Time Variability Studies with Photon-counting Imaging Detectors. I. A Maximum Likelihood Technique

A new method is presented for characterizing the variability properties of a preselected class of celestial objects which are repeatedly observed with the same photon-counting imaging detector. Instrument-specific characteristics, such as detector instrument point response function and mirror system off-axis response, are separated and taken into account in the form of input parameters. All collected source data, both in the form of detections and upper bounds at putative source positions, are retained and fully used in determining the maximum likelihood (ML) estimator of the intrinsic source count rate. For each distinct observation it is determined, at the chosen significance level based on Poisson statistics, whether the observed flux (or upper bound) undergoes a statistically significant variation with respect to the derived ML flux estimator, and variation amplitude, or an upper bound for those cases where significant variations have not been detected is evaluated. It is concluded that, on the basis of presently limited sensitivity data, the variability behavior of the X-ray coronal emission of Pleaides and Hyades stars cannot be distinguished.