SIMBAD references

In the study of the AGNs variability the search for possible relations between the shape of the spectral energy distribution and the source luminosity is usually performed through the evaluation of the linear correlation coefficient between the flux in one band and the spectral index, derived from a set of photometric measures in various bands. The dependence of the spectral index upon the fluxes introduces a bias in the correlation coefficient in the sense of a spectral hardening (or softening) related to increasing fluxes at the higher (lower) frequencies, which can mimic the spectral changes expected from both thermal and non thermal theoretical models. In this paper we derive explicit expressions for the correlation coefficient when the flux changes are due to random fluctuations and found that it is linearly depending on the frequency; this analysis is also applied to some examples, based on literature data which demonstrate this effect. Correct approaches to evaluate the unbiased correlation coefficient are presented.