Self-consistent Modeling of the logN-logS in the Poisson Limit

Details Self-consistent Modeling of the logN-logS in the Poisson Limit Self-consistent Modeling of the logN-logS in the Poisson Limit

Aug 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004head....8.1632s&link_type=abstract

American Astronomical Society, HEAD meeting #8, #16.32; Bulletin of the American Astronomical Society, Vol. 36, p.934

Mathematics

Logic

Scientific paper

logN-logS curves are a fundamental tool in the study of source populations, luminosity functions, and cosmological parameters. However, their determination is hampered by statistical effects such as the Eddington bias, incompleteness due to detection efficiency, faint source flux fluctuations, etc. Here we present a new and powerful method using the full Poisson machinery that allows us to model the logN-logS distribution of X-ray sources in a self-consistent manner. Because we properly account for all the above statistical effects, our modeling is valid over the full range of the data.
We use a Bayesian approach, modeling the fluxes with known functional forms such as simple or broken power-laws. The expected photon counts are conditioned on the fluxes, the background contamination, effective area, detector vignetting, and detection probability. The built-in flexibility of the algorithm also allows a simultaneous analysis of multiple datasets.
We demonstrate the power of our algorithm by applying it to a set of Chandra observations.
This project is part of the California-Harvard/CXC AstroStatistics Collaboration. The authors gratefully acknowledge funding for this project partially provided by NSF grant DMS-01-04129 and by NASA Contract NAS8-39073, and NASA grants NCC2-1350 and NAG5-13056.

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