This dissertation examines the relationship between galaxy clusters and the brightestcluster galaxies (BCGs) of those clusters. It has been known for a while that the state of the hot intracluster medium (ICM) gas in the core of a galaxy cluster, quantified as the central entropy of the gas, can be found in two particular states. Galaxy clusters with central entropies greater than 30 keV cm2 are typically disturbed clusters with no radio activity or line emission in their BCG. On the other hand, those clusters with low central entropy can host BCGs, which are considered "active" and contain strong central radio sources as well as line emission suggesting star formation. While there is this dichotomy, the relative importance of physical processes which may help to create this dichotomy, is not well determined. In Chapter 2, we examine the ultraviolet and infrared properties of BCGs in a heterogeneous sample of clusters. We find that the dichotomy still holds when investigating star formation in both the obscured and unobscured regimes. In these low entropy clusters ~40% have a BCG with some form of star formation such that star formation in BCGs is enabled by the dense X-ray emitting ICM gas. The results we find are consistent with other star formation indicators, such as Hα, but we are able to create a more complete picture of the star formation occurring in the BCG.In Chapter 3 we conduct an in depth investigation of the cool core galaxy cluster RXJ2014.8-2430. Based on Chandra X-ray data, we find the cluster core is sloshing. However,the BCG is still located near the X-ray peak and the metallicity is still centrally peaked,which suggests sloshing is a recent phenomenon. Also, we do not find X-ray cavities even though they are expected in a cool core with radio emission. We simulate X-ray images with various bubble configurations and sizes to set limits on what we could have missed in thedata. We analyze narrow band Hα imaging and optical spectra and find elongation of the Hα filaments along the same east-west axis of the sloshing. The emission line spectra show a velocity gradient across the central Hα region, suggesting the galaxy is getting pulled into or out of the cluster. The weak sloshing as well as the limit on X-ray cavities suggests we may be observing RXJ 2014.8-2430 during a rare period where sloshing and the AGN are beginning to heat the cluster core.In Chapter 4 we present results from our polarimetry pilot study for the optical imager onthe Southern Astrophysical Research (SOAR) Telescope. We discuss the methodology used to collect the data and determine data quality for appropriate analysis. We verify that we can reproduce polarization fractions and angles in sources that are polarization standards.We attempt to measure polarization in the Hα filaments in the BCG M87, but do not finda statistically significant measurement of polarization in the filaments and place an upperlimit on their total polarization. The limit on polarization of emission from the filaments inM87 limits the role saturated thermal conduction can play at the interface of the hot ICMand the cold filaments. We summarize the results of the dissertation in Chapter 5.
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