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Correlations between the quasi-periodic oscillations (QPOs) and the spectral power-law index have been reported for a number of black hole candidate sources and for four neutron star (NS) sources, 4U 0614+09, 4U 1608-52, 4U 1728-34 and Sco X-1. An examination of QPO frequencies and index relationship in Cyg X-2 is reported herein. The RXTE spectrum of Cyg X-2 can be adequately represented by a simple two-component model of Compton up-scattering with a soft photon electron temperature of about 0.7 keV and an iron K-line. Inferred spectral power-law index shows correlation with the low QPO frequencies. We find that the Thomson optical depth of the Compton cloud (CC) tau, in framework of spherical geometry, is in the range of ~4-6, which is consistent with the neutron star's surface being obscured. The NS high frequency pulsations are presumably suppressed as a result of photon scattering off CC electrons because of such high values of tau. We also point out a number of similarities in terms timing (presence of low and high frequency QPOs) and spectral (high CC optical depth and low CC plasma temperature) appearances between Cyg X-2 and Sco X-1., Comment: 7 pages, 4 figures, accepted for publication in ApJ (October 1, 2007, v667n2 issue)

Correlations between 1-10 Hz quasi-periodic oscillations (QPOs) and spectral power law index have been reported for black hole (BH) candidate sources and one neutron star source, 4U 1728-34. An examination of QPO frequency and index relationships in Sco X-1 is reported herein. We discovered that Sco X-1, representing Z-source groups, can be adequately modeled by a simple two-component model of Compton up-scattering with a soft photon electron temperature of about 0.4 keV, plus an Iron K-line. The results show a strong correlation between spectral power law index and kHz QPOs. Because Sco X-1 radiates near the Eddington limit, one can infer that the geometrical configuration of the Compton cloud (CC) is quasi-spherical because of high radiation pressure in the CC. Thus, we conclude that the high Thomson optical depth of the Compton cloud, in the range of ~5-6 from the best-fit model parameters, is consistent with the neutron star's surface being obscured by material. Moreover, a spin frequency of Sco X-1 is likely suppressed due to photon scattering off CC electrons. Additionally, we demonstrate how the power spectrum evolves when Sco X-1 transitions from the horizontal branch to the normal branch., Comment: 7 pages, 4 figures, accepted for publication in ApJ (July 1, 2007, v663n1 issue)

We present numerical verification of hyperbolic nature for chaotic attractor in a system of two coupled non-autonomous van der Pol oscillators (Kuznetsov, Phys. Rev. Lett., 95, 144101, 2005). At certain parameter values, in the four-dimensional phase space of the Poincare map a toroidal domain (a direct product of a circle and a three-dimensional ball) is determined, which is mapped into itself and contains the attractor we analyze. In accordance with the computations, in this absorbing domain the conditions of hyperbolicity are valid, which are formulated in terms of contracting and expanding cones in the tangent spaces (the vector spaces of the small state perturbations)., Comment: 14 pages, 7 figures

We consider the dynamics of small perturbations of stable two-frequency quasiperiodic orbits on an attracting torus in the quasiperiodically forced Henon map. Such dynamics consists in an exponential decay of the radial component and in a complex behaviour of the angle component. This behaviour may be two- or three-frequency quasiperiodicity, or it may be irregular. In the latter case a graphic image of the dynamics of the perturbation angle is a fractal object, namely a strange nonchaotic attractor, which appears in auxiliary map for the angle component. Therefore, we claim that stable trajectories may approach the attracting torus either in a regular or in an irregular way. We show that the transition from quasiperiodic dynamics to chaos in the model system is preceded by the appearance of an irregular behaviour in the approach of the perturbed quasiperiodic trajectories to the smooth attracting torus. We also demonstrate a link between the evolution operator of the perturbation angle and a quasiperiodically forced circle mapping of a special form and with a Harper equation with quasiperiodic potential., Comment: 22 pages, 5 figures

A simple and transparent example of a non-autonomous flow system, with hyperbolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and the parameters controlling generation in both oscillators undergo a slow periodic counter-phase variation in time. In terms of stroboscopic Poincar\'{e} section, the respective four-dimensional mapping has a hyperbolic strange attractor of Smale - Williams type. Qualitative reasoning and quantitative data of numerical computations are presented and discussed, e.g. Lyapunov exponents and their parameter dependencies. A special test for hyperbolicity based on statistical analysis of distributions of angles between stable and unstable subspaces of a chaotic trajectory has been performed. Perspectives of further comparative studies of hyperbolic and non-hyperbolic chaotic dynamics in physical aspect are outlined., Comment: 7 pages, 4 figures

We present a first INTEGRAL observation of the 42s transient X-ray pulsar EXO 2030+375 with IBIS/ISGRI. The source was detected during Cyg X-1 observations in December 2002. We analyzed observations during the outburst period from 9 to 21 December 2002 with a total exposure time of ~770 kiloseconds. EXO 2030+375 was almost always detected during single ~30 minute exposures in the 18-45 energy bands. The source light curve shows the characteristic outburst shape observed in this source., Comment: 4 pages, 3 figures (1 in CMYK color), accepted by Astronomy and Astrophysics, INTEGRAL special issue, 2003

