Modeling the response of a standard accretion disc to stochastic viscous fluctuations

Ahmad, Naveel; Misra, Ranjeev; Iqbal, Naseer; Maqbool, Bari; Hamid, Mubashir

doi:10.1016/j.newast.2017.07.011

Cited by 7 publications

(5 citation statements)

References 29 publications

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“…We characterise the coherence and frequency dependent time lags of the the local accretion rate at different radii, finding that the fluctuations are coherent on timescales longer than the viscous time and also time delayed by the viscous travel time. The local dissipation/emission at different radii is also coherent on timescales longer than the viscous time, but with a time-delay that is appreciably smaller (in agreement with Ahmad et al (2018)). Finally, we recover non-linear variability even for rapidly modulated viscosity, and we reconcile differences with Cowperthwaite & Reynolds (2014) as being due to the form of the viscosity prescription (with the 𝛼-prescription introducing stronger non-linearities).…”

Section: Introductionsupporting

confidence: 78%

“…They employed a slightly simpler viscosity prescription, but did not restrict to small stochastic viscosity perturbations. Their numerical solution of the disc evolution equation confirmed that propagating fluctuations produced log-normal flux distributions, linear rms-flux relations, and frequency-dependent time-lags (on this last point, also see Ahmad et al 2018). Cowperthwaite & Reynolds (2014) suggested that the viscosity fluctuations needed to be driven sufficiently slowly, on the order of the viscous timescale, in order to produce this non-linear variability.…”

Section: Introductionmentioning

confidence: 87%

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Investigating the Theory of Propagating Fluctuations with Numerical Models of Stochastic Accretion Discs

Turner,

Reynolds

2021

Preprint

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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 rootmean 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 𝛼-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.

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Section: Introductionsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 87%

Investigating the Theory of Propagating Fluctuations with Numerical Models of Stochastic Accretion Discs

Turner,

Reynolds

2021

Preprint

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“…According to Cowperthwaite & Reynolds (2014), the time-lag expected in stochastic propagation is frequency dependent. Ahmad et al (2018) have shown that for standard stable gas pressure dominated disk the propagation timescale is frequency dependent for frequencies higher than the local viscous time-scale. While these results are indicative, one should bear in mind that they are for standard optically thick disks, and it is not certain how quantitatively different would the results be for a hot optically thin, geometrically thick flow and when the propagation time being considered is from the transition region on wards.…”

Section: Comparison With Other Propagation Modelsmentioning

confidence: 99%

“…However, one interesting feature of these simulations is that the propagation time-scales can be frequency dependent and are not necessarily the same as the viscous ones. Using simple time dependent standard disk equations, Ahmad et al (2018) also showed that this is the case and quantify the frequency dependent behaviours. However, these results are for standard outer disks extending to the last stable orbit and it is not clear how the results would change if the standard outer disk is truncated at some distance from the black hole and has a hot inner flow (Yuan & Narayan 2014).…”

Section: Introductionmentioning

confidence: 97%

A stochastic propagation model to the energy dependent rapid temporal behaviour of Cygnus X-1 as observed by AstroSat in the hard state

Maqbool

Mudambi

Misra

et al. 2019

Monthly Notices of the Royal Astronomical Society

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We report the results from analysis of six observations of Cygnus X-1 by Large Area X-ray Proportional Counters (LAXPC) and Soft X-ray Telescope (SXT) on-board AstroSat, when the source was in the hard spectral state as revealed by the broad band spectra. The spectra obtained from all the observations can be described by a single temperature Comptonizing region with disk and reflection components. The event mode data from LAXPC provides unprecedented energy dependent fractional root mean square (rms) and time-lag at different frequencies which we fit with empirical functions. We invoke a fluctuation propagation model for a simple geometry of a truncated disk with a hot inner region. Unlike other propagation models, the hard X-ray emission (> 4 keV) is assumed to be from the hot inner disk by a single temperature thermal Comptonization process. The fluctuations first cause a variation in the temperature of the truncated disk and then the temperature of the inner disk after a frequency dependent time delay. We find that the model can explain the energy dependent rms and time-lag at different frequencies.

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“…On the other hand, we follow numerically the flow dynamics so all the aspects of the variability model based on the idea of the propagating fluctuations (Lyubarskii 1997;Kotov et al 2001;Ingram & Done 2012) are automatically included by us. We do not have to restore to semi-analytical approach as done for example by Ingram & Klis (2013) who use analytic expressions for the power spectrum for models with propagating fluctuations but with zero-centred Lorentzian of a width 1/t visc , or by Ahmad et al (2018) for the geometrically thin disc who modelled the variability characteristic in the Soft State.…”

Section: Parametersmentioning

confidence: 99%

Clumpy wind accretion in Cygnus X-1

Palit,

Janiuk,

Czerny

2020

Preprint

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Cygnus X-1 is one of the brightest X-ray sources observed and shows the X-ray intensity variations on time scales from milliseconds to months in both the soft and hard X-rays. The accretion onto the black hole is believed to be wind fed due to focused stellar wind from the binary companion HDE-226868. We aim to understand the physical mechanism responsible for the short timescale X-ray variability (<100 s) of the source in its Hard/Low state. We compute the 2D relativistic hydrodynamic simulation of the low angular momentum accretion flow with a time dependent outer boundary condition that reflects the focused, clumpy wind from the super-giant in this X-ray binary system. We follow the dynamical evolution of our model for about 100 s and present the results showing an oscillatory shock, being a potential explanation of variability observed in hard X-rays. The simulated model with shock solutions is in good agreement with the observed power density spectra of the source.

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Modeling the response of a standard accretion disc to stochastic viscous fluctuations

Cited by 7 publications

References 29 publications

Investigating the Theory of Propagating Fluctuations with Numerical Models of Stochastic Accretion Discs

Investigating the Theory of Propagating Fluctuations with Numerical Models of Stochastic Accretion Discs

A stochastic propagation model to the energy dependent rapid temporal behaviour of Cygnus X-1 as observed by AstroSat in the hard state

Clumpy wind accretion in Cygnus X-1

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