Period Variations and Possible Third Components in the Eclipsing Binaries AH Tauri and ZZ Cassiopeiae

TL;DR

This study analyzes period variations in eclipsing binaries AH Tau and ZZ Cas, suggesting the presence of third components affecting their orbits and providing estimated parameters and masses for these unseen companions.

Contribution

The paper introduces a Python-based modeling method to estimate third component orbits and masses from O-C data, incorporating errors and using extensive observational data.

Findings

Third components are likely stars based on mass estimates.

Period variations are caused by mass transfer and third components.

A modeling program was developed to analyze orbital parameters.

Abstract

We investigated two variable stars AH Tau and ZZ Cas. They are eclipsing binaries of W UMa and $\beta$ Lyr types. The period changes with time. The reason for steady changes of the period could be the mass transfer (the flow of matter) between components of these stellar systems. For ZZ Cas the changes of the period are cyclic caused by the presence of the hypothetical third component (either a small star or a large planet). The cyclic changes of the period for AH Tau superimpose on steady ones (the period decrease) indicating for a third component and mass transfer. The third components do not take part in the eclipses. However, due to their gravity, they make the visible close binary systems rotate and become closer or further to an observer, causing the Light-Time Effect (LTE). Generally, an orbit of a third component is not a circle, but an ellipse and it is inclined relatively to the observer's line of sight. Using the O-C curve, we estimated the parameters of a third component's orbit, such as a semi-major axis, an eccentricity, angles of orientation and a period of a third component's rotation. We elaborated a modeling program using the computer language Python. We calculated errors of third component's orbit parameters and even estimated its mass. The values of masses of the third components within errors of calculations show that the third components are probably stars. All these calculations were made using all available data from international database BRNO (Brno Regional Network for Observers). Moreover, we used moments of minima which we calculated as the result of observation processing from the AAVSO database.