Neutrino fluxes obtained for the models with an opacity increase and planet formation. Shown are the models with an opacity increase (circles; see also Fig. 1) and with both an opacity increase and a variable Z_accretion (i.e., planet formation processes; star symbols). The colors show the opacity increase A₂ ∈ [0.12, 0.18]. The opacity increase in this range leads to a better match with spectroscopic and helioseismic observations (χ² ≲ 0.5 indicated by the size). A higher opacity increase leads to lower Φ(⁸B), Φ(7Be), and Φ(CNO) values, whereas the planet formation processes lead to higher values. Consequently, our best model with both an opacity increase of A₂ = 0.12 and planet formation processes (i.e., star symbol with white color) reproduces not only the observed constraints of neutrino fluxes (green circles with error bars) but also the spectroscopic and helioseismic observations. (See “K2-MZvar-A2-12” and “K2-A2-12” in Table A.1 and the CDS table for more details about the models with A₂ = 0.12 and with and without planet formation processes, respectively.)