Lev Titarchuk

Millisecond X-Ray Variability from an Accreting Neutron Star System

We report the detection with the Proportional Counter Array (PCA) on board the Rossi X-Ray Timing Explorer (RXTE) of millisecond variability in the X-ray emission from the low-mass X-ray binary 4U 1728-34. Pulsations at 363 Hz with amplitudes (rms) of 2.5%-10% are present in six of the eight bursts analyzed to date. The strongest were seen in two successive bursts recorded on 1996 February 16 when the quiescent count rate was near the highest seen by PCA. The pulsations during these bursts show frequency changes of 1.5 Hz during the first few seconds but become effectively coherent as the burst decays. We interpret the 363 Hz pulsations as rotationally induced modulations of inhomogeneous burst emission. This represents the first compelling evidence for a millisecond spin period in a low-mass X-ray binary. Complex, intensity-dependent, millisecond X-ray variability is also present in all the quiescent flux intervals we examined. Most interesting was the behavior as the count rate approached its highest observed level. Two quasi-periodic oscillations (QPOs) were simultaneously observed in the 650-1100 Hz range. Both QPOs increased in frequency together, maintaining a nearly constant frequency separation of about 363 Hz, the spin period inferred from the burst oscillations. This phenomenology is strongly suggestive of the magnetospheric beat frequency model proposed for the horizontal-branch oscillations (HBOs) seen in Z sources. We discuss this and several other possible physical interpretations for the observed X-ray variability.

X-Ray Spectral Formation in a Converging Fluid Flow: Spherical Accretion into Black Holes

We study Compton upscattering of low-frequency photons in a converging flow of thermal plasma. The photons escape diffusively, and electron scattering is the dominant source of opacity. We solve the equation of radiative transfer in the case of spherical, steady state accretion into black holes numerically and approximately analytically. Unlike previous work on this subject, we consider the inner boundary at a finite radius, and this has a significant effect on the emergent spectrum. It is shown that the bulk motion of the converging flow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the flow is of order a few keV or less. In this case, the spectrum observed at infinity consists of a soft component coming from input photons that escaped after a few scatterings without any significant energy change and of a power law that extends to high energies and is made of those photons that underwent significant upscattering. The luminosity of the power law is relatively small compared to that of the soft component. The more reflective the inner boundary is, the flatter the power-law spectrum becomes. The spectral energy power-law index for black hole accretion is always higher than 1, and it is approximately 1.5 for high accretion rates. This result tempts us to say that bulk motion Comptonization might be the mechanism behind the power-law spectra seen in black hole X-ray sources.

Temporal and Spectral Properties of Comptonized Radiation and Its Applications

We have found relations between the temporal and spectral properties of radiation Comptonized in an extended atmosphere associated with compact accreting sources. We demonstrate that the Nuctuation power spectrum density (PSD) imposes constraints on the atmosphere scale and pro-le. Furthermore, we indicate that the slope and low-frequency break of the PSD are related to the Thomson depth, of the q 0 , atmosphere and the radius of its physical size, respectively. Since the energy spectrum of the escaping radiation also depends on (and the electron temperature the relation between spectral and tem- q 0 kT e ), poral properties follows. This relation allows, for the -rst time, an estimate of the accreting matter Thomson depth, independent of arguments involving Comptonization. We present -gures for the q 0 , light curves and PSDs of di†erent energy bands, the photon energy spectra, and the phase lags as func- tions of the variability frequency. The temporal properties of the high (soft) and low (hard) state of black hole sources are discussed in this context. Subject headings: accretion, accretion disks E black hole physics E radiation mechanisms: nonthermal E stars: neutron

The Converging Inflow Spectrum Is an Intrinsic Signature for a Black Hole: Monte Carlo Simulations of Comptonization on Free-falling Electrons

