Variability studies in blazar jets with SF analysis: caveats and problems

Blazars are radio-loud active galactic nuclei (AGN) dominated by relativistic jets seen at small angles to the line-of-sight. They exhibit dramatic flux variations across the electromagnetic spectrum. The fastest variations are observed in the X-ray and γ-ray bands on time-scales of hours or even minutes. Currently, a substantial part of the blazar literature has been based on the study of these temporal variations through the use of structure function (SF) analysis, the results of which are believed to put great constrains on the jet-physics. The SF is often invoked in the framework of shot-noise models to determine the temporal properties of individual shots within the jet as well as their geometrical sizes. We argue, that for blazar variability studies, the SF-results are sometimes erroneously interpreted leading to misconceptions about the actual source properties. Based on extensive simulations we caution that spurious breaks will appear in the SFs of almost all light-curves, even though these lightcurves may contain no intrinsic characteristic time-scale. Finally, it is also commonly thought that SFs are immune to the sampling problems, such as data-gaps, which affects the estimators of the underlying power spectra density function such as the periodogram. However, we show that SFs are also troubled by gaps which can induce artefacts.