217 research outputs found
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&
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
Kilohertz QPOs in Neutron Star Binaries modeled as Keplerian Oscillations in a Rotating Frame of Reference
Since the discovery of kHz quasi-periodic oscillations (QPO) in neutron star
binaries, the difference between peak frequencies of two modes in the upper
part of the spectrum, i.e. Delta (omega)=omega_h-omega_K has been studied
extensively. The idea that the difference Delta(omega) is constant and (as a
beat frequency) is related to the rotational frequency of the neutron star has
been tested previously. The observed decrease of Delta(omega) when omega_h and
omega_k increase has weakened the beat frequency interpretation. We put forward
a different paradigm: a Keplerian oscillator under the influence of the
Coriolis force. For such an oscillator, omega_h and the assumed Keplerian
frequency omega_k hold an upper hybrid frequency relation:
omega^2_h-omega^2_K=4*Omega^2, where Omega is the rotational frequency of the
star's magnetosphere near the equatorial plane. For three sources (Sco X-1, 4U
1608-52 and 4U 1702-429), we demonstrate that the solid body rotation
Omega=Omega_0=const. is a good first order approximation. Within the second
order approximation, the slow variation of Omega as a function of omega_K
reveals the structure of the magnetospheric differential rotation. For Sco X-1,
the QPO have frequencies approximately 45 and 90 Hz which we interpret as the
1st and 2nd harmonics of the lower branch of the Keplerian oscillations for the
rotator with vector Omega not aligned with the normal of the disk: omega_L/2
pi=(Omega/pi)(omega_K/omega_h)sin(delta) where delta is the angle between
vector Omega and the vector normal to the disk.Comment: 13 pages, 3 figures, accepted for publications in ApJ Letter
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
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
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