LINEAR AND NON-LINEAR TIME SERIES ANALYSIS OF CYG X-1

J. Timmer, I. Wardinski, H. Voss, U. Schwarz, G. Hasinger, Tomaso Belloni (EXSAS), Michael van der Klis, J. Kurths

PRE 61 (2) 1 February 2000, Preprint

We analyze the variability in the X-ray lightcurves of the black hole candidate Cygnus X-1 by linear and nonlinear time series analysis methods. While a linear model describes the over-all second order properties of the observed data well, surrogate data analysis reveals a significant deviation from linearity. We discuss the relation between shot noise models usually applied to analyze these data and linear stochastic autoregressive models. We debate statistical and interpretational issues of surrogate data testing for the present context. Finally, we suggest a combination of tools from linear and nonlinear time series analysis methods as a procedure to test the predictions of astrophysical models on observed data.

Light curve from 1996 to 2001


X-Ray Flux: Low State Feb 12, 1996, Low State Feb 18, 1998 and Intermediate State May 25, 1998


X-Ray Flux Densities


X-Ray Flux Log-Lin-Periodogram: Data + LSSM Fit


X-Ray Flux Log-Log-Periodogram: Data + LSSM Fit


Evolutionary Q(t,m) of the Intermediate State, Q(m)

Q(m) statistics and twice the standard error calculated from the 32 segments of length 20000 of the second time series based on the estimated denoised data by the Kalman filter.

Relaxating shot


Relaxating oscillator shot


Q(m)