Comparative study of spectral lines with different Landé factors observed in sunspots

We analyze the spectra of two sunspots of July 8, 2015 and September 5, 2021 which were observed with the ATsU-5 solar telescope of the Main Astronomical Observatory of the National Academy of Sciences of Ukraine. The main goal of the study was to search for signs of superstrong magnetic fields in the sunspots (> 10(3) G), taking into account the fact that such magnetic fields can have mixed magnetic polarity. An SBIG ST-8300 CCD camera was used to record a spectral interval of about 8 angstrom near the Fe I 5434.5 angstrom line, where six metal lines with effective Lande factors g(eff) from -0.014 to 2.14 are located. Also, FeI 5397.1 line with g(eff) = 1.426 was studied too for the second sunspot. In the first spot, we found a splitting of the I +/- V profiles in the FeI 5434.5 line, corresponding to a magnetic field with a strength of approximate to 25 kG, which has the opposite magnetic polarity with respect to the "kilogaussian" magnetic field approximate to 2 kG) determined from lines with large Lande factors. A detailed comparison of the spectral widths in the Stokes I profiles of two lines of the 15th iron multiplet, FeI 5434.5 and 5397.1 angstrom showed that their additional widening (local peaks of splitting) sometimes occurs at different places on the Sun. Considering that these lines have almost the same temperature sensitivity and formation height in the atmosphere, it is unlikely that this is a non-magnetic effect due to variations in thermodynamic conditions and the velocity field. Regarding the possible influence of spectral blends, the paradox is that it is the more "clean" line Fe I 5434.5 that demonstrates the most incomprehensible splitting peaks. This strengthens the assumption that the observed splitting peaks are of a magnetic nature. But then, if we assume that the additional widening of the 5434.5 line is due to the magnetic field, then its value should be similar to 10(5) G. The semi-empirical model for the first sunspot was built using the so-called Tikhonov stabilizers, which modify the objective function to ensure the smoothness and stability of the solutions of the inverse problem. This model has an anomalous feature, namely, the maximum of micro-turbulent velocities in the region of the temperature minimum, i. e. where the minimum of these velocities is present in the model of a quiet photosphere. Perhaps this feature indicates very strong magnetic fields in this sunspot. On the whole, we cannot draw a final conclusion about the existence of the above mentioned superstrong magnetic fields in the sunspots, but we draw attention to interesting and mysterious effects in the line profiles, which require additional studies.