Multiple matches

This section describes how multiple matches are handled by catpair. Multiple matches can arise because the pairing techniques are matching objects with similar rather than identical positions and an object in one catalogue can pair with several in the other catalogue. The terminology used in this section is:

match

a match is any object which lies within the critical distance, $D$, for an object in the other catalogue,

pair

a pair is any object chosen from amongst the set of matches to correspond to an object in the other catalogue.

That is, any match is potentially a pair and the pairing algorithm must prescribe which matches are considered pairs. There are three cases for multiple matches:

1. a single object in the primary matches several objects in the secondary (see Figure ),

2. a single object in the secondary is matched by several objects in the primary (see Figure ),

3. in crowded catalogues more complicated situations can arise, as illustrated in Figure . The results of pairing such catalogues are, in general, unpredictable.

catpair is unsuitable for handling the third case, and should not be used with catalogues where it is likely to be important. There are, however, several options for handling the first two cases:

1. only accept the closest of the matches as the pair,

2. accept all the matches as pairs,

3. use further information from the catalogues (such as magnitude or colour) to disambiguate a single pair from amongst the matches.

The third option is not practical in a general purpose program such as catpair because it relies on astronomical knowledge about the catalogues being paired. Either of the first two options may be appropriate, depending on the details of the pairing being performed. catpair provides both options separately for multiple matches in the primary and secondary, and you should choose the alternatives appropriate for your work.

Figure: A single primary object matches several secondary objects

Figure: A single secondary object is matched by several primary objects

Figure: A crowded field with multiple matches of both primary and secondary objects

An example might help to illustrate the difference between multiple matches in the primary and secondary. Suppose the primary was a private list of target objects and the secondary was the NGC catalogue. Table  shows the equatorial coordinates for the triplet of galaxies NGC 3623, NGC 3627 and NGC 3628¹². Consider the following two cases.

• If a target object in the primary had coordinates $11^{\rm h}\,19\mbox{$^{\rm m}\!\!.$}5$, $+13^{\circ}\,20\raisebox{-0.5ex}{$^{'}$}$ with an error circle of 30$^{'}$ then all three galaxies would be matches. This case is an example of multiple matches in the secondary.

• Conversely, if there were two target objects with coordinates of $11^{\rm h}\,18\mbox{$^{\rm m}\!\!.$}8$, $+13^{\circ}\,01\raisebox{-0.5ex}{$^{'}$}$ and $11^{\rm h}\,18\mbox{$^{\rm m}\!\!.$}9$, $+13^{\circ}\,07\raisebox{-0.5ex}{$^{'}$}$ and both with an error circle of 10$^{'}$ then they would both match NGC 3623 and neither would match the other members of the triplet. This case is an example of multiple matches in the primary.

Table: Coordinates for a triplet of galaxies

NGC		$\alpha$			$\delta$
		h	m		$^{\circ}$	$^{'}$
3623		11	18.9		+13	05
3627		11	20.2		+12	59
3628		11	20.3		+13	36