UNIVERSITY OF KWAZULU-NATAL EVOLUTION OF GALAXY CLUSTER SCALING RELATIONS OVER HALF A HUBBLE TIME by Susan Wilson Submitted in fulfillment of the academic requirements for the degree of Doctor of Philosophy (Science) in the School of Mathematics, Statistics, and Computer Science, University of KwaZulu-Natal Durban December, 2016 As the candidate’s supervisor I have approved this thesis for submission. Signed: .............................. Name: .............................. Date: .................... “A mathematician may say anything he pleases, but a physicist must be at least partially sane.” - J. Willard Gibbs ABSTRACT In this thesis, we observe a sample of 38 galaxy clusters drawn with 0:1 < z < 1 from the XMM Cluster Survey in order to study scaling relations and their evolution. The two scaling relations discussed are the velocity dispersion–temperature (σv–TX) and the mass–temperature relation (M − TX ). We measure the evolution of the σv–TX for our sample using an orthogonal regression method. This work improves upon previous studies by the use of a homogeneous cluster sample and in terms of the number of high redshift clusters included. We present here new redshift and velocity dispersion measurements for 12 z > 0:5 clusters observed with the GMOS instruments on the Gemini telescopes. We find that the slope of the relation is steeper than that expected if clusters were self-similar, and that the evolution of the normalisation is slightly negative, but not signifi- 0:86±0:14 −0:37±0:33 cantly different from zero (σv / T E(z) ). We verify our results by applying our methods to cosmological hydrodynamical simulations. The lack of evolution seen in our data is consistent with simulations that include both feedback and radiative cooling. Since we find no evidence of evolution in the σv–TX relation, and the dynamical mass of the cluster is dependent on σ we can conclude that the M − TX relation is not evolving. We measure dyn the M − TX relation for our sample using two methods, an orthogonal regression method i ii 2:44±0:37 and a Bayesian Gaussian mixture model fitting method, and find a slope of M500 / TX 1:11±0:97 and M500 / TX , respectively. The expected relation from the self-similar model is 1:5 M500 / TX . Although both our fit results are within 3σ of the expected result, the orthogo- nal method slope is steeper than expected and the Gaussian mixture model fitting method gives a shallower than expected slope. We tested the effectiveness of retrieving a fit from a simulated set of data and found the Gaussian mixture model fitting method to provide a more consistent and re- liable result in comparison to the orthogonal method. However, we also found that the steepness of the slope for the orthogonal method is biased high when there is large scatter in the data. The Gaussian mixture model data over-estimates the scatter and therefore in low scatter systems, the slope is under-estimated. The fit for our M − TX relation was compared to the small population of previous studies and was found to be consistent within 3σ. However, all previous methods fitted their relation using a hydrostatic mass which requires the assumption that the clusters are in hydrostatic equilibrium. A comparison between hydrostatic and dynamical masses is given and the hydrostatic mass bias is discussed. In order to gain further knowledge about galaxy clusters we consider what information the radio wavelength can provide. The presence of diffuse radio emission, in the form of radio ha- los, radio relics and mini halos, has been linked to cluster mergers but the exact model for its origin is still not understood. Two competing models exist, but studies of galaxy clusters seem to be more in favour of the primary electron model rather than the hadronic model. Since the presence of a merger will have an effect on the properties of a galaxy cluster, we considered how they will change the known scaling relations. Although literature provides a change in the X-ray luminosity relation, the effect on the σv–TX relation has not been studied. To gain some insight into this we compare the position of a sample of clusters with and without radio halos, which are traces of a merger, on the σv–TX plane. We find no obvious population difference but a larger, homogeneous sample will be required to validate this result. iii We also provide 3 new VLA observations for galaxy clusters from our XCS sample as part of a pilot project to search for radio halos in low mass clusters. Due to an insufficient observation time and corrupted data, the images we obtain have a high rms noise, and no detection of a radio halo is found. The expected average size of a radio halo is 1 Mpc but we discuss the correlation between the radio halo size and the cluster mass. To see if it has an effect on radio power and detections we simulate radio halos of two different sizes, 400 kpc and 1 Mpc. We determine power upper limit estimates at the 3σ level for our 3 clusters, with radio halo sizes of 400 kpc, 24 −1 24 of: P1:4GHz < 1:67 × 10 W Hz in XMMXCS J111515.6+531949.5, P1:4GHz < 4:15 × 10 −1 25 −1 W Hz in XMMXCS J104044.4+395710.4, and P1:4GHz < 5:88 × 10 W Hz in XMMXCS J151618.6+000531.3. We compare the positions of our upper limit estimates, to other known radio halo detections and upper limits, on the P1:4GHz − LX and P1:4GHz − M500 plane. Using the reduced simulated halo size, our radio power upper limits are decreased by a factor of 2∼10. Although, our upper limits still do not rule out the presence of a radio halo at this smaller size, it does bring into question the accepted method for calculating radio halo upper limits. The results obtained in this thesis have provided us with more knowledge of scaling relations of galaxy clusters but has also shown us how much there is still left unknown. Further spec- troscopic observations of galaxy clusters will allow us to increase our sample size and further constrain the σv–TX and M − TX relation. Radio observations of a large homogeneous selected sample of galaxy clusters will allow us to further investigate the presence of radio halos and their effect on scaling relations. ACKNOWLEDGMENTS This research was possible due to funding from the National Research Foundation (NRF) and the Square Kilometer Array South Africa (SKA) through the postgraduate bursary. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the Na- tional Aeronautics and Space Administration. This research has made use of the X-Rays Clusters Database (BAX) which is operated by the Laboratoire d’Astrophysique de Tarbes-Toulouse (LATT), under contract with the Centre Na- tional d’Etudes Spatiales (CNES) This research obtained results based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a co- operative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). iv v “Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t. - Rikki Rogers There were often moments when I was completing my thesis, that I thought I would never finish. This is a thank you to everyone who believed in me and encouraged me to continue so I could complete my dream. Special mention must be given to the following people. My supervisor Dr Matt Hilton - Thank you for giving me the opportunity to work with you and thank you for having with patience me. I really appreciate all your help. You were always available and ready to answer questions and encourage me to think through problems for myself. Thank you for making these last 4 years bearable and interesting. My co-supervisor Dr Nadeem Oozeer - Although I was not able to physically consult you on this project, you were always available to offer help over email. Thank you for the skype conversations and encouragement. My two best friends: Nikhita Madhanpall although we have not studied in the same city over the past four years you have been a constant rock and support for me. Thank you for your cheerfulness and belief in me on my disheartening days. I am so grateful to call you my friend. Kenda Knowles thank you for everything you have done in the last four years. Your unwavering support and friendship has helped me to achieve my dream of completing my PhD. From the late night chats, to the constant supply of tea and chocolate, and the extensive grammar checking and proof reading during the last push. You have made these last four years a wonderful journey and now it’s time to celebrate - cheers! My family: My sisters and brothers-in-law - Thank you for believing in me and loving me even when I was having a bad day. I love you all so much and promise to visit more often now. My parents - Thank you for your patience and love these last four years. For pushing me to work on days when I didn’t want to, I may not have shown it at the time but I am extremely grateful and love you so much.