  We investigate the detectability of Zeeman broadening in optical Stokes I
spectra of slowly rotating sun-like stars. To this end, we apply the LTE
spectral line inversion package SPINOR to very-high quality CES data and
explore how fit quality depends on the average magnetic field, Bf .
One-component (OC) and two-component (TC) models are adopted. In OC models, the
entire surface is assumed to be magnetic. Under this assumption, we determine
formal 3{\sigma} upper limits on the average magnetic field of 200 G for the
Sun, 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). A
distinction between magnetic and non-magnetic regions is made in TC models,
while assuming a homogeneous distribution of both components. In our TC
inversions of 59 Vir, we investigate three cases: both components have equal
temperatures; warm magnetic regions; cool magnetic regions. Our TC model with
equal temperatures does not yield significant improvement over OC inversions
for 59 Vir. The resulting Bf values are consistent for both. Fit quality is
significantly improved, however, by using two components of different
temperatures. The inversions for 59 Vir that assume different temperatures for
the two components yield results consistent with 0 - 450 G at the formal
3{\sigma} confidence level. We thus find a model dependence of our analysis and
demonstrate that the influence of an additional temperature component can
dominate over the Zeeman broadening signature, at least in optical data.
Previous comparable analyses that neglected effects due to multiple temperature
components may be prone to the same ambiguities.
