5,822 research outputs found
Solutions to the relativistic precession model
The relativistic precession model (RPM) can be used to obtain a precise
measurement of the mass and spin of a black hole when the appropriate set of
quasi periodic oscillations is detected in the power-density spectrum of an
accreting black hole. However, in previous studies the solution of the RPM
equations could be obtained only through numerical methods at a price of an
intensive computational effort. Here we demonstrate that the RPM system of
equations can be solved analytically, drastically reducing the computational
load, now limited to the Monte-Carlo simulation necessary to estimate the
uncertainties. The analytical method not only provides an easy solution to the
RPM system when three oscillations are detected, but in all the cases where the
detection of two simultaneous oscillations is coupled with an independent mass
measurement. We also present a computationally inexpensive method to place
limits on the black hole mass and spin when only two oscillations are observed.Comment: Accepted to MNRAS; 8 pages, 3 figure
An observational method for fast stochastic X-ray polarimetry-timing
The upcoming launch of the first space based X-ray polarimeter in
years will provide powerful new diagnostic information to study accreting
compact objects. In particular, analysis of rapid variability of the
polarisation degree and angle will provide the opportunity to probe the
relativistic motions of material in the strong gravitational fields close to
the compact objects, and enable new methods to measure black hole and neutron
star parameters. However, polarisation properties are measured in a statistical
sense, and a statistically significant polarisation detection requires a fairly
long exposure, even for the brightest objects. Therefore, the sub-minute
timescales of interest are not accessible using a direct time-resolved analysis
of polarisation degree and angle. Phase-folding can be used for coherent
pulsations, but not for stochastic variability such as quasi-periodic
oscillations. Here, we introduce a Fourier method that enables statistically
robust detection of stochastic polarisation variability for arbitrarily short
variability timescales. Our method is analogous to commonly used
spectral-timing techniques. We find that it should be possible in the near
future to detect the quasi-periodic swings in polarisation angle predicted by
Lense-Thirring precession of the inner accretion flow. This is contingent on
the mean polarisation degree of the source being greater than ,
which is consistent with the best current constraints on Cygnus X-1 from the
late 1970s.Comment: Accepted for publication in MNRA
A unified Lense-Thirring precession model for optical and X-ray quasi-periodic oscillations in black hole binaries
Recent observations of accreting black holes reveal the presence of
quasi-periodic oscillations (QPO) in the optical power density spectra. The
corresponding oscillation periods match those found in the X-rays, implying a
common origin. Among the numerous suggested X-ray QPO mechanisms, some may also
work in the optical. However, their relevance to the broadband -- optical
through X-ray -- spectral properties have not been investigated. For the first
time, we discuss the QPO mechanism in the context of the self-consistent
spectral model. We propose that the QPOs are produced by Lense-Thirring
precession of the hot accretion flow, whose outer parts radiate in the optical
wavelengths. At the same time, its innermost parts are emitting the X-rays,
explaining the observed connection of QPO periods. We predict that the X-ray
and optical QPOs should be either in phase or shifted by half a period,
depending on the observer position. We investigate the QPO harmonic content and
find that the variability amplitudes at the fundamental frequency are larger in
the optical, while the X-rays are expected to have strong harmonics. We then
discuss the QPO spectral dependence and compare the expectations to the
existing data.Comment: 9 pages, 5 figures; ApJ, in pres
Phase-resolved spectroscopy of low frequency quasi-periodic oscillations in GRS 1915+105
X-ray radiation from black hole binary (BHB) systems regularly displays
quasi-periodic oscillations (QPOs). In principle, a number of suggested
physical mechanisms can reproduce their power spectral properties, thus more
powerful diagnostics which preserve phase are required to discern between
different models. In this paper, we first find for two Rossi X-ray Timing
Explorer (RXTE) observations of the BHB GRS 1915+105 that the QPO has a well
defined average waveform. That is, the phase difference and amplitude ratios
between the first two harmonics vary tightly around a well defined mean. This
enables us to reconstruct QPO waveforms in each energy channel, in order to
constrain QPO phase-resolved spectra. We fit these phase resolved spectra
across 16 phases with a model including Comptonisation and reflection (Gaussian
and smeared edge components) to find strong spectral pivoting and a modulation
in the iron line equivalent width. The latter indicates the observed reflection
fraction is changing throughout the QPO cycle. This points to a geometric QPO
origin, although we note that the data presented here do not entirely rule out
an alternative interpretation of variable disc ionisation state. We also see
tentative hints of modulations in the iron line centroid and width which,
although not statistically significant, could result from a non-azimuthally
symmetric QPO mechanism.Comment: Accepted for publication in MNRA
Propagating mass accretion rate fluctuations in X-ray binaries under the influence of viscous diffusion
Many statistical properties of X-ray aperiodic variability from accreting
compact objects can be explained by the propagating fluctuations model applied
to the accretion disc. The mass accretion rate fluctuations originate from
variability of viscosity, which arises at every radius and causes local
fluctuations of the density. The fluctuations diffuse through the disc and
