cosmic value measured by WMAP, while the f 500 stars+gas+depl+ICL found for an average group differs from it at more than 3σ. Given the heterogeneity of the sample (see e.g. Figure 16b), for some objects the gap between f 500 stars+gas+depl+ICL and the WMAP5 value could be negligible or, conversely, statistically more significant for objects in the same bin of total mass, but at the two extremes of the distribution in f stars 500 . Unfortunately we do not have a measure of the gas mass fraction for individual objects, therefore we focus on the behaviour of the average object. We did likewise for the ICL by assuming a fixed fractional contribution of 11–22% across the entire mass range. Possible systematic effects introduced by our definition and estimate of the ICL contribution are discussed in § 2.4.5. Here we stress that they do not lead to an anomalously low BCG+ICL contribution to the total mass of the system. Thus the discrepancy at the groups regime in not erased by uncertainties on the stellar mass fraction. In the absence of evidence for a systematic and relevant underestimation of the gas mass fraction in our systems (see § 2.4.5), we interpret the discrepancy as a lack of gas, by 33%, at the group regime. This may be produced by feedback (stellar and/or AGN), as suggested by high-resolution cosmological simulations including cooling, star formation, supernova feedback, and AGN radio–mode feedback in galaxy clusters and groups (Puchwein et al. 2008, Bower et al. 2008, Short & Thomas 2008). Since supernova feedback appears to be insufficient to explain the L X –T relation (Puchwein
Galaxy clusters are the signature of the primordial density fluctuations that have grown via hierarchical accretion since the epoch of recombination. Because their abundance at different epochs is extremely sensitive to the matter content and accel- eration of the universe, clusters are sensitive probes for testing different cosmological models. In addition, they are cosmiclaboratories in which complex processes that shape galaxyevolution can be studied in great detail. Nowadays many efforts are invested into the observational challenge of providing sizable samples of galaxy clus- ters at high redshift (z > 0.8) to trace the evolution of the cluster population and its matter components back to the first half of the universe lifetime, corresponding to lookback times of 7 − 10 Gyr. Many surveys have been designed to efficiently detect distant clusters by means of their red galaxy population (e.g., SpARCS, Wilson et al. 2006), their Sunyaev − Zel’dovich (SZ) effect signature (e.g., SPT, Williamson et al. (2011); ACT, Menanteau et al. (2010)) or the diffuse X-ray emission originating from the hot intracluster medium. The last approach, in particular, has proved very pow- erful to the above aim as shown e.g. by the XMM -Newton Distant Cluster Project (XDCP, B¨ohringer et al. 2005; Fassbender et al. 2011a). This is a serendipitous X-ray survey specifically designed for finding and studying distant X-ray luminous galaxy clusters at z ≥ 0.8 and it has compiled the largest sample of such systems to date. For a comprehensive overview of the survey and an extensive discussion on its strategy and results we refer the reader to Fassbender et al. (2011a).
