Improvement of the photometric sunspot index and changes of the disk-integrated sunspot contrast with time

The photometric sunspot index (PSI) was developed to study the effects of sunspots on solar irradiance. It is calculated from the sunspot data published in the Solar-Geophysical Data catalog. It has been shown that the former PSI models overestimate the effect of dark sunspots on solar irradiance; furthermore results of direct sunspot photometry indicate that the contrast of spots depends on their area. An improved PSI calculation is presented; it takes into account the area dependence of the contrast and calculates `true' daily means for each observation using the differential rotation of the spots. Moreover, the observations are screened for outliers which improves the homogeneity of the data set substantially, at least for the period after December 1981 when NOAA started to report data from a few instead of one to two stations. A detailed description of the method is provided. The correlation between the newly calculated PSI and total solar irradiance is studied for different phases of the solar cycles 21 and 22 using bi-variate spectral analysis. The results can be used as a `calibration' of PSI in terms of gain, the factor by which PSI has to be multiplied to yield the observed irradiance change. The factor changes with time from about 0.6 in 1980 to 1.1 in 1990. This unexpected result cannot be interpreted by a change of the contrast relative to the quiet Sun (as it is normally defined and determined by direct photometry) but rather as a change of the contrast between the spots and their surrounding as seen in total irradiance (integrated over the solar disk). This may partly be explained by a change in the ratio between the areas of the spots and the surrounding faculae.