XMM-Newton Science Analysis System


catcorr (catcorr-0.11.2) [xmmsas_20230412_1735-21.0.0]

Statistical method

If $r_{ij}$ is the great-circle distance between an X-ray detection (i) and an optical or infra-red source (j), and $\sigma_{ij}$ is the associated error, then the probability of match $P_{ij}$ is given as:

  $$p_{ij} = \exp{ -0.5 (\frac{r_{ij}}{\sigma_{ij}} )^2 }$$ (1)

while the probability of a coincidence with a optical/infra-red object within a radius $r_{ij}$ when there are $n_{o}$ optical/infra-red objects in the field of view of radius $r_{f}$ is given by:

  $$q_{ij} = n_{o} (\frac{r_{ij}}{r_{f}})^2$$ (2)

The net probability is the difference of these, subject to being above zero. Thus the overall goodness-of-fit is computed as:

  $$L = \sum_{i=1}^{n_x} \sum_{j=1}^{n_o} max(0.0, p_{ij} - q_{ij})$$ (3)

Note that there are three components in $\sigma_{ij}$ which are summed in quadrature:

• The estimated X-ray positional error in the OBSMLI file which is given in the column RADEC_ERR,
• The corresponding positional error in the reference catalogue,
• An additional systematic error determined to be 0.35 arc-seconds.

The procedure maximises L over all possible matching pairs as the frame shifts and rotations are applied.

The parameter minfit determines the minimum value of L for which the fit is accepted. It defaults to 10.0. Extensive trials have shown that a useful positional correction can be obtained if the goodness-of-fit $L\geq 5$.