An imprint of planet formation in the deep interior of the Sun

Our goal is to determine whether processes that led to the formation of planets in the solar system may have left an observational signature in the Sun's composition. We calculate the evolution of the Sun from the protostellar phase to the present age. We perform chi-squared tests to optimize our input parameters (mixing length, overshooting parameter, initial compositions, the parameters for the opacity increase, and the evolution of accreting materials' composition) using spectroscopic and helioseismic constraints (i.e., effective temperature, luminosity, surface composition, convective envelope thickness, and sound speed profile). We first determine which classes of models best reproduce the observational constraints. We then account for variations of the composition of accreted gas and compare the resulting internal compositions obtained for the present-day Sun. We find that solar models best matching all available constraints require an opacity increase of 12 to 18% centered on 2.5 million K, slightly higher but qualitatively in good agreement with measurements of higher Fe opacities by Bailey et al. (2015). During the planet formation phase, the accretion of dust into pebbles and their inward drift leads to a temporary ``pebble wave'' of increased metallicity. It is followed by metal-poor accretion due to exhaustion of solids in the disk and the formation of planetesimals and planets. Because this lasts only for a few million years, we find that most of the signature of this phase is erased by the initially large solar convective zone. However, we find that the metallicity of the solar core (inner 20% in radius) is enhanced by up to 5%. This may be tested from an accurate measurement of the solar neutrino flux.