Conclusions

The comparison of the properties of the XMM-LSS and SpARCS distant cluster samples has revealed a number of physical differences between the two cluster samples.

6.4 Wavelength bias in distant galaxy cluster samples: A case study using the XMM-LSS and SpARCS cluster samples

Figure 6.8:The cumulative angular X-ray surface brightness distribution of each cluster sub-sample: XMM-LSS (blue), X-ray-bright SpARCS (green), X-ray-faint+MIR-faint SpARCS (red), X-ray-faint+MIR-bright (black). For the SpARCS sub-samples solid coloured lines indicate the measurements applying the BCG position of each cluster whereas dashed lines indicate barycentre positions. The cyan line indicates the average cumulative surface brightness distribution computed from 100 randomly placed apertures. The upper panel shows all cluster sub- samples, the lower panel presents a zoomed view of the low surface brightness sub-samples.

massive cluster population. This is primarily evident from the comparison of the MIR surface brightness distribution of the XMM-LSS and X-ray-bright SpARCS clusters. This result can be understood in terms of X-ray selection in the following manner. X-ray selection of extended sources is biased to those of higher surface brightness which, in turn, is proportional to the square of the projected electron density in galaxy clusters. At fixed cluster mass, a relaxed cluster will display a more concentrated mass distribution than a cluster which is more dynamically disturbed. This statement applies equally to the gas of the intra cluster medium (ICM) which loses energy via collisional cooling as to the bright (i.e. massive) galaxy distribution which loses energy via dynamical friction with the fainter (less massive) galaxies within each cluster3_.

A second conclusion regarding X-ray selection is that it identifies clusters equivalent in mass yet pos- sessing a wider range of optical-MIR properties than identified by optical-MIR searches alone. Evidence for this statement is drawn from the comparison of the red sequence properties of the XMM-LSS and X-ray bright SpARCS samples (Figure 7 of Willis et al. in preparation). At comparable X-ray bright- ness (and therefore approximately comparable mass) the X-ray selected clusters display a lower average red sequence normalisation compared to X-ray bright optical-MIR red sequence selected clusters. X-ray selection therefore identifies clusters displaying a broader range of star formation histories than methods which rely upon the presence of the red sequence – a conclusion previously noted by Donahue et al. (2002).

A third conclusion is that colour-overdensity searches, such as SpARCS, identify a broader range of

3_{Note that these considerations ignore two secondary physical considerations: at fixed mass a relaxed cluster will display}

a marginally lower X-ray temperature than a disturbed cluster - with a consequently slightly lower surface brightness as a result (however, the changes in the square of the gas density dominate). Secondly, if clusters are indeed described by the distribution of collisionless cold dark matter, then one should also compare the properties at fixed mass and collapse epoch.

cluster dynamical states (at fixed mass) than X-ray selected samples. This statement is not simply the converse of the first conclusion as it also concerns the nature of the X-ray-faint+MIR-bright sub- sample of SpARCS clusters. The lack of detectable X-ray emission in the stacked image of the X- ray-faint+MIR-bright clusters provides a strong indication that the majority of these systems are not collapsed structures in virial equilibrium.

Two possibilities present themselves: firstly these systems could be projected large-scale structures along the line-of-sight which mimic the signal associated with bona-fide clusters in the Spitzer-adapted red sequence cluster finding method. The evidence for this conclusion is the similarity between the projected MIR surface brightness in such systems and the distribution measured for the stacked random apertures. However, the average red sequence for the X-ray-faint+MIR-bright SpARCS clusters is marginally different from the random line-of-sight distribution. Whether this is a bias associated with the application of the red sequence criterion to line-of-sight large-scale structure variations is not clear. A second possibility is that X-ray-faint+MIR-bright clusters represent gravitationally bound, collapsing structures which have not yet reached virial equilibrium. Although this explanation is consistent with the majority of the measurements of these systems, it does rely on fortuitous timing in the sense that the majority of these systems must be being observed early in the collapse phase, i.e. before the formation of a virialised core which might be detected via weak X-ray emission or central galaxy concentration.

