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Register a new userModeling the response of a standard accretion disc to stochastic viscous fluctuations
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Naveel Ahmad Wani Mr.
Publication date
2017
fields
Physics
and research's language is
English
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The observed variability of X-ray binaries over a wide range of time-scales can be understood in the framework of a stochastic propagation model, where viscous fluctuations at different radii induce accretion rate variability that propagate inwards to the X-ray producing region. The scenario successfully explains the power spectra, the linear rms-flux relation as well as the time-lag between different energy photons. The predictions of this model have been obtained using approximate analytical solutions or empirically motivated models which take into account the effect of these propagating variability on the radiative process of complex accretion flows. Here, we study the variation of the accretion rate due to such viscous fluctuations using a hydro-dynamical code for the standard geometrically thin, gas pressure dominated $alpha$-disc with a zero torque boundary condition. Our results confirm earlier findings that the time-lag between a perturbation and the resultant inner accretion rate variation depends on the frequency (or time-period) of the perturbation. Here we have quantified that the time-lag $t_{lag} propto f^{-0.54}$, for time-periods less than the viscous time-scale of the perturbation radius and is nearly constant otherwise. This, coupled with radiative process would produce the observed frequency dependent time-lag between different energy bands. We also confirm that if there are random Gaussian fluctuations of the $alpha$-parameter at different radii, the resultant inner accretion rate has a power spectrum which is a power-law.
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We analyze several outbursts of a few transient sources using Proportional Counter Array (PCA) data (2.5-25 keV) as well as All Sky Monitor (ASM) data (1.5-12 keV) of Rossi X-ray Timing Explorer (RXTE) satellite. We find a time delay between the arrival times of the Keplerian disc component and the halo of the Two-Component Advective Flow (TCAF) when the spectral data is fitted with TCAF solution. We compare this time delay from the spectral fits with the TCAF solution of the transient low mass X-ray binaries (LMXBs) e.g., GX 339-4, H 1743-322 and MAXI J1836-194 with that of the high mass X-ray Binary (HMXB), Cyg X-1. We find that several days of time delays are observed in LMXBs while for Cyg X-1 the delay is negligible. We interpret the large delay to be due to the viscous delay of a large Keplerian component to reach the inner region as compared to nearly free-fall time taken by the low angular momentum halo component. The delay is of the order of a few days for the low mass X-ray binaries (LMXBs) where the feeding is primarily through the Roche-lobe. However, it is negligible in a wind-fed system like Cyg X-1 since a very small Keplerian disc is created here by slowly redistributing the low angular momentum of the wind. As a consequence, sporadic soft or intermediate spectral states are observed.
Microlensing observations indicate that quasar accretion discs have half-light radii larger than expected from standard theoretical predictions based on quasar fluxes or black hole masses. Blackburne and colleagues have also found a very weak wavelength dependence of these half-light radii. We consider disc temperature profile models that might match these observations. Nixon and colleagues have suggested that misaligned accretion discs around spinning black holes will be disrupted at radii small enough for the Lense-Thirring torque to overcome the discs viscous torque. Gas in precessing annuli torn off a disc will spread radially and intersect with the remaining disc, heating the disc at potentially large radii. However, if the intersection occurs at an angle of more than a degree or so, highly supersonic collisions will shock-heat the gas to a Compton temperature of T~10^7 K, and the spectral energy distributions (SEDs) of discs with such shock-heated regions are poor fits to observations of quasar SEDs. Torn discs where heating occurs in intermittent weak shocks that occur whenever the intersection angle reaches a tenth of a degree pose less of a conflict with observations, but do not have significantly larger half-light radii than standard discs. We also study two phenomenological disc temperature profile models. We find that discs with a temperature spike at relatively large radii and lowered temperatures at radii inside the spike yield improved and acceptable fits to microlensing sizes in most cases. Such temperature profiles could in principle occur in sub-Keplerian discs partially supported by magnetic pressure. However, such discs overpredict the fluxes from quasars studied with microlensing except in the limit of negligible continuum emission from radii inside the temperature spike.
Across a large range of scales, accreting sources show remarkably similar patterns of variability, most notably the log-normality of the luminosity distribution and the linear root-mean square (rms)-flux relationship. These results are often explained using the theory of propagating fluctuations in which fluctuations in the viscosity create perturbations in the accretion rate at all radii, propagate inwards and combine multiplicatively. While this idea has been extensively studied analytically in a linear regime, there has been relatively little numerical work investigating the non-linear behaviour. In this paper, we present a suite of stochastically driven 1-d $alpha$-disc simulations, exploring the behaviour of these discs. We find that the eponymous propagating fluctuations are present in all simulations across a wide range of model parameters, in contradiction to previous work. Of the model parameters, we find by far the most important to be the timescale on which the viscosity fluctuations occur. Physically, this timescale will depend on the underlying physical mechanism, thought to be the magnetorotational instability (MRI). We find a close relationship between this fluctuation timescale and the break frequency in the power spectral density (PSD) of the luminosity, a fact which could allow observational probes of the behaviour of the MRI dynamo. We report a fitting formula for the break frequency as a function of the fluctuation timescale, the disc thickness and the mass of the central object.
The power spectral density (PSD) of the X-ray emission variability from the accretion disc-corona region of black hole X-ray binaries and active galactic nuclei has a broken power law shape with a characteristic break time-scale. If the disc and the jet are connected, the jet variability may also contain a characteristic time-scale related to that of the disc-corona. Recent observations of the blazar Mrk 421 have confirmed the broken power law shape of the PSD of its jet X-ray variability. We model the time variability of a blazar, in which emitting particles are assumed to be accelerated by successive shock waves flowing down the jet with a varying inter-shock time-scale. We investigate the possible relation between the characteristic time-scales in the disc and jet variability based on the above model, along with mathematically and physically simulated disc variability. We find that both the PSD of the jet and disc variability may have a broken power law shape but the break time-scales are not related in general except only in systems with a small range of BH mass. The break in the jet and the disc PSD are connected to the interval between large amplitude outbursts in the jet (inter-shock time-scale) and to the viscous time-scale in the disc, respectively. In frequency bands where multiple emission processes are involved or emission is from lower energy particles, the break in the PSD may not be prominent enough for detection.
Black hole binary transients undergo dramatic evolution in their X-ray timing and spectral behaviour during outbursts. In recent years a paradigm has arisen in which soft X-ray states are associated with an inner disc radius at, or very close to, the innermost stable circular orbit (ISCO) around the black hole, while in hard X-ray states the inner edge of the disc is further from the black hole. Models of advective flows suggest that as the X-ray luminosity drops in hard states, the inner disc progressively recedes, from a few to hundreds gravitational radii. Recent observations which show broad iron line detections and estimates of the disc component strength suggest that a non-recessed disc could still be present in bright hard states. In this study we present a comprehensive analysis of the spectral components associated with the inner disc, utilising data from instruments with sensitive low-energy responses and including reanalyses of previously published results. A key component of the study is to fully estimate systematic uncertainties by e.g. investigating in detail the effect of having a hydrogen column density that is fixed or free to vary. We conclude that for L_x > 0.01 of the Eddington limit, spectral fits allow us to constrain the disc to be < 10R_g. There is, however, clear evidence that when L_x is between 10^-2-- 10^-3 Eddington, the disc does begin to recede. We include measurements of disc radii in two quiescent black hole binaries, and present the inferred evolution of accretion parameters in the entire range of bolometric luminosities 10^-8 -- 1 Eddington. We compare our results with theoretical models and note that the implied rate of disc recession with luminosity is consistent with recent empirical results on the X-ray timing behaviour of black holes of all masses.
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