This Thesis addresses the topic of galaxy formation and evolution in the universe. In collaboration with D. Croton, G. de Lucia, V. Springel, and S.D.M. White, I made use of the Millennium simulation, a very large N-body simulation of dark- matter evolution in a cosmological volume carried out at the MPA in 2005 by Springel et al. (2005), to explore the predictions made by the most recent generation of semi- analytic models for galaxy formation. These models are incorporating a new mode of feedback from active galactic nuclei (AGN), which have their origins in super- massive black holes accreting mass and turning it into energy. Because of its ob- servational signature in the radio regime this feedback is called “radio mode” and it counteracts the cooling flows of cold gas in undisturbed dark-matter haloes hosting galaxy clusters, which would otherwise show much higher star-formation of their central object than is observed. Previous work by Croton et al. (2006) and De Lucia & Blaizot (2007) has shown that with the new semi-analytic model the population of local galaxies can be reproduced quite accurately. In order to study the evolution of the population out to higher redshifts, the semi-analytic predictions have been com- pared to a number of observations in various filter bands, in particular to two recent efforts to get a comprehensive multi-wavelength dataset of high redshift galaxies car- ried out by the DEEP2 (Davis et al. 2001) and COSMOS (Scoville et al. 2006) col- laborations. The approach taken was to perform as broad a comparison as possible to gain firm constraints on the assumed physics in our model. Therefore a multi- tude of observational properties was contrasted with the model predictions such as clustering, luminosity functions, stellar mass functions, number counts per area and redshift to a certain magnitude limit. In order to facilitate the comparison between simulations and recent intermediate and high-redshift surveys, it is very useful to have a number of independent mock observations of the simulated galaxies, which provide good enough statistics to get a handle on cosmic variance. To this end I have devised a computer program that calculates the simulated galaxies lying on the backward light cone of a hypothetical observer out to arbitrarily high redshifts, tak- ing advantage of the periodicity of the simulation box but avoiding replications. The output provides accurately interpolated redshifts, positions, observer frame and rest- frame magnitudes, dust extinction, as well as all the intrinsic galaxy properties like stellar mass and star formation rate. Utilising this tool it is also possible to make predictions for future galaxy surveys, deeper in magnitude and redshift than current
Another important source of uncertainty is the cell-to-cell variance due to large-scale structure (Hu & Kravtsov 2003; Lima & Hu 2004), usually called sample variance (or cosmic variance). In fact, observational estimates of number densities of a clus- tered population in finite volumes are subject to uncertainties which exceed the Poisson noise, arising from the underlying large-scale density fluctuations. If the typical clustering scale of the observed objects is much smaller than the sample vol- ume, then cosmic variance is negligible. On the contrary, if the observed volumes are smaller than the clustering scale, one might count more or less objects with respect to the average number: in this case, cosmic variance becomes dominant and should be taken into account. For example, cosmic variance is relevant for deep galaxies surveys, because galaxies at high redshifts are more strongly clustered than dark matter compared to the local Universe (Kauffmann et al. 1999b). To check if a sur- vey is independent of cosmic variance and accurately samples the Universe, one can compare the variation between the number counts for samples of different angular sizes which mimic different survey fields. In the case of strong cosmic variance, the number counts depend on where the samples are located in the sky and differ signif- icantly for each region. If instead the counts agree while approaching the total size of the survey, the cosmic variance can be neglected. For clusters, we can recast the counts of Eq. (3.3) as
tained for the SEGUE Stellar Parameter Pipeline (Lee et al. 2008a), which reports results from a number of different methods. The results from MAχ agree well with those of the various pipelines, and any differences are consistent with those between the various ac- cepted approaches. We are aware of the MATISSE (Recio-Blanco et al. 2006) method of parameter estimation, which uses a different combination of weighting data but is closer to the MAχ approach than the standard pipeline methods. We look forward to comparing our results with those of MATISSE when they become available. More specifically, tem- perature agrees excellently with the averaged temperature of SSPP, with a negligible offset of -61 K and low scatter of 112 K. Our metallicities show a tendency to be -0.32 dex lower than SSPP averages. The small scatter of 0.23 dex suggests that the different spectral features used in the analysis (mainly Ca II lines) could shift the zero point of the metallic- ity. In any case this offset should not be matter of concern, since recently Carollo et al. (2010) has commented on a probable conservative assignment by 0.2- 0.3 dex of [Fe/H] by the SSPP for stars with low metallicities. The most pronounced discrepancy is found in surface gravity, where MAχ reports values 0.51 dex (σ = 0.39) higher than the averaged value of the pipeline. We saw that this is consistent with the discrepancies seen between other methods.
