Advanced MAVKA software for the approximation of extrema observations is used to analyze the variability of the brightness of pulsating and eclipsing stars, but may be useful in analyzing signals of any nature. A new algorithm using a parabolic (quadratic) spline is proposed. In contrast to the traditional definition of a spline as a piecewise-defined function at fixed intervals, a spline is proposed to be divided into three intervals, but the positions of the boundaries between the intervals are additional parameters. The spline defect is 1, that is, the function and its first derivative are continuous and the second derivative can be discontinuous at the boundaries. Such a function is an enhancement of the "asymptotic parabola" (Marsakova and Andronov 1996). The dependence of the fixed signal approximation accuracy on the location of the boundaries of the interval is considered. The parameter accuracy estimates using the least squares method and bootstrap are compared. The variability of the semi-regular pulsating star Z UMa is analyzed. The presence of multicomponent variability of an object, including, four periodic oscillations and significant variability of the amplitudes and phases of individual oscillations is shown.

MAVKA: Program of Statistically Optimal Determination of Phenomenological Parameters of Extrema. Parabolic Spline Algorithm And Analysis of Variability of The Semi-Regular Star Z UMa

Methods for time series analysis (TSA) are reviewed. Special attention is paid to multicomponent signals with irregularly spaced arguments, what is typical for geoscience and astronomy. Examples are the satellite photometrical surveys (GAIA, KEPLER, HIPPARCOS/TYCHO, WISE, TESS, etc.), ground-based CCD projects (CRTS, SuperWASP, NSVS, ASAS, OGLE, ZTF, etc.), and collections of photographic negatives (Harvard, Sonneberg, Odessa, etc.). Even for “continuous” time series without gaps, the duration of observations is generally not equal to an integer number of periods. In this case (and many others), the basic functions are not orthogonal, so common simplified methods give biased parameters of the approximations. We review improved algorithms and programs (including our own) for statistically correct analysis, and illustrate results for real and model data.

Advanced Time Series Analysis of Generally Irregularly Spaced Signals: Beyond the Oversimplified Methods

In our research, we investigated two variable stars: AH Tau and ZZ Cas. They are eclipsing binary stars of W Ursae IMajories 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.

/pdf/period-variations-and-possible-third-components-in-the-muq78r1rd1.pdf

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

In our research, we studied 9 eclipsing binary stars: AR Lac, U CrB, S Equ, SU Boo, VV UMa, WW Gem, YY Eri, V0404 Lyr, HP Aur. We collected large sets of moments of minima from BRNO and observational data from AAVSO databases. Then, we obtained moments of minima for AAVSO observations (totally - 397 minima) using method of approximation with symmetric polynomial, realized in software MAVKA. This software was provided by Kateryna D. Andrych and Ivan L. Andronov. After we combined obtained moments of minima with data taken from BRNO and plotted O-C diagrams. For all stars these diagrams represented sinusoidal-like oscillations with superposition of linear (for SU Boo, VV UMa, WW Gem, V0404 Lyr and HP Aur) or parabolic trend (for AR Lac, U CrB, S Equ and YY Eri). The oscillations could be described as presence of the third component, which does not take part in eclipses, but causes the well-known light-time effect (LTE). That effect could be easily detected using long data series of observations. However, the oscillations have clear asymmetry, which we interpreted as elliptical shape of the third components orbit. Parabolic trend we explained as mass transfer between components of binary system. For all stars we computed minimal possible mass of the third component. In addition, we developed our own code in computed language Python and using it we computed orbital elements of the third component. Moreover, for stars with parabolic trend we calculated rate of the mass transfer. Finally, for all computed values we estimated errors.

/pdf/third-components-with-elliptical-orbits-in-the-eclipsing-edp20655nv.pdf

Third Components With Elliptical Orbits in the Eclipsing Binaries

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.

Abstract The aim of this paper is to introduce the software and astronomical web-services developed in frame of the Ukraine Virtual Observatory (UkrVO) and VIrtual Roentgen and Gamma Observatory (VIRGO) to the broad astronomical community. We report briefly on such web-services as the public databases “Sky Maps” of X-ray observations by XMM-Newton, the Earth Orbital Parameters for International Earth Rotation System, and the UkrVO Joint Digitized Archive of astroplates. We refer to such software as the “Multi-Column View”, “Variable Stars Calculator”, “FrameSmooth” for variable star’s research and “Collection Light Technology” (CoLiTec) software for search and discovery of new Solar System bodies.

/pdf/ukrvo-astroinformatics-software-and-web-services-2enti1oipz.pdf

Yaroslav S. Yatskiv

Papers

UkrVO Astroinformatics Software and Web-services.