A comparative analysis of the special shapes (patterns, profiles) of the eclipses applied for the phenomenological modeling of the light curves of eclipsing binary stars is conducted. Families of functions are considered, generalizing local approximations (Andronov, 2010, 2012) and the functions theoretically unlimited in a width, based on a Gaussian (Mikulasek, 2015). For an analysis, the light curve of the star V0882 Car = 2MASS J11080308 - 6145589 of the classic Algol - subtype (βPersei) is used. By analyzing dozens of modified functions with additional parameters, it was chosen the 14 best ones according to the criterion of the least sum of squares of deviations. The best are the functions with an additional parameter, describing profiles, which are limited in phase.
The observed light curves of most eclipsing binaries and stars with transiting planets can be well described and interpreted by current advanced physical models which also allow for the determination of many physical parameters of eclipsing systems. However, for several common practical tasks there is no need to know the detailed physics of a variable star, but only the shapes of their light curves or other phase curves. We present a set of phenomenological models for the light curves of eclipsing systems. We express the observed light curves of eclipsing binaries and stars, transited by their…
In-depth analysis of eclipsing binary (EB) observational data collected for several decades can inform us about a lot of astrophysically interesting processes taking place in the systems. We have developed a wide-ranging method for the phenomenological modelling of eclipsing binary phase curves that enables us to combine even very disparate sources of phase information. This approach is appropriate for the processing of both standard photometric series of eclipses and data from photometric surveys of all kind. We conclude that mid-eclipse times, determined using the latest version of our 'hi-f…
The Phenomenological Classification of TESS Eclipsing Binaries
Shandong University（山东大学）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；University of the Chinese Academy of Sciences（中国科学院大学）
We discuss methods for modeling eclipsing binary stars using the "physical", "simplified" and "phenomenological" models. There are few realizations of the "physical" Wilson-Devinney (1971) code and its improvements, e.g. Binary Maker, Phoebe. A parameter search using the Monte-Carlo method was realized by Zola et al. (2010), which is efficient in expense of too many evaluations of the test function. We compare existing algorithms of minimization of multi-parametric functions and propose to use a "combined" algorithm, depending on if the Hessian matrix is positively determined. To study methods…
The dependence of the test function on the phenomenological parameters used in the "NAV" ("New Algol Variable") algorithm (Andronov, 2012Ap.....55..536A) is studied. Due to a presence of local minima, the method of minimization contains two steps: the "brute force" minimization at a grid in the 4D parameter space, and further iterations using the differential corrections. This method represents an effective approximation of the light curve using the special pattern (shape) separately for the primary and secondary minima. The application of the method to concrete stars is briefly reviewed.
The phenomenological parameters of eclipsing binary stars, which are the prototypes of the EA, EB and EW systems are determined using the expert complex of computer programs, which realizes the NAV ("New Algol Variable") algorithm (Andronov 2010, 2012) and its possible modifications are discussed, as well as constrains for estimates of some physical parameters of the systems in a case of photometric observations only, such as the degree of eclipse, ratio of the mean surface brightnesses of the components. The half-duration of the eclipse is 0.0617(7), 0.1092(18) and 0.1015(7) for Algol, $β$ Ly…
We report on analysis of the two-color VR CCD observations of the newly discovered variable 2MASS J18024395+4003309=VSX J180243.9+400331 obtained using the 1-m telescope of the Mt. Lemmon Observatory (LOAO) in the field of the intermediate polar V1323 Her. The extended version of this conference talk we published in 2015JASS...32..127A. The variability was reported in 2012OAP....25..150A, and the object was monitored. The two-color observations covered all phase interval. The object is classified as an Algol-type variable with tidally distorted components, and shows an asymmetry of the maxima …
We introduce a special class of functions for mathematical modeling of periodic signals of special shape with irregularly spaced arguments. This method was developed for determination of phenomenological characteristics of the light curves, which are necessary for registration in the "General Catalogue of Variable Stars" and other databases. For eclipsing binary stars with smooth light curves - of types EB and EW - it is recommended a trigonometric polynomial of optimal degree in a complete or symmetric form. For eclipsing binary systems with narrow minima (EA-type), statistically optimal is a…
We present a new few-parameter phenomenological model of light curves of eclipsing binaries and stars with transiting planets that is able to fit the observed light curves with the accuracy better than 1\% of their amplitudes. The model can be used namely for appropriate descriptions of light curve shapes, classification, mid-eclipse time determination, and fine period analyses.
