Method of Running Sines: Modeling Variability in Long-Period Variables

TL;DR

The paper reviews the 'Running Sines' method for analyzing nearly periodic signals with variable periods, demonstrating its effectiveness on astrophysical data like long-period variables and binary star oscillations.

Contribution

It introduces and evaluates the 'Running Sines' method as a tool for modeling variability in irregularly spaced time series, especially in astrophysical contexts.

Findings

Effective for signals with large period variations

Applicable to irregularly spaced data

Successfully applied to various variable stars

Abstract

We review one of complementary methods for time series analysis - the method of "Running Sines". "Crash tests" of the method include signals with a large period variation and with a large trend. The method is most effective for "nearly periodic" signals, which exhibit "wavy shape" with a "cycle length" varying within few dozen per cent (i.e. oscillations of low coherence). This is a typical case for brightness variations of long-period pulsating variables and resembles QPO (Quasi-Periodic Oscillations) and TPO (Transient Periodic Oscillations) in interacting binary stars - cataclysmic variables, symbiotic variables, low-mass X-Ray binaries etc. General theory of "running approximations" was described by Andronov (1997A &AS..125..207A), one of realizations of which is the method of "running sines". The method is related to Morlet-type wavelet analysis improved for irregularly spaced data (Andronov, 1998KFNT...14..490A, 1999sss..conf...57A), as well as to a classical "running mean" (="moving average"). The method is illustrated by an application to a model signal with strongly variable period, as well as to a semi-regular variable AF Cyg. Some other stars studied with this method are discussed, e.g. RU And (switching between "Mira-type" large amplitude oscillations and time intervals of "constancy"), intermediate polars MU Cam (1RXS J062518.2+733433) and BG CMi, magnetic dwarf nova DO Dra, symbiotic stars UV Aur and V1329 Cyg.