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

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.