Abstract: Ultra-diffuse galaxies are inefficient at star-formation, and have been difficult to detect historically. Within the last four years, improvements in optical telescope resolution capabilities has led to the discovery of a large number of ultra-diffuse galaxies that are not contained in galaxy clusters (field ultra-diffuse galaxies). Because of the relative isolation of these galaxies in space, field ultra-diffuse galaxies can be used as laboratories for star formation and galactic feedback mechanisms. A luminosity function has not yet been determined for the population of field ultra-diffuse galaxies. A luminosity function expresses the distribution of luminosities among a population of galaxies and is one of the most fundamental observables in astronomy. I have identified the redshifts for a sample of 14 field ultra-diffuse galaxies, spectroscopically observed by the Southern African Large Telescope. Based on apparent magnitude data from the Hyper Suprime-Cam, along with their redshifts, I have been able to calculate properties such as their physical size as well as their closest neighboring galaxy using the NASA Sloan-Atlas Catalog. Moreover, I have made a preliminary estimate of the shape of the luminosity function for field ultra-diffuse galaxies, finding that the characteristic luminosity scale of field ultra-diffuse galaxies differs significantly in the i-band from the general galaxy population. My luminosity function will help to constrain models of star-formation and feedback mechanisms in galaxies with low surface-brightnesses.
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