Global magnetic fields of active solar-like stars are nowadays routinely detected with spectropolarimetric measurements and are mapped with Zeeman-Doppler imaging (ZDI). However, due to the cancellation of opposite field polarities, polarimetry captures only a tiny fraction of the magnetic flux and cannot assess the overall stellar surface magnetic field if it is dominated by a small-scale component. Analysis of Zeeman broadening in high-resolution intensity spectra can reveal these hidden complex magnetic fields. Historically, there were very few attempts to obtain such measurements for G dwarf stars due to the difficulty of disentangling Zeeman effect from other broadening mechanisms affecting spectral lines. Here we developed a new magnetic field diagnostic method based on relative Zeeman intensification of optical atomic lines with different magnetic sensitivity. Using this technique we obtained 78 field strength measurements for 15 Sun-like stars, including some of the best-studied young solar twins. We find that the average magnetic field strength $Bf$ drops from 1.3-2.0 kG in stars younger than about 120 Myr to 0.2-0.8 kG in older stars. The mean field strength shows a clear correlation with the Rossby number and with the coronal and chromospheric emission indicators. Our results suggest that magnetic regions have roughly the same local field strength $Bapprox3.2$ kG in all stars, with the filling factor $f$ of these regions systematically increasing with stellar activity. Comparing our results with the spectropolarimetric analyses of global magnetic fields in the same stars, we find that ZDI recovers about 1% of the total magnetic field energy in the most active stars. This figure drops to just 0.01% for the least active targets.
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