When we go through multiple astronomy catalogs, we often do Cross-matching. We compare the position parameters $(\alpha, \delta)$ of different sources (galaxies, quasars, etc.) in the equatorial coordinate, where $\alpha$ is the right ascension and $\delta$ is the declination.
However, it is possible that two completely different sources are on almost the same position. We might make make mistakes if: $$ \alpha_1 \approx \alpha_2,\ \delta_1 \approx \delta_2 $$ The question here How can we be sure that we have identified very distant stars correctly? pointed out the redshift features could be very important in this problem.
My question is:
- Does the phenomenon often occur when we are doing cross matching?
- In specific, how can we use the redshift features in cross matching programs?
- Do we have any other way (some special statistics techniques, for example) to solve the problem?