Characterizing black hole variability with nonlinear methods: the case of the X-ray Nova 4U 1543-47

Aims. We investigate the possible nonlinear variability properties of the black hole X-ray nova 4U 1543-47 with a dual goal: 1) to complement the temporal studies based on linear techniques, and 2) to search for signs of (deterministic and stochastic) nonlinearity in Galactic black hole (GBH) light curves. The proposed analysis may provide additional model-independent constraints to shed light on black hole systems and may strengthen the unification between GBHs and active galactic nuclei (AGN). Methods. First, we apply the weighted scaling index method (WSIM) to characterize the X-ray variability properties of 4U 1543-47 in different spectral states during the 2002 outburst. Second, we use surrogate data to investigate whether the variability is nonlinear in any of the different spectral states. Results. The main findings from our nonlinear analysis can be summarized as follows: 1) The mean weighted scaling index <alpha > appears to be able to uniquely parametrize the temporal variability properties of GBHs. The three different spectral states of the 2002 outburst of 4U 1543-47 are characterized by different and well constrained values of <alpha > satisfying the following relationship: <alpha > VHS < <alpha >(LS) < <alpha >(HS). 2) The search for nonlinearity reveals that the variability is linear in all light curves with the notable exception of the very high state (VHS). Conclusions. Our results imply that we can use the WSIM to assign a single number, namely the mean weighted scaling index <alpha >, to a light curve, and in this way distinguish between the different spectral states of a source. The detection of nonlinearity in the VHS which is characterized by the presence of most prominent QPOs disfavors intrinsically linear models which have been proposed to account for the low frequency QPOs in GBHs. Finally, as the WSIM results are scarcely affected by the noise level and length of the light curve, this naturally suggests an application to AGN variability with the possibility of a direct comparison with GBHs. However, before deriving more general conclusions, it is first necessary to carry out a systematic nonlinear analysis on several GBHs in different spectral states to assess whether the results obtained for 4U 1543-47 can be considered as representative for the entire class of GBHs.