Interstellar dust is a ubiquitous component of galaxies, but some of its most fundamental properties are still poorly understood. This work analyzes the average extinction properties of dust in the Small Magellanic Cloud (SMC) through color-magnitude diagrams (CMDs) of resolved stars observed with the Hubble Space Telescope (HST). It also investigates the three-dimensional structure of the SMC, since the galaxy's proximity and dynamic interaction history provide a unique way to simultaneously study both dust extinction and galactic geometry. The observations are taken as part of the Small Magellanic Cloud Investigation of Dust and Gas Evolution (SMIDGE) program examining a 200 $\times$ 100 parsec region in the SW bar of the SMC.
SMC-like dust extinction is frequently used to correct observations of high-redshift or low-metallicity galaxies due to SMC's own low metallicity \citep{Gordon:2003}. The dust extinction law or curve describing the stellar extinction in magnitudes as a function wavelength is the quantity used for this purpose. Fundamentally, the extinction law holds information about the dust grain size and composition. The SMIDGE survey has made it possible to find the average dust extinction properties in the SMC and build upon the handful of measurements in existence prior to the survey.
Chapter \ref{ch:intro} is an introduction to the importance of SMC dust extinction curve and galactic geometry measurements, and to the approach taken here to answer questions about these two measurements. Chapter \ref{ch:paper1} explores the average SMC dust extinction curve through multiband HST photometric observations of evolved red clump stars. The study focuses on the measurement of the slope of the red clump reddening vector from the CMD relying on a simple model which takes into account the extinction curve shape, a log-normal distribution of extinctions, and the distance distribution of the stellar component along the line of sight. The results for the shape of the average SMC extinction curve are consistent with prior measurements, and also point to a significant galactic depth along the line-of-sight, in line with recent studies.
Chapter \ref{ch:paper2} describes work on a more complex model for the SMC, using red clump and red giant branch stars on a CMD. The model simulates the dust-stars offset and the stellar distance distribution, yielding the reddened fraction of stars. It also simulates a dust layer with a log-normal extinction distribution $A_V$ - the extinction in magnitudes in the optical $V$ photometric band - with width $\sigma_{A_V}$. This work results in the first detailed dust extinction and 3D geometry properties in a key region in the SMC. It also produces a photometry-based $A_V$ result allowing for a measurement of the dust mass content of the galaxy which is independent from infrared dust emission observations. This is one of a few measurements of $A_V$ at low metallicity which can be compared to gas and dust content measured from infrared emission. Similarly to other photometry-based extinction results in Andromeda and the Milky Way, it points to a potential overestimation of the dust mass derived from dust grain models relying on IR dust emission data.
Chapter \ref{ch:paper3} summarizes this dissertation and describes future work on SMC's dust extinction properties. This future study relies on the results derived in Chapter \ref{ch:paper2} to obtain a refined SMC average dust extinction curve. It also aims to obtain spatially-resolved maps of the extinction curve and $A_V$ in order to answer questions about the true distribution of SMC extinction curves.
