Aperture Photometry Values and Errors
Users should be aware that the values of aperture photometry quantities such as src_cnts_aper, src_rate_aper, photflux_aper, and flux_aper cited in the catalog are maximum-likelihood estimators (MLE), computed from the relation
where n and m are total counts in the source and background apertures, respectively; f and g are encircled counts fractions in the apertures; and r is a ratio of aperture areas and exposures.
However, the confidence limits on the photometry quantities are derived from the Bayesian background-marginalized posterior probability distribution for the photometry quantity, assuming non-informative priors. In particular, the limits are intended to define the smallest, non-negative interval that includes the mode of the distribution and corresponds to the desired confidence level. However, there is no guarantee that the MLE will be included in the interval.
To investigate this issue, we have examined the MLEs and modes of the B band photflux_aper quantities for ~15,000 sources in a pre-release version of the catalog. We find that only <~ 0.5% of the sources have MLEs and modes that differ by more than ±5%, and <~ 0.1% have medians and modes that differ by more than ±10%. We find only one (low-count) source for which the MLE is not included in the 68% confidence interval.
We conclude that the effect is negligible, although users should take care to check the consistency of the photometry values and their errors. In future catalog releases, we plan to modify our algorithms to force consistency of photometry values and their errors.
Complete details of the aperture photometry algorithms are contained in the documents "Background marginalized X-ray source intensity" and "Revised Specifications for Computing Aperture Photometry Quantities".