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Hot accretion flows contain collisionless plasmas that are believed to be capable of accelerating particles to very high energies, as a result of turbulence generated by the magnetorotational instability (MRI). We conduct unstratified shearing-box simulations of the MRI turbulence in ideal magnetohydrodynamic (MHD), and inject energetic (relativistic) test particles in simulation snapshots to conduct a detailed investigation on particle diffusion and stochastic acceleration. We consider different amount of net vertical magnetic flux to achieve different disk magnetizations levels at saturated states, with sufficiently high resolution to resolve the gyro-radii ($R_g$) of most particles. Particles with large $R_g$ ($\gtrsim0.03$ disk scale height $H$) show spatial diffusion coefficients of $\sim30$ and $\sim5$ times Bohm values in the azimuthal and poloidal directions, respectively. We further measure particle momentum diffusion coefficient $D(p)$ by applying the Fokker-Planck equation to particle momentum evolution. For these particles, contribution from turbulent fluctuations scales as $D(p)\propto p$, and shear acceleration takes over when $R_g\gtrsim0.1H$, characterized by $D(p)\propto p^3$. For particles with smaller $R_g$ ($\lesssim0.03H$), their spatial diffusion coefficients roughly scale as $\sim p^{-1}$, and show evidence of $D(p)\propto p^2$ scaling in momentum diffusion but with large uncertainties. We find that multiple effects contribute to stochastic acceleration/deceleration, and the process is also likely affected by intermittency in the MRI turbulence. We also discuss the potential of accelerating PeV cosmic-rays in hot accretion flows around supermassive black holes., Comment: 22 pages, 18 figures, accepted for publication in MNRAS

The stability of magnetized flows of a nonuniformly rotating layer of an electrically conducting nanofluid is investigated with regard to the effects of Brownian diffusion and thermophoresis. In the absence of a temperature gradient, new types of magnetorotational instability (MRI) are considered in axial, azimuthal, and helical magnetic fields in thin layers of a nanofluid. The increments and development regions of these instabilities are obtained depending on the angular velocity profile (Rossby number Ro) and the radial wavenumber k. In the presence of temperature and nanoparticle concentration gradients, stationary regimes of nonuniformly rotating convection in axial and helical magnetic fields are studied. Expressions are obtained for the critical Rayleigh numbers Rast, and neutral stability curves are plotted depending on the angular velocity profile, the profile of the external azimuthal magnetic field (the magnetic Rossby number Rb), and the radial wavenumber k. Conditions for stabilization and destabilization of stationary convection in axial and helical magnetic fields are found.

The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary disks (PPDs). While there is extensive literature on the VSI in the hydrodynamic limit, PPDs are expected to be magnetized and their extremely low ionization fractions imply that non-ideal magneto-hydrodynamic (MHD) effects should be properly considered. To this end, we present linear analyses of the VSI in magnetized disks with Ohmic resistivity. We primarily consider toroidal magnetic fields, which are likely to dominate the field geometry in PPDs. We perform vertically global and radially local analyses to capture characteristic VSI modes with extended vertical structures. To focus on the effect of magnetism, we use a locally isothermal equation of state. We find that magnetism provides a stabilizing effect to dampen the VSI, with surface modes, rather than body modes, being the first to vanish with increasing magnetization. Subdued VSI modes can be revived by Ohmic resistivity, where sufficient magnetic diffusion overcome magnetic stabilization, and hydrodynamic results are recovered. We also briefly consider poloidal fields to account for the magnetorotational instability (MRI), which may develop towards surface layers in the outer parts of PPDs. The MRI grows efficiently at small radial wavenumbers, in contrast to the VSI. When resistivity is considered, we find the VSI dominates over the MRI for Ohmic Els\"{a}sser numbers $\lesssim 0.09$ at plasma beta parameter $\beta_Z \sim 10^4$., Comment: 17 pages, 11 figures, accepted for publication in MNRAS

Convection has been discussed in the field of accretion discs for several decades, both as a means of angular momentum transport and also because of its role in controlling discs' vertical structure via heat transport. If the gas is sufficiently ionized and threaded by a weak magnetic field, convection might interact in non-trivial ways with the magnetorotational instability (MRI). Recently, vertically stratified local simulations of the MRI have reported considerable variation in the angular momentum transport, as measured by the stress to thermal pressure ratio $\alpha$, when convection is thought to be present. Although MRI turbulence can act as a heat source for convection, it is not clear how the instabilities will interact dynamically. Here we aim to investigate the interplay between the two instabilities in controlled numerical experiments, and thus isolate the generic features of their interaction. We perform vertically stratified, 3D MHD shearing box simulations with a perfect gas equation of state with the conservative, finite-volume code PLUTO. We find two characteristic outcomes of the interaction between the two instabilities: straight MRI and MRI/convective cycles, with the latter exhibiting alternating phases of convection-dominated flow (during which the turbulent transport is weak) and MRI-dominated flow. During the latter phase we find that $\alpha$ is enhanced by nearly an order of magnitude, reaching peak values of $\sim 0.08$. In addition, we find that convection in the non-linear phase takes the form of large-scale and oscillatory convective cells. Convection can also help the MRI persist to lower Rm than it would otherwise do. Finally we discuss how our results help interpret simulations of Dwarf Novae., Comment: Accepted for publication in MNRAS (23 pages, 14 figures, 1 table)

Instability modes of viscoelastic Taylor–Couette flow in the Keplerian regime are investigated using both linear stability analysis and experimental detection of critical states. A generalised Rayl...

We investigate whether the regular Galilean satellites could have formed in the dead zone of a circumplanetary disc. A dead zone is a region of weak turbulence in which the magnetorotational instability (MRI) is suppressed, potentially an ideal environment for satellite formation. With the grid-based hydrodynamic code, FARGO3D, we examine the evolution of a circumplanetary disc model with a dead zone. Material accumulates in the dead zone of the disc leading to a higher total mass and but a similar temperature profile compared to a fully turbulent disc model. The tidal torque increases the rate of mass transport through the dead zone leading to a steady state disc with a dead zone that does not undergo accretion outbursts. We explore a range of disc, dead zone and mass inflow parameters and find that the maximum mass of the disc is around 0.001 MJ . Since the total solid mass of such a disc is much lower, we find that there is not sufficient material in the disc for in situ formation of the Galilean satellites and that external supplement is required., Comment: 10 pages, 6 figures

We explore the pulsationally driven orbital mass ejection mechanism for Be star disc formation using isothermal, 3D magnetohydrodynamic (MHD) and hydrodynamic simulations. Non-radial pulsations are added to a star rotating at 95\% of critical as an inner boundary condition that feeds gas into the domain. In MHD, the initial magnetic field within the star is weak. The hydrodynamics simulation has limited angular momentum transport, resulting in repeating cycles of mass accumulation into a rotationally-supported disc at small radii followed by fall-back onto the star. The MHD simulation, conversely, has efficient (Maxwell $\alpha_{\rm M}$ $\sim$ 0.04) angular momentum transport provided by both of turbulent and coherent magnetic fields; a slowly decreting midplane driven by the magnetorotational instability and a supersonic wind on the surface of the disc driven by global magnetic torques. The angle and time-averaged properties near the midplane agree reasonably well with a 1D viscous decretion disc model with a modified $\tilde\alpha=0.5$, in which the gas transitions from a subsonic thin disc to a supersonic spherical wind at the critical point. 1D models, however, cannot capture the multi-phase decretion/angular structure seen in our simulations. Our results demonstrate that, at least under certain conditions, non-radial pulsations on the surface of a rapidly rotating, weakly magnetized star can drive a Keplerian disc with the basic properties of the viscous decretion disc paradigm, albeit coupled to a laminar wind away from the midplane. Future modeling of Be star discs should consider the possible existence of such a surface wind., Comment: Accepted by MNRAS. 16 pages, 10 figures