An accreting black hole is, by definition, characterized by the drain. Namely, matter falls into a black hole much the same way as water disappears down a drain: matter goes in and nothing comes out. As this can only happen in a black hole, it provides a way to see a black hole, a unique observational signature of black holes. The accretion proceeds almost in a free-fall manner close to the black hole horizon, where the strong gravitational field dominates the pressure forces. In this paper we calculate (by using Monte Carlo simulations) the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) within about 3 Schwarzschild radii of the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems (BHS) can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread (Greens) function. The latter boosted photon component is seen as an extended power law at energies much higher than the characteristic energy of the soft photons. We demonstrate the stability of the power spectral index (α=1.8±0.1) over a wide range of the plasma temperature, 0-10 keV, and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high-energy cutoff occurs at energies of 200-400 keV, which are related to the average energy of electrons mec2 impinging on the event horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum (Hua & Titarchuk) when the CI plasma temperature is getting of order of 50 keV (the typical ones for the hard state of BHS). In this case one can see the effect of the bulk motion only at high energies, where there is an excess in the CI spectrum with respect to the pure thermal one. Furthermore, we demonstrate that the change of spectral shapes from the soft X-ray state to the hard X-ray state is clearly to be related to the temperature of the bulk flow. We derive a generic formula for the temperature of the emitting region (CI) that depends on the ratio of the energy release in this very region and in the disk. Using this formula, we demonstrate that the temperature of the emission region in the hard state of the BHS is approximately 2 times higher than the ones of neutron star systems (NSS) in the hard state, which is confirmed by recent RXTE and Beppo-SAX observations of the hard state of NSS. The effect of the bulk Comptonization compared with the thermal one is getting stronger when the plasma temperature drops below 10 keV. These Monte Carlo simulated CI spectra are an inevitable stamp of the BHS where the strong gravitational field dominates the pressure forces.An accreting black hole is, by definition, characterized by the drain. Namely, the matter falls into a black hole much the same way as water disappears down a drain - matter goes in and nothing comes out. As this can only happen in a black hole, it provides an unique way to see it. The accretion proceeds almost in free fall close to the black hole horizon. In this paper we calculate (by using Monte -Carlo simulations) the specific features of X-ray spectra formed as a result of upscattering of the soft (disk) photons in the converging inflow (CI) within about 3 Schwarzschild radii of the black hole. The full relativistic treatment has been implemented to reproduce these spectra. We show that spectra in the soft state of black hole systems can be described as the sum of a thermal (disk) component and the convolution of some fraction of this component with the CI upscattering spread function. The latter boosted photon component is seen as an extended power-law at energies much higher than the characteristic soft photons energy. We demonstrate the stability of the power spectral index (alpha= 1.8) over a wide range of the plasma temperature 0-10 keV and mass accretion rates (higher than 2 in Eddington units). We also demonstrate that the sharp high energy cutoff occurs at energies of 200-400 keV which are related to the average rest energy of electrons impinging upon the horizon. The spectrum is practically identical to the standard thermal Comptonization spectrum when the CI plasma temperature is getting of order of 50 keV (hard state of BHS). Also, the change of spectral shapes from the soft to the hard X-ray state is clearly to be related with the temperature of the bulk flow. These Monte-Carlo simulated CI spectra are then a inevitable stamp of the BHS.

Correlations between Kilohertz Quasi-periodic Oscillations and Low-Frequency Features Attributed to Radial Oscillations and Diffusive Propagation in the Viscous Boundary Layer around a Neutron Star

We present a dimensional analysis of two characteristic timescales in the boundary layer where the disk adjusts to the rotating neutron star (NS). The boundary layer is treated as a transition region between the NS surface and the first Keplerian orbit. The radial transport of the angular momentum in this layer is controlled by a viscous force defined by the Reynolds number, which in turn is related to the mass accretion rate. We show that the observed low-Lorentzian frequency is associated with radial oscillations in the boundary layer, where the observed break frequency is determined by the characteristic diffusion time of the inward motion of the matter in the accretion flow. Predictions of our model regarding relations between those two frequencies and the frequencies of kilohertz quasi-periodic oscillations (kHz QPOs) compare favorably with recent observations of the source 4U 1728-34. This Letter contains a theoretical classification of kHz QPOs in NS binaries and the related low-frequency features. Thus, results concerning the relationship between the low-Lorentzian frequency of viscous oscillations and the break frequency are presented in the framework of our model of kHz QPOs viewed as Keplerian oscillations in a rotating frame of reference.

