[vsnet-chat 7870] Paper: "Method of Running Sines: Modeling Variability..."

[Ivan Andronov]

http://arxiv.org/abs/1308.1129

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

Ivan L. Andronov^1, Lidia L. Chinarova^1

1 Department “High and Applied Mathematics”, Odessa National Maritime University, Ukraine
2 Astronomical Observatory, Odessa National University, Ukraine


                 “Even Ptolomeus knew the Fourier transform.
                  Thus no new methods for time series analysis are needed.”
                                    Anonymous referee, 1997

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.