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

Transcription

1 Kwee-van Woerden method: To use or not to use? Zdeněk Mikulášek, Marek Chrastina, Jiří Liška, Miloslav Zejda, Jan Janík, Department of Theoretical Physics and Astrophysics, FS of Masaryk University, Brno, Czech Republic Observational techniques, instrumentation and science for metre-class telescopes, Tatranská Lomnica 2013

2 Motivation O-C diagram of eclipsing binaries (EB) is one of the most powerful instrument of the modern stellar astrophysics. It serves for the sophisticated period analyses enabling to reveal a number of intimate details of star couple lives. The reliability of conclusions based on O-C EB analyses strictly depends also on the correctness of the observed mid-eclipse times and sureness of knowledge of their uncertainty. Well-known lack of practically all EB O-C diagrams the observed scatter of measurements is many times larger than scatter expected from their uncertainties. Mathematically: the reduced χ 2 r>>1. AR Aur - χ 2 r = 158! Why? a) uncertainties underestimated (why?), b) incorrect mid- eclipse times bad method of O + δo O determination K-W method

3 Kwee van Woerden method The majority of EB minimum times O and δo has been determined by means of the famous K-W method from Many advantages: indisputable results, no assumptions about the LC courses (except its symmetry), no need of computers, general acceptance of EB astronomers all over the world. Nowadays observers use their KWM codes on their PCs: {t i,m(t i )} KWM black box O + δo, nobody now knows the details of the original KWM and the true content of its KW black box. There are also another possibility e.g. to use physical models of EB or LC templates and to determine O + δo using LSM.. We prefer this approach.

4 Simulations Aim: : to compare results of K-W and LSM methods by means of computer simulation. Object: model LC of the vicinity of AR Aur V primary minimum scattered by normal pseudorandom numbers. The K-W method code was written strictly according to the original K-W paper (the interior of BB is known). The template LC for the LSM method was the non-scattered model LC. We did simulations with σ = mag, duration of observations h for three situations: 1) Strictly symmetric LC without any trend, 2) Originally strictly symmetric LC influenced by the typical trend of dm/dd /dt = mag/h, and 3) Asymmetrically placed minimum (hockey stick) 2:3, without any trend.

5 Conclusions I The original K-W method is usable only for LCs sparsely covered by measurements with small and moderate scatter it cannot be used for standard CCD observations. There are some modification which allowed it unfortunately the KW uncertainty estimate then cannot be used anymore. Minima times determined by the true K-W method and exact LSM approach are the same the published O s published obtained by KWM can be used. The scatter of LSM times is always smaller than the scatter of KWM times. It is a bonus for the additional information hidden in the assumption of the true course of the LC. The uncertainty estimations of KWM times are always strongly underestimated by a factor of 1.4. Both methods are identically influenced by uneliminated trends common for CCD observations. The shift arises with the duration of observations too many data harms the theory. A typical trend of dm/dt = mag/h (only linear term is decisive) causes the shift min, depending on duration.

6 Conclusions II LSM approach enables to correct mid-eclipse times for linear trends it diminishes the scatter of O-C values three times. At the same time the uncertainties of O times arise roughly two times (more observing intervals). Both effects suppress χ 2 r from allarming158 to also bad, but more acceptable 12. KWM is also much worse in the case of incomplete LCs or hockey sticks. To use or not use the Kwee van Woerden method, one of the most favorite method for variable star data processing? We think that the time for the KWM retiring is just coming. Thank you for your attention!