Influence of the magnetic activity cycle on mean density and acoustic radius inversions

Context. Asteroseismic modelling is set to play a crucial role in upcoming space-based missions such as PLATO, CubeSpec, and Roman. Despite the significant progress made in this field, asteroseismology has uncovered notable discrepancies between observations and theoretical predictions. These discrepancies introduce non-negligible biases in stellar characterisation at the precision levels required by PLATO. Present modelling strategies typically disregard magnetic activity, assuming its impacts are concealed within the parametrisation of the so-called ‘surface effects’. However, this assumption has recently been challenged, as a significant imprint of magnetic activity on the asteroseismic characterisation of the Sun using forward modelling methods has been demonstrated. Aims. Based on GOLF and BiSON observations of two full activity cycles of the Sun, a reference target for assessing the PLATO mission requirements, we quantified the impact of magnetic activity on solar mean density and acoustic radius inversions. Methods. The GOLF and BiSON observations were segmented into yearly overlapping snapshots, each offset by 91.25 days. For each snapshot, we performed inversions to determine the mean density and acoustic radius. This approach enabled us to track the apparent temporal evolution of these two quantities and to estimate the systematic uncertainty associated with magnetic activity. Results. Similar to the findings obtained using forward methods, we observe a discernible imprint of the magnetic activity cycle on the solar mean density and acoustic radius as determined through helioseismic inversions. This imprint is consistent across both GOLF and BiSON datasets, and constitutes the largest source of systematic uncertainty in the solar asteroseismic characterisation. Additionally, the effects of magnetic activity are mitigated by the inclusion of low radial-order modes in the dataset, consistently with the literature, but we observe a significantly larger mitigation factor than previous measurements for other stellar variables such as the stellar age. Conclusions. We recommend asteroseismic values for the solar mean density and acoustic radius: ρ̄ inv = 1.4104 ± 0.0051 g/cm 3 and τ inv = 3722.0 ± 4.1 s. The suggested values correspond to the average over the two full activity cycles and the suggested uncertainties take into account the major sources of systematic errors, including the choice of physical ingredients in stellar models, stellar activity, and the surface effect prescription. We achieved a high precision of 0.36% for the mean density and 0.11% for the acoustic radius. These results are promising, as they demonstrate the potential to attain high precision levels for these quantities in Sun-like stars. A better-constrained mean density can be used to enhance the precision of the stellar radius, which is crucial for characterising exoplanetary systems. A more accurately determined stellar radius indeed leads to better estimates of the orbital distance and planetary radius of exoplanets.