We investigate the detectability of Zeeman broadening in optical Stokes Ispectra of slowly rotating sun-like stars. To this end, we apply the LTEspectral line inversion package SPINOR to very-high quality CES data andexplore how fit quality depends on the average magnetic field, Bf .One-component (OC) and two-component (TC) models are adopted. In OC models, theentire surface is assumed to be magnetic. Under this assumption, we determineformal 3{\sigma} upper limits on the average magnetic field of 200 G for theSun, and 150 G for 61 Vir (G6V). Evidence for an average magnetic field of ~500 G is found for 59 Vir (G0V), and of ~ 1000 G for HD 68456 (F6V). Adistinction between magnetic and non-magnetic regions is made in TC models,while assuming a homogeneous distribution of both components. In our TCinversions of 59 Vir, we investigate three cases: both components have equaltemperatures; warm magnetic regions; cool magnetic regions. Our TC model withequal temperatures does not yield significant improvement over OC inversionsfor 59 Vir. The resulting Bf values are consistent for both. Fit quality issignificantly improved, however, by using two components of differenttemperatures. The inversions for 59 Vir that assume different temperatures forthe two components yield results consistent with 0 - 450 G at the formal3{\sigma} confidence level. We thus find a model dependence of our analysis anddemonstrate that the influence of an additional temperature component candominate over the Zeeman broadening signature, at least in optical data.Previous comparable analyses that neglected effects due to multiple temperaturecomponents may be prone to the same ambiguities.
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