Cases for the critical distance

The following three cases for the value of the critical distance, $D$, are supported by catpair.

1. It is a constant, for example twenty-three minutes of arc. Any objects in the catalogues correspond if their positions differ by twenty-three minutes of arc or less. Of the various cases this is the simplest.

2. It adopts the value of a column in the primary. Typically such a column would be an error associated with the position; objects with a small error would only pair with a nearby object, but objects with a large error would pair with objects further away.

3. It adopts a value computed from an expression involving columns in the primary. This case is a generalisation of the preceding one.

A fourth case in which the critical distance is computed from an expression involving columns in both catalogues is not supported in catpair. A special instance of this case which sometimes arises is where both input catalogues have errors in their coordinates which vary with the objects in the catalogues and thus are stored as columns, one in each catalogue. Objects are considered to pair when their error circles overlap. Here the expression for the critical distance, $D$, would involve columns (containing the errors) from both catalogues and hence this case is not supported.