The primary aim of this dissertation was to develop and validate a methodology for identifying spatial clusters (hotspots) of various paediatric cancers within South Africa by using GIS software. The Hotspot Analysis (Getis-Ord Gi*) Tool was used for this purpose. A series of spatial clusters (hotspots) were identified by the tool for each cancer type and these clusters were compared with the exiting literature regarding known environmental and other carcinogens. The quality of the cancer data used in the dissertation was however found to be questionable and significantly underreported. This caused the results of the tool to also be questionable. The dissertation therefore concluded that the tool could be successfully used to identify spatial clusters of cancer in principle. It was however found that the results of the tool needed to be viewed without caution in this dissertation due to the low quality of the cancer data used. / MSc (Geography and Environmental Management), North-West University, Potchefstroom Campus, 2014

Located in the Large Magellanic Cloud, R136 is a rare example of a nearby young and dense massive star cluster in which individual stars can be resolved. Often suggested as a globular cluster in formation, its study is of great interest and promises to provide insights into the early dynamical evolution of massive star clusters. This is crucial to understand more extreme and distant starburst clusters, which contribute to a significant fraction of all current star formation in the Local Universe, in particular in interacting galaxies. The majority of this thesis is based on multi-epoch spectroscopic observations in and around R136 obtained as part of the VLT-FLAMES Tarantula Survey (VFTS), an ambitious programme which targeted nearly 1 000 massive stars in the intricate 30 Doradus star-forming region. The motivations and observing strategy of this survey, designed to address key questions about the evolution of massive stars and clusters, are first introduced. The data reduction procedures applied to VFTS data are described, with an emphasis on the tasks accomplished in the context of this thesis. The VFTS data are first used to perform a detailed kinematic study of R136, determine its dynamical state, and evaluate the importance of gas expulsion in the early evolution of massive star clusters. Orbital motions of binary stars are found to dominate the line- of-sight velocity dispersion of the cluster, illustrating the risk of interpreting velocity dispersion measurements for unresolved extragalactic young massive clusters. However, once the detected binaries are rejected and the contribution of undetected binaries is accounted for through Monte Carlo simulations, the true velocity dispersion of the cluster is found to be low and consistent with it being in virial equilibrium. This suggests that gas expulsion has not had a dramatic effect on the early dynamical evolution of R136. Using the velocity measurements of R136 as a test case, a maximum likelihood method that fits the velocity dispersion of a cluster from a single epoch of radial velocity data is then tested. The method must be applied with care given the high binary fraction of massive stars and the large uncertainties in their binary orbital parameter distributions, but for typical velocity dispersions of young massive clusters (& 4 kms−1), it is shown that the velocity dispersion can be measured with an accuracy of 40% or better. This offers an efficient way of constraining the dynamics of these systems. The radial velocity measurements of apparently single stars in R136 are also used to investigate the internal rotation of the cluster, a potentially important but largely unexplored characteristic of young clusters. Evidence is found, at the 95% confidence level, for rotation of the cluster as a whole. A simple maximum likelihood method is presented to fit rotation curves to the data, from which a typical rotational velocity of 3 kms−1 is found. When compared to the low velocity dispersion of R136, this suggests that star clusters may form with as much as 20% of their kinetic energy in rotation. Finally, a smaller-scale survey of massive stars in the Wing of the Small Magellanic Cloud is introduced. As an example of the particularly interesting massive binaries that can be revealed by the synergy between large optical spectroscopic surveys of young clusters and observations at other wavelengths, the discovery of a new Be/X-ray pulsar binary and associated supernova remnant is reported. With a long spin period of over 1 000 seconds and a young age of 104 years constrained by its association with the supernova remnant, the pulsar in this system is quickly emerging as a unique object that challenges our understanding of the spin evolution of accreting neutron stars.

