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On the Statistical Properties of Cospectra

Huppenkothen, D. and Bachetti, M. (2018) On the Statistical Properties of Cospectra. Astrophysical Journal Supplement Series, 236 (1). Art. No. 13. ISSN 1538-4365. doi:10.3847/1538-4365/aabe38.

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In recent years, the cross-spectrum has received considerable attention as a means of characterizing the variability of astronomical sources as a function of wavelength. The cospectrum has only recently been understood as a 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 timescales. 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, under the assumption that the same source is observed simultaneously in independent detectors in the same energy range. This case is especially relevant for detecting faint X-ray pulsars in detectors heavily affected by instrumental effects, including NuSTAR, Astrosat, and IXPE, which allow for even sampling and where the cospectrum can act as an effective way to mitigate dead time. 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.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Huppenkothen, D.0000-0002-1169-7486
Bachetti, M.0000-0002-4576-9337
Additional Information:© 2018 The American Astronomical Society. Received 2017 September 27; revised 2018 January 16; accepted 2018 January 16; published 2018 May 11. The authors thank the anonymous referee for their helpful comments. The authors also thank Thomas Laetsch for helpful suggestions regarding the mathematical derivations, and Peter Bult for spotting a mathematical error. D.H. is supported by the James Arthur Postdoctoral Fellowship and the Moore-Sloan Data Science Environment at New York University. D.H. acknowledges support from the DIRAC Institute in the Department of Astronomy at the University of Washington. The DIRAC Institute is supported through generous gifts from the Charles and Lisa Simonyi Fund for Arts and Sciences, and the Washington Research Foundation. M.B. is supported in part by the Italian Space Agency through agreement ASI-INAF n.2017-12-H.0 and ASI-INFN agreement n.2017-13-H.0.
Subject Keywords:methods: data analysis – methods: statistical – X-rays: general
Issue or Number:1
Record Number:CaltechAUTHORS:20171002-134855167
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Official Citation:D. Huppenkothen and M. Bachetti 2018 ApJS 236 13
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81958
Deposited By: Joy Painter
Deposited On:02 Oct 2017 23:20
Last Modified:15 Nov 2021 19:47

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