result in local variability of the mass accretion rate, which modulates the
X-ray flux from the inner disc in the case of black holes, or from the surface
in the case of neutron stars. A key role in the theoretical explanation of fast
variability belongs to the description of the diffusion process. The
propagation and evolution of the fluctuations is described by the diffusion
equation, which can be solved by the method of Green functions. We implement
Green functions in order to accurately describe the propagation of fluctuations
in the disc. For the first time we consider both forward and backward
propagation. We show that (i) viscous diffusion efficiently suppress
variability at time scales shorter than the viscous time, (ii) local
fluctuations of viscosity affect the mass accretion rate variability both in
the inner and the outer parts of accretion disc, (iii) propagating fluctuations
give rise not only to hard time lags as previously shown, but also produce soft
lags at high frequency similar to those routinely attributed to reprocessing,
(iv) deviation from the linear rms-flux relation is predicted for the case of
very large initial perturbations. Our model naturally predicts bumpy power
spectra.Comment: 20 pages, 17 figures, accepted for publication in MNRA
A physical model for the variability properties of X-ray binaries
Emission from X-ray binaries is variable on a wide range of
timescales. On long timescales, changes in mass accretion rate drive changes in spectral state. There is also rapid variability, the power spectrum of which consists of a low frequency quasi-periodic oscillation (QPO) superimposed on a broad band noise continuum. Here I investigate a model intended to quantitatively explain the observed spectral and variability properties. I consider a truncated disc geometry whereby the inner regions of an optically thick, geometrically thin accretion disc evaporate to form an optically thin, large scale height accretion flow.
The QPO is driven by Lense-Thirring precession of the entire hot flow and the broad band noise is due to fluctuations in mass accretion rate which propagate towards the central object. Mass conservation ties these two processes together, enabling me to define a model for the QPO and broad band noise which uses only one set of parameters. I am thus able fit the model to data. The accretion rate fluctuations drive fluctuations in the precession frequency, giving rise to a quasi-periodic oscillation rather than a pure periodicity. The model thus predicts recent observations which show the QPO frequency to
correlate with flux on short timescales. I then investigate a more unique model prediction. As the flow precesses, the patch of the disc preferentially illuminated by the flow rotates such that a non face on observer sees a quasi-periodic shift between blue and red shift in the iron K alpha line. An observation of such an effect would constitute excellent evidence for the model
Optically thick envelopes around ULXs powered by accreating neutron stars
Magnetized neutron stars power at least some ultra-luminous X-ray sources.
The accretion flow in these cases is interrupted at the magnetospheric radius
and then reaches the surface of a neutron star following magnetic field lines.
Accreting matter moving along magnetic field lines forms the accretion envelope
around the central object. We show that, in case of high mass accretion rates
the envelope becomes closed and optically
thick, which influences the dynamics of the accretion flow and the
observational manifestation of the neutron star hidden behind the envelope.
Particularly, the optically thick accretion envelope results in a multi-color
black-body spectrum originating from the magnetospheric surface. The spectrum
and photon energy flux vary with the viewing angle, which gives rise to
pulsations characterized by high pulsed fraction and typically smooth pulse
profiles. The reprocessing of radiation due to interaction with the envelope
leads to the disappearance of cyclotron scattering features from the spectrum.
We speculate that the super-orbital variability of ultra-luminous X-ray sources
powered by accreting neutron stars can be attributed to precession of the
neutron star due to interaction of magnetic dipole with the accretion disc.Comment: 8 pages, 6 figures, accepted for publication in MNRA
Timing properties of ULX pulsars: optically thick envelopes and outflows
It has recently been discovered that a fraction of ultra-luminous X-ray
sources (ULXs) exhibit X-ray pulsations, and are therefore powered by
super-Eddington accretion onto magnetized neutron stars (NSs). For typical ULX
mass accretion rates (), the inner parts of
the accretion disc are expected to be in the supercritical regime, meaning that
some material is lost in a wind launched from the disc surface, while the rest
forms an optically thick envelope around the NS as it follows magnetic field
lines from the inner disc radius to the magnetic poles of the star. The
envelope hides the central object from a distant observer and defines key
observational properties of ULX pulsars: their energy spectrum, polarization,
and timing features. The optical thickness of the envelope is affected by the
mass losses from the disc. We calculate the mass loss rate due to the wind in
ULX pulsars, accounting for the NS magnetic field strength and advection
processes in the disc. We argue that the detection of strong outflows from ULX
pulsars can be considered evidence of a relatively weak dipole component of the
NS magnetic field. We estimate the influence of mass losses on the optical
thickness of the envelope and analyze how the envelope affects broadband
aperiodic variability in ULXs. We show that brightness fluctuations at high
Fourier frequencies can be strongly suppressed by multiple scatterings in the
envelope and that the strength of suppression is determined by the mass
accretion rate and geometrical size of the magnetosphere.Comment: 12 pages, 11 figures, accepted for publication in MNRA
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