Statistically Optimal Modeling of Flat Eclipses and Exoplanet  Transitions.  the “Wall-Supported Polynomial”  (Wsp) Algoritms

Andrych, Kateryna D.; Андронов, И. Л.; Chinarova, L. L.

doi:10.18524/1810-4215.2017.30.118521

Cited by 13 publications

(10 citation statements)

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“…Also, we used the abbreviated Taylor series for the functions proposed by Mikulášek (2015) and Andronov (2012). Andrych et al (2017) introduced the "Wall-Supported Polynomial" (WSP) algoritms for statistically optimal modeling of flat eclipses and exoplanet transitions.…”

Section: Algorithms Used In Mavkamentioning

confidence: 99%

Astroinformatics: Statistically Optimal Approximations of Near-Extremal Parts with Application to Variable Stars

Андронов

Andrych

Chinarova

et al. 2020

ComBAO

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The software MAVKA is described, which was elaborated for statistically optimal determination of the characteristics of the extrema of 1000+ variable stars of different types, mainly eclipsing and pulsating. The approximations are phenomenological, but not physical. As often, the discovery of a new variable star is made on time series of a single-filter (single-channel) data, and there is no possibility to determine parameters needed for physical modelling (e.g. temperature, radial velocities, mass ratio of binaries). Besides classical polynomial approximation "AP" (we limited the degree of the polynomial from 2 to 9), there are realized symmetrical approximations (symmetrical polynomials "SP", "wall-supported" horizontal line "WSL" and parabola "WSP", restricted polynomials of non-integer order based on approximations of the functions proposed by Andronov (2012) and Mikulasek (2015) and generally asymmetric functions (asymptotic parabola "AP", parabolic spline "PS", generalized hyperbolic secant function "SECH" and "log-normal-like" "BSK"). This software is a successor of the "Observation Obscurer" with some features for the variable star research, including a block for "running parabola" "RP" scalegram and approximation. Whereas the RP is oriented on approximation of the complete data set. MAVKA is pointed to parts of the light curve close to extrema (including total eclipses and transits of stars and exoplanets). The functions for wider intervals, covering the eclipse totally, were discussed in Andronov (2017). Global and local approximations are reviewed in Andronov (2020). The software is available at http://uavso.org.ua/mavka and https://katerynaandrych.wixsite.com/mavka. We have analyzed the data from own observations, as well as from monitoring obtained at ground-based and space (currently, mainly, TESS) observatories. It may be used for signals of any nature.

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Section: Algorithms Used In Mavkamentioning

confidence: 99%

Astroinformatics: Statistically Optimal Approximations of Near-Extremal Parts with Application to Variable Stars

Андронов

Andrych

Chinarova

et al. 2020

ComBAO

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“…For studies of "near extremum" parts of the light curve, including the determination of ToM (Time of Minimum/Maximum), 19 functions (9 types of functions) were realized in the software MAVKA Andronov, 2019, , Andrych et al 2020). Some of the functions were previously introduced by Andronov (2005), Andrych et al (2015Andrych et al ( , 2017. These methods were applied to determine ToM of a group of eclipsing variables (e.g.…”

Section: Special Shapes (Patterns)mentioning

confidence: 99%

Variable Stars: A Net of Complementary Methods for Time Series Analysis. Application to RY UMa

Andronov,

Chinarova

2019

Preprint

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cyclic change of semi-amplitude of pulsations between 0.01 to 0.37mag, which is interpreted as a bias between the waves with close periods and a beat period of 4000d (11yr). The dominating period has changed from 307.35(8)d before 1993 to 285.26(6)d after 1993. The initial epoch of the maximum brightness for the recent interval is 2454008.8(5). It is suggested that the apparent period switch is due to variability of amplitudes of these two waves and an occasional swap of the dominating wave.

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“…Most of them were taken from Brno Regional Network of Observers (BRNO). In addition, we computed moments of minima for all available data from American Association of Variable Stars Observers database (AAVSO) using the software MAVKA (Andrych et al, 2017). For all available moments of minima, we calculated the values of O−C and built the O−C curve.…”

Section: O-c Analysismentioning

confidence: 99%

Period Variations and Possible Third Components in the Eclipsing Binaries Ah Tauri and Zz Cassiopeiae

Tvardovskyi

Marsakova

Андронов

et al. 2018

OAP

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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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Statistically Optimal Modeling of Flat Eclipses and Exoplanet Transitions. the “Wall-Supported Polynomial” (Wsp) Algoritms

Cited by 13 publications

References 1 publication

Astroinformatics: Statistically Optimal Approximations of Near-Extremal Parts with Application to Variable Stars

Astroinformatics: Statistically Optimal Approximations of Near-Extremal Parts with Application to Variable Stars

Variable Stars: A Net of Complementary Methods for Time Series Analysis. Application to RY UMa

Period Variations and Possible Third Components in the Eclipsing Binaries Ah Tauri and Zz Cassiopeiae

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