The evolution of current sheets in accretion flows undergoing magnetorotational instability (MRI) is examined through two and three dimensional numerical modelling of the resistive MHD equations in global cylindrical geometry. With an initial uniform magnetic field aligned in the vertical ($z$) direction, MRI produces radially extended toroidal (azimuthal) current sheets. In both 2D and 3D when axisymmetric modes dominate, these current sheets attract each other and merge in the poloidal ($rz$) plane, driving magnetic reconnection when the Lundquist number $S > 3 \times 10^2$, making it a possible source of plasmoids (closed magnetic loops) in accretion disks. At high Lundquist numbers in the 2D regime, starting at $S = 5 \times 10^3$, self-consistent MRI-generated current sheets become thin and subject to plasmoid instability, and therefore spontaneous magnetic reconnection. When non-axisymmetric 3D modes dominate, turbulence makes the azimuthal current sheets further unstable, and stretch vertically. Toroidally extended vertical current sheets in the inner region, as well as larger 3D magnetic islands in the outer regions of the disks are also formed. These findings have strong ramifications for astrophysical disks as potential sources of plasmoids that could cause local heating, particle acceleration, and high energy EM radiation., 12 pages, 6 figures, Accepted for publication to ApJ Letters

In the present study, we addressed the question of how the growth rate of the magnetorotational instability is modified when the radial component of the stellar dipole magnetic field is taken into account in addition to the vertical component. Considering a fiducial radius in the disc where diamagnetic currents are pronounced, we carried out a linear stability analysis to obtain the growth rates of the magnetorotational instability for various parameters such as the ratio of the radial-to-vertical component and the gradient of the magnetic field, the Alfvenic Mach number and the diamagnetization parameter. Our results show that the interaction between the diamagnetic current and the radial component of the magnetic field increases the growth rate of the magnetorotational instability and generates a force perpendicular to the disc plane which may induce a torque. It is also shown that considering the radial component of the magnetic field and taking into account a radial gradient in the vertical component of the magnetic field causes an increase in the magnitudes of the growth rates of both the axisymmetric ($m=0$) and the non-axisymmetric ($m=1$) modes., Comment: 9 pages, 5 figures, published in MNRAS, 2020, vol. 491, pages 5481-5488

We investigate acceleration and propagation processes of high-energy particles inside hot accretion flows. The magnetorotational instability (MRI) creates turbulence inside accretion flows, which triggers magnetic reconnection and may produce non-thermal particles. They can be further accelerated stochastically by the turbulence. To probe the properties of such relativistic particles, we perform magnetohydrodynamic simulations to obtain the turbulent fields generated by the MRI, and calculate orbits of the high-energy particles using snapshot data of the MRI turbulence. We find that the particle acceleration is described by a diffusion phenomenon in energy space with a diffusion coefficient of the hard-sphere type: $D_\epsilon\propto \epsilon^2$, where $\epsilon$ is the particle energy. Eddies in the largest scale of the turbulence play a dominant role in the acceleration process. On the other hand, the stochastic behaviour in configuration space is not usual diffusion but superdiffusion: the radial displacement increases with time faster than that in the normal diffusion. Also, the magnetic field configuration in the hot accretion flow creates outward bulk motion of high-energy particles. This bulk motion is more effective than the diffusive motion for higher energy particles. Our results imply that typical active galactic nuclei that host hot accretion flows can accelerate CRs up to $\epsilon\sim 0.1-10$ PeV., Comment: 17 pages, 16 figures, Figure 4 is corrected, conclusions are unchanged, published in MNRAS