Spectral Index and Quasi-Periodic Oscillation Frequency Correlation in Black Hole Sources: Observational Evidence of Two Phases and Phase Transition in Black Holes

Recent studies have shown that strong correlations are observed between the low frequencies (1-10 Hz) of quasi-periodic oscillations (QPOs) and the spectral power law index of several black hole (BH) candidate sources, in low (hard) states, steep power law (soft) states, and transitions between these states. The observations indicate that the X-ray spectra of such state (phases) show the presence of a power-law component and are sometimes related to simultaneous radio emission, indicating the probable presence of a jet. Strong QPOs (>20% rms) are present in the power density spectrum in the spectral range where the power-law component is dominant (i.e., 60%90%). This evidence contradicts the dominant, long-standing interpretation of QPOs as a signature of the thermal accretion disk. We present the data from the literature and our own data to illustrate the dominance of power-law index-QPO frequency correlations. We provide a model that identifies and explains the origin of the QPOs and how they are imprinted on the properties of the power-law flux component. We argue for the existence of a bounded compact coronal region that is a natural consequence of the adjustment of the Keplerian disk flow to the innermost sub-Keplerian boundary conditions near the central object and that ultimately leads to the formation of a transition layer (TL) between the adjustment radius and the innermost boundary. The model predicts two phases or states dictated by the photon upscattering produced in the TL: (1) a hard state, in which the TL is optically thin and very hot (kT approximately greater than 50 keV), producing photon upscattering via thermal Comptonization (the photon spectrum index Gamma approximates 1.7 for this state is dictated by gravitational energy release and Compton cooling in an optically thin shock near the adjustment radius), and (2) a soft state that is optically thick and relatively cold (kT approximately less than 5 keV the index for this state, Gamma approximates 2.8, is determined by soft-photon upscattering and photon trapping in a converging flow into the BH). In the TL model for the corona, the QPO frequency V(sub high) is related to the gravitational (close to Keplerian) frequency V(sub K) at the outer (adjustment) radius and v(sub low) is related to the TLs normal mode (magnetoacoustic) oscillation frequency v(sub MA) . The observed correlations between index and low and high QPO frequencies are readily explained in terms of this model. We also suggest a new method for evaluation of the BH mass using the index-frequency correlation.

The Extended Power Law as an Intrinsic Signature for a Black Hole

We analyze the exact general relativistic integrodifferential equation of radiative transfer describing the interaction of low-energy photons with a Maxwellian distribution of hot electrons in the gravitational field of a Schwarzschild black hole. We prove that, owing to Comptonization, an initial arbitrary spectrum of low-energy photons unavoidably results in spectra characterized by an extended power-law feature. We examine the spectral index by using both analytical and numerical methods for a variety of physical parameters as such the plasma temperature and the mass accretion rate. The presence of the event horizon as well as the behavior of the null geodesics in its vicinity largely determine the dependence of the spectral index on the flow parameters. We come to the conclusion that the bulk motion of a converging flow is more efficient in upscattering photons than thermal Comptonization, provided that the electron temperature in the flow is of order of a few kilo-electron volts or less. In this case, the spectrum observed at infinity consists of a soft component, which is produced by those input photons that escape after a few scatterings without any significant energy change, and a hard component (described by a power law), which is produced by the photons that underwent significant upscattering. The luminosity of the power-law component is relatively small compared to that of the soft component. For accretion into a black hole, the spectral energy index of the power law is always higher than 1 for plasma temperatures of order of a few kilo-electron volts. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black hole X-ray sources.

