Fine-tuning of light-time effect in triple systems

TL;DR

This paper refines the mathematical modeling of the light-time effect in triple star systems, providing more accurate formulas and estimating the impact of dynamical coupling on eclipse timing variations.

Contribution

It introduces generalized analytic formulations for LITE and assesses the significance of dynamical coupling effects in triple systems.

Findings

Corrected LITE formula may be detectable in systems with P2/P1 ≤ 20

Dynamical coupling effects are small but potentially relevant for future observations

Analytical models facilitate analysis of photometric data in triple star systems

Abstract

The sequence of eclipses of binary stars is subject to inequalities for various reasons. The presence of a third component in the system causes periodic motion of the binary's center of mass along the line of sight of an observer. The finite value of the light velocity implies that the epochs of eclipses periodically advance and delay with respect to the exact orbital period of the binary, a phenomenon termed the light-time effect (LITE). We aim to refine two aspects of the mathematical treatment of LITE. First, we provide both generalized and more accurate analytic formulation describing the light-travel time in the binary system itself presented in previous works. Second, we analytically estimate the so far neglected coupling of LITE with the dynamical interaction of the binary orbit with the motion of the third star. Our principal results are given in a simple analytical form, which is suitable for the analysis of photometric observations that require minimization over a multidimensional parameter space of the triple system. The leading correction to the traditional formulation of LITE due to the light-travel time in the binary system may be detectable for triple systems with a period ratio of $P_2/P_1\lesssim 20$, for which accurate photometric observations are available. On the other hand, the correction due to the dynamical coupling of the two orbits with $P_2$ periodicity is small, but may become relevant in the future.