Viscosity In Accretion Disks Research Articles

Emergence of vortices at the edges of planet-driven gaps in protoplanetary discs

ABSTRACT Young planets embedded in protoplanetary discs (PPDs) excite spiral density waves, which propagate shock and deposit angular momentum in the disc. This results in gap opening around the planetary orbit, even for low (sub-thermal) mass planets, provided that the effective viscosity in the disc is low. The edges of these planet-induced gaps are known to be prone to emergence of observable vortices via the Rossby wave instability (RWI). We study time-scales for the development of vortices driven by low-mass planets in inviscid discs. We employ a recently developed semi-analytical theory of vortensity production by the planet-driven shock to predict vortensity evolution near the planet, from which we derive the radial profile of the planet-induced gap as a function of time (this procedure can have multiple other uses, e.g. to study dust trapping, suppression of pebble accretion, etc.). We then analyse the linear stability of the gap edges against the RWI, obtaining the time-scales for the first appearance of unstable modes and (later) fully developed vortices at gap edges. We present useful formulae for these time-scales as functions of planetary and disc parameters and provide their physical justification. We also thoroughly test our semi-analytical framework against high-resolution 2D hydrodynamic simulations, confirming the accuracy of our theoretical predictions. We discuss ways in which our semi-analytical framework can be extended to incorporate additional physics, e.g. planetary accretion, migration, and non-zero disc viscosity. Our results can be used to interpret observations of PPDs and to predict emergence of vortices in simulations.

High-resolution parameter study of the vertical shear instability – II: dependence on temperature gradient and cooling time

ABSTRACT A certain appeal to the alpha model for turbulence and related viscosity in accretion discs was that one scales the Reynolds stresses simply on the thermal pressure, assuming that turbulence driven by a certain mechanism will attain a characteristic Mach number in its velocity fluctuations. Besides the notion that there are different mechanism driving turbulence and angular momentum transport in a disc, we also find that within a single instability mechanism, here the vertical shear instability, stresses do not linearly scale with thermal pressure. Here, we demonstrate in numerical simulations the effect of the gas temperature gradient and the thermal relaxation time on the average stresses generated in the non-linear stage of the instability. We find that the stresses scale with the square of the exponent of the radial temperature profile at least for a range of dlog T/dlog R = [−0.5, −1], beyond which the pressure scale height varies too much over the simulation domain, to provide clear results. Stresses are also dependent on thermal relaxation times, provided they are longer than 10−3 orbital periods. The strong dependence of viscous transport of angular momentum on the local conditions in the disc (especially temperature, temperature gradient, and surface density/optical depth) challenges the ideas of viscosity leading to smooth density distributions, opening a route for structure (ring) formation and time variable mass accretion.

Accretion bursts in high-mass protostars: A new test bed for models of episodic accretion

Aims. It is well known that low-mass young stellar objects (LMYSOs) gain a significant portion of their final mass through episodes of very rapid accretion, with mass accretion rates up to Ṁ∗ ∼ 10−4 M⊙ yr−1. Recent observations of high-mass young stellar objects (HMYSOs) with masses M∗ ≳ 10 M⊙ uncovered outbursts with accretion rates exceeding Ṁ∗ ∼ 10−3 M⊙ yr−1. Here, we examine which scenarios proposed in the literature so far to explain accretion bursts of LMYSOs can also apply to the episodic accretion in HMYSOs. Methods. We utilise 1D time-dependent models of protoplanetary discs around HMYSOs to study burst properties. Results. We find that discs around HMYSOs are much hotter than those around their low-mass cousins. As a result, a much more extended region of the disc is prone to the thermal hydrogen ionisation and magnetorotational activation instabilities. The former, in particular, is found to be ubiquitous in a very wide range of accretion rates and disc viscosity parameters. The outbursts triggered by these instabilities, however, always have too low of an Ṁ∗ and are one to several orders of magnitude too long compared to those observed from HMYSOs to date. On the other hand, bursts generated by tidal disruptions of gaseous giant planets formed by the gravitational instability of the protoplanetary discs yield properties commensurate with observations, provided that the clumps are in the post-collapse configuration with planet radius Rp ≳ 10 Jupiter radii. Furthermore, if observed bursts are caused by disc ionisation instabilities, then they should be periodic phenomena with the duration of the quiescent phase comparable to that of the bursts. This may yield potentially observable burst periodicity signatures in the jets, the outer disc, or the surrounding diffuse material of massive HMYSOs. Bursts produced by disruptions of planets or more massive objects are not expected to be periodic phenomena, although multiple bursts per protostar are possible. Conclusions. Observations and modelling of episodic accretion bursts across a wide range of young stellar object (YSO) masses is a new promising avenue to break the degeneracy between models of episodic accretion in YSOs.