In order to determine redshifts, I adapted the ZSPEC software, originally developed by Renbin Yan and used by the DEEP2 redshift survey (Davis et al., 2003, 2007), for use with our FORS2 MXU data. In ZSPEC, an Interactive Data Language (IDL) based tool, spectra are first cross- correlated to eigen-templates (stellar, galaxy, and QSO templates) and the ten best-fitted redshifts and χ 2 are provided. The spectra (both 2D and 1D) and their redshift fits were then visually examined in order to confirm or determine the correct redshift. Usually the first or second best χ 2 fit provided is a good fit. Instances where artifacts from sky line subtraction confuse the fitting, the signal-to-noise of the spectrum is relatively low, only a single emission line is detected, the spectrum is relatively featureless, or a bad pixel column exists, often result in the first or second-ranked fits being incorrect. In these cases, the appropriate solution often appears in a fit with a higher χ 2 . When none of the ten choices was a good match, any spectral features easily identified by eye were used to identify a probable redshift, which could be confirmed by manual cross-correlation. Fig. 4.5 shows an example of the ZSPEC redshift evaluation.
We model all seven galaxies with five lines of sight each with our fiducial mod- elling setup. Generally, the asymmetric kinematics along the major axis as dis- cussed above hamper successfull modelling with dysmal because the code as- sumes axisymmetric mass distributions. One case with relatively symmetric one- dimensional kinematics is shown in Figure 4.19 (black points with errors) for galaxy #5, sightline 1, together with our best fit (red diamonds) as constrained through the medians of the posterior probability distributions from the MCMC chains (Figure 4.20). In Figure 4.20, best-fit parameters are indicated by the blue squares and vertical lines, while the true values are indicated by green stars and vertical dash-dotted lines or regions. In the bottom row we also show the cor- responding histograms for the inferred dark matter fraction within the effective radius. We recover the central dark matter fraction f DM (R e ) within one standard
for the lower mass cut we used, therefore we can relate the two distributions). Unlike for the blue galaxies, the population mix of green galaxies shows a slight dependence on environment: the fraction of galaxies with a post-starburst signature (PC2>0) and emission lines is smaller in the cluster, whereas the fraction of galaxies with PC2<0, and no emission lines is larger in the cluster. It is not easy to connect these two classes with a single evolutionary model, and any attempt would be quite contrived. Possibly, there are two processes involved: the low– density field and poor groups environment may be more efficient at triggering post-starbursts e.g. by an increased merger rate. On the other hand, we have argued that star formation in the cluster is not shut off immediately, i.e. without inducing post-starburst signatures. Galaxies with an exponentially declining star formation rate would move to the green valley, and at the same time, the star formation activity would decline and fall below the threshold. The majority of green galaxies have emission lines, although the fraction is lower than for blue galaxies. In the local sample, we found that & 50% of green galaxies host an optical AGN. This might be the case also for the EDisCS galaxies, although we lack other emission lines to fully classify them into star-forming / AGN. But very few galaxies in our sample have a post- starburst signature, and no emission lines, which would correspond to the classical ‘E+A’ classification. Our data do not support previous claims that post-starbursts are associated with the cluster environment.
Understanding this low luminosity radio source population, and its cosmic evolu- tion, is not only important for understanding the physical origin of the radio activity, but also for understanding galaxyevolution. There is growing evidence that low- luminosity radio-loud AGN play a critical role in regulating the masses and star formation rates of galaxies. Semi-analytic models of galaxy formation (for exam- ple see White and Frenk 1991 and Cole et al. 2000) successfully reproduce many of the the observed properties of galaxies. However, these models over-predict the abundance of galaxies at the bright end of the luminosity function. This problem arises because many massive galaxies are predicted to sit at the center of hot hy- drostatic halos, in which cooling flows are expected to develop. If the gas cools and forms stars, central group and cluster galaxies are too massive by the present day and have much bluer colors than observed. Tabor and Binney  first suggested that radio galaxies could in principle regulate these cooling flows, preventing sig- nificant accretion of gas and limiting the mass of galaxies. This concept of AGN feedback has now been successfully incorporated into the semi-analytic models of Bower et al.  and Croton et al. .
