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This paper presents a comprehensive analysis of four triply eclipsing triplestar systems, namely TIC 88206187, TIC 14839347, TIC 298714297, and TIC66893949. The four systems with third-body eclipses were found in the TESSlightcurves from among a sample of ~400 matches between known eclipsingbinaries and the Gaia DR3 Non-Single Star (NSS; Gaia Collaboration 2022;Pourbaix et al. 2022) solution database. We combined photometric lightcurves,eclipse timing variations, archival spectral energy distributions, andtheoretical evolution tracks in a robust photodynamical analysis to determinethe orbital and system parameters. The triples have outer periods of 52.9,85.5, 117, and 471 days, respectively. All dozen stars have masses $\lesssim$2.6 M$_\odot$. The systems are quite flat with mutual inclination anglesbetween the inner and outer orbital planes that are all $\lesssim 4^\circ$. Theouter mass ratios range from 0.39--0.76, consistent with our earlier collectionof compact triply eclipsing triples. TIC 88206187 exhibits a fractional radiusof the outer tertiary component $(r_B \equiv R_B/a_{\rm out})$ exceeding 0.1(only the third such system known), and we consider its future evolution.Finally, we compare our photodynamical analysis results and the orbitalparameters given in the Gaia DR3 NSS solutions, indicating decent agreement,but with the photodynamical results being more accurate.

Four New Compact Triply Eclipsing Triples found with Gaia and TESS