Saturation mechanism and generated viscosity in gravito-turbulent accretion disks

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.

On the physical nature of accretion disc viscosity

We use well–established observational evidence to draw conclusions about the fundamental nature of the viscosity in accretion discs. To do this, we first summarise the observational evidence for the value of the dimensionless accretion disc viscosity parameter α, defined by Shakura and Sunyaev (1973, 1976). We find that, for fully ionized discs, the value of α is readily amenable to reliable estimation and that the observations are consistent with the hypothesis that α∼0.2−0.3. In contrast in discs that are not fully ionized, estimates of the value of α are generally less direct and the values obtained are generally < 0.01 and often ≪ 0.01. We conclude that this gives us crucial information about the nature of viscosity in accretion discs. First, in fully ionized discs the strength of the turbulence is always limited by being at most trans-sonic. This implies that it is necessary that credible models of the turbulence reflect this fact. Second, the smaller values of α found for less ionized, and therefore less strongly conducting, discs imply that magnetism plays a dominant role. This provides important observational support for the concept of magneto-rotational instability (MRI) driven hydromagnetic turbulence.

Modified viscosity in accretion disks

Black holes (BHs) surrounded by accretion disks are present in the Universe at different scales of masses, from microquasars up to the active galactic nuclei (AGNs). The current picture remains ad hoc due to the complexity of the magnetic field action. In addition, accretion disks at high Eddington rates can be radiation-pressure dominated and, according to some of the heating prescriptions, thermally unstable. The observational verification of their resulting variability patterns may shed light on both the role of radiation pressure and magnetic fields. We compute the structure and time evolution of an accretion disk, using the code GLADIS (which models the global accretion disk instability). We supplement this model with a modified viscosity prescription, which can to some extent describe the magnetisation of the disk. We study the results for a large grid of models, to cover the whole parameter space, and we derive conclusions separately for different scales of black hole masses, which are characteristic for various types of cosmic sources. We show the dependencies between the flare or outburst duration, its amplitude, and period, on the accretion rate and viscosity scaling. We show that if the heating rate in the accretion disk grows more rapidly with the total pressure and temperature, the instability results in longer and sharper flares. In general, we confirm that the disks around the supermassive black holes are more radiation-pressure dominated and present relatively brighter bursts. Our method can also be used as an independent tool for the black hole mass determination, which we confront now for the intermediate black hole in the source HLX-1.

Accretion disc viscosity: a limit on the anisotropy

Observations of warped discs can give insight into the nature of angular momentum transport in accretion discs. Only a few objects are known to show strong periodicity on long timescales, but when such periodicity is present it is often attributed to precession of the accretion disc. The X-ray binary Hercules X-1/HZ Herculis (Her X-1) is one of the best examples of such periodicity and has been linked to disc precession since it was first observed. By using the current best-fitting models to Her X-1, which invoke precession driven by radiation warping, I place a constraint on the effective viscosities that act in a warped disc. These effective viscosities almost certainly arise due to turbulence induced by the magneto-rotational instability. The constraints derived here are in agreement with analytical and numerical investigations into the nature of magneto-hydrodynamic disc turbulence, but at odds with some recent global simulations.

Flickering in CVs and Accretion Disc Viscosity

I review observational constraints on accretion disc viscosity inferred from changes of disc structure with time and from disc flickering distributions. The radial run of the disc viscosity parameter in four cases are presented and discussed.

Anomalous magnetic viscosity in accretion disks with q-distributed plasmas

Based on the equations of the self-generated magnetic field in the q-distributed plasmas, the studies show that the magnetic field is modulationally unstable by the perturbation method and the equations have self-similar collapse solution. The anomalous magnetic viscosity of accretion disks generates from highly spatially intermittent flux of the self-generated magnetic field. In addition, the anomalous viscosity coefficient is 8 orders more than the molecular viscosity and is modified by the adjustable index q, which may preferably explain the observations.

Accretion disc viscosity: what do warped discs tell us?

