Fast Spectral Variability from Cygnus X-1

📝 Abstract

We have developed an algorithm that, starting from the observed properties of the X-ray spectrum and fast variability of an X-ray binary allows the production of synthetic data reproducing observables such as power density spectra and time lags, as well as their energy dependence. This allows to reconstruct the variability of parameters of the energy spectrum and to reduce substantially the effects of Poisson noise, allowing to study fast spectral variations. We have applied the algorithm to Rossi X-ray Timing Explorer data of the black-hole binary Cygnus X-1, fitting the energy spectrum with a simplified power law model. We recovered the distribution of the power law spectral indices on time-scales as low as 62 ms as being limited between 1.6 and 1.8. The index is positively correlated with the flux even on such time-scales.

💡 Analysis

We have developed an algorithm that, starting from the observed properties of the X-ray spectrum and fast variability of an X-ray binary allows the production of synthetic data reproducing observables such as power density spectra and time lags, as well as their energy dependence. This allows to reconstruct the variability of parameters of the energy spectrum and to reduce substantially the effects of Poisson noise, allowing to study fast spectral variations. We have applied the algorithm to Rossi X-ray Timing Explorer data of the black-hole binary Cygnus X-1, fitting the energy spectrum with a simplified power law model. We recovered the distribution of the power law spectral indices on time-scales as low as 62 ms as being limited between 1.6 and 1.8. The index is positively correlated with the flux even on such time-scales.

📄 Content

arXiv:1007.0474v1 [astro-ph.HE] 3 Jul 2010 Mon. Not. R. Astron. Soc. 000, 1–14 () Printed 18 November 2018 (MN LATEX style file v2.2) Fast Spectral Variability from Cygnus X-1 Y. X. Wu1,2⋆, T. M. Belloni2 and L. Stella3 1Department of Engineering Physics and Center for Astrophysics, Tsinghua University, Beijing 100084, China 2INAF-Osservatorio Astronomico di Brera, Via Bianchi 46, I-23807 Merate, Italy 3INAF-Osservatorio Astronomico di Roma, via Frascati 33, I-00040 Monteporzio Catone, Italy ABSTRACT We have developed an algorithm that, starting from the observed properties of the X- ray spectrum and fast variability of an X-ray binary allows the production of synthetic data reproducing observables such as power density spectra and time lags, as well as their energy dependence. This allows to reconstruct the variability of parameters of the energy spectrum and to reduce substantially the effects of Poisson noise, allowing to study fast spectral variations. We have applied the algorithm to Rossi X-ray Timing Explorer data of the black-hole binary Cygnus X-1, fitting the energy spectrum with a simplified power law model. We recovered the distribution of the power law spectral indices on time-scales as low as 62 ms as being limited between 1.6 and 1.8. The index is positively correlated with the flux even on such time-scales. Key words: X-rays: binaries – X-rays: individual: Cygnus X-1 – methods: statistical – methods: data analysis 1 INTRODUCTION Black hole binaries (BHB) exhibit considerable X-ray vari- ability on a wide range of time-scales. The study of X-ray fast time variability has become an important astrophysical research tool that helps us gain better insight into the physi- cal process at work near the black hole (see the recent review of van der Klis 2004). For instance, the dynamic time-scale for the motion within a few Schwarzschild radii of a 10 M⊙ black hole is at the order of milliseconds. Further consider- ing that most of the gravitational energy of accretion matter is released in the inner area of a few Schwarzschild radii, the variability at short time-scales can be used to probe the accretion-flow dynamics and geometries within the strong- field region. Time variability can be studied in the time domain or in the frequency domain. The latter is based on the Fourier transform (FT) and usually is based upon two basic tech- niques, the Power Density Spectrum (PDS) and the time lag spectrum. The square of Fourier transform amplitudes as a function of Fourier frequency constitutes the PDS, which provides the estimate of variance at different frequencies. The time lag spectrum is obtained from the phase lag, i.e. the phase angle difference between the Fourier vectors at different energy channels. In practice, the PDS and the lag spectra are usually averaged over many segments of obser- vation and frequencies in order to increase the statistical significance. The Fourier transform is reversible: the time series can be reconstructed from its Fourier transform by ⋆E-mail: wuyx@mails.thu.edu.cn; tomaso.belloni@brera.inaf.it means of Inverse Fourier transform (IFT). On the contrary, the PDS is not reversible, since the phase information in the FT is lost. In principle there is an infinite variety of different signals that will yield the same PDS. The fast variability observed from BHB is of stochas- tic nature and as such cannot be modeled directly. In other words, it is not possible to reproduce the exact observed variations. The aim of time-series analysis is to character- ize the average properties that give rise to the fluctuations, under the assumption that the process is stationary. A suc- cessful model should reproduce the PDS and the lag spec- trum, as well as other statistical properties of the signal (see, e.g. Uttley et al. 2005). A conventional model describ- ing the temporal fluctuation is the shot-noise model (Terrell 1972; Negoro et al. 1994). It has become clear, however, that in this framework complex shot profiles or distribu- tions of shot durations and amplitudes have to be assumed to model the variability of BHBs (e.g. Miyamoto et al. 1988; Belloni & Hasinger 1990; Lochner et al. 1991). An alternative way is to apply Linear State Space Models (LSSMs) which are based on stochastic processes, or au- toregressive (AR) processes to describe the temporal vari- ability (K¨onig & Timmer 1997; Pottschmidt et al. 1998). Uttley et al. (2005) use a non-linear model to explain the lognormal flux distribution and rms-flux relation. All these models are phenomenological; based on the PDS alone they try to reproduce the observed properties through a mathe- matical model, which can provide constraints on physical models. On the other hand, Ar´evalo & Uttley (2006) at- tempted a more physically-constrained generating process to model all the spectral-timing properties simultaneously. 2 Y. X. Wu, T. M. Belloni and L. Stella The usual course of action is to extract information in the frequency domain, such as a P

This content is AI-processed based on ArXiv data.