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Register a new userZero net flux MRI-turbulence in disks $-$ sustenance scheme and magnetic Prandtl number dependence
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George Mamatsashvili
Publication date
2020
fields
Physics
and research's language is
English
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We investigate sustenance and dependence on magnetic Prandtl number (${rm Pm}$) for magnetorotational instability (MRI)-driven turbulence in astrophysical Keplerian disks with zero net magnetic flux using standard shearing box simulations. We focus on the turbulence dynamics in Fourier space, capturing specific/noncanonical anisotropy of nonlinear processes due to disk flow shear. This is a new type of nonlinear redistribution of modes over wavevector orientations in Fourier space -- the nonlinear transverse cascade -- which is generic to shear flows and fundamentally different from usual direct/inverse cascade. The zero flux MRI has no exponentially growing modes, so its growth is transient, or nonmodal. Turbulence self-sustenance is governed by constructive cooperation of the transient growth of MRI and the nonlinear transverse cascade. This cooperation takes place at small wavenumbers (on the flow size scales) referred to as the vital area in Fourier space. The direct cascade transfers mode energy from the vital area to larger wavenumbers. At large ${rm Pm}$, the transverse cascade prevails over the direct one, keeping most of modes energy contained in small wavenumbers. With decreasing ${rm Pm}$, however, the action of the transverse cascade weakens and can no longer oppose the action of direct cascade which more efficiently transfers energy to higher wavenumbers, leading to increased resistive dissipation. This undermines the sustenance scheme, resulting in the turbulence decay. Thus, the decay of zero net flux MRI-turbulence with decreasing ${rm Pm}$ is attributed to topological rearrangement of the nonlinear processes when the direct cascade begins to prevail over the transverse cascade.
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We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier (${bf k}$-)space, we identified three types of active modes that define turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled the vital area and are: (i) the channel mode - uniform in the disk plane with the smallest vertical wavenumber,(ii) the zonal flow mode - azimuthally and vertically uniform with the smallest radial wavenumber and (iii) the rest modes. The rest modes comprise those harmonics in the vital area whose energies reach more than $50 %$ of the maximum spectral energy. The rest modes individually are not so significant compared to the channel and zonal flow modes, however, the combined action of their multitude is dominant over these two modes. These three mode types are governed by interplay of the linear and nonlinear processes, leading to their interdependent dynamics. The linear processes consist in disk flow nonmodality-modified classical MRI with a net vertical field. The main nonlinear process is transfer of modes over wavevector angles in Fourier space - the transverse cascade. The channel mode exhibits episodic bursts supplied by linear MRI growth, while the nonlinear processes mostly oppose this, draining the channel energy and redistributing it to the rest modes. As for the zonal flow, it does not have a linear source and is fed by nonlinear interactions of the rest modes.
Accretion disks are likely threaded by external vertical magnetic flux, which enhances the level of turbulence via the magnetorotational instability (MRI). Using shearing-box simulations, we find that such external magnetic flux also strongly enhances the amplitude of banded radial density variations known as zonal flows. Moreover, we report that vertical magnetic flux is strongly concentrated toward low-density regions of the zonal flow. Mean vertical magnetic field can be more than doubled in low-density regions, and reduced to nearly zero in high density regions in some cases. In ideal MHD, the scale on which magnetic flux concentrates can reach a few disk scale heights. In the non-ideal MHD regime with strong ambipolar diffusion, magnetic flux is concentrated into thin axisymmetric shells at some enhanced level, whose size is typically less than half a scale height. We show that magnetic flux concentration is closely related to the fact that the magnetic diffusivity of the MRI turbulence is anisotropic. In addition to a conventional Ohmic-like turbulent resistivity, we find that there is a correlation between the vertical velocity and horizontal magnetic field fluctuations that produces a mean electric field that acts to anti-diffuse the vertical magnetic flux. The anisotropic turbulent diffusivity has analogies to the Hall effect, and may have important implications for magnetic flux transport in accretion disks. The physical origin of magnetic flux concentration may be related to the development of channel flows followed by magnetic reconnection, which acts to decrease the mass-to-flux ratio in localized regions. The association of enhanced zonal flows with magnetic flux concentration may lead to global pressure bumps in protoplanetary disks that helps trap dust particles and facilitates planet formation.
(abriged) MRI turbulence is a leading mechanism for the generation of an efficient turbulent transport of angular momentum in an accretion disk through a turbulent viscosity effect. It is believed that the same process could also transport large-scale magnetic fields in disks, reshaping the magnetic structures in these objects. This process, known as turbulent resistivity, has been suggested and used in several accretion-ejection models and simulations to produce jets. Still, the efficiency of MRI-driven turbulence to transport large-scale magnetic fields is largely unknown. We investigate this problem both analytically and numerically. We introduce a linear calculation of the MRI in the presence of a spatially inhomogeneous mean magnetic field. We show that, in this configuration, MRI modes lead to an efficient magnetic field transport, on the order of the angular momentum transport. We next use fully non linear simulations of MRI turbulence to compute the turbulent resistivity in several magnetic configurations. We find that the turbulent resistivity is on the order of the turbulent viscosity in all our simulations, although somewhat lower. The turbulent resistivity tensor is found to be highly anisotropic with a diffusion coefficient 3 times greater in the radial direction than in the vertical direction. These results support the possibility of driving jets from turbulent disks; the resulting jets may not be steady.
Accreting supermassive binary black holes (SMBBHs) are potential multi-messenger sources because they emit both gravitational wave and electromagnetic (EM) radiation. Past work has shown that their EM output may be periodically modulated by an asymmetric density distribution in the circumbinary disk, often called an overdensity or lump; this modulation could possibly be used to identify a source as a binary. We explore the sensitivity of the overdensity to SMBBH mass ratio and magnetic flux through the accretion disk. We find that the relative amplitude of the overdensity and its associated EM periodic signal both degrade with diminishing mass ratio, vanishing altogether somewhere between 1:2 and 1:5. Greater magnetization also weakens the lump and any modulation of the light output. We develop a model to describe how lump formation results from internal stress degrading faster in the lump region than it can be rejuvenated through accretion inflow, and predicts a threshold value in specific internal stress below which lump formation should occur and which all our lump-forming simulations satisfy. Thus, detection of such a modulation would provide a constraint on both mass-ratio and magnetic flux piercing the accretion flow.
In their early stages, protoplanetary discs are sufficiently massive to undergo gravitational instability (GI). This instability is thought to be involved in mass accretion, planet formation via gas fragmentation, the generation of spiral density waves, and outbursts. A key and very recent area of research is the interaction between the GI and magnetic fields in young protoplanetary discs, in particular whether this instability is able to sustain a magnetic field via a dynamo. We conduct three-dimensional, stratified shearing-box simulations using two independent codes, PLUTO and Athena++, to characterise the GI dynamo in poorly ionised protostellar discs subject to ambipolar diffusion. We find that the dynamo operates across a large range of ambipolar Elssaser number Am (which characterises the strength of ambipolar diffusion) and is particularly strong in the regime Am=10-100, with typical magnetic to thermal energy ratios of order unity. The dynamo is only weakly dependent on resolution (at least for Am <100), box size, and cooling law. The magnetic field is produced by the combination of differential rotation and large-scale vertical roll motions associated with spiral density waves. Our results have direct implications for the dynamo process in young protoplanetary discs and possibly some regions of AGN discs.
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