Localized magnetorotational instability and its role in the accretion disc dynamo

(Abriged) The magnetorotational instability (MRI) is believed to be an efficient way to transport angular momentum in accretion discs. It has also been suggested as a way to amplify magnetic fields in discs, the instability acting as a nonlinear dynamo. Recent numerical work has shown that a large-scale magnetic field, which is predominantly azimuthal, can be sustained by motions driven by the MRI of this same field. Following this idea, we present an analytical calculation of the MRI in the presence of an azimuthal field with a non-trivial vertical structure. We find that the mean radial EMF associated to MRI modes tends to reduce the magnetic energy, acting like a turbulent resistivity by mixing the non-uniform azimuthal field. Meanwhile, the azimuthal EMF generates a radial field that, in combination with the Keplerian shear, tends to amplify the azimuthal field and can therefore assist in the dynamo process. This effect, however, is reversed for sufficiently strong azimuthal fields, naturally leading to a saturation of the dynamo and possibly to a cyclic behaviour of the magnetic field, as found in previous numerical works.Comment: 15 pages, 5 figure

On the interaction between tides and convection

We study the interaction between tides and convection in astrophysical bodies by analysing the effect of a homogeneous oscillatory shear on a fluid flow. This model can be taken to represent the interaction between a large-scale periodic tidal deformation and a smaller-scale convective motion. We first consider analytically the limit in which the shear is of low amplitude and the oscillation period is short compared to the timescales of the unperturbed flow. In this limit there is a viscoelastic response and we obtain expressions for the effective elastic modulus and viscosity coefficient. The effective viscosity is inversely proportional to the square of the oscillation frequency, with a coefficient that can be positive, negative or zero depending on the properties of the unperturbed flow. We also carry out direct numerical simulations of Boussinesq convection in an oscillatory shearing box and measure the time-dependent Reynolds stress. The results indicate that the effective viscosity of turbulent convection falls rapidly as the oscillation frequency is increased, attaining small negative values in the cases we have examined, although significant uncertainties remain because of the turbulent noise. We discuss the implications of this analysis for astrophysical tides.Comment: 14 pages, 5 figures, to be published in MNRA

On the angular momentum transport due to vertical convection in accretion discs

The mechanism of angular momentum transport in accretion discs has long been debated. Although the magnetorotational instability appears to be a promising process, poorly ionized regions of accretion discs may not undergo this instability. In this letter, we revisit the possibility of transporting angular momentum by turbulent thermal convection. Using high-resolution spectral methods, we show that strongly turbulent convection can drive outward angular momentum transport at a rate that is, under certain conditions, compatible with observations of discs. We find however that the angular momentum transport is always much weaker than the vertical heat transport. These results indicate that convection might be another way to explain global disc evolution, provided that a sufficiently unstable vertical temperature profile can be maintained.Comment: 6 pages, 5 figures, accepted in MNRA

Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes.Comment: 7 pages, 6 figure

Magnetorotational dynamo chimeras. The missing link to turbulent accretion disk dynamo models?

In Keplerian accretion disks, turbulence and magnetic fields may be jointly excited through a subcritical dynamo process involving the magnetorotational instability (MRI). High-resolution simulations exhibit a tendency towards statistical self-organization of MRI dynamo turbulence into large-scale cyclic dynamics. Understanding the physical origin of these structures, and whether they can be sustained and transport angular momentum efficiently in astrophysical conditions, represents a significant theoretical challenge. The discovery of simple periodic nonlinear MRI dynamo solutions has recently proven useful in this respect, and has notably served to highlight the role of turbulent magnetic diffusion in the seeming decay of the dynamics at low magnetic Prandtl number Pm (magnetic diffusivity larger than viscosity), a common regime in accretion disks. The connection between these simple structures and the statistical organization reported in turbulent simulations remained elusive, though. Here, we report the numerical discovery in moderate aspect ratio Keplerian shearing boxes of new periodic, incompressible, three-dimensional nonlinear MRI dynamo solutions with a larger dynamical complexity reminiscent of such simulations. These "chimera" cycles are characterized by multiple MRI-unstable dynamical stages, but their basic physical principles of self-sustainment are nevertheless identical to those of simpler cycles found in azimuthally elongated boxes. In particular, we find that they are not sustained at low Pm either due to subcritical turbulent magnetic diffusion. These solutions offer a new perspective into the transition from laminar to turbulent instability-driven dynamos, and may prove useful to devise improved statistical models of turbulent accretion disk dynamos.Comment: 12 pages, 8 figures, submitted to A&

Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows

The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic field and non-axisymmetric perturbations amplified by the magnetorotational instability. We demonstrate that this large scale dynamo mechanism is overall intrinsically nonlinear and not reducible to the standard mean-field dynamo formalism. Our results therefore provide clear evidence for a generic nonlinear generation mechanism of time-dependent coherent large-scale magnetic fields in shear flows and call for new theoretical dynamo models. These findings may offer important clues to understand the transitional and statistical properties of subcritical magnetorotational turbulence.Comment: 10 pages, 6 figures, accepted for publication in Physical Review

On Self-Sustained Dynamo Cycles in Accretion Discs

(abridged) MHD turbulence is known to exist in shearing boxes with either zero or nonzero net magnetic flux. However, the way turbulence survives in the zero-net-flux case is not explained by linear theory and appears as a purely numerical result. Aims: We look for a nonlinear mechanism able to explain the persistence of MHD turbulence in shearing boxes with zero net magnetic flux, and potentially leading to large-scale dynamo action. Method: Spectral nonlinear simulations of the magnetorotational instability are shown to exhibit a large-scale axisymmetric magnetic field, maintained for a few orbits. The generation process of this field is investigated using the results of the simulations and an inhomogeneous linear approach. Results: The mechanism by which turbulence is sustained in zero-net-flux shearing boxes is shown to be related to the existence of a large-scale azimuthal field, surviving for several orbits. In particular, it is shown that MHD turbulence in shearing boxes can be seen as a dynamo process coupled to a magnetorotational-type instability.Comment: 11 pages, 11 figures, Accepted in A&

Dissipative effects on the sustainment of a magnetorotational dynamo in Keplerian shear flow.

The magnetorotational (MRI) dynamo has long been considered one of the possible drivers of turbulent angular momentum transport in astrophysical accretion disks. However, various numerical results suggest that this dynamo may be difficult to excite in the astrophysically relevant regime of magnetic Prandtl number (Pm) significantly smaller than unity, for reasons currently not well understood. The aim of this article is to present the first results of an ongoing numerical investigation of the role of both linear and nonlinear dissipative effects in this problem. Combining a parametric exploration and an energy analysis of incompressible nonlinear MRI dynamo cycles representative of the transitional dynamics in large aspect ratio shearing boxes, we find that turbulent magnetic diffusion makes the excitation and sustainment of this dynamo at moderate magnetic Reynolds number (Rm) increasingly difficult for decreasing Pm. This results in an increase in the critical Rm of the dynamo for increasing kinematic Reynolds number (Re), in agreement with earlier numerical results. Given its very generic nature, we argue that turbulent magnetic diffusion could be an important determinant of MRI dynamo excitation in disks, and may also limit the efficiency of angular momentum transport by MRI turbulence in low Pm regimes

Effects of agonists of peroxisome proliferator-activated receptor γ on proteoglycan degradation and matrix metalloproteinase production in rat cartilage in vitro

AbstractObjective To examine the effects of agonists of peroxisome proliferator-activated receptor (PPAR) γ on proteoglycan degradation induced by interleukin (IL)-1β or tumor necrosis factor (TNF)α in cartilage in vitro.Design Proteoglycan degradation was measured as release of radioactivity from rat cartilage explants previously labeled with 35SO2−4. Western blots were used to examine tissue levels of aggrecan neoepitopes NITEGE and VDIPEN, generated by aggrecanases and matrix metalloproteinases (MMP), respectively. Production of MMP-2, -3 and -9 by cultured rat chondrocytes was measured by zymography and by fluorimetric assay.Results IL-1β-induced proteoglycan degradation was likely due to aggrecanase, since it was associated with a strong increase of NITEGE signal. MMP-dependent VDIPEN signal increased only after further incubation with pro-MMP activator APMA. PPAR agonists 15d-PGJ2 and GI262570 (10μM) inhibited IL-1β- and TNFα-induced proteoglycan degradation measured both before and after addition of APMA. The agonists also inhibited cytokine-induced MMP production by isolated chondrocytes.Conclusion This study shows that PPARγ agonists inhibit cytokine-induced proteoglycan degradation mediated by both aggrecanase and MMP. This effect is associated with inhibition of production of MMP-3 and -9. These results support the interest for PPARγ agonists as candidate inhibitors of pathological cartilage degradation. Copyright 2002 OsteoArthritis Research Society International. Published by Elsevier Science Ltd. All rights reserved

Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

Magnetorotational dynamo action in Keplerian shear flow is a three-dimensional, non-linear magnetohydrodynamic process whose study is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics of transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to turbulent injection of both kinetic and magnetic energy in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to better understand the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows