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Context. Zeeman-Doppler imaging (ZDI) is used to reconstruct the surface magnetic field of late-type stars from high-resolution spectropolarimetric observations. The results are usually described in terms of characteristics of the field topology, such as poloidality versus toroidality and axisymmetry versus non-axisymmetry, in addition to the field strength. Aims. In this study, we want to test how well these characteristics are preserved when applying the ZDI method to simulated data. We are particularly interested in how accurately the field topology is preserved and to what extent stellar parameters, such as projected rotation velocity and rotation axis inclination, influence the reconstruction. Methods. For these tests, we used published magnetic field vector data from direct numerical magnetohydrodynamic simulations taken near the surface of the simulation domain. These simulations have variable rotation rates and therefore represent different levels of activity of an otherwise Sun-like setup with a convective envelope of solar thickness. Our ZDI reconstruction is based on spherical harmonics expansion. By comparing the original values to those of the reconstructed images, we study the ability to reconstruct the surface magnetic field in terms of various characteristics of the field. Results. In general, the ZDI method works as expected. The main large-scale features are reasonably well recovered, but the strength of the recovered magnetic field is just a fraction of the original input. The quality of the reconstruction shows clear correlations with the data quality. Furthermore, there are some spurious dependencies between stellar parameters and the characteristics of the field. Conclusions. Our study uncovers some limits of ZDI. Firstly, the recovered field strength will generally be lower than the 'real' value, as smaller structures with opposite polarities will be blurred in the inversion. This is also seen in the relative distribution of magnetic energy in

In this article we review small-scale dynamo processes that are responsible for magnetic field generation on scales comparable to and smaller than the energy carrying scales of turbulence. We provide a review of critical observation of quiet Sun magnetism, which have provided strong support for the operation of a small-scale dynamo in the solar photosphere and convection zone. After a review of basic concepts we focus on numerical studies of kinematic growth and non-linear saturation in idealized setups, with special emphasis on the role of the magnetic Prandtl number for dynamo onset and saturation. Moving towards astrophysical applications we review convective dynamo setups that focus on the deep convection zone and the photospheres of solar-like stars. We review the critical ingredients for stellar convection setups and discuss their application to the Sun and solar-like stars including comparison against available observations. © 2023, The Author(s).

Context. The origins of quiet-Sun magnetism (QS) is still under debate and investigating the solar cycle variation observationally in greater detail can provide clues on how to resolve the ensuing controversies. Aims. We investigate the solar cycle variation of the most magnetically quiet regions and their surface gravity oscillation (f-) mode-integrated energy, E-f. Methods. We used 12 years of Helioseismic and Magnetic Imager (HMI) data and applied a stringent selection criteria based on spatial and temporal quietness to avoid any influence from active regions (ARs). We developed an automated high-throughput pipeline to go through all available magnetogram data and to compute the value of E-f for the selected quiet regions. Results. We observed a clear solar cycle dependence of the magnetic field strength in the most quiet regions containing several supergranular cells. For patch sizes smaller than a supergranular cell, no significant cycle dependence was detected. The E-f at the supergranular scale is not constant over time. During the late ascending phase of Cycle 24 (SC24, 2011-2012), it is roughly constant, but starts diminishing in 2013, as the maximum of SC24 is approached. This trend continues until mid-2017, when hints of strengthening at higher southern latitudes are seen. Slow strengthening continues, stronger at higher latitudes than at the equatorial regions, but E-f never returns to the values seen in 2011-2012. In addition, the strengthening trend continues past the solar minimum, to the years when SC25 is already clearly ascending. Hence, the E-f behavior is not in phase with the solar cycle. Conclusions. The dependence of E-f on the solar cycle at supergranular scales is indicative of the fluctuating magnetic field being replenished by tangling from the large-scale magnetic field - and not solely due to the action of a fluctuation dynamo process in the surface regions. The absence of variations on smaller scales might be an effect of the limited sp, QC 20220930