Quantifying the effect of passband on observations in the Ca II K line

Full-disk observations of the Sun in the Ca II K line have been carried out since the late 19th century at various observatories worldwide. These long-term records of solar activity are crucial for reducing discrepancies among solar irradiance reconstructions and for advancing our understanding of the solar dynamo. To construct a consistent composite record, data from different observatories must be cross-calibrated to account for variations in spectral passband and spatial resolution, which are the primary sources of discrepancies between archives. In this study, we use high spectral and spatial resolution observations in the Ca II K line from the state-of-the-art Sunrise III mission to emulate different passbands and derive empirical contrast-contrast relationships between them. We find that these relationships are well described by a power law and provide coefficients for different combinations of passband widths in the range 0.1--9 Angstroms and spatial resolutions between 1 arcsec and 6 arcsec. Applying such a relationship to observations from two major Ca II K archives demonstrates its potential to improve their cross-calibration. The results provide a foundation for the construction of a consistent, century-long time series of solar activity from historical and modern Ca II K observations.