Abstract
Context. Catalogue cross-correlation is essential to building large sets of multi-wavelength data, whether it be to study the properties of populations of astrophysical objects or to build reference catalogues (or timeseries) from survey observations. Nevertheless, resorting to automated processes with limited sets of information available on large numbers of sources detected at different epochs with various filters and instruments inevitably leads to spurious associations. We need both statistical criteria to select detections to be merged as unique sources, and statistical indicators helping in achieving compromises between completeness and reliability of selected associations. Aims. We lay the foundations of a statistical framework for multi-catalogue cross-correlation and cross-identification based on explicit simplified catalogue models. A proper identification process should rely on both astrometric and photometric data. Under some conditions, the astrometric part and the photometric part can be processed separately and merged a posteriori to provide a single global probability of identification. The present paper addresses almost exclusively the astrometrical part and specifies the proper probabilities to be merged with photometric likelihoods. Methods. To select matching candidates in n catalogues, we used the Chi (or, indifferently, the Chi-square) test with 2(n−1) degrees of freedom. We thus call this cross-match a χ-match. In order to use Bayes’ formula, we considered exhaustive sets of hypotheses based on combinatorial analysis. The volume of the χ-test domain of acceptance – a 2(n−1)-dimensional acceptance ellipsoid – is used to estimate the expected numbers of spurious associations. We derived priors for those numbers using a frequentist approach relying on simple geometrical considerations. Likelihoods are based on standard Rayleigh, χ and Poisson distributions that we normalized over the χ-test acceptance domain. We validated our theoretical results by generating and cross-matching synthetic catalogues. Results. The results we obtain do not depend on the order used to cross-correlate the catalogues. We applied the formalism described in the present paper to build the multi-wavelength catalogues used for the science cases of the Astronomical Resource Cross-matching for High Energy Studies (ARCHES) project. Our cross-matching engine is publicly available through a multi-purpose web interface. In a longer term, we plan to integrate this tool into the CDS XMatch Service.
Highlights
The development of new detectors with high throughput over large areas has revolutionized observational astronomy during recent decades
We applied the formalism described in the present paper to build the multi-wavelength catalogues used for the science cases of the Astronomical Resource Cross-matching for High Energy Studies (ARCHES) project
ARCHES was originally focusing on the cross-matching of XMM-Newton sources, the algorithms developed in this context are clearly applicable to any combination of catalogues and energy bands
Summary
The development of new detectors with high throughput over large areas has revolutionized observational astronomy during recent decades These technological advances, aided by a considerable increase of computing power, have opened the way to outstanding ground-based and space-borne all-sky or very large area imaging projects (e.g. the 2MASS Skrutskie et al 2006; Cutri et al 2003; SDSS Ahn et al 2012, 2013; and WISE Wright et al 2010; Cutri et al 2014, surveys). At the 2020 horizon, European space missions such as Gaia and Euclid together with the Large Synoptic Survey Telescope (LSST) will provide a several-fold increase in the number of catalogued optical objects while providing measurements of exquisite astrometric and photometric quality This exponentially increasing flow of high quality multiwavelength data has radically altered the way astronomers design observing strategies and tackle scientific issues. ARCHES was originally focusing on the cross-matching of XMM-Newton sources, the algorithms developed in this context are clearly applicable to any combination of catalogues and energy bands (see for example Mingo et al 2016)
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