The effects of periodically gapped time series on cross-correlation lag determinations

The three bright TeV blazars Mrk 421, Mrk 501 and PKS 2155-404 are highly variable in synchrotron X-ray emission. In particular, these sources may exhibit variable time lags between flux variations at different X-ray energy bands. However, there are a number of issues that may significantly bias lag determinations. Edelson et al. (2001) recently proposed that the lags on timescales of hours, discovered by ASCA and BeppoSAX, could be an artifact of periodic gaps in the light curves introduced by the Earth occultation every \~1.6 hr. Using Monte Carlo simulations, in this paper we show that the lags over timescales of hours can not be the spurious result of periodic gaps, while periodic gaps indeed introduces uncertainty larger than what present in the evenly sampled data. The results also show that time lag estimates can be substantially improved by using evenly sampled light curves with large lag to bin-size ratio. Furthermore, we consider an XMM-Newton observation without interruptions and re-sample the light curves using the BeppoSAX observing windows, and then repeat the same cross correlation function (CCF) analysis on both the real and fake data. The results also show that periodic gaps in the light curves do not significantly distort the CCF characters, and indeed the CCF peak ranges of the real and fake data overlap. Therefore, the lags discovered by ASCA and BeppoSAX are not due to periodic gaps in the light curves.