Photometric Analysis of Candidate Quadruple Eclipsing Binary Systems: Dynamical Evolution of TIC 63459761

Quadruple Eclipsing Binaries [QEBs] are gravitationally bound, hierarchical stellar binaries consisting of at least four bodies, generally corresponding to 2+2 system architecture, though 2+(2+1), 1+(2+1), 2+2+2 , etc. arrangements are possible. Single and double eclipsing binary systems are well-known to serve as excellent testbeds for determining stellar and orbital parameters (Torres et al. 2009). QEBs, while exceedingly rare, offer unique opportunities to contribute insights into binary star system evolution and inter-binary interaction. For a significant subsample of the QEB candidate lists derived from the Transiting Exoplanet Survey Satellite (TESS) presented in Kostov et al. (2022) and Kostov et al. (2023), extensive ground-based photometry via the 0.6m Rapid Response Robotic Telescope [RRRT] at Fan Mountain Observatory, VA, and the 0.5m Astrophysical Research Consortium Small Aperture Telescope [ARCSAT] at Apache Point Observatory, NM, in conjunction with speckle interferometry, were obtained to constrain system parameters and identify Eclipse Timing Variations [ETVs]. The program to obtain these observations is described, including a planning tool designed to optimize observing around capturing QEB eclipses. We then describe a systematic error discovered in the determination of distances for QEBs using Gaia trigonometric parallaxes, π, for those QEBs resolved by speckle imaging into two subsystems, with the size of that systematic error reaching a peak in επ/π when the angular separation of the resolved QEB subcomponents becomes comparable to the native resolution of the Gaia satellite; clearly Gaia astrometry is failing for sources that it marginally resolves. Finally, we focus on a case study of one QEB for which we have extensive multi-epoch observations: TIC 63459761, a 2+2 QEB with primary and secondary orbital periods of 4.362d and 4.244d, respectively, in the Cygnus OB2 association. The degeneracies and potential contributions of various perturbative effects are explored in Section 4, alongside a description of future observations of ETVs and Relative Eclipse Timing Variations [RETVs] that will constrain the system’s architecture.