How can we make sure that it is physically the same source when we do cross matching?

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:

1. Does the phenomenon often occur when we are doing cross matching?
2. In specific, how can we use the redshift features in cross matching programs?
3. Do we have any other way (some special statistics techniques, for example) to solve the problem?

Thanks!

• I think you should narrow your question down. Of course if you cross-match using only coordinates then there can be spurious correlations, since all positions have uncertainties or correspond to sources where the flux has been gathered from a finite positional area. How you resolve (if you can) this problem just depends on exactly what science you are trying to do. Q2 isn't going to be relevant in many (most) cases unless you have a specific application you want to ask about? Dec 21, 2022 at 9:30