Investigating Period Variability Mechanisms in Eclipsing Binary Stars through Eclipsing Time Variation Analysis: A Case Study of TZ Bootis

We present an effective strategy for extensive analysis of eclipsing time variations (ETVs) using modern and sophisticated optimization methods that comprise a set of tools to investigate period variability mechanisms in eclipsing binary stars such as the light-time effect, the Applegate mechanism, and mass transfer. We implement these methods for the first time assuming that the above mechanisms can act simultaneously in the puzzling W UMa–type binary star TZ Bootis by using archival and new TESS data spanning 75 yr and reexamining the up-to-date ETVs. Preliminary analysis of the TESS data revealed for the first time the presence of a second binary in agreement with previous spectroscopic data and astrometric results from Gaia DR3. We consider the most credible scenario for the ETV: two stellar circumbinary companions of minimum masses M 3 = 0.5 M ☉ and M 4 = 0.14 M ☉ in highly eccentric orbits e 3 = 0.70 and e 4 = 0.82 with periods P 3 = 38 yr and P 4 = 20 yr along with a 24 yr magnetic activity of the secondary component and a long-term period increase ( dP / dt = 1.2 × 10 −8 days yr −1 ), interpreted as a conservative mass transfer from the secondary to the primary component at a rate of dM 1 / dt = 3.7 × 10 −9 days yr −1 . Further spectroscopic observations, analytical modeling of the second pair, and ETV analysis of both pairs are needed to investigate the quadruple nature of the system.