Effects of Downscattering on the Continuum and Line Spectra in a Powerful Wind Environment: Monte Carlo Simulations, Analytical Results, and Data Analysis

In an earlier paper, the general formulation and results for photon reprocessing (downscattering) that included recoil and Comptonization effects due to divergence of the flow were presented. In a second paper we showed the Monte Carlo (MC) simulated continuum and line spectra. We also provided an analytical description of the simulated continuum spectra using the diffusion approximation. We have simulated the propagation of monochromatic and continuum photons in a bulk outflow from a compact object. Electron scattering of the photons within the expanding flow leads to a decrease of their energy, which is of first order in V/c (where V is the outflow velocity). The downscattering effect of first order in V/c in the diverging flow is explained by semianalytical calculations and confirmed by MC simulations. We conclude that redshifted lines and downscattering bumps are intrinsic properties of the powerful outflows for which the Thomson optical depth is greater than 1. We fitted our model line profiles to the observations using four free parameters, β = V/c, the optical depth of the wind τ, the wind temperature kTe, and the original line photon energy E0. We show how the primary spectrum emitted close to the black hole is modified by reprocessing in the warm wind. In the framework of our wind model, the fluorescent iron line Kα is formed in the partly ionized wind as a result of illumination by central source continuum photons. The demonstrated application of our outflow model to the XMM-Newton observations of MCG -6-30-15 and to the ASCA observations of GRO J1655-40 points out a potential powerful spectral diagnostic for probes of the outflow-central object connection in Galactic and extragalactic black hole sources.

Do the Spectra of Soft X-Ray Transients Reveal Bulk-Motion Inflow Phenomenon?

We present our analysis of the high-energy radiation from black hole (BH) transients using archival data obtained primarily with RXTE and a comprehensive test of the bulk-motion Comptonization (BMC) model for the high-soft state continuum. The emergent spectra of over 30 separate measurements of the GRO J1655-40, GRS 1915+105, GRS 1739-278, 4U 1630-47 XTE J1755-32, and EXO 1846-031 X-ray sources are successfully fitted by the BMC model, which has been derived from basic physical principles in previous work. This in turn provides direct physical insight into the innermost observable regions, where matter impinging on the event horizon can effectively be directly viewed. The BMC model is characterized by three parameters: the disk color temperature, a geometric factor related to the illumination of the BH site by the disk, and a spectral index related to the efficiency of the bulk-motion upscattering. For the case of GRO J1655-40, where there are distance and mass determinations, a self-consistency check of the BMC model has been made, in particular of the assumption regarding the dominance of gravitational forces over the pressure forces within the inner few Schwarzschild radii. We have also examined the time behavior of these parameters, which can provide information on the source structure. Using our inferred model parameters: color temperature, spectral index, and an absolute normalization, we present new, independently derived constraints on the BH mass, mass accretion rate, and the distance for the aforementioned sources. Also notable is the relationship between the color temperature and flux, which for GRO J1655-40 is entirely distinct from a simple T4 dependence and strikingly consistent with the disk model we have invoked: a standard Shakura-Sunyaev disk with the modification to the electron scattering. This provides insight into the origin of the seed soft photons and allows us to impose an important estimation of the hardening parameter, Th, which is the ratio of the color temperature to the effective temperature: we find Th2.6, higher than previous estimates used in the literature.

Soft phase lags of pulsed emission from the millisecond x-ray pulsar sax j1808.4-3658

We report the discovery of phase shifts between X-ray pulses at different energies in the newly discovered millisecond X-ray pulsar SAX J1808.4-3658. The results show that low-energy pulses lag high-energy pulses by as much as ~0.2 ms (or ~8% of the pulse period). The measurements were made in two different ways: (1) computing cross-power spectra between different energy bands, and (2) cross-correlating the folded pulse profiles in different energy bands; consistent results were obtained. We speculate that the observed soft lags might be related to the lateral expansion and subsequent cooling of a hot spot on the neutron star surface in which the pulsed X-ray emission originates. Also presented is the possibility of producing soft lags via Compton downscattering of hard X-ray photons from the hot spot in the cool surrounding atmosphere. We will discuss possible X-ray production mechanisms for SAX J1808.4-3658 and constraints on the emission environment, based on the observed soft lags, pulse profiles, and energy spectrum.