Numerical solution of the radiative transfer equation: X-ray spectral formation from cylindrical accretion onto a magnetized neutron star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. To this aim, we have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system tau using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth tau produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. The algorithm has been implemented in the XSPEC package for X-ray spectral fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (> 10^{12} G), which is expected to be typical of accreting systems such as X-ray pulsars and supergiant fast X-ray transients.Comment: 13 pages, 20 figures, accepted for publication in A&

On the stability of the thermal Comptonization index in neutron star low-mass X-ray binaries in their different spectral states

Most of the spectra of neutron star low mass X-ray binaries (NS LMXBs), being them persistent or transient, are characterized by the presence of a strong thermal Comptonization bump, thought to originate in the transition layer (TL) between the accretion disk and the NS surface. The observable quantities which characterize this component dominating the emission below 30 keV, are the spectral index alpha and the rollover energy, both related to the electron temperature and optical depth of the plasma. Starting from observational results on a sample of NS LMXBs in different spectral states, we formulate the problem of X-ray spectral formation in the TL of these sources. We predict a stability of the thermal Comptonization spectral index in different spectral states if the energy release in the TL is much higher than the intercepted flux coming from the accretion disk. We use an equation for the energy balance and the radiative transfer diffusion equation for a slab geometry in the TL, to derive a formula for the thermal Comptonization index alpha. We show that in this approximation the TL electron temperature kTe and optical depth tau_0 can be written as a function of the energy flux from the disk intercepted by the corona (TL) and that in the corona itself Qdisk/Qcor, in turn leading to a relation alpha=f(Qdisk/Qcor), with alpha ~ 1 when Qdisk/Qcor <<1. We show that the observed spectral index alpha for the sample of sources here considered lies in a belt around 1 +/- 0.2 a part for the case of GX 354--0. Comparing our theoretical predictions with observations, we claim that this result, which is consistent with the condition Qdisk/Qcor <<1, can give us constraints on the accretion geometry of these systems, an issue that seems difficult to be solved using only the spectral analysis method.Comment: 7 pages, 3 figures, accepted for publication in A&

Analysis of X-ray spectral variability and black hole mass determination of the NLS1 galaxy Mrk 766

We present an XMM-Newton time-resolved spectral analysis of the NLS1 galaxy Mrk 766. We analyse eight available observations of the EPIC-pn camera taken between May 2000 and June 2005 to investigate the X-ray spectral variability as produced by changes in the mass accretion rate. The 0.2-10 keV spectra are extracted in time bins longer than 3 ks to accurately trace the variations of the best fit parameters of our adopted Comptonisation spectral model. We test a bulk-motion Comptonisation (BMC) model which is in general applicable to any physical system powered by accretion onto a compact object, and assumes that soft seed photons are efficiently up-scattered via inverse Compton scattering in a hot and dense electron corona. The Comptonised spectrum has a characteristic power-law shape, whose slope was found to increase for large values of the normalisation of the seed component, that is proportional to the mass accretion rate (in Eddington units). Our baseline spectral model also includes a warm absorber lying on the line of sight and radiation reprocessing from the accretion disk or from outflowing matter in proximity of the central compact object. Our study reveals that the normalisation-slope correlation, observed in Galactic Black Hole sources (GBHs), also holds for Mrk 766: variations of the photon index in the range Gamma~1.9-2.4 are indeed likely to be related to the variations of m-dot, as observed in X-ray binary systems. We finally applied a scaling technique based on the observed correlation to estimate the BH mass in Mrk 766. This technique is commonly and successfully applied to measure masses of GBHs, and this is the first time it is applied in detail to estimate the BH mass in an AGN. We obtain a value of M_{BH}=1.26^{+1.00}_{-0.77}x10^6 M_{sun} that is in very good agreement with that estimated by the reverberation mappingComment: 26 pages, 7 figures, 4 tables to be published in Astronomy and Astrophysic

On the Low and High Frequency Correlation in Quasi-Periodic Oscillations Among White Dwarfs, Neutron Star and Black Hole Binaries