Investigations into the structure of the model yielded a surprise for Galactic kinematics. At least since the work of Delhaye (1965) it was common knowledge that the Local Standard of Rest (LSR) could be determined via the Str¨omberg equation, or in other name asymmetric drift relation that states a linear relationship between the asymmetric drift (i.e. the velocity difference between the circular speed of the Galaxy and the azimuthal velocity component of a population in question) and its squared velocity dispersion. Intuitively this relationship is clear as a lack of angular momentum and hence kinetic energy in the azimuthal velocity component can be made up by random energy in the other components, formally it can be directly derived from the Jeans equations. Dissecting a sample into kinematically hot and cool objects, this linear relationship can in principle be measured and by extrapolation to zero asymmetric drift the LSR and the solar azimuthal velocity against this circular speed can be recovered. Until now an important aspect of the asymmetric drift relation has been overlooked throughout the history of its use: The relation contains the radial density gradient of a population. The gradient is remarkably stable for populations of different ages, but if we select a sample by metallicity, we select for inner and outer disc stars respectively. For moderately metal poor objects born in the outer disc, this gradient will even reverse leading in extreme cases up to a sign change in the asymmetric drift relation. And indeed the classic selection of stars involves metallicity: Having no other parameters at hand, stars were selected by their colour. This strategy uses the fact that blue stars have higher stellar masses, which makes them die young and hence the average age of a population of main sequence stars increases from blue to red until the red-most turn-off point that is set by the oldest stellar populations of our Galaxies, also called Parenago’s discontinuity (Parenago, 1950), from where the dispersion should remain constant. However, as higher metallicity implies redder colours for stars of the same mass, the colour selection leads to metal-poor stars being preferentially in the young bins and metal-rich stars on the old, red side. This distorts the expected linear relationship and thus an unphysical linear relationship is faked on the red side. This novel view explains also the large systematic aberration observed for young stars from the slope defined by the linear relation and led to a correction of the standard value for the solar azimuthal velocity from (5.25 ± 0.54) km s − 1 to now (12.24 ± 0.47) km s − 1 with an assumed systematic uncertainty of 2 km s − 1 . Some observational data are presented that confirm the predictions made in this paper.
For all DM haloes identified by the FOF group finder, gravitationally bound substruc- ture haloes are identified with subfind (Springel et al. 2001a). This selects candidate substructure haloes by lowering a density threshold starting from the particle with the highest local halo density. For this, the particles are sorted according to density. If during the lowering of the threshold particles are treated that are close to the already processed ones, they are attached to corresponding substructure candidate. If the particle under consideration however is separated by any of the processed particles by more than a few softening lengths, then this particle is taken to be the seed of a new substructure halo. Once all particles are processed and all substructure candidates are determined, sub- structure particles that are not gravitationally bound are removed from the subhaloes. This is repeated iteratively until the gravitationally bound substructure is determined. (Springel et al. 2001a) show that a semi-analytic galaxy formation model that correctly follows the evolution of the substructure haloes performs significantly better than one which does not follow substructure.
The existence of dark matter is indicated in clusters and groups of galaxies by their high mass-to-light ratio. One can estimate the cluster total mass by assuming that the member galaxies have become dynamically relaxed and that they are in an equilibrium configuration: hence the virial theorem can be used (U = − 2 K, where U and K are the potential and the kinetic ener- gies respectively) to obtain the virial mass (once the radial velocity dispersion σ r 2 has been measured). The observed optical luminosity of the galaxies was found to correspond to a mass that is much lower than the total cluster mass, pointing at the presence of a large quantity of matter not visible as stars (i.e. in the optical). X-ray emitting gas constitutes a portion of this ”missing mass”, but most of it is ”dark” and it remains unexplained. The formation of the dark matter haloes and the clustering of galaxies are highly nonlinear phenomena. They can be studied for example through numerical simulations (e.g. Springel et al. 2006): billions of cold dark matter particles (they are assumed to be elementary particles that interact only gravitationally) are cre- ated and followed starting 400, 000 years after the Big Bang (see Figure 1.2).
