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

The three bright TeV blazars Mrk 421, Mrk 501, and PKS 2155 - 304 are highly variable in synchrotron X-ray emission. In particular, these sources can 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 similar to 1.6 hr. Using Monte Carlo simulations, we show in this paper that the lags over timescales of hours cannot be the spurious result of periodic gaps, although periodic gaps do indeed introduce greater uncertainty than is 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 ratios. Furthermore, we consider an XMM-Newton observation without interruptions and resample 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.