XMM-Newton Science Analysis System
catcorr (catcorr-0.11.1) [xmmsas_20190531_1155-18.0.0]
If
is the great-circle distance between an X-ray detection (i) and
an optical or infra-red source (j), and
is the associated
error, then the probability of match
is given as:
![\begin{displaymath}
p_{ij} = \exp{ -0.5 (\frac{r_{ij}}{\sigma_{ij}} )^2 }
\end{displaymath}](img4.png) |
(1) |
while the probability of a coincidence with a optical/infra-red object within
a radius
when there are
optical/infra-red objects in the field
of view of radius
is given by:
![\begin{displaymath}
q_{ij} = n_{o} (\frac{r_{ij}}{r_{f}})^2
\end{displaymath}](img7.png) |
(2) |
The net probability is the difference of these, subject to being above zero.
Thus the overall goodness-of-fit is computed as:
![\begin{displaymath}
L = \sum_{i=1}^{n_x} \sum_{j=1}^{n_o} max(0.0, p_{ij} - q_{ij})
\end{displaymath}](img8.png) |
(3) |
Note that there are three components in
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
.
XMM-Newton SOC/SSC -- 2019-06-02