This cross-match is a simple cross-match: for each source of the catalogue A, it returns the sources of the catalogue B lying at an angular distance less than Radius () from the catalogue A source.
In other words, for each source of the catalogue A, it returns the sources of the catalogue B which are inside the cone of aperture having for apex (also called vertex) the center of the ICRS frame and for axis the direction of the catalogue A source in the ICRS frame.
This cross-match is a cross-match based on the positional uncertainties of both catalogue A and catalogue B sources. The selection of the candidates is the same as described in section 3.1.1 of Pineau et al. (2011b).
Sigma correspond to in eq. 3 of Pineau et al. (2011b).
Max. distance is a safeguard preventing from correlating sources having a too high angular separation.
To look for candidates, we first estimate the maximum of the semi-major axis of errors on the positions of catalogue B sources by a boxplot: where and are the lower and upper quartiles respectively.
For each source of the catalogue A, the search radius we use to look for catalogue B source candidates is the minimum between (in which is the semi-major axis of the error on the source of the catalogue A), and the watchdog Max. distance. We then keep only candidates satisfying eq. 3 of Pineau et al. (2011b).
USNO-B1.0: a systematic error of 0.2 arcsec is quadratically added to positional errors on both e_RAJ2000 and e_DEJ2000
Sources having for positional error a NULL (or a NaN) value are ignored.
Because of the use of a boxplot on positional errors to avoid outliers, the result of the cross-match of 2 catalogues is not necessarily symmetric: the number of associations between A and B can be different from the number of associations between B and A.