Phase Lags and Coherence of X-Ray Variability in Black Hole Candidates

The ``low'' (hard or ``non-thermal'') state of black hole candidates is sometimes modelled via an optically thick, hot Compton cloud that obscures a softer input source such as an accretion disk. In these models the observed output spectra consist entirely of photons reprocessed by the cloud, making it difficult to extract information about the input spectra. Recently Miller (1995) has argued that the Fourier phase (or time) lag between hard and soft X-ray photons in actuality represents the phase lags intrinsic to the input source, modulo a multiplicative factor. The phase lags thus would be a probe of the input photon source. In this paper we examine this claim and find that, although true for the limited parameter space considered by Miller, the intrinsic phase lag disappears whenever the output photon energy is much greater than the input photon energy. The remaining time lags represent a ``shelf'' due to differences between mean diffusion times across the cloud. As pointed out by Miller, the amplitude of this shelf -- which is present even when the intrinsic time lags remain -- is indicative of the size and temperature of the Compton cloud and is a function of the two energies being compared. However, we find that with previous instruments such as Ginga the shelf, if present, was likely obscured by counting noise. A more sensitive measure of Compton cloud parameters may be obtainable from the coherence function, which is derived from the amplitude of the Fourier cross power spectral density. This function has been seen to exponentially decrease at high Fourier frequencies in Cygnus X-1. Coherence loss is characteristic of Compton clouds that undergo large variations of size and/or temperature on time scales longer than about 10 seconds. We argue that observing phase lags and coherenceComment: 14 pages, uuencoded postscript, accepted for publication in Monthly Notice

RXTE Observation of Cygnus X-1: II. Timing Analysis

We present timing analysis for a Rossi X-ray Timing Explorer observation of Cygnus X-1 in its hard/low state. This was the first RXTE observation of Cyg X-1 taken after it transited back to this state from its soft/high state. RXTE's large effective area, superior timing capabilities, and ability to obtain long, uninterrupted observations have allowed us to obtain measurements of the power spectral density (PSD), coherence function, and Fourier time lags to a decade lower in frequency and half a decade higher in frequency than typically was achieved with previous instruments. Notable aspects of our observations include a weak 0.005 Hz feature in the PSD coincident with a coherence recovery; a `hardening' of the high-frequency PSD with increasing energy; a broad frequency range measurement of the coherence function, revealing rollovers from unity coherence at both low and high frequency; and an accurate determination of the Fourier time lags over two and a half decades in frequency. As has been noted in previous similar observations, the time delay is approximately proportional to f^(-0.7), and at a fixed Fourier frequency the time delay of the hard X-rays compared to the softest energy channel tends to increase logarithmically with energy. Curiously, the 0.01-0.2 Hz coherence between the highest and lowest energy bands is actually slightly greater than the coherence between the second highest and lowest energy bands. We carefully describe all of the analysis techniques used in this paper, and we make comparisons of the data to general theoretical expectations. In a companion paper, we make specific comparisons to a Compton corona model that we have successfully used to describe the energy spectral data from this observation.Comment: To Be Published in the Astrophysical Journal. 18 pages. Uses emulatepaj.st

RXTE Observation of Cygnus X-1: Spectral Analysis

We present the results of the analysis of the broad-band spectrum of Cygnus X-1 from 3.0 to 200 keV, using data from a 10 ksec observation by the Rossi X-ray Timing Explorer. The spectrum can be well described phenomenologically by an exponentially cut-off power law with a photon index Gamma = 1.45 +/- 0.02 (a value considerably harder than typically found), e-folding energy E_fold = 162 +/- 9 keV, plus a deviation from a power law that formally can be modeled as a thermal blackbody with temperature kT_bb = 1.2 +/1 0.2 keV. Although the 3 - 30 keV portion of the spectrum can be fit with a reflected power law with Gamma = 1.81 +/- 0.01 and covering fraction f = 0.35 +/- 0.02, the quality of the fit is significantly reduced when the HEXTE data in the 30 - 100 keV range is included, as there is no observed hardening in the power law within this energy range. As a physical description of this system, we apply the accretion disc corona models of Dove, Wilms & Begelman (1997) --- where the temperature of the corona is determined self-consistently. A spherical corona with a total optical depth tau = 1.6 +/- 0.1 and an average temperature kT_c = 87 +/- 5 keV, surrounded by an exterior cold disc, does provide a good description of the data (reduced chi-squared = 1.55). These models deviate from the data by up to 7% in the 5 - 10 keV range, and we discuss possible reasons for these discrepancies. However, considering how successfully the spherical corona reproduces the 10 - 200 keV data, such ``photon-starved'' coronal geometries seem very promising for explaining the accretion processes of Cygnus X-1.Comment: Revised version (added content). 8 pages, 6 figures, 1 table.tex file, latex, uses mn.sty. Accepted for publication in MNRA

