measuring the solar neutrino flux. In the improved models, the protosolar molecular cloud core is characterized by a primordial metallicity in the range Zproto = 0.0127-0.0157 and a helium mass fraction in the range Yproto = 0.268-0.274.

Supplemental materials of Kunitomo & Guillot (2021), A&A. The stellar evolution code MESA version 12115 was used.