# Cross-matched Catalogues

## X-Matched Catalogues

Each of the archival catalogues used for the crossmatch is referenced by single letter: *3XMM: x, Galex: g, UCAC:u CMC: c, SDSS: s, UKIDSS LAS: l, KIDS GPS: k ALLWISE; w AKARI: a* and

*FIRST_NVSS_COMBO:*

**r**The cross-matched consist of reference catalogues which contains for each entry of the enhanced 3XMM catalogue the best multi-wavelength source identifications extracted from selected archival catalogues.

The first table is the result of the cross-correlation of the 3XMMe (A) catalogue version 1.2 with GALEX DR5 , UCAC4 , 2MASS , AllWISE, the merge of SUMSS and NVSS and the AKARI FIS catalogues.

Probabilities of associations are computed for all possible sets of candidates in GALEX DR5, UCAC4, 2MASS and AllWISE. Candidates from SUMSS, NVSS and AKARI FIS are selected based on a chi-square criteria.

The second table is similar to the first one but the the UCAC4 is replaced by the SDSS DR9.

Each row of the table contains one set of candidates and all probabilities associated with each possible partition of this set. Each possible partition corresponds to one Bayesian hypothesis. For example, if a given XMM source has two candidates, one in catalogue B and one in C, the possible partitions of this 3 elements set are:

- ABC: A associated with B and C
- AB_C: A associated with B but not with C
- AC_B: A associated with C but not with B
- A_BC: A as no counterpart but B and C are associated
- A_B_C: None of the 3 sources are associated

The number of possible partitions for a set containing n elements is given by the BELL number B(n).

- b(2) = 2
- b(3) = 5 (the example above)
- b(4) = 15
- b(5) = 52

The number of possible subsets of catalogues C(n,m) in which there are candidates depends on the presence or not of a candidate in each catalogue. We consider XMM and four other catalogues (m=4), and we call n the number of candidates in a subset. Then C(n,4) is given by the binomial coefficients as follow:

- C(1,4) = 4
- C(2,4) = 6
- C(3,4) = 4
- C(4,4) = 1

So the number of different probabilities for all possible sets of candidates is given by:

- np = sum over n from 1 to 4 of C(n, 4) B(n+1) = 150

The tables contain all computed probabilities for all subsets of candidates selected by our chi-square criterion. In many cases (20-25%) the highest probability is found for the following hypothesis: « none of the candidates is a real counterpart, i.e. all matches are spurious ». It is interesting to keep those sets at this stage to test the validity of the cross-correlation process.

##### All sky Products

- Allsky file with all probabilities [download]
- Allsky file with a limited subset of probabilities [download]

##### LAS Products

This products contain the following set of catalogues: 3XMMe - Galex GR6/7 - SDSS DR9 - UCAC4 - UKIDSS DR10 LAS - AllWISE (+ MINGO (FIRST-NVSS combined) - AKARI FIS).

This set of catalogues is the same as the Allsky products one except that 2MASS is replaced by UKIDSS LAS. This products thus contains only XMM FOVs covered by UKIDSS LAS.