a maximum characteristic timescale.

### Effects of Pileup {#sfpileupsection}

We measure the presence of pile-up in our observations by using the SAS task EPATPLOT and find that the majority of our sources show varying degrees of pile-up. For example, as previously shown in Section \[obssection\], MKN 421 Obs. ID: 0099280101 has a modest amount of pile-up (see Figure \[epatplot\]). In the structure function of this observation (left panel, Figure  \[structpileup\]), the flat portion of the structure function curve should have a value of $log(SF)=1$, which corresponds to the Poisson photon noise inherent in the photon statistics. However, here it falls below the Poisson photon noise level. To remove the pile-up we exclude the central core of the source in the event file since pile-up is more likely to occur here. For this subtracted data, the EPATPLOT output indicates that there is no pile-up and the SF curve is then at the expected value for Poisson photon noise (right panel, Figure \[structpileup\]). Pile-up affects the SF because it lowers the overall count rate and thereby Poisson photon noise is underreported.

We correct for pile-up in the rest of our data by adding a fixed value to $log(SF)$, moving the flat part 