Kwee-van Woerden method: To use or not to use?

TL;DR

This paper critically evaluates the Kwee-van Woerden method for determining mid-eclipse times in eclipsing binaries, comparing it with least squares methods and recommending its retirement due to underestimation of uncertainties.

Contribution

The study provides a comparative analysis showing that the Kwee-van Woerden method underestimates uncertainties and is less reliable than least squares approaches.

Findings

LSM yields smaller scatter than KWM.

KWM systematically underestimates uncertainties.

Results suggest retiring the Kwee-van Woerden method.

Abstract

The trustworthiness of orbital period analyses of eclipsing binaries strictly depends on the correctness of the observed mid-eclipse time determination, as well the reliability of its uncertainty estimation. The majority of them has been determined by means of the Kwee-van Woerden method (KWM). There are also other possibilities: to use physical models of eclipsing binaries or light curve templates and to determine mid-eclipse times using the least square method (LSM). We compared results yielded by both methods by means of a computer simulation on the synthetic model of AR\,Aur primary minimum. Minima times determined by the KWM and the exact LSM approach are nearly the same, while the scatter of LSM times is always smaller than the scatter of KWM times. KWM uncertainties are systematically underestimated. We think that the time is ripe for the Kwee-van Woerden method to retire.