We explore in situ formation and subsequent evolution of close-in super-Earths and mini-Neptunes. We adopt a steady-state inner protoplanetary gas disc structure that arises from viscous accretion due to the magneto-rotational instability (MRI). We consider the evolution of dust in the inner disc, including growth, radial drift and fragmentation, and find that dust particles that radially drift into the inner disc fragment severely due to the MRI-induced turbulence. This result has two consequences: (1) radial drift of grains within the inner disc is quenched, leading to an enhancement of dust in the inner regions which scales as dust-to-gas-mass-flux-ratio at ~1 AU; (2) however, despite this enhancement, planetesimal formation is impeded by the small grain size. Nevertheless, assuming that planetary cores are present in the inner disc, we then investigate the accretion of atmospheres onto cores and their subsequent photoevaporation. We then compare our results to the observed exoplanet mass-radius relationship. We find that: (1) the low gas surface densities and high temperatures in the inner disc reduce gas accretion onto cores compared to the minimum mass solar nebula, preventing the cores from growing into hot Jupiters, in agreement with the data; (2) however, our predicted envelope masses are still typically larger than observed ones. Finally, we sketch a qualitative picture of how grains may grow and planetesimals form in the inner disc if grain effects on the ionization levels and the MRI and the back-reaction of the dust on the gas (both neglected in our calculations) are accounted for., Comment: Accepted for publication in MNRAS

The Magnetorotational Instability (MRI) has long been considered a plausibly ubiquitous mechanism to destabilize otherwise stable Keplerian flows to support radially outward transport of angular momentum. Such an efficient transport process would allow fast accretion in astrophysical objects such as stars and black holes to release copious kinetic energy that powers many of the most luminous sources in the universe. But the standard MRI under a purely vertical magnetic field has heretofore never been directly measured despite numerous efforts over more than a decade. Here we report an unambiguous laboratory demonstration of the spring-mass analogue to the standard MRI by comparing motion of a spring-tethered ball within different rotating flows. The experiment corroborates the theory: efficient outward angular momentum transport manifests only for cases with a weak spring in quasi-Keperian flow. Our experimental method accomplishes this in a new way, thereby connecting solid and fluid mechanics to plasma astrophysics., Comment: 7 pages; 4 figures; accepted by Communications Physics

Worldwide very long baseline radio interferometry arrays are expected to obtain horizon-scale images of supermassive black hole candidates as well as of relativistic jets in several nearby active galactic nuclei. This motivates the development of models for magnetohydrodynamic flows in strong gravitational fields. The Black Hole Accretion Code (BHAC) intends to aid with the modelling of such sources by means of general relativistic magnetohydrodynamical (GRMHD) simulations in arbitrary stationary spacetimes. New additions were required to guarantee an accurate evolution of the magnetic field when small and large scales are captured simultaneously. We discuss the adaptive mesh refinement (AMR) techniques employed in BHAC, essential to keep several problems computationally tractable, as well as staggered-mesh-based constrained transport (CT) algorithms to preserve the divergence-free constraint of the magnetic field, including a general class of prolongation operators for face-allocated variables compatible with them. Through several standard tests, we show that the choice of divergence-control method can produce qualitative differences in simulations of scientifically relevant accretion problems. We demonstrate the ability of AMR to reduce the computational costs of accretion simulations while sufficiently resolving turbulence from the magnetorotational instability. In particular, we describe a simulation of an accreting Kerr black hole in Cartesian coordinates using AMR to follow the propagation of a relativistic jet while self-consistently including the jet engine, a problem set up-for which the new AMR implementation is particularly advantageous. The CT methods and AMR strategies discussed here are being employed in the simulations performed with BHAC used in the generation of theoretical models for the Event Horizon Telescope Collaboration., Comment: 21 pages, 16 figures, accepted for publication in Astronomy & Astrophysics. Link to www.bhac.science will soon be active

