On the Statistical Properties of Cospectra

Abstract

In recent years, the cross spectrum has received considerable attention as a means of characterising the variability of astronomical sources as a function of wavelength. While much has been written about the statistics of time and phase lags, the cospectrum has only recently been understood as means of mitigating instrumental effects dependent on temporal frequency in astronomical detectors, as well as a method of characterizing the coherent variability in two wavelength ranges on different time scales. In this paper, we lay out the statistical foundations of the cospectrum, starting with the simplest case of detecting a periodic signal in the presence of white noise. This case is especially relevant for detecting faint X-ray pulsars in detectors heavily affected by instrumental effects, including NuSTAR, Astrosat and IXPE. We show that the statistical distributions of both single and averaged cospectra differ considerably from those for standard periodograms. While a single cospectrum follows a Laplace distribution exactly, averaged cospectra are approximated by a Gaussian distribution only for more than ~30 averaged segments, dependent on the number of trials. We provide an instructive example of a quasi-periodic oscillation in NuSTAR and show that applying standard periodogram statistics leads to underestimated tail probabilities for period detection. We also demonstrate the application of these distributions to a NuSTAR observation of the X-ray pulsar Hercules X-1.

12 pages, 8 figures, submitted to ApJ; reproducible code available at https://github.com/dhuppenkothen/cospectra-paper ; Comments welcome

References in corpus (12)

• X-ray reverberation around accreting black holes
• A quasi-periodic modulation of the iron line centroid energy in the black hole binary H 1743-322
• No Time for Dead Time: Timing analysis of bright black hole binaries with NuSTAR
• HZ Her: Stellar Radius from X-ray Eclipse Observations, Evolutionary State and a New Distance
• NuSTAR observation of a Type I X-ray burst from GRS 1741.9-2853
• Internal Gravity Waves in the Magnetized Solar Atmosphere. I. Magnetic Field Effects
• Disk-Wind Connection During the Heartbeats of GRS 1915+105
• Statistical properties of Fourier-based time-lag estimates
• Ultraluminous X-ray sources: three exciting years
• Detection of Very Low-Frequency Quasi-Periodic Oscillations in the 2015 Outburst of V404 Cygni
• NuSTAR and XMM-Newton observations of the 2015 outburst decay of GX 339-4
• Discovery of a soft X-ray 8 mHz QPO from the accreting millisecond pulsar IGR J00291+5934

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