We interpret the correlation over five orders of magnitude between high frequency and low frequency in a quasi-periodic oscillations (QPO) found by Psaltis, Belloni & van der Klis (1999) for black hole (BH), neutron star (NS) systems and then extended by Mauche (2002) to white dwarf (WD) binaries. We argue that the observed correlation is a natural consequence of the Keplerian disk flow adjustment to the innermost sub-Keplerian boundary conditions near the central object. In the framework of the transition layer model the high frequency is related to the Keplerian frequency at the outer (adjustment) radius and the low frequency is related to the magnetoacoustic oscillation (MA) frequency. Using a relation between the MA frequency the magnetic and gas pressure and the density and the hydrostatic equilibrium condition in the disk we infer a linear correlation the Keplerian frequency and the MA frequency. We estimate the magnetic field strength near the TL outer radius for BHs NSs and WDs. The fact that the observed high-low frequency correlation over five orders of magnitude is valid for BHs, NSs, and down to WDs strongly rules out relativistic models for QPO phenomena. We come to the conclusion that the QPOs observations indicate the adjustment of the geometrically thin disk to sub-Keplerian motion near the central object. This effect is a common feature for a wide class of systems, starting from white dwarf binaries up to black hole binaries.Comment: 8 pages, 1 figure, accepted for publication in the ApJ. Letters 2002 August

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 X-ray spectral evolution of Cyg X-2 in the framework of bulk Comptonization

We used the newly developed thermal plus bulk Comptonization model comptb to investigate the spectral evolution of the neutron star LMXB Cyg X-2 along its Z-track. We selected a single source in order to trace in a quantitative way the evolution of the physical parameters of the model. We analyzed archival broad-band BeppoSAX spectra of Cyg X-2. Five broad-band spectra have been newly extracted according to the source position in the Z-track described in the colour-colour and colour-intensity diagrams. We have fitted the spectra of the source with two comptb components. The first one, with bulk parameter delta=0, dominates the overall source broad-band spectrum and its origin is related to thermal upscattering (Comptonization) of cold seed photons off warm electrons in high-opacity enviroment. We attribute the origin of these seed photons to the part of the disk which illuminates the outer coronal region (transition layer) located between the accretion disk itself and the neutron star surface. This thermal component is roughly constant with time and with inferred mass accretion rate. The second comptb model describes the overall Comptonization (thermal plus bulk, delta > 0) of hotter seed photons which come from both the inner transition layer and from the neutron star surface. The appearance of this component in the colour-colour or hardness-intensity diagram is more pronounced in the horizontal branch and is progressively disappearing towards the normal branch, where a pure blackbody spectrum is observed. The spectral evolution of Cyg X-2 is studied and interpreted in terms of changes in the innermost environmental conditions of the system, leading to a variable thermal-bulk Comptonization efficiency.Comment: 10 pages, 7 figures, accepted for publication in A&

Evidence for a Neutron Star in the non-pulsating massive X-ray binary 4U2206+54

We present an analysis of archival RXTE and BeppoSAX data of the X-ray source 4U2206+54 . For the first time, high energy data (> 30 kev) are analyzed for this source. The data are well described by comptonization models (CompTT and BMC) in which seed photons with temperatures between 1.1 kev and 1.5 kev are comptonized by a hot plasma at 50 kev thereby producing a hard tail which extends up to, at least, 100 kev. We offer a new method of identification of neutron star systems using a temperature - luminosity relation. If a given X-ray source is characterized by a low bolometric luminosity and a relatively high color blackbody temperature (>1 kev) it has necessarily to be a neutron star rather than a black hole. From these arguments it is shown that the area of the soft photon source must be small (r ~ 1 km) and that the accretion disk, if present, must be truncated very far from the compact object. Here we report on the possible existence of a cyclotron line around 30 kev. The presence of a neutron star in the system is strongly favored by the available data.Comment: Accepted for publication in A&A. 9 pages, 7 figures. Submitted to journal in November 200

Spectral evolution of bright NS LMXBs

Theoretical and observational support suggests that the spectral evolution of neutron-star LMXBs, including transient hard X-ray tails, may be explained by the interplay between thermal and bulk motion Comptonization. In this framework, we developed a new model for the X-ray spectral fitting XSPEC package which takes into account the effects of both thermal and dynamical (i.e. bulk) Comptonization, CompTB. Using data from the INTEGRAL satellite, we tested our model on broad band spectra of a sample of persistently low magnetic field bright neutron star Low Mass X-ray Binaries, covering different spectral states. The case of the bright source GX 5-1 is presented here. Particular attention is given to the transient powerlaw-like hard X-ray (above 30 keV) tail that we interpret in the framework of the bulk motion Comptonization process, qualitatively describing the physical conditions of the environment in the innermost part of the system.Comment: 6 pages, 4 figures. Accepted for publication on PoS (contribution PoS(extremesky2009)059), proceedings of "The Extreme sky: Sampling the Universe above 10 keV", held in Otranto (Italy) in October 200