Many high-energy astrophysical systems contain magnetized collisionless plasmas with relativistic particles, in which turbulence can be driven by an arbitrary mixture of solenoidal and compressive motions. For example, turbulence in hot accretion flows may be driven solenoidally by the magnetorotational instability or compressively by spiral shock waves. It is important to understand the role of the driving mechanism on kinetic turbulence and the associated particle energization. In this work, we compare particle-in-cell simulations of solenoidally driven turbulence with similar simulations of compressively driven turbulence. We focus on plasma that has an initial beta of unity, relativistically hot electrons, and varying ion temperature. Apart from strong large-scale density fluctuations in the compressive case, the turbulence statistics are similar for both drives, and the bulk plasma is described reasonably well by an isothermal equation of state. We find that nonthermal particle acceleration is more efficient when turbulence is driven compressively. In the case of relativistically hot ions, both driving mechanisms ultimately lead to similar power-law particle energy distributions, but over a different duration. In the case of non-relativistic ions, there is significant nonthermal particle acceleration only for compressive driving. Additionally, we find that the electron-to-ion heating ratio is less than unity for both drives, but takes a smaller value for compressive driving. We demonstrate that this additional ion energization is associated with the collisionless damping of large-scale compressive modes via perpendicular electric fields., 29 pages, 28 figures, accepted for publication in ApJ

Aims. Accretion and luminosity bursts triggered by three distinct mechanisms: the magnetorotational instability in the inner disk regions, clump infall in gravitationally fragmented disks and close encounters with an intruder star, were studied to determine the disk kinematic characteristics that can help to distinguish between these burst mechanisms. Methods. Numerical hydrodynamics simulations in the thin-disk limit were employed to model the bursts in disk environments that are expected for each burst mechanism. Results. We found that the circumstellar disks featuring accretion bursts can bear kinematic features that are distinct for different burst mechanisms, which can be useful when identifying the burst origin. The disks in the stellar encounter and clump-infall models are characterized by tens of percent deviations from the Keplerian rotation, whie the disks in the MRI models are characterized only a few percent deviation, which is mostly caused by the gravitational instability that fuels the MRI bursts. Velocity channel maps also show distinct kinks and wiggles, which are caused by gas disk flows that are peculiar to each considered burst mechanism. The deviations of velocity channels in the burst-hosting disks from a symmetric pattern typical of Keplerian disks are strongest for the clump-infall and collision models, and carry individual features that may be useful for the identification of the corresponding burst mechanism. The considered burst mechanisms produce a variety of light curves with the burst amplitudes varying in the \Delta m=2.5-3.7 limits, except for the clump-infall model where \Delta m can reach 5.4, although the derived numbers may be affected by a small sample and boundary conditions. Conclusions. Burst triggering mechanisms are associated with distinct kinematic features in the burst-hosting disks that may be used for their identification. Abridged., Comment: Accepted for publication by Astronomy & Astrophysics

We revealed a novel type of linear axisymmetric helical magnetorotational instability in viscous and resistive rotating flows with radially increasing angular velocity, or positive shear, exposed to a helical magnetic field. It operates for a broad range of positive shear, provided that magnetic Prandtl number is not unity. This instability can play an important role in the magnetic activity of the equatorial parts of the solar tachocline, where the shear of differential rotation is positive.

We study the convective and absolute forms of azimuthal magnetorotational instability (AMRI) in a Taylor-Couette (TC) flow with an imposed azimuthal magnetic field. We show that the domain of the convective AMRI is wider than that of the absolute AMRI. Actually, it is the absolute instability which is the most relevant and important for magnetic TC flow experiments. The absolute AMRI, unlike the convective one, stays in the device, displaying a sustained growth that can be experimentally detected. We also study the global AMRI in a TC flow of finite height using DNS and find that its emerging butterfly-type structure -- a spatio-temporal variation in the form of upward and downward traveling waves -- is in a very good agreement with the linear stability analysis, which indicates the presence of two dominant absolute AMRI modes in the flow giving rise to this global butterfly pattern., Comment: 11 pages, 6 figures, accepted for publication in J. Fluid Mech. Rapids

DW Cnc is an intermediate polar which has previously been observed in both high and low states. Observations of the high state of DW Cnc have previously revealed a spin period at ~ 38.6 min, however observations from the 2018/19 low state showed no evidence of the spin period. We present results from our analysis of 12 s cadence photometric data collected by NGTS of DW Cnc during the high state which began in 2019. Following the previously reported suppression of the spin period signal we identify the return of this signal during the high state, consistent with previous observations of it. We identify this as the restarting of accretion during the high state. We further identified three short outbursts lasting ~ 1 d in DW Cnc with a mean recurrence time of ~ 60 d and an amplitude of ~ 1 mag. These are the first outbursts identified in DW Cnc since 2008. Due to the short nature of these events we identify them not as a result of accretion instabilities but instead either from instabilities originating from the interaction of the magnetorotational instability in the accretion disc and the magnetic field generated by the white dwarf or the result of magnetic gating., Comment: Accepted to MNRAS; 8 pages, 4 figues

