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Number-counts slope estimation in the presence of Poisson noiseThe slope determination of a power-law number flux relationship in the case of photon-limited sampling. This case is important for high-sensitivity X-ray surveys with imaging telescopes, where the error in an individual source measurement depends on integrated flux and is Poisson, rather than Gaussian, distributed. A bias-free method of slope estimation is developed that takes into account the exact error distribution, the influence of background noise, and the effects of varying limiting sensitivities. It is shown that the resulting bias corrections are quite insensitive to the bias correction procedures applied, as long as only sources with signal-to-noise ratio five or greater are considered. However, if sources with signal-to-noise ratio five or less are included, the derived bias corrections depend sensitively on the shape of the error distribution.
Document ID
19870035028
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Schmitt, Juergen H. M. M. (Max-Planck-Institut fuer Physik und Astrophysik Garching, Germany)
Maccacaro, Tommaso (Harvard-Smithsonian Center for Astrophysics Cambridge, MA, United States)
Date Acquired
August 13, 2013
Publication Date
November 1, 1986
Publication Information
Publication: Astrophysical Journal, Part 1
Volume: 310
ISSN: 0004-637X
Subject Category
ASTROPHYSICS
Funding Number(s)
CONTRACT_GRANT: NAS8-30751
Distribution Limits
Public
Copyright
Other