The study of the formation and growth of cosmic structures is one of the most fascinat- ing and challenging fields of astrophysics. In the currently favoured cosmological model, the so-called ΛCDM cosmogony, dark matter structures grow hierarchically, with small clumps forming first at very early epochs. The merging of these dark matter halos in the following evolution leads to the formation of more massive objects with time, ultimately resulting in a complex cosmic web composed of filaments of dark matter and galaxies, rich galaxy clusters, and voids in between. While we have some knowledge how these dark matter structures evolve with cosmic time, the relationship between the “dark” and the “luminous” content of the Universe is still far from being fully understood and it poses many puzzling questions, both for observational and theoretical investigations. Galaxy clusters, the largest virialized objects in the Universe, are especially interesting for cosmo- logical studies because they are ideal laboratories to study the physical processes relevant in structure formation, like those that shape the properties of galaxies, the intergalactic and intracluster media, and the active galactic nuclei (AGN) that originate from super- massive black holes (BHs) in cluster centres. The study of clusters is remarkably promising right now, both because of the wealth of new data from X-ray telescopes such as XMM- Newton and Chandra or from optical surveys such as SDSS, and also due to the increasing power of cosmological simulations as a theoretical tool. The latter can track the growth of cosmological structures far into the highly non-linear regime, and have recently become faithful enough to include for the first time physical processes such as AGN activity and its effect on galaxyevolution.
The WFPC2 data in filters F555W and F814W come from HST proposal 6004 by Tyson (1995). We use pipeline flatfielded images which were combined using iraf 1 tasks in combination with psf fitting cosmic ray rejection algorithms developed in house (G¨ossl & Riffeser, 2002). The steps of data reduction were as follows. First all features with FWHM less than 1 pixel and a high signal to noise were marked as cosmic rays and not used in any further analysis. In the second step the four chips of each WFPC2 exposure were transformed to a single coordinate system. In this step both the geo- metrical distortions of the WFPC2 chips as well as translation and rotation between the different CCDs and exposures were taken care off. The description of Holtzman et al. (1995) was used to remove the geometrical distortions. The different chips have slightly different photometric zeropoints and before the images were stacked all the im- ages were normalised to the zeropoint of the planetary camera. The stacking was done by taking a kappa-sigma clipped mean of each pixel. It was found during the reduction process that the two stage cosmic ray rejection was necessary in order to remove all the cosmic rays efficiently. Most of the cosmic rays were removed by psf- fitting in the first stage and larger pointlike cosmic rays were removed in the stacking stage by the kappa-sigma clipping.
Heat conduction in the intracluster medium (ICM) is primarily along the field lines because the Larmor radius of the particles is very small compared to the collisional mean free path (Braginskii, 1965). The ICM undergoes turbulent motion in a range of spatial scales (Inogamov & Sunyaev, 2003; Schuecker et al., 2004; Schekochihin & Cowley, 2006; Subramanian et al., 2006; Zhuravleva et al., 2011). As the magnetic field is, to a good approximation, frozen into the ICM, the field lines become tangled by gas motions and their topology changes constantly. Four main eﬀects should be considered. First, parallel thermal conduction along stochastic magnetic field lines may be reduced because the heat- conducting electrons become trapped and detrapped between regions of strong magnetic field (magnetic mirrors; see Chandran & Cowley 1998; Chandran et al. 1999; Malyshkin & Kulsrud 2001; Albright et al. 2001). Secondly, diﬀusion in the transverse direction may be boosted due to spatial divergence of the field lines (Skilling et al., 1974; Rechester & Rosenbluth, 1978; Chandran & Cowley, 1998; Narayan & Medvedev, 2001; Chandran & Maron, 2004). Thirdly, there is eﬀective diﬀusion due to temporal change in the magnetic field (‘field-line wandering’). Finally, if one is interested in temperature fluctuations and their diﬀusion, one must be mindful of the fact that the temporal evolution of the magnetic field is correlated with the evolution of the temperature field because the field lines and the temperature are advected by the same turbulent velocity field.
