Timescale Resolved Spectroscopy of Cyg X-1

arXiv:0903.4118v1 [astro-ph.IM] 24 Mar 2009 Timescale Resolved Spectroscopy of Cyg X-1 Y. X. Wu1, T. P. Li1, 2, 3, T. M. Belloni4, T. S. Wang2 and H. Liu3 ABSTRACT We propose the timescale-resolved spectroscopy (TRS) as a new method to combine the timing and spectral study. TRS is based on the time domain power spectrum and reflects the variable amplitudes of spectral components on different timescales. We produce the TRS with the RXTE PCA data for Cyg X-1 and studied the spectral parameters (the power law photon index and the equivalent width of the iron fluorescent line) as a function of timescale. The results of TRS and frequency-resolved spectra (FRS) have been compared, and similarities have been found for the two methods with the identical motivations. We also discover the correspondences between the evolution of photon index with timescale and the evolution of the equivalent width with timescale. The observations can be divided into three types according to the correspondences and different type is connected with different spectral state. Subject headings: methods: data analysis — stars: binaries: general — stars: individual: Cyg X-1 — X-rays: general 1. INTRODUCTION The X-ray emission from an accreting compact object (neutron star or black hole) carries information concerning geometry and physical conditions in the vicinity of the central com- pact object. One way to study the X-ray data is to fit various models to the time-averaged energy spectra. For hard spectral states of black-hole binaries, the spectra are well under- stood with a model consisting of weak disk emission, its Comptonization by a hot corona, 1Department of Engineering Physics & Center for Astrophysics, Tsinghua University, Beijing, China. E-mail: wuyx@mails.thu.edu.cn 2Department of Physics & Center for Astrophysics, Tsinghua University, Beijing, China 3Particle Astrophysics Lab., Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China 4INAF-Osservatorio Astronomico di Brera, Via Bianchi 46, I-23807 Merate, Italy – 2 – and reflection or reprocessing of the hard X-ray photons by the disk. Other mechanisms as alternatives to Comptonization, such as jet models, have also been discussed in the litera- ture (e.g. Markoffet al. 2005; Tomsick et al. 2008). The spectra of the soft spectral states are characterized with a dominant soft disk component. In the past few years, efforts have been made to combine the spectral and variability information to investigate geometry and dynamics of the X-ray sources. A novel technique is known as frequency-resolved spectrum or Fourier-resolved spectrum (FRS), which is based on both power spectrum and average energy spectrum. This method accumulates the variability amplitudes (or power spectral density amplitudes) within a well-defined frequency range for each energy bin to produce the “energy spectrum”1 for the specific frequency band. Therefore it provides an opportunity to explore the variability properties of different spectral components (e.g. disk emission, power law and iron fluorescent line); as such, it allows certain immediate insight into the spatial locations or dynamics responsible for the emission of the specific spectral components. For example, the FRS can indicate the geometrical size of the reprocessing medium, because the light crossing time of the reflector provides a natural frequency filter. Since it was first proposed by Revnivtsev et al. (1999), the FRS has been successfully applied to Galac- tic black-hole binaries (Revnivtsev et al. 1999, 2001; Gilfanov et al. 2000; Reig et al. 2006), neutron star low mass X-ray binaries (LMXBs) (Gilfanov et al. 2003; Revnivtsev & Gilfanov 2006; Shrader et al. 2007) and active galactic nuclei (AGN) (Papadakis et al. 2005, 2007; Ar´evalo et al. 2008). In interpreting a Fourier spectrum in the time domain, one usually takes 1/f, the reciprocal of a Fourier frequency f, as a timescale. A time domain power spectrum can be derived directly from a time series without using the Fourier transform (Li 2001), where the definition of power is based only on the original meaning of rms variation and the power spectrum represents the distribution of the variability amplitude versus timescale. The Fourier domain power spectrum is not an accurate representation of rms variations in the time domain, i.e., for a stochastic process the Fourier spectrum underestimates the signal power on timescales shorter than the characteristic time of the process, whereas the time domain spectrum can correctly estimate it. For the X-ray emission of black-hole binaries, Fourier spectra and time domain spectra differ from each other in short timescales or high frequency regions (less than ∼0.1 s): power densities from time domain spectra are significantly higher than that from Fourier spectra (Li & Muraki 2002). For investigating the geometry and dynamics of black-hole binaries, it is interesting to study the fast variability of the black-hole 1The term of “energy spectrum”

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