Characterizing Quadruple Eclipsing Binary Systems Through Combined TESS Photometry and Speckle Imaging During Eclipses (SIDE) Observations

Eclipsing binary stars (EBs) have long been valued as important tools in establishing fundamental properties and relationships in stellar astrophysics. With the discovery of systems with multiple families of eclipses, the importance of EBs extends to the study of hierarchical, multiple star systems. The primary objective of this thesis is to analyze several TESS-identified quadruple eclipsing binaries (QEBs) using both space and ground-based photometry, as well as high resolution speckle imaging obtained with the Differential Speckle Survey Instrument, DSSI [Horch et al., 2009] on the Astrophysical Research Consortium 3.5-meter telescope at Apache Point Observatory (APO) in Sunspot, NM with the goal of ascertaining detailed architectures of these hierarchical, multiple star systems. This is the first systematic application of Speckle Imaging During Eclipse (SIDE) applied to eclipsing binary starts. All systems discussed in this thesis were identified from photometric data obtained with NASA's Transiting Exoplanet Survey Satellite (TESS) by Kostov et al. [2022] and Kostov et al. [2024], whose work is essential to the creation of this thesis. The first aspect of the present analysis attempts to verify the times of current eclipses for each system using ground-based photometry collected with the 0.5-meter Astrophysical Research Consortium Small Aperture Telescope (ARCSAT) based at APO, and the 0.6-meter Rapid Response Robotic Telescope (RRRT) at Fan Mountain Observatory in Covesville, VA. These verifications are necessary to ensure that eclipse timings remain accurate after originally observed with TESS. After the original observations by TESS several years ago, both because the original derivations of some eclipse periods and durations had non-negligible errors, and because some systems were identified by Kostov et al. as showing evidence of eclipse timing variations (ETVs), predicted eclipse times could have shifted since the original observations. Due to these factors, further verification is necessary to ensure that our predicted eclipse times are still correct. The second portion of our analysis uses diffraction-limited speckle imaging to resolve the QEBs into two subcomponents, to measure the photometric difference between these two components, and, most uniquely, to make these measurements both in and out of eclipses. By monitoring the changes in photometric difference during eclipses we show that it is possible to gain further insights into the architectures of the QEB systems, making it possible to determine which speckle-resolved source can be associated with which family of eclipses. The usage of high-resolution speckle imaging to analyze TESS-identified QEb candidates is currently in its infancy, and the results described will be among the first published analysis of these systems using this method. Ultimately, the goal of this analysis is to determine whether both binary pairs of the TESS-identified QEB reside in one of the speckle-resolved subcomponents or if each of the resolved subcomponents contains one of the EB pairs.