Improvement of Simplified Models of Variability of Stars: A review

TL;DR

This review discusses advanced algorithms and methods for analyzing irregular astronomical data of variable stars, improving accuracy in period detection and light curve approximation without traditional detrending.

Contribution

The paper introduces novel algorithms for statistically correct analysis of irregular stellar variability data, enhancing periodogram analysis, light curve approximation, and coherence estimation.

Findings

Improved periodogram analysis without detrending.

Enhanced light curve approximation with additional harmonic waves.

Effective analysis of irregularly spaced data using ACF and scalegram methods.

Abstract

Astronomical data are typically irregular in time, e.g. the space (HIPPARCOS/TYCHO, KEPLER, GAIA, WISE etc.) and ground-based CCD (NSVS, ASAS, CRTS, SuperWASP etc.) and photographic (Harvard, Sonneberg, Odessa etc.) photometrical surveys. This leads to cancellation of the conditions, which lead to the orthogonality of the basic functions, and thus the simplified methods give biased parameters of the approximations. We have elaborated a series of algorithms and programs for statistically correct analysis, and have applied them to 2000+ variable stars of different types. The data were obtained from an international collaboration in a frame of the "Inter-Longitude Astronomy" (ILA) campaign. Some highlights of our studies are presented, with an extended list of our original publications. The main improvements were done: 1) for the periodogram analysis - the parameters are determined from a complete set of equations containing the (algebraic polynomial) trend superimposed on the (multi-) harmonic wave, so no "detrending", no "prewhitening" are used; 2) for the approximations - we use additional (multi-) harmonic waves, and also "special shapes" (patterns) for parts of the light curve, which correspond to relatively fast changes (minima of the eclipsing binaries, minima and maxima for the pulsating variables); 3) "auto correlation analysis" (ACF) - taking into account the bias due to a trend removal (previously - only a subtraction of the sample mean was taken into account); ACF for the irregularly spaced data; 4) for the signals with bad coherence, the "scalegram" analysis is proposed, which allows to estimate a characteristic cycle length and the amplitude, as well as to provide a realistic approximation; 5) the extension of the Morlet-type wavelet for more periodic signals and 6) "running" (parabola, sine) approximations for aperiodic and "nearly periodic" variations, respectively.