Observing the simulations: Applying ZDI to 3D non-potential magnetic field simulations

The large-scale magnetic fields of stars can be obtained with the Zeeman-Doppler-Imaging (ZDI) technique, but their interpretation is still challenging as the contribution of the small-scale field or the reliability of the reconstructed field properties is still not fully understood. To quantify this, we use 3D non-potential magnetic field simulations for slowly rotating solar-like stars as inputs to test the capabilities of ZDI. These simulations are based on a flux transport model connected to a non-potential coronal evolution model using the observed solar flux emergence pattern. We first compare four field prescriptions regarding their reconstruction capabilities and investigate the influence of the spatial resolution of the input maps on the corresponding circularly polarised profiles. We then generate circularly polarised spectra based on our high resolution simulations of three stellar models with different activity levels, and reconstruct their large-scale magnetic fields using a non-potential ZDI code assuming two different stellar inclination angles. Our results show that the ZDI technique reconstructs the main features of slowly rotating solar-like stars but with $\sim\,$one order of magnitude less magnetic energy. The large-scale field morphologies are recovered up to harmonic modes $\ell \sim 5$, especially after averaging over several maps for each stellar model. While ZDI is not able to reproduce the input magnetic energy distributions across individual harmonic modes, the fractional energies across the modes are generally within $20\,\%$ agreement. The fraction of axisymmetric and toroidal field tends to be overestimated for stars with solar flux emergence patterns for more pole-on inclination angles.