Extraction of a deterministic component from ROSAT X-ray data using a wavelet transform and the principal component analysis

¹ Steward Observatory, University of Arizona, Tucson, AZ, U.S.A.
² Swedish Institute of Space Physics, S-981 28 Kiruna, Sweden

Send offprint request to: L. Liszka, e-mail: ludwik@irf.se

Received: 23 April 1999
Accepted: 23 August 1999

Abstract

In the present work wavelet transform methods together with principal component analysis and non-linear filtering are used to extract the deterministic components in AGN X-ray variability from the photon event history files. The photon history files are converted into so called ampligrams using the Morlet wavelet transform. The ampligram may be considered as an analogy to signal decomposition into Fourier components. In that case different components correspond to different frequencies. In the present case different components correspond to different wavelet coefficient magnitudes, being equivalent to spectral densities. In addition to the ampligram a time scale spectrum is defined, being a forward wavelet transform of each row (wavelet coefficient magnitude) in the ampligram. The time scale spectrum of the ampligram tells us more than the original wavelet spectrum does. The time scale spectrum reveals individual signal components and indicates the statistical properties of each component: deterministic or stochastic. The ampligram and its time scale spectrum seems to be a useful tool to study processes resulting in a mixture of stochastic and deterministic components. In the case of X-ray luminosity variations in the AGN it is expected that the described data analysis technique will provide a conclusive proof of the existence of building blocks. The efficient decomposition of the luminosity variation data may be used to study the deterministic, quasi-periodic phenomena, like tones and chirps. The most important point of the method is that it may be used to remove the influence of the Poisson statistics in the photon data and in this way to extract real deterministic luminosity variations. As it is shown by simulations in the final part of this work, the method is capable to extract weak, of the order of few percent, deterministic variations embedded in a totally Poisson-like series of events. There may be also other applications of the method in astrophysics, for example to study X-ray pulsars.