Phenomenological modeling of variable stars allows determination of a set of the parameters, which are needed for classification in the "General Catalogue of Variable Stars" and similar catalogs. We apply a recent method NAV ("New Algol Variable") to eclipsing binary stars of different types. Although all periodic functions may be represented as Fourier series with an infinite number of coefficients, this is impossible for a finite number of the observations. Thus one may use a restricted Fourier series, i.e. a trigonometric polynomial (TP) of order s either for fitting the light curve, or to …
We report an analysis of two poorly studied systems GSC 04396-00605 and GSC 04395-00485, which were recently named as V0455 Dra and V0454 Dra, respectively. For two eclipsing stars, the periods and epochs were significantly corrected using our extensive data. The phenomenological characteristics of the mean light curves were determined using the "New Algol Variable" (NAV) algorithm. The individual times of Maxima/Minima (ToM) were determined using the newly developed software MAVKA, which outputs the accurate parameters using the "asymptotic parabola" approximations. The light curves were appr…
We present the first results obtained from an extensive study of eclipsing binary (EB) system candidates recently detected in the VISTA Variables in the Vía Láctea (VVV) near-infrated (NIR) Survey. We analyze the VVV tile d040 in the southern part of the Galactic disc wherein the interstellar reddening is comparatively low, which makes it possible to detect hundreds of new eclipsing binary candidates. We present here the light curves and the determination of the geometric and physical parameters of the best candidates found in this "NIR window", including 37 contact, 50 detached and 13 semi-de…
We present an updated catalog of 4680 northern eclipsing binaries (EBs) with Algol-type light curve morphology (i.e., with well-defined beginning and end of primary and secondary eclipses), using data from the Catalina Sky Surveys. Our work includes revised period determinations, phenomenological parameters of the light curves, and system morphology classification based on machine learning techniques. While most of the new periods are in excellent agreement with those provided in the original Catalina catalogs, improved values are now available for ~10% of the stars. A total of 3456 EBs were c…
During processing the observations of the intermediate polar 1RXS J180340.0+401214, obtained 26.05.2012 at the 60-cm telescope of the Mt. Suhora observatory (Krakow, Poland), variability of 2MASS J18024395+4003309 was discovered. As this object was not listed in the "General Catalogue of Variable Stars" or "Variable Stars Index", we registered it as VSX J180243.9+400331. Additionally we used 189 separate observations from the Catalina Sky Survey spread over 7 years. The periodogram analysis yields the period of 0d.3348837{\pm}0d.0000002.The object was classified as the Algol-type eclipsing bin…
Phenomenological characteristics of the sample of the Algol-type stars are revised using a recently developed NAV ("New Algol Variable") algorithm (2012Ap.....55..536A, 2012arXiv 1212.6707A) and compared to that obtained using common methods of Trigonometric Polynomial Fit (TP) or local Algebraic Polynomial (A) fit of a fixed or (alternately) statistically optimal degree (1994OAP.....7...49A, 2003ASPC..292..391A). The computer program NAV is introduced, which allows to determine the best fit with 7 "linear" and 5 "non-linear" parameters and their error estimates. The number of parameters is mu…
A spectroscopic study was carried out on the surface chemical abundances of CNO and several heavier elements in the primary and secondary components of 5 eclipsing close binaries around A-type (AR Aur, beta Aur, YZ Cas, WW Aur, and RR Lyn), in order to investigate the nature of chemical differences between both components (being comparatively slow rotators alike due to tidal synchronization). Regarding the systems comprising similar components, beta Aur and WW Aur were confirmed to exhibit no compositional difference between the primary and secondary both showing almost the same Am anomaly, th…
Context. Discovery of new variability classes in large surveys using multivariate statistics techniques such as clustering, relies heavily on the correct understanding of the distribution of known classes as point processes in parameter space. Aims. Our objective is to analyze the correspondence between the classical stellar variability types and the clusters found in the distribution of light curve parameters and colour indices of stars in the CoRoT exoplanet sample. The final aim is to help in the identification on new types of variability by first identifying the well known variables in the…
We review the method NAV (New Algol Variable) first introduced in 2012Ap.....55..536A, which uses the locally-dependent shapes of eclipses in an addition to the trigonometric polynomial of the second order (which typically describes the "out-of-eclipse" part of the light curve with effects of reflection, ellipticity and O'Connell). Eclipsing binary stars are believed to show distinct eclipses only if belonging to the EA type. With a decreasing eclipse width, the statistically optimal value of the trigonometric polynomial s (2003ASPC..292..391A) drastically increases from ~2 for elliptic (EL) v…
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 …
Flickering is a universal phenomenon in accreting astronomical systems which still defies detailed physical understanding. It is particularly evident in cataclysmic variables (CVs). Attempting to define boundary conditions for models, the strength of the flickering is measured in several thousand light curves of more than 100 CVs. The flickering amplitude is parameterized by the FWHM of a Gaussian fit to the magnitude distribution of data points in a light curve. This quantity requires several corrections before a comparison between different sources can be made. While no correlations of the f…
Binary systems anchor many of the fundamental relations relied upon in asteroseismology. Masses and radii are rarely constrained better than when measured via orbital dynamics and eclipse depths. Pulsating binaries have much to offer. They are clocks, moving in space, that encode orbital motion in the Doppler-shifted pulsation frequencies. They offer twice the opportunity to obtain an asteroseismic age, which is then applicable to both stars. They enable comparative asteroseismology -- the study of two stars by their pulsation properties, whose only fundamental differences are the mass and rot…
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 th…
We carried out high-precision photometric observations of three eclipsing ultrashortperiod contact binaries (USPCBs). Theoretical models were fitted to the light-curves by means of the Wilson-Devinney code. The solutions suggest that the three targets have evolved to a contact phase. The photometric results are as follows: a) 1SWASP J030749.87-365201.7, q=0.439\pm0.003, f=0.0\pm3.6%; b) 1SWASP J213252.93-441822.6, q=0.560\pm0.003, f=14.2\pm1.9%; c) 1SWASP J200059.78+054408.9, q=0.436\pm0.008, f=58.4\pm1.8%. The light curves show O'Connell effects, which can be modeled by assumed cool spots. Th…
Prompted by X-ray detections from multiple surveys, we investigated the A-type star HD 63021 and found that it is a double-lined spectroscopic binary with highly variable emission associated with the primary star. Analysis of our multi-epoch spectroscopic observations, the majority of which were carried out on small aperture telescopes, indicates a very short orbital period of just $2.9$ days, and a mass ratio M$_2$/M$_1$ of $0.23$. The A1 V star is a slow rotator, with a rotational speed of $\sim34$ km/s. Assuming its mass is $2.3$ M$_{\odot}$, the present-day secondary is an evolved star of …
