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.