X-Ray Variability Coherence: How to Compute it, What it Means, and How it Constrains Models of Cyg X-1 and GX 339-4

We describe how the coherence function, a Fourier frequency-dependent measure of the linear correlation between time series measured simultaneously in two energy channels, can be used in conjunction with energy spectra, power spectra, and time delays between energy channels to constrain models of the spectrum and variability of x-ray binaries. Here we present a procedure for estimating the coherence function in the presence of counting noise. We apply this method to the black hole candidates Cyg X--1 and GX 339--4, and find that the near perfect coherence between low and high energy x-ray photons rules out a wide range of models that postulate: spatially extended fluctuating emission, thermal flares, and overlapping shot-noise.Comment: Latex file (emulateapj macro included, see comments at beginning of file), 1 eps figure. To be published in ApJ Letters, Jan. 1, 199

X-Ray Variability Coherence: How to Compute It, What It Means, and How It Constrains Models of GX 339-4 and Cygnus X-1

We describe how the coherence function—a Fourier frequency–dependent measure of the linear correlation between time series measured simultaneously in two energy channels—can be used in conjunction with energy spectra, power spectra, and time delays between energy channels to constrain models of the spectrum and variability of X-ray binaries. Here we present a procedure for estimating the coherence function in the presence of counting noise. We apply this method to the black hole candidates Cyg X-1 and GX 33924 and find that the near-perfect coherence between low- and high-energy X-ray photons rules out a wide range of models that postulate spatially extended fluctuating emission, thermal flares, and overlapping shot noise

On the Correlation of Torque and Luminosity in GX 1+4

Over five years of daily hard X-ray (>20 keV) monitoring of the 2-min accretion-powered pulsar GX 1+4 with the Compton Gamma Ray Observatory/BATSE large-area detectors has found nearly continuous rapid spin-down, interrupted by a bright 200-d spin-up episode. During spin-down, the torque becomes more negative as the luminosity increases (assuming that the 20-60 keV pulsed flux traces bolometric luminosity), the opposite of what is predicted by standard accretion torque theory. No changes in the shape of the 20-100 keV pulsed energy spectrum were detected, so that a very drastic change in the spectrum below 20 keV or the pulsed fraction would be required to make the 20-60 keV pulsed flux a poor luminosity tracer. These are the first observations which flatly contradict standard magnetic disk accretion theory, and they may have important implications for understanding the spin evolution of X-ray binaries, cataclysmic variables, and protostars. We briefly discuss the possibility that GX 1+4 may be accreting from a retrograde disk during spin-down, as previously suggested.Comment: 10 pages including 3 PS figures. To appear in ApJ Letter

RXTE Observation of Cygnus X-1

We present timing analysis for a Rossi X-ray Timing Explorer (RXTE) observation of Cygnus X-1 in its hard/low state. This was the first RXTE observation of Cyg X-1 taken after it transited back to this state from its soft/high state. RXTE's large effective area, superior timing capabilities, and ability to obtain long, uninterrupted observations have allowed us to obtain measurements of the power spectral density (PSD), coherence function, and Fourier time lags to a decade lower in frequency and half a decade higher in frequency than typically was achieved with previous instruments. Notable aspects of our observations include a weak 0.005 Hz feature in the PSD coincident with a coherence recovery; a 'hardening' of the high-frequency PSD with increasing energy; a broad frequency range measurement of the coherence function, revealing rollovers from unity coherence at both low and high frequency; and an accurate determination of the Fourier time lags over two and a half decades in frequency. As has been noted in previous similar observations, the time delay is approximately proportional to f(exp -0.7), and at a fixed Fourier frequency the time delay of the hard X-rays compared to the softest energy channel tends to increase logarithmically with energy. Curiously, the 0.01-0.2 Hz coherence between the highest and lowest energy bands is actually slightly greater than the coherence between the second highest and lowest energy bands. We carefully describe all of the analysis techniques used in this paper, and we make comparisons of the data to general theoretical expectations. In a companion paper, we make specific comparisons to a Compton corona model that we have successfully used to describe the energy spectral data from this observation