The RXTE observations of Scorpius X-1 in 1996-1999 are presented. The properties of its quasi-periodic X-ray oscillations are studied in detail. The results obtained are used for analysis in terms of the transition-layer model (TLM) and the relativistic-precession model (RPM) for a slowly rotating neutron star. Theoretical predictions of the two models are compared and their self-consistency is verified. The tilt of the magnetosphere to the accretion-disk plane, the neutron-star mass, and its angular momentum are determined in the model frameworks., Comment: 17 pages, 9 figures, uses pstricks package. To be published in Astronomy Letters, Vol. 28, No. 12, 2002, pp. 811-820 (English version by "MAIK Nauka")

Using large number of Rossi X-ray Time Explorer observations of Sco X-1 we present a detailed investigation of the transition layer (TL) and the relativistic precession (RP) models. These models predict the existence of the invariant quantities: an inclination angle delta of the magnetospheric axis with the normal to the disk for the TLM and a neutron star (NS) mass M_{NS} for the RPM. Theoretical predictions of both models are tested and their self-consistency is checked. We establish that: (1) The inferred delta angle is 5.56+/-0.09 degrees. Correlation of the delta-values with the horizontal branch oscillation (HBO) frequency is rather weak. (2) There is a strong correlation between an inferred M_{NS} and the HBO frequency in the RPM frameworks. (3) We infer M_{NS} for different assumptions regarding the relations between the HBO frequency and the nodal frequency. We find that the inferred M_{NS}=2.7+/-0.1 M_sun cannot be consistent with any EOS of NS matter. We conclude that RPM fails to describe the data while TLM seems to be compatible., Comment: Accepted for publication in Astrophysical Journal Letters (2002 June/571 issue), 5 pages, 4 figures, uses emulateapj5.sty

The bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type-I, but generalized for the presence of a quasiperiodic external force. The analysis is concentrated on the torus-fractalization (TF) critical point that occurs at some critical amplitude of driving. (At smaller amplitudes the bifurcation corresponds to a collision and subsequent disappearance of two smooth invariant curves, and at larger amplitudes it is a touch of fractal attractor and repeller at some set of exceptional points, without coincidence.) For the TF critical point, renormalization group (RG) analysis is developed. For the golden mean rotation number a nontrivial fixed-point solution of the RG equation is found in a class of fractional-linear functions with coefficients depending on the phase variable. Universal constants are computed responsible for scaling in phase space ($\alpha=2.890053...$ and $\beta=-1.618034...$) and in parameter space ($\delta_1=3.134272...$ and $\delta_2=1.618034...$). An analogy with the Harper equation is outlined, which reveals important peculiarities of the transition. For amplitudes of driving less than the critical value the transition leads (in the presence of an appropriate re-injection mechanism) to intermittent chaotic regimes; in the supercritical case it gives rise to a strange nonchaotic attractor., Comment: 16 pages, 16 figures, 4 tables. Physical Review E, submitted

We present results of RXTE observations of the X-ray source Cyg X-2 during 1996-1999. Its power density spectra in the 0.1-128-Hz band are fitted by a model that takes into account the power-law spectral behavior at frequencies below and above the break frequency, with an introduction of one or more Lorenz lines to describe the peaks of quasi-periodic oscillations that correspond to the horizontal branch of the Z track. The RXTE observations have revealed a positive correlation between the break frequency and the indices of the two parts of the spectrum. The spectrum steepens with increasing break frequency both above and below the break frequency., Comment: 7 pages, 2 figures, To be published in Astronomy Letters, Vol. 27, No. 12, 2001, pp. 790-793 (English version by "MAIK Nauka")

Precise simultaneous measurements of the frequencies of the two kiloHertz quasi-periodic oscillations (referred in the literature as upper and lower kHz QPOs) cast doubts on the validity of the simple beat-frequency interpretation and some of the modifications introduced to explain the results of the varying frequency difference. A new model explains the variation of the frequency difference suggesting that the upper kHz QPO,namely nu_h is an upper hybrid frequency of the Keplerian oscillator under the influence of the Coriolis force and the lower kHz QPO is the Keplerian frequency nu_K. Such an oscillator has two branches characterized by high frequency nu_h (around 1 kHz) and by low frequency nu_L (around 50 Hz). The frequency nu_L depends strongly on the angle, delta between the normal to the neutron star disk and Omega - the angular velocity of the magnetosphere surrounding the neutron star. In the lower part of the QPO spectrum (around 10 Hz), this model identifies the frequency of radial viscous oscillations nu_v (previously called "extra noise component") and the break frequency nu_b, which is associated with the diffusive process in the transition region (the innermost part of the disk). According to this model, all frequencies (namely nu_h, nu_L, nu_b and nu_v) have specific dependences on nu_K. This paper focuses on the verification of the predicted relations. For the source 4U 1728-34, the best theoretical fit is obtained for delta=8.3+/-1.0^o, which is slightly larger than delta=5.5+/- 0.5^o previously found for Sco X-1. In addition, we show that the theoretically derived power law relation, nu_b proportional to nu_v^{1.61} is consistent with the recent observations of other atoll and Z-sources., Comment: 12 pages, 4 figures, accepted by ApJ Letters