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Register a new userInvestigating the Theory of Propagating Fluctuations with Numerical Models of Stochastic Accretion Discs
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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 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.
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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.
We perform a set of numerical experiments studying the interaction of Type I X-ray bursts with thin, Shakura-Sunyaev type accretion discs. Careful observations of X-ray spectra during such bursts have hinted at changes occurring in the inner regions of the disc. We now clearly demonstrate a number of key effects that take place simultaneously, including: evidence for weak, radiation-driven outflows along the surface of the disc; significant levels of Poynting-Robertson (PR) drag, leading to enhanced accretion; and prominent heating in the disc, which increases the height, while lowering the density and optical depth. The PR drag causes the inner edge of the disc to retreat from the neutron star surface toward larger radii and then recover on the timescale of the burst. We conclude that the rich interaction of an X-ray burst with the surrounding disc provides a novel way to study the physics of accretion onto compact objects.
We present a non-linear numerical model for a geometrically thin accretion disk with the addition of stochastic non-linear fluctuations in the viscous parameter. These numerical realizations attempt to study the stochastic effects on the disk angular momentum transport. We show that this simple model is capable of reproducing several observed phenomenologies of accretion driven systems. The most notable of these is the observed linear rms-flux relationship in the disk luminosity. This feature is not formally captured by the linearized disk equations used in previous work. A Fourier analysis of the dissipation and mass accretion rates across disk radii show coherence for frequencies below the local viscous frequency. This is consistent with the coherence behavior observed in astrophysical sources such as Cygnus X-1.
The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed analytic expression for the front diffusion coefficient in the weak noise limit. Here we test this theory in stochastic simulations involving reacting and diffusing particles on a one-dimensional lattice. We also investigate a small noise-induced systematic shift of the front velocity compared to the prediction from the spatially continuous deterministic reaction-diffusion equation.
Standard accretion disc model relies upon several assumptions, the most important of which is geometrical thinness. Whenever this condition is violated, new physical effects become important such as radial energy advection and mass loss from the disc. These effects are important, for instance, for large mass accretion rates when the disc approaches its local Eddington limit. In this work, we study the upper limits for standard accretion disc approximation and find the corrections to the standard model that should be considered in any model aiming on reproducing the transition to super-Eddington accretion regime. First, we find that for thin accretion disc, taking into account relativistic corrections allows to increase the local Eddington limit by about a factor of two due to stronger gravity in General Relativity (GR). However, violation of the local Eddington limit also means large disc thickness. To consider consequently the disc thickness effects, one should make assumptions upon the two-dimensional rotation law of the disc. For rotation frequency constant on cylinders $rsintheta=const$, vertical gravity becomes stronger with height on spheres of constant radius. On the other hand, effects of radial flux advection increase the flux density in the inner parts of the disc and lower the Eddington limit. In general, the effects connected to disc thickness tend to increase the local Eddington limit even more. The efficiency of accretion is however decreased by advection effects by about a factor of several.
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