10 Statistics of the X-ray properties of the cluster sources and the sample contamination

The GCA X-ray source analysis returns two source quality parameters, the spectral hardness ratio and the source extent. These two parameters are not used for the selection of the candidate sample. We have only used this information in conjunction with optical data as a justification to remove a number of obviously contaminating sources. Therefore the distribution of these source properties gives a practically independent information on the nature of the REFLEX cluster sample and it is interesting to study them in comparison to the properties of the non-cluster sources. (The results for the spectral hardness ratios are used here in comparison to the expected values that can be well calculated for cluster type spectra (5 keV) and given interstellar HI column density in the light of sight. The parameter quoted is the difference between the measurement and the prediction in units of $\sigma$ of the measurement uncertainty). In Fig. 27 we show the distribution of the two X-ray parameters for the 452 REFLEX clusters. The figure also shows the boundaries used for the decision as dotted lines: a source is considered to be very likely extended if it has a Kolmogorov-Smirnov probability of less than 0.01 ( $-\log P = 2$); and a deviation from the expected hardness ratio of more than 3$\sigma$ (to the soft side) is considered as an argument against a cluster identification. Based on these cuts we find that 81% of the REFLEX clusters feature an X-ray source extent. (This sample fraction of course depends on the threshold value used in the KS-test. For a less stringent threshold value of 0.05 for the probability of a source to be point-like we could characterize more than 90% of the sources as extended. The merits of relaxing the threshold condition are currently tested with Monto Carlo simulations and will be described in a following paper.) How the non-extended sources and their fraction as compared to the REFLEX total are distributed in redshift is shown in Fig. 26. While among nearby objects only for a very small number of groups no significant extent was found, the extent fraction is increasing clearly with redshift. At high redshifts, where only the most luminous clusters are found, still more than half of the clusters feature a measurable extent. Only 6% of all the sources have an observed spectral parameter which appears too soft (Fig. 27). This is a small failure rate which is partly due to statistical fluctuations, possibily due to an inaccurate acount of the interstellar absorption for some of the sources, and also partly due to the contamination of an AGN in the cluster for some of these few sources. But since the overall deviation is only significant for 6% of the sources the contamination by AGN which might be indicated here is not a problem for the statistical use of the overall sample.

Figure 26: Redshift distribution of the non-extended X-ray cluster sources in the REFLEX sample (solid line). The fraction of non-extended sources compared to the total REFLEX sample for each redshift bin is shown as dashed line (in units of percent)

It is interesting to compare these source parameters with those for non-cluster sources. In Fig. 28 we show the distribution of the hardness ratio deviations and the source extent probabilities for the sample of 221 cluster candidates flagged by the galaxy counts but excluded from the sample in the subsequent identification process. (Note that this sample has some bias in comparison to a random non-cluster sample since e.g. (i) in some cases the optical selection may be due an extended object falsely split up into galaxies (ii) contaminating sources may be preferentially recognized if they have a soft spectrum). There is a large fraction of much softer sources. About 13% percent feature an apparent extent, however (after a few spurious sources located at exposure edges were removed). This is more than the failure rate typically found in the analysis of a test sample of already identified AGN which are known point sources and the statistics of the falsely flagged extended sources shown in Sect. 8 (<6%). The higher rate of detection of extended sources among these non-cluster sources as compared to the false classification rate found in Sect. 8 is partly due to really extended X-ray emission from nearby galaxies and due to close, blended double sources. The latter two source types are easily recognized by inspection and therefore the actual false classification rate of point sources as extended including the inspection is at most about half of these 13%.

Figure 27: Hardness ratio deviation and extent probability distribution of the REFLEX clusters. The vertical axis gives the deviation of the measured hardness ratio from the theoretically calculated value in units of the standard deviation. For the detailed definition of the parameters and the threshold values see the text

Figure 28: Hardness ratio deviation and extent probability distribution of stars and AGN excluded from the REFLEX sample clusters

We can use the difference in the spectral hardness ratio distribution of the two samples of cluster and non-cluster sources to test for the possible contamination of the REFLEX cluster sample by AGN which are producing the dominant X-ray emission in a cluster. First of all the high fraction of extended sources guarantees that the emission of most of these 81% of the X-ray sources is extended emission from the intracluster medium of a cluster. The question is more critical for the non-extended sources. One way of checking the AGN contamination among them is to make a statistical comparison between the spectral parameters of the extended and non-extended cluster sources in REFLEX. This is done in the form of histograms for the deviation of the measured and expected hardness ratio for the two REFLEX subsamples in Fig. 29. We note that the two distributions are very similar, quite in contrast to the very different distribution of the non-cluster sources shown in the same figure. Thus there is no indication that the point-like REFLEX clusters are spectrally significantly different from the extended ones.

This can be more critically tested with cumulative and normalized plots of these same distributions as shown in Fig. 30. Here we note again the similarity of the distributions for the two REFLEX subsamples. They have the same median and the only difference is a slightly broader distribution for the extended cluster sources. We noted this behaviour already for the NORAS cluster sample (Böhringer 2000) and it is most probably due to the fact that the extended sources contain many more photons on average and therefore systematic deviations play an increasing role compared to the pure photon statistics which is the only aspect included in the error calculation. The non-cluster sources labeled c have a completely different distribution. To test the sensitivity of this comparison we have artificially contaminated the point-like X-ray source cluster sample by 20 randomly selected non-cluster sources. The resulting distribution function is labeled with an asterisk in Fig. 30. This sample is significantly different from the cluster distribution and such a deviation would easily be recognized. Thus the contamination in the total sample as introduced by the false identification of non-extended REFLEX sources is less than 4%. To this we have to add the possible contamination in the sample of extended sources which could in principle be due to non-cluster sources falsely flagged as extended. Making the following very extreme assumptions: (i) there are as many non-cluster sources as cluster sources in the candidate sample, (ii) the false classification rate is as high as 6% as found in Sect. 8, (iii) all these falsely classified objects have escaped our careful inspection in the sample cleaning process, we find an upper limit for the possible contamination of this part of the sample of less than 5%. Therefore the overall contamination cannot be larger than 9% and is probably much less.

Figure 29: Distribution of the significance of the deviation of the measured from the expected hardness ratio: extended REFLEX clusters (thin line), REFLEX clusters with no significant extent (thick line), non-cluster sources excluded from the REFLEX sample (dashed line). The plot shows that the extended and non-extended REFLEX clusters do belong to the same spectral class of X-ray sources. Note that the amplitudes of the extended cluster source and non-cluster source histograms have been scale down by a factor of 2 for better comparison with the smaller cluster point source sample

Figure 30: Cumulative distribution of the significance of the deviation of the measured from the expected hardness ratio: extended REFLEX clusters (dashed line, b), REFLEX clusters with no significant extent (thick line, a), non-cluster sources excluded from the REFLEX sample (c), non-extended REFLEX clusters artificially contaminated by 20 non-cluster sources (*)