The Aspects code for probabilistic cross-identification of astrophysical sources: documentation and complements

Aspects ([asp{epsilon}], ASsociation PositionnellE/ProbabilistE de CaTalogues de Sources in French) is a Fortran 95 code for the cross-identification of astrophysical sources. Its source files are freely available. Given the coordinates and positional uncertainties of all the sources in two catalogs K and K, Aspects computes the probability that an object in K and one in K are the same or that they have no counterpart. Three exclusive assumptions are considered: (1) Several-to-one associations: a K-source has at most one counterpart in K, but a K-source may have several counterparts in K; (2) One-to-several associations: the same with K and K swapped; (3) One-to-one associations: a K-source has at most one counterpart in K and vice versa. To compute the probabilities of association, Aspects needs the a priori (i.e. ignoring positions) probability that an object has a counterpart. The code obtains estimates of this quantity by maximizing the likelihood to observe all the sources at their effective positions under each assumption. The likelihood may also be used to determine the most appropriate model, given the data, or to estimate the typical positional uncertainty if unknown.

Probabilistic positional association of catalogs of astrophysical sources: the Aspects code

We describe a probabilistic method of cross-identifying astrophysical sources in two catalogs from their positions and positional uncertainties. The probability that an object is associated with a source from the other catalog, or that it has no counterpart, is derived under two exclusive assumptions: first, the classical case of several-to-one associations, and then the more realistic but more difficult problem of one-to-one associations. In either case, the likelihood of observing the objects in the two catalogs at their effective positions is computed and a maximum likelihood estimator of the fraction of sources with a counterpart -- a quantity needed to compute the probabilities of association -- is built. When the positional uncertainty in one or both catalogs is unknown, this method may be used to estimate its typical value and even to study its dependence on the size of objects. It may also be applied when the true centers of a source and of its counterpart at another wavelength do not coincide. To compute the likelihood and association probabilities under the different assumptions, we developed a Fortran 95 code called Aspects ([asp{epsilon}], ASsociation PositionnellE/ProbabilistE de CaTalogues de Sources in French); its source files are made freely available. To test Aspects, all-sky mock catalogs containing up to 10^5 objects were created, forcing either several-to-one or one-to-one associations. The analysis of these simulations confirms that, in both cases, the assumption with the highest likelihood is the right one and that estimators of unknown parameters built for the appropriate association model are reliable.

Probabilistic positional association of astrophysical sources between catalogs

We describe a simple probabilistic method to cross-identify astrophysical sources from different catalogs and provide the probability that a source is associated with a source from another catalog or that it has no counterpart. When the positional uncertainty in one of the catalog is unknown, this method may be used to derive its typical value and even to study its dependence on the size of objects. It may also be applied when the true centers of a source and of its counterpart at another wavelength do not coincide. We extend this method to the case when there are only one-to-one associations between the catalogs.