No Time for Dead Time: Use the Fourier Amplitude Differences to Normalize Dead-time-affected Periodograms

Dead time affects many of the instruments used in X-ray astronomy, by producing a strong distortion in power density spectra. This can make it difficult to model the aperiodic variability of the source or look for quasi-periodic oscillations. Whereas in some instruments a simple a priori correction for dead-time-affected power spectra is possible, this is not the case for others such as NuSTAR, where the dead time is non-constant and long (~2.5 ms). Bachetti et al. 2015 suggested the cospectrum obtained from light curves of independent detectors within the same instrument as a possible way out, but this solution has always only been a partial one: the measured rms was still affected by dead time, because the width of the power distribution of the cospectrum was modulated by dead time in a frequency-dependent way. In this Letter we suggest a new, powerful method to normalize cospectra and, with some caveats, even power density spectra. Our approach uses the difference of the Fourier amplitudes from two independent detectors to characterize and filter out the effect of dead time. This method is crucially important for the accurate modelling of periodograms derived from instruments affected by dead time on board current missions like NuSTAR and ASTROSAT, but also future missions such as IXPE