Standard, planar accretion discs operate through a dissipative mechanism, usually thought to be turbulent, and often modelled as a viscosity. This acts to take energy from the radial shear, enabling the flow of mass and angular momentum in the radial direction. In a previous paper we discussed observational evidence for the magnitude of this viscosity, and pointed out discrepancies between these values and those obtained in numerical simulations. In this paper we discuss the observational evidence for the magnitude of the dissipative effects which act in non--planar discs, both to transfer and to eliminate the non--planarity. Estimates based on the model by Ogilvie (1999), which assumes a small--scale, isotropic viscosity, give alignment timescales for fully ionized discs which are apparently too short by a factor of a few compared with observations, although we emphasize that more detailed computations as well as tighter observational constraints are required to verify this conclusion. For discs with low temperature and conductivity, we find that the timescales for disc alignment based on isotropic viscosity are too short by around two orders of magnitude. This large discrepancy suggests that our understanding of viscosity in quiescent discs is currently inadequate.

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (η) to entropy density (s) for any matter to be ∼μℏ/4πkB, when ℏ and kB are reduced Planck and Boltzmann constants respectively and μ⩽1. Motivated by this, we explore η/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest η/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford–Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In addition, certain optically thin, hot, accretion flows, of temperature ≳109 K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that η/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on η/s also leads to an upper bound on the Reynolds number of the flow.

DO JETS PRECESS… OR EVEN MOVE AT ALL?

Observations of accreting black holes often provoke suggestions that their jets precess. The precession is usually supposed to result from a combination of the Lense-Thirring effect and accretion disc viscosity. We show that this is unlikely for any type of black hole system, as the disc generally has too little angular momentum compared with a spinning hole to cause any significant movement of the jet direction across the sky on short timescales. Uncorrelated accretion events, as in the chaotic accretion picture of active galactic nuclei, change AGN jet directions only on timescales \gtrsim 10^7 yr. In this picture AGN jet directions are stable on shorter timescales, but uncorrelated with any structure of the host galaxy, as observed. We argue that observations of black-hole jets precessing on timescales short compared to the accretion time would be a strong indication that the accretion disc, and not the standard Blandford-Znajek mechanism, is responsible for driving the jet. This would be particularly convincing in a tidal disruption event. We suggest that additional disc physics is needed to explain any jet precession on timescales short compared with the accretion time. Possibilities include the radiation warping instability, or disc tearing.

Angular Momentum Transport in Accretion Disk Boundary Layers Around Weakly Magnetized Stars

The standard model for turbulent shear viscosity in accretion disks is based on the assumption that angular momentum transport is opposite to the radial angular frequency gradient of the disk. This implies that the turbulent stress must be negative and thus transport angular momentum inwards, in the boundary layer where the accretion disk meets the surface of a weakly magnetized star. However, this behavior is not supported by numerical simulations of turbulent magnetohydrodynamic (MHD) accretion disks, which show that angular momentum transport driven by the magnetorotational instability (MRI) is inefficient in disk regions where, as expected in boundary layers, the angular frequency increases with radius. Motivated by the need of a deeper understanding of the behavior of an MHD fluid in a differentially rotating background that deviates from a Keplerian profile, we study the dynamics of MHD waves in configurations that are stable to the standard MRI. Employing the shearing-sheet framework, we show that transient amplification of shearing MHD waves can generate magnetic energy without leading to a substantial generation of hydromagnetic stresses. While these results are in agreement with numerical simulations, they emphasize the need to better understand the mechanism for angular momentum transport in the inner disk regions on more solid grounds.

Anomalous magnetic viscosity in relativistic accretion disks

It has been proved that the self-generated magnetic fields by transverse plasmons in the relativistic regime are modulationally unstable, leading to a self-similar collapse of the magnetic flux tubes and resulting in local magnetic structures; highly spatially intermittent flux is responsible for generating the anomalous viscosity. We derive the anomalous magnetic viscosity coefficient, in accretion disks around compact objects, such as black holes, pulsars and quasars, where the plasmas are relativistic, in order to help clarify the nature of viscosity in the theory of accretion disks. The results indicate that, the magnetic viscosity is modified by the relativistic effects of plasmas, and its’ strength would be 1015 stronger than the molecular viscosity, which may be helpful in explaining the observations.

