B-field Determination from Magnetoacoustic Oscillations in kHz QPO Neutron Star Binaries: Theory and Observations

We present a method for determining the B-field around neutron stars based on observed kHz and viscous QPO frequencies used in combination with the best-fit optical depth and temperature of a Comptonization model. In the framework of the transition layer QPO model, we analyze magnetoacoustic wave formation in the layer between a neutron star surface and the inner edge of a Keplerian disk. We derive formulas for the magnetoacoustic wave frequencies for different regimes of radial transition layer oscillations. We demonstrate that our model can use the QPO as a new kind of probe to determine the magnetic field strengths for 4U 1728-42, GX 340+0, and Sco X-1 in the zone where the QPOs occur. Observations indicate that the dependence of the viscous frequency on the Keplerian frequency is closely related to the inferred dependence of the magnetoacoustic wave frequency on the Keplerian frequency for a dipole magnetic field. The magnetoacoustic wave dependence is based on a single parameter, the magnetic moment of the star as estimated from the field strength in the transition layer. The best-fit magnetic moment parameter is about (0.5-1)x 10^{25} G cm^3 for all studied sources. From observational data, the magnetic fields within distances less 20 km from neutron star for all three sources are strongly constrained to be dipole fields with the strengths 10^{7-8} G on the neutron star surface.Comment: 10 pages, 1 figure, accepted for the Astrophysical Journal Letter

The Extended Power Law as Intrinsic Signature For a Black Hole

We analyze the exact general relativistic exact integro-differential equation of radiative transfer describing the interaction of low energy photons with a Maxwellian distribution of hot electrons in gravitational field of a Schwarzschild black hole. We prove that due 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 behaviour 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 keV or less. In this case, the spectrum observed at infinity consists of a soft component produced by those input photons that escape after a few scatterings without any significant energy change and of hard component (described by a power law) 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 black hole the spectral energy index of the power-law is always higher than one for plasma temperature of order of a few keV. This result suggests that the bulk motion Comptonization might be responsible for the power-law spectra seen in the black-hole X-ray sources.Comment: 31 pages, 3 figures; Astrophysical Journal accepte

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 numerically and approximately analytically the equation of radiative transfer in the case of spherical, steady state accretion into black holes. 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 those input photons which escaped after a few scatterings without any significant energy change and of a power law which extends to high energies and is made of those photons which 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.Comment: 37 pages, LaTex, AAS Macros, 8 ps figures, to appear in Ap

On the spectral slopes of hard X-ray emission from black hole candidates

Most black hole candidates exhibit characteristic power-law like hard X-ray emission above \sim 10 keV. In the {\em high state}, in which 2 -- 10 keV luminosity is relatively high, the energy index of the hard X-ray emission is usually greater than 1 --- typically \sim 1.5. On the other hand, in the {\em low state}, the hard X-ray energy index is 0.3 -- 0.9. In this paper, we suggest that this difference of the hard X-ray spectral slopes may be due to two different Comptonization mechanisms. We propose that, in the high state, the hard component is governed by the Comptonization due to the bulk motion of the almost freely falling (convergent accretion) flow close to the black hole, rather than thermal Comptonization. The spectral slope of the hard component is insensitive to the disk accretion rate governing the soft component, hence is nearly invariant in spite of the soft component variations. The power-law component due to the bulk motion Comptonization has a sharp cut-off at around the electron rest mass energy, which is consistent with high energy observations of the high state. In the low state, the spectrum is formed due to thermal Comptonization of the low-frequency disk radiation by a sub-Keplerian component (possibly undergoing a centrifugally-supported shock) which is originated from the Keplerian disk. In the limit of low disk accretion rate, the power law index is uniquely determined by the mass accretion rate of the sub-Keplerian component

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, 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.Comment: 30 pages TeX format, 6 PS figures, accepted for ApJ Main Journa

Broad redshifted line as a signature of outflow

We formulate and solve the diffusion problem of line photon propagation in a bulk outflow from a compact object (black hole or neutron star) using a generic assumption regarding the distribution of line photons within the outflow. Thomson scattering of the line 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 and c is the speed of light. We demonstrate that the emergent line profile is closely related to the time distribution of photons diffusing through the flow (the light curve) and consists of a broad redshifted feature. We analyzed the line profiles for the general case of outflow density distribution. We emphasize that the redshifted lines are intrinsic properties of the powerful outflow that are supposed to be in many compact objects.Comment: 16 pages, 1 black-white figure and 2 color figures; accepted for publication in the Astrophysical Journa

Power-law Tails from Dynamical Comptonization in Converging Flows

The effects of bulk motion comptonization on the spectral formation in a converging flow onto a black hole are investigated. The problem is tackled by means of both a fully relativistic, angle-dependent transfer code and a semi-analytical, diffusion-approximation method. We find that a power-law high-energy tail is a ubiquitous feature in converging flows and that the two approaches produce consistent results at large enough accretion rates, when photon diffusion holds. Our semi-analytical approach is based on an expansion in eigenfunctions of the diffusion equation. Contrary to previous investigations based on the same method we find that, although the power-law tail at really large energies is always dominated by the flatter spectral mode, the slope of the hard X-ray portion of the spectrum is dictated by the second mode and it approaches Gamma=3 at large accretion rate, irrespective of the model parameters. The photon index in the tail is found to be largely independent on the spatial distribution of soft seed photons when the accretion rate is either quite low ( 10). On the other hand, the spatial distribution of source photons controls the photon index at intermediate accretion rates, when Gamma switches from the first to the second mode. Our analysis confirms that a hard tail with photon index Gamma <3 is produced by the up-scattering of primary photons onto infalling electrons if the central object is a black hole.Comment: to be published in the Astrophysical Journal, 16 pages and 9 figure

Mechanisms for High-frequency QPOs in Neutron Star and Black Hole Binaries

We explain the millisecond variability detected by Rossi X-ray Timing Explorer (RXTE) in the X-ray emission from a number of low mass X-ray binary systems (Sco X-1, 4U1728-34, 4U1608-522, 4U1636-536, 4U0614+091, 4U1735-44, 4U1820-30, GX5-1 and etc) in terms of dynamics of the centrifugal barrier, a hot boundary region surrounding a neutron star. We demonstrate that this region may experience the relaxation oscillations, and that the displacements of a gas element both in radial and vertical directions occur at the same main frequency, of order of the local Keplerian frequency. We show the importance of the effect of a splitting of the main frequency produced by the Coriolis force in a rotating disk for the interpretation of a spacing between the QPO peaks. We estimate a magnitude of the splitting effect and present a simple formula for the whole spectrum of the split frequencies. It is interesting that the first three lowest-order overtones fall in the range of 200-1200 Hz and match the kHz-QPO frequencies observed by RXTE. Similar phenomena should also occur in Black Hole (BH) systems, but, since the QPO frequency is inversely proportional to the mass of a compact object, the frequency of the centrifugal-barrier oscillations in the BH systems should be a factor of 5-10 lower than that for the NS systems. The X-ray spectrum formed in this region is a result of upscattering of a soft radiation (from a disk and a NS surface) off relatively hot electrons in the boundary layer. We also briefly discuss some alternative QPO models, including a possibility of acoustic oscillations in the boundary layer, the proper stellar rotation, and g-mode disk oscillations.Comment: The paper is coming out in the Astrophysical Journal in the 1st of May issue of 199