6.5 Summary and outlook

The Poisson nature of the X-ray data demands a careful treatment and the development of sophisticated tools to extract useful information from it. In this regard, Bayesian statistics plays an important role in the low-counts regime, where the Gaussian statistics is not longer valid. This chapter presents two techniques to analyse faint X-ray sources: a Bayesian aperture photometry method and a source stacking procedure.

The Bayesian aperture photometry method basically computes values and confidence regions of the source intensity (count-rates, flux, luminosity) by using counts and exposure data obtained in source and background apertures. The approach consists in calculating the background marginalized posterior probability distribution function of the source counts assuming Poisson likelihoods for the source and background components. The mode of this distribution is determined, and the lower and upper bounds of the confidence region are calculated by summing values of the distribution alternately above and below the mode until the desired confidence level is reached. This approach works fine in the low- counts regime, where the classical aperture photometry method fails and reproduces the results of the classical approach in the high-counts regime, where the Gaussian statistics works appropriately. In principle, this method can be used by any imaged X-ray data from any instrument, but in this work it is shown its application to XMM-Newton data. Since this X-ray telescope has two different types of CCD cameras, the source posterior probability distributions of each CCD are corrected by the different camera sensitivities, and the final source aperture photometry is obtained from the multiplication of the three corrected distributions.

The stacking technique creates stacked X-ray images of a given source population. In this way, the average X-ray emission properties of a given sample can be investigated, especially if the sources of interest are X-ray faint. The stacking technique is particularly complex to implement on XMM-Newton

6.5 Summary and outlook

data since one has to combine data from two different types of CCD cameras and the XMM-Newton PSF and background varies considerably across the field-of-view.

In this regard, a novel stacking technique has been developed. Basically, the stacking procedure adds together cut-outs of source images and their corresponding exposure maps. It also creates corresponding background maps, which are carefully modelled. The final count-rate image is obtained by subtracting the stacked background map from the stacked photon image and dividing by the stacked exposure map. Moreover, this technique has been optimized to stack objects in physical radius, i.e. in the rest frame of each cluster.

The two techniques have been used in the study of wavelength bias in high-redshift galaxy cluster samples. The goals of this research are to consistently study different wavelength-selected cluster samples and to provide evidence of the astrophysics that influences the cluster observed waveband- dependent properties. For this research, z > 0.8 mid-infrared (MIR) and X-ray selected galaxy cluster samples have been used. Then, the Bayesian aperture photometry method and the source stacking pro- cedure are used in the study of the MIR-selected clusters in X-rays.

The X-ray (18 systems) and MIR (95 systems) selected galaxy clusters were taken from a common area (∼ 9 deg2_{) between the XMM-Newton Large Scale Structure Survey (XMM-LSS, ∼ 11 deg}2_{) and the} Spitzer Adaptation of the Red Sequence Cluster Survey (SpARCS), respectively. Only 33% of the X-ray selected clusters can be related to one of the MIR selected clusters. The comparison of the properties of both distant cluster samples reveals a number of physical differences:

• X-ray surveys identify a dynamically relaxed subset of the massive cluster population at high red-

shift, where the intra-cluster gas has settled and started to emit in X-ray. This is confirmed by the compact MIR surface brightness of such clusters, meaning that these systems have a concentrated mass distribution.

• In contrast to the above, MIR surveys identify clusters exhibiting a broader range of dynamical

states and, therefore, offer a useful complement to X-ray studies. However, our comparisons also identify a population of low X-ray emission MIR clusters (e.g. some bright MIR systems have a lack of X-ray emission) which may well represent non-virialised large-scale structure.

This successful pilot study indicates that multi-wavelength studies of galaxy cluster populations are an effective method of revealing physical bias in such samples.