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Context. A number of studies have aimed at defining the exact form of the relation between magnetic field strength and CaII H and K core brightness. All previous studies have however been restricted to isolated regions on the solar disc or to a limited set of observations.
Aims. We reassess the relationship between the photospheric magnetic field strength and the CaII K intensity for a variety of surface features as a function of the position on the disc and the solar activity level. This relationship can be used to recover the unsigned photospheric magnetic field from images recorded in the core of CaII K line.
Methods. We have analysed 131 pairs of high-quality, full-disc, near-co-temporal observations from the Helioseismic and Magnetic Imager (SDO/HMI) and Precision Solar Photometric Telescope (Rome/PSPT) spanning half a solar cycle. To analytically describe the observationally determined relation, we considered three different functions: a power law with an offset, a logarithmic function, and a power-law function of the logarithm of the magnetic flux density. We used the obtained relations to reconstruct maps of the line-of-sight component of the unsigned magnetic field (unsigned magnetograms) from CaII K observations, which were then compared to the original magnetograms.
Results. We find that both power-law functions represent the data well, while the logarithmic function is good only for quiet periods. We see no significant variation over the solar cycle or over the disc in the derived fit parameters, independently of the function used. We find that errors in the independent variable, which are usually not accounted for, introduce attenuation bias. To address this, we binned the data with respect to the magnetic field strength and CaII K contrast separately and derived the relation for the bisector of the two binned curves. The reconstructed unsigned magnetograms show good agreement with the original ones. Root mean square differences are less than 90 G. The results were unaffected by the stray-light correction of the SDO/HMI and Rome/PSPT data.
Conclusions. Our results imply that accurately processed and calibrated CaII K observations can be used to reconstruct unsigned magnetograms by using the relations derived in our study.