BCG is substantially flattened: in Fig. 3.6 we have shown that the ICL is significantly more flattened both than the BCG “core” itself and than the galaxy distribution. Examples of flattening of the BCG’s outer halo with re- spect to its inner parts have been known since the late 1970s (Dressler 1979; Porter, Schneider, & Hoessel 1991), as an association with a similar flattening of the galaxy distribution (e.g. Binggeli 1982). Our ellipticities and the corre- sponding radial dependences are completely consistent with those of Gonzalez, Zabludoff, & Zaritsky (2004). Moreover, extending the observed radial range well beyond 100–200 kpc, we can present evidence for an asymptotic value for this ellipticity, which is only suggested by their data, although predicted by the two-component de Vaucouleurs models which they fit to the BCG+ICL surface brightness distribution. The fact that this asymptotic ellipticity is first reached where the slope of the SB of the diffuse light flattens lends fur- ther support to the hypothesis of a distinct second component responsible for the outer profile. In addition to this, it is intriguing that the change in slope and ellipticity occurs where the galaxy component begins to dominate the to- tal SB, apparently establishing a link between the galaxies and the “true” ICL. During the last decade many attempts have been made to assess the total amount of ICL and its contribution to the total cluster light. Current esti- mates based on different methods range from less than 10 per cent for poor groups of galaxies (Feldmeier et al. 2004a) to . 20 per cent for non-cD clus- ters (Feldmeier et al. 2004b), to 20–40 per cent for cD clusters (Schombert 1988; Feldmeier et al. 2002) and up to ∼ 50 per cent for Coma (R . 500 kpc, Bernstein et al. 1995, but at < 25 per cent according to Melnick, Hoessel, & White 1977). The results presented in Sec. 3.5.6 indicate that in the mean the ICL contributes 10.9 ± 1 per cent of the flux within 500 kpc, while the de Vaucouleurs component of the BCG contributes 21.9 ± 1 per cent. We warn that the uncertainties reflect the measurement errors only, and we expect the overall uncertainty (sampling plus systematic) in this measure to be about 5 per cent for the ICL and 3 per cent for the BCG. Variations between individual clusters are of course likely to be much larger. Our results thus favour a quite low average ICL fraction, compared to previous estimates. This conclusion is not particularly biased by the properties of our sample, where intermedi- ate and low mass clusters dominate: similar fractions are obtained almost independent of cluster richness and BCG luminosity. This apparent discrep- ancy points to the problem of how estimates of ICL are derived with different methods and to the need to obtain reliable cross calibrations.
X-ray luminosity was attributed to the evolution of the X-ray luminosity function between z = 0 and z ∼ 0.4. On the other side, the existence of X-ray underluminous clusters at low redshift suggests this effect is not due to evolution. The same results were obtained by Holden et al. (1997). Donahue et al. (2002) using the ROSAT Optical X-ray Survey (ROXS), found that using both X-ray and optical methods to identify clusters of galaxies, the overlap was poor. About 20% of the optically selected clusters were found in X-rays while 60% of the X-ray clusters were identified also in the optical sample. Furthermore, not all of their X-ray detected clusters had a prominent red-sequence, a fact that could introduce a bias in constructing cluster samples using only color information (Goto et al. 2002, Gladders et al. 2000). Ledlow at al. (2003) analyzed the X-ray properties of a sample of nearby bright Abell clusters with the ROSAT All-Sky Survey (RASS). They found an X- ray detection rate of 83%. Gilbank at al. (2004) explored the biases due to optical and X-ray cluster selection techniques in the X-ray Dark Cluster Survey (XDCS). They found that a considerable fraction of the optically selected clusters do not have a clear X-ray counterpart. Moreover, spectroscopic follow-up of a subsample of X-ray underluminous systems confirmed they reality. Lubin et al. (2004) analyzed the first XMM-Newton results of two optically selected clusters at z ≥ 0.7. They found that their X-ray luminosity and temperature are low for their measured velocity dispersion. Similar results were obtained in the XMM-2dF Survey of Basilakos et al. (2004). They found many more optical cluster candidates than X- ray ones. Moreover, they found that using deeper XMM data many of the optically selected clusters are faint X-ray emitters with fluxes below the limit of their shallow survey. Thus, are there X-ray (optical) underluminous clusters, that is clusters extremely faint in X-rays (optical) and normally bright in the optical (X-rays)?
