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Turbulence in Accretion Disks – New Perspectives

Periodic Reporting for period 1 - MRI-Turbulent-Disk (Turbulence in Accretion Disks – New Perspectives)

Reporting period: 2018-07-01 to 2020-06-30

Astrophysical disks rotating around young stellar objects, black holes and binary stars, attract great interest because one of the fundamental phenomena in the Universe – mass accretion and radiation – occur via such disks. Disks are involved in a range of spectacular phenomena, from planet formation to X-ray binaries and collimated jets from protostars and black holes. Knowledge of the basic physics of mass accretion onto the central object is essential for understanding its evolution and observational characteristics. Disks evolve by accreting matter to the central object as a result of losing angular momentum. The gravitational energy released during accretion is converted into radiation, which can be observed and give clues on the accretion rate – one of the central quantities for deducing the structure and evolution of disk. However, gas viscosity is too low to yield sufficiently rapid transport of angular momentum and hence consistent with observations inward accretion rates of disk matter. So, identifying mechanisms for more efficient redistribution of angular momentum has been a puzzle for decades.

It is widely accepted today that such an enhanced transport is achieved by turbulence due to the magnetorotational instability (MRI), which arises from the combination of disk’s differential rotation and magnetic field and grows fast, on orbital time. The nonlinear development of MRI breaks down into turbulence which transports angular momentum outwards. Theoretically estimated accretion rates due to this turbulent transport are orders of magnitude higher than that due to viscosity and comparable to observed values. The main goal of frontier research in MRI in disks is to understand its key aspects – saturation and sustenance of resulting turbulence – and to compare corresponding mass accretion rates with observations. Because of enormous complexity of turbulence, these are tackled via numerical simulations. A great progress in this field over the last decade, thanks to powerful computers, demonstrated that various physical factors: strength and configuration of disk’s magnetic field, numerical resolution, stratification, non-ideal effects (viscosity, Ohmic resistivity), etc. play a crucial role in the dynamics of MRI-turbulence and its transport capability. However, MRI-turbulence theory has not yet grown sufficiently to have strong predictive power. In particular, accretion rates from theoretical studies still appear to depend on these factors and hence often do not agree with observations. Many key unresolved issues still remain from which the most important ones of the frontier research are:
1. Convergence problem of MRI-turbulence, i.e. decrease in the turbulent transport with increasing numerical resolution
2. Dependence of MRI-turbulent transport on viscous and resistive dissipation
3. Magnetic dynamo and its role in the sustenance of MRI-turbulence and transport
Our main goal was to address these issues from a new perspective of analysis of the dynamical processes in Fourier space.
We performed simulations of unstratified MRI-turbulence in disks and then analyzed in detail the energy spectra as well as energy-injecting linear and nonlinear terms. It was shown that action of nonlinear terms in Fourier space displays a new – transverse – type of cascade due to flow shear and, based on this, identified basic sustaining mechanism of the turbulence. The nonlinear transverse cascade plays a crucial role here, since the sustenance relies on the interplay between the linear growth of MRI and the transverse cascade. We showed that with increasing vertical size of the domain, transverse cascade pumps more energy in lower wavenumber modes, leading to the dynamo action and emergence of large-scale azimuthal field.

Next, we analyzed how sustenance and transport of the turbulence is affected by viscosity and resistivity via computing nonlinear interactions between small-scale and large-scale modes, mostly responsible for the transport. This analysis provided essential insights into physical grounds for the convergence problem for MRI-turbulence and the effects of viscosity and resistivity on the transport. These effects have been previously investigated, but only in physical space, offering a limited understanding of the dynamics.

Finally, we explored the MRI-turbulence in stratified disks. By analyzing in detail the nonlinear transfers among modes in Fourier space, we showed how such a mode interaction gives rise to large-scale dynamo action in the presence of stratification, with quasi-periodic spatio-temporal variations of the mean azimuthal field. This large-scale azimuthal field was previously observed in other studies, but again explored in physical space using mean-field approach, where one uses spatially averaged equations and misses out the essential dynamics of smaller-scale modes that drive large-scale dynamo via nonlinearity.
The project, going beyond the state-of-the-art, aimed at clarifying these issues by in-depth investigation of the dynamics of MRI in disks – its linear growth, nonlinear saturation and energetic balances in the resulting turbulence, associated transport and dynamo action under different physical conditions in disks, building on my previous findings in shear flow turbulence theory. First of all, these are the new concepts of shear-induced spectral anisotropy, nonlinear transverse cascade and vital area of turbulence, which I elaborated and which lie at the heart of sustaining dynamics of turbulence in shear flows, whose special case is MRI-turbulence in disks. This new approach consists in a combination of simulations of equations of magnetohydrodynamics and, on their basis, a detailed analysis of the dynamical process in Fourier space, where much richer dynamics unfolds than that in physical (coordinate) space. It has offered a deeper understanding of the sustenance and evolution of MRI-turbulence in disks and, importantly, enabled further progress in the resolution of the above three main issues, which, however, are not accessible to an analysis in physical space, as done before in most studies. Thus, with this new approach, we have gone beyond the state-of-the-art in MRI studies, providing a new perspective on MRI-turbulence dynamics that contributes to clarification of the main outstanding issues still persisting due to conservative approaches used so far.

The project will have a wide impact, since the elaborated methods and obtained results are of interdisciplinary value that can be of interest to different (e.g. hydrodynamical, plasma physics, geophysical, etc.) communities studying shear flow turbulence. The new concepts and processes studied in the project, such as anisotropic spectra and transverse cascade, are in fact generic to any shear flow in nature, industry and lab and will form a basis for new studies in shear flow turbulence in Fluid Dynamics, Plasma Physics, Geophysics, Space Physics, etc. The main goal of the project was to study sustaining dynamics of turbulence in disks, which are special cases of shear flows, and to show the role of the transverse cascade therein. In this way, the project has also contributed to an establishment of the transverse cascade as a necessary alternative to usual inverse/direct cascades in shear flows. The transverse cascade calls for revision of these well-known cascade processes of Kolmogorov’s theory of turbulence in relation to shear flows.
Structure of the azimuthal field in physical space in a developed MRI-turbulence in stratified disks