We perform a measurement of the mass-richness relation of the redMaPPer galaxy cluster catalogue using weak lensing data from the Sloan Digital Sky Survey (SDSS). We have carefully characterized a broad range of systematic uncertainties, including shear calibration errors, photo-z biases, dilution by member galaxies, source obscuration, magnification bias, incorrect assumptions about cluster mass profiles, cluster centring, halo triaxiality and projection effects. We also compare measurements of the lensing signal from two independently produced shear and photometric redshift catalogues to characterize systematic errors in the lensing signal itself. Using a sample of 5570 clusters from 0.1 <= z <= 0.33, the normalization of our power-law mass versus. relation is log(10)[M-200m/ h-M-1(circle dot)] = 14.344 +/- 0.021 (statistical) +/- 0.023 (systematic) at a richness lambda= 40, a 7 per cent calibration uncertainty, with a power-law index of 1.33(- 0.10)(+0.09) (1 sigma). The detailed systematics characterization in this work renders it the definitive weak lensing mass calibration for SDSS redMaPPer clusters at this time.

The confirmation of a globular cluster (GC) in the recently discovered ultrafaint galaxy Eridanus II (Eri II) motivated us to examine the question posed in the title. After estimating the halo mass of Eri II using a published stellar mass-halo mass relation, the one GC in this galaxy supports extending the relationship between the number of GCs hosted by a galaxy and the galaxy's total mass about two orders of magnitude in stellar mass below the previous limit. For this empirically determined specific frequency of between 0.06 and 0.39 GCs per 10(9)M(circle dot) of total mass, the surviving Milky Way (MW) subhalos with masses smaller than 10(10)M(circle dot) could host as many as 5-31 GCs, broadly consistent with the actual population of outer halo MW GCs, although matching the radial distribution in detail remains a challenge. Using a subhalo mass function from published high-resolution numerical simulations and a Poissonian model for populating those halos with the aforementioned empirically constrained frequency, we find that about 90% of these GCs lie in lower-mass subhalos than that of Eri II. From what we know about the stellar mass-halo mass function, the subhalo mass function, and the mass-normalized GC specific frequency, we conclude that some of the MW's outer halo GCs are likely to be hosted by undetected subhalos with extremely modest stellar populations.

The shapes of cluster central galaxies are not randomly oriented, but rather exhibit coherent alignments with the shapes of their parent clusters as well as with the surrounding large-scale structures. In this work, we aim to identify the galaxy and cluster quantities that most strongly predict the central galaxy alignment phenomenon among a large parameter space with a sample of 8237 clusters and 94 817 members within 0.1 < z < 0.35, based on the red-sequence Matched-filter Probabilistic Percolation cluster catalogue constructed from the Sloan Digital Sky Survey. We first quantify the alignment between the projected central galaxy shapes and the distribution of member satellites, to understand what central galaxy and cluster properties most strongly correlate with these alignments. Next, we investigate the angular segregation of satellites with respect to their central galaxy major axis directions, to identify the satellite properties that most strongly predict their angular segregation. We find that central galaxies are more aligned with their member galaxy distributions in clusters that are more elongated and have higher richness, and for central galaxies with larger physical size, higher luminosity and centring probability, and redder colour. Satellites with redder colour, higher luminosity, located closer to the central galaxy, and with smaller ellipticity show a stronger angular segregation towards their central galaxy major axes. Finally, we provide physical explanations for some of the identified correlations, and discuss the connection to theories of central galaxy alignments, the impact of primordial alignments with tidal fields, and the importance of anisotropic accretion.

We use simulated galaxy surveys to study: (i) how galaxy membership in redMaPPer clusters maps to the underlying halo population, and (ii) the accuracy of a mean dynamical cluster mass, M-sigma(lambda), derived from stacked pairwise spectroscopy of clusters with richness lambda. Using similar to 130 000 galaxy pairs patterned after the Sloan Digital Sky Survey (SDSS) redMaPPer cluster sample study of Rozo et al., we show that the pairwise velocity probability density function of central-satellite pairs with m(i) < 19 in the simulation matches the form seen in Rozo et al. Through joint membership matching, we deconstruct the main Gaussian velocity component into its halo contributions, finding that the top-ranked halo contributes similar to 60 per cent of the stacked signal. The halo mass scale inferred by applying the virial scaling of Evrard et al. to the velocity normalization matches, to within a few per cent, the log-mean halo mass derived through galaxy membership matching. We apply this approach, along with miscentring and galaxy velocity bias corrections, to estimate the log-mean matched halo mass at z = 0.2 of SDSS redMaPPer clusters. Employing the velocity bias constraints of Guo et al., we find aEuroln (M-200c)|lambda aEuro parts per thousand = ln (< M-30) + alpha(m) ln (lambda/30) with M-30 = 1.56 +/- 0.35 x 10(14) M-aS (TM) and alpha(m) = 1.31 +/- 0.06(stat) +/- 0.13(sys). Systematic uncertainty in the velocity bias of satellite galaxies overwhelmingly dominates the error budget.

In this paper we propose an unsupervised voting-merging scheme that is capable of clustering data sets, and also of finding the number of clusters existing in them. The voting part of the algorithm allows us to combine several runs of clustering algorithms resulting in a common partition. This helps us to overcome instabilities of the clustering algorithms and to improve the ability to find structures in a data set. Moreover, we develop a strategy to understand, analyze and interpret these results. In the second part of the scheme, a merging procedure starts on the clusters resulting by voting, in order to find the number of clusters in the data set. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

In this paper we present an unsupervised algorithm which performs clustering given a data set and which can also find the number of clusters existing in it. This algorithm consists of two techniques. The first, the voting technique, allows us to combine several runs of clustering algorithms, with the number of clusters predefined, resulting in a common partition. We introduce the idea that there are cases where an input point has a structure with a certain degree of confidence and may belong to more than one cluster with a certain degree of "belongingness". The second part consists of an index measure which receives the results of every voting process for diffrent number of clusters and makes the decision in favor of one. This algorithm is a complete clustering scheme which can be applied to any clustering method and to any type of data set. Moreover, it helps us to overcome instabilities of the clustering algorithms and to improve the ability of a clustering algorithm to find structures in a data set. / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest systematic all-sky survey of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data sets, and is the first SZ-selected cluster survey containing > 10(3) confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the estimates of the SZ strength parameter Y-5R500 are robust to pressure-profile variation and beam systematics, but accurate conversion to Y-500 requires the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical, and X-ray data sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under-luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples.

A thesis submitted in ful lment of the requirements for the degree of Doctor of Philosophy in the School of Physics July 2017. / Based on the Marenostrum-MultiDark Simulation of galaxy Clusters (MUSIC) we develop semi-analytical models which provide multi-wavelength emission maps generated by dark matter (DM) annihilation processes in galaxy clusters and their sub-halos. We focus on radio and gamma-ray emission maps from neutralino DM annihilation processes testing two different neutralino masses, Mx = 35 GeV and 60 GeV along with two different models of the magnetic elds. A comparison of the radio ux densities from our DM annihilation model with the observed difuse radio emission from the Coma cluster shows that they are of the same order of magnitude. We determine the DM densities with a Smoothed Particle Hydrodynamics (SPH) kernel. This enables us to integrate the DM annihilation signal along any given line-of-sight through the volume of the cluster. In particular it allows us to investigate the contribution of sub-halos to the DM annihilation signal with very high resolution. Zooming in on a subset of high mass-to-light ratio (M/L) DM sub-halos, i.e. DM sub-halos with very low baryon content, we demonstrate that such targets can generate prominent annihilation signals. The radial distribution of high M/L DM sub-halos is more strongly peaked at R200crit = 1 compared to the distribution of all sub-halos which may suggest that the search for DM annihilation signals from sub-halos in clusters is most promising at R200crit. The radio ux densities from DM sub-halos are well within the sensitivity limit of the Square Kilometer Array (SKA) with an integration time of 1000 hours, and unlike clusters their gamma-ray spectrum is seen to be dominated by pion decay over a wide range of gamma-ray energies. Our model makes clear predictions for future radio and gamma-ray observations of the DM annihilation signals in clusters and their sub-halos. / LG2018