This body of work has demonstrated that while galaxy mergers are an important aspect of the evolution of the galaxy population, they do not simply parallel the mergers of dark halos. As White & Rees (1978) stressed, galaxies must remain distinct after the merger of their halos if we are to understand the formation of galaxy clusters. Fall (1979) noted that late-type giant galaxies cannot have undergone recent major mergers since these would destroy their stellar disks. While many more recent studies have followed Toomre (1976) in arguing that massive elliptical galaxies assembled relatively recently through mergers (e.g. Kauffmann & Charlot 1998; van Dokkum 2005; De Lucia et al. 2006) other authors have used the age and uniformity of their stellar populations and their apparently undiminished abundance at high redshift to argue against such late assembly (e.g. Cimatti et al. 2006). Observational estimates of merging rates, based primarily on counts of very close pairs of galaxies, or of morphological evidence for recent merging, have varied widely due to un- certainties in the associated timescales (Le F`evre et al. 2000; Lin et al. 2004). In addition, attempts to measure the evolution of the merger rate, usually parametrised as proportional to (1 + z) α have obtained values for the exponent α ranging from 0 to 6. (Bell et al. 2006; Carlberg et al. 2000; Patton et al. 2002; Conselice et al. 2003; Bundy et al. 2004; Lin et al. 2004).
In the weak lensing regime it is possible to extend the analysis to the periphery of the clusters and groups as well as to encompass those systems which do not show any strong lensing signature. In this lensing regime, the distortion or shear that a halo imprint on the shape of background galaxies is very small. This distortion can not be observed by eye nor measured for individual galaxies, so the weak lensing signal is quantified by averaging the shear over many galaxies. Furthermore, the shear is measured in terms of ellipticities, but since galaxies have their own intrinsic ellipticity which is not known a priori, the intrinsic shape of galaxies adds white noise to the shear measurements. In order to eliminate this source of noise, this method requires a high-density of background galaxies that can only be achieved with very deep observations. The current systems analyzed using the weak lensing method are biased towards galaxy clusters (& 10 14 M ⊙ ) and intermediate redshifts (z < 1), for which the weak lensing signal is more efficient and therefore not so strongly affected by the white noise introduced by intrinsic ellipticities. However, weak lensing detections of high- redshift clusters (z > 1) using deep space-based data have been reported recently in the literature.
36 ′ sky patch and statistically subtracted. For each X-ray cluster candidate the whole redshift range from z = 0 to z = 1.05 is scanned through using simultaneously two colors that bracket the 4000 Å break at the given redshift. This suppresses false overdensity peaks at transitional redshifts where the 4000 Å break moves between two adjacent bands (e.g. the transition between the g and r band around z ≈ 0.35). Once a peak in redshift space is identified, we refine the redshift estimate by fitting a Gaussian function to the redshift density distribution. We then select cluster members in a stripe (0.05 width in color) around the estimated red-sequence. The final cluster redshift value is calculated as the inverse color error weighted mean redshift of the selected member galaxies. This assures that the reliability of the photo-z values for the whole system is always better than for any individual galaxy. An example of the galaxy density distribution in the redshift space for cluster ID 018 is shown in Fig. 5.5 (its redshift is close to the median redshift of the cluster sample). In a few cases two or more solutions were found by our algorithm. For these systems we visually check the obtained redshift distributions and select the more likely solution given the positions of galaxies with respect to the X-ray emission.