In our research, we investigated two variable stars: AH Tau and ZZ Cas. They are eclipsing binary stars of W Ursae Majories and Lyrae types. The period between eclipses of these stars 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. That is why we assume the cyclic changes could be 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). Thus we assume the third component and mass transfer are present. We also assume that 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. This explanation is called 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 special plot called 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. The O-C curve is the plot which shows how the difference between an observed and calculated moment of minimal brightness changes during a long period of time (usually it is several decades). To do this we created a modeling computer program using the computer language Python. In addition, we can calculate errors of third component's orbit parameters and even estimate 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 AAVSO database (American Association of Variable Stars Observers). These results are provided in the tables and plots. Абстракт: У нашій роботі було досліджено дві змінні зорі: AH Tau та ZZ Cas. Вони є затемнювано-подвійними зорями типів W Великої Ведмедиці та β Ліри. Період між затемненнями цих зір змінюється з часом. Причиною постійних змін періоду може бути перетікання речовини (потік речовини) між зорями. У ZZ Cas зміни періоду є циклічними. Тому ми припускаємо, що вони можуть бути викликані наявністю гіпотетичного третього компонента (малої зорі або великої планети). У AH Tau циклічні зміни періоду накладаються на постійні (період зменшується). Отже ми припускаємо, що присутні й перетікання речовини, й третій компонент. Ми також припускаємо, що треті компоненти не беруть участі в затемненнях, але завдяки своїй силі тяжіння вони змушують видимі тісні подвійні системи наближатися або віддалятися від спостерігача. Це пояснення називається ефектом затримки світлового сигналу (LTE). У загальному випадку орбіта третього к...
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We developed the software package MAVKA for the determination of characteristics of extrema (moment of extremum, magnitude) and their errors. The program realizes the application of 11 basic functions for approximation of extrema. We tested all these methods in two parts. In the first part we used generated data sets (various smooth curves with noise). We investigated deviations between generated and computed values of moments of extremum and magnitude, as well as execution time for different extrema parameters. In the second part we used real observations of different variable stars using photometric and visual observations from different databases.
We have studied three binary stellar systems KR Cyg, V382 Cyg and BX And, which are eclipsing variables of the β Lyrae -type. We have studied the phase curves and O-C curves. The forms of their O-C curves are sinusoidal with a trend, so we made the conclusion that the periods of binary systems change periodically and we suppose that the systems have third components that do not take part in the eclipses, but produce a periodic light time eect, as the inner eclipsing binary rotates around the common centre of masses of the triple system. For the analysis, we used data published in the AAVSO and NSVS databases, as well as our own observations. For the O-C curves, the data were taken from the BRNO database, as well as from our own calculations of the moments of minima from the light curves. We determined secondary periods, calculated the minimal masses of the third components, estimated the mass transfer rate for the system V382 Cyg and corrected the ephemeris for these three eclipsing variables.
In our research, we have studied 6 close binary stellar systems which are eclipsing variables of β Lyrae and W Ursae Majoris types of variability. We have studied their O-C curves. To build them, we used moments of minima, listed in the BRNO database. Also, we used ones, which we obtained as the result of processing of observational data taken from AAVSO database. As the result of the O-C analysis, we detected that all of these stars have parabolic O-C curves, which might be caused by mass transfer from one component to another. In an addition, 3 from researched stars (U Peg, V0523 Cas and WZ Cyg) have superimposed parabolic and cyclic O-C changes that could be caused by presence of the third components in the systems. Also, we calculated minimal possible masses of third components, rates of the mass transfer for these systems and corrected the ephemerides.
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