The viscosity parameterαand the properties of accretion disc outbursts in close binaries

The physical mechanisms driving angular momentum transport in accretion discs are still unknown. Although it is generally accepted that, in hot discs, the turbulence triggered by the magneto-rotational instability is at the origin of the accretion process in Keplerian discs, it has been found that the values of the stress-to-pressure ratio (the alpha "viscosity" parameter) deduced from observations of outbursting discs are an order of magnitude higher than those obtained in numerical simulations. We test the conclusion about the observation-deduced value of alpha using a new set of data and comparing the results with model outbursts. We analyse a set of observations of dwarf-nova and AM CVn star outbursts and from the measured decay times determine the hot-disc viscosity parameter alpha_h. We determine if and how this method is model dependent. From the dwarf-nova disc instability model we determine an amplitude vs recurrence-time relation and compare it to the empirical Kukarkin-Parenago relation between the same, but observed, quantities. We found that all methods we tried, including the one based on the amplitude vs recurrence-time relation, imply alpha_h ~ 0.1 - 0.2 and exclude values an order of magnitude lower. The serious discrepancy between the observed and the MRI-calculated values of the accretion disc viscosity parameter alpha is therefore real since there can be no doubt about the validity of the values deduced from observations of disc outbursts.

Anomalous gravitomagnetic viscosity in accretion disks

We propose a viscosity prescription in a self-gravitating system based on the self-generated gravitomagnetic field. It has been proved that the self-generated gravitomagnetic field with very low frequency is modulational unstable, leading to a self-collapse, and resulting in the enhancement of perturbed matter density and gravitomagnetic field in a small region; the interactions between highly spatially intermittent gravitomagnetic structures and the macrofluid with differential rotation are responsible for the anomalous gravitomagnetic viscosity. The result indicates that, the gravitomagnetic viscosity would be nearly 108 stronger than the molecular viscosity, which maybe useful for investigating the structures and instabilities in the self-gravitating accretion disks; provide an explanation for the transportion of angular momentum and the formation of gravitomagnetic jets.

A possible origin of viscosity in Keplerian accretion disks due to secondary perturbation: Turbulent transport without magnetic fields

The origin of hydrodynamic turbulence in rotating shear flow is a long standing puzzle. Resolving it is especially important in astrophysics when the flow's angular momentum profile is Keplerian which forms an accretion disk having negligible molecular viscosity. Hence, any viscosity in such systems must be due to turbulence, arguably governed by magnetorotational instability, especially when temperature T ≳ 105. However, such disks around quiescent cataclysmic variables, protoplanetary and star-forming disks, and the outer regions of disks in active galactic nuclei are practically neutral in charge because of their low temperature, and thus are not expected to be coupled with magnetic fields enough to generate any transport due to the magnetorotational instability. This flow is similar to plane Couette flow including the Coriolis force, at least locally. What drives their turbulence and then transport, when such flows do not exhibit any unstable mode under linear hydrodynamic perturbation? We demonstrate that the three-dimensional secondary disturbance to the primarily perturbed flow that triggers elliptical instability may generate significant turbulent viscosity in the range 0.0001 ≲ νt ≲ 0.1, which can explain transport in accretion flows.

Reduction of boundary effects in the spiralMRI experiment PROMISE

AbstractMagnetorotational instability (MRI) is one of the most important and most common instabilities in astrophysics. It is widely accepted that it serves as a source of turbulent viscosity in accretion disks – the most energy efficient objects in the Universe. However it is very difficult to bring this process down on earth and model it in a laboratory experiment. Several different approaches have been proposed, one of the most recent is PROMISE (Potsdam‐ROssendorf Magnetorotational InStability Experiment). It consists of a flow of a liquid metal between two rotating cylinders under applied current‐free spiral magnetic field. The cylinders must be covered with plates which introduce additional end‐effects which alter the flow and make it more difficult to clearly distinguish between MRI stable and unstable state. In this paper we propose simple and inexpensive improvement to the PROMISE experiment which would reduce those undesirable effects. (© 2007 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Accretion disc viscosity: how big is alpha?

We consider observational and theoretical estimates of the accretion disc viscosity parameter a. We find that in thin, fully ionized discs, the best observational evidence suggests a typical range a ∼ 0.1-0.4, whereas the relevant numerical simulations tend to derive estimates for a which are an order of magnitude smaller. We discuss possible reasons for this apparent discrepancy.

A Gravitational Instability-driven Viscosity in Self-gravitating Accretion Disks

We derive a viscosity from gravitational instability in self-gravitating accretion disks, which has the required properties to account for the observed fast formation of the first supermassive black holes in highly redshifted quasars and for the cosmological evolution of the black hole mass distribution.