We investigate the possibility of the growth of magnetorotational instability (MRI) in disks around Class 0 protostars. We construct a disk model and calculate the chemical reactions of neutral and charged atoms, molecules and dust grains to derive the abundance of each species and the ionization degree of the disk. Then, we estimate the diffusion coefficients of non-ideal magnetohydrodynamics effects such as ohmic dissipation, ambipolar diffusion and the Hall effect. Finally, we evaluate the linear growth rate of MRI in each area of the disk. We investigate the effect of changes in the strength and direction of the magnetic field in our disk model and we adopt four different dust models to investigate the effect of dust size distribution on the diffusion coefficients. Our results indicate that an MRI active region possibly exists with a weak magnetic field in a region far from the protostar where the Hall effect plays a role in the growth of MRI. On the other hand, in all models the disk is stable against MRI in the region within $, Accepted for publication in MNRAS. 43 pages, 12 figures

In the early stages of a protoplanetary disk, when its mass is a significant fraction of its star's, turbulence generated by gravitational instability (GI) should feature significantly in the disk's evolution. At the same time, the disk may be sufficiently ionised for magnetic fields to play some role in the dynamics. Though usually neglected, the impact of magnetism on the GI may be critical, with consequences for several processes: the efficiency of accretion, spiral structure formation, fragmentation, and the dynamics of solids. In this paper, we report on global three-dimensional magnetohydrodynamical simulations of a self-gravitating protoplanetary disk using the meshless finite mass (MFM) Lagrangian technique. We confirm that GI spiral waves trigger a dynamo that amplifies an initial magnetic field to nearly thermal amplitudes (plasma beta < 10), an order of magnitude greater than that generated by the magneto-rotational instability alone. We also determine the dynamo's nonlinear back reaction on the gravitoturbulent flow: the saturated state is substantially hotter, with an associated larger Toomre parameter and weaker, more 'flocculent' spirals. But perhaps of greater import is the dynamo's boosting of accretion via a significant Maxwell stress; mass accretion is enhanced by factors of several relative to either pure GI or pure MRI. Our simulations use ideal MHD, an admittedly poor approximation in protoplanetary disks, and thus future studies should explore the full gamut of non-ideal MHD. In preparation for that, we exhibit a small number of Ohmic runs that reveal that the dynamo, if anything, is stronger in a non-ideal environment. This work confirms that magnetic fields are a potentially critical ingredient in gravitoturbulent young disks, possibly controlling their evolution, especially via their enhancement of (potentially episodic) accretion., Happy Chinese new year

Magnetars are highly magnetized neutron stars whose magnetic dipole ranges from $10^{14}$ to $10^{15}$ G. The MRI is considered to be a promising mechanism to amplify the magnetic field in fast-rotating protoneutron stars and form magnetars. This scenario is supported by many local studies showing that magnetic fields could be amplified by the MRI on small scales. However, the efficiency of the MRI at generating a dipole field is still unknown. To answer this question, we study the MRI dynamo in an idealized global model of a fast rotating protoneutron star with differential rotation. We perform 3D incompressible MHD simulations in spherical geometry with explicit diffusivities where the differential rotation is forced at the outer boundary. We vary the initial magnetic field and investigated different magnetic boundary conditions. These simulations were compared to local shearing box simulations. We obtain a self-sustained turbulent MRI-driven dynamo, whose saturated state is independent of the initial magnetic field. The MRI generates a strong turbulent magnetic field of $B \geq 2\times 10^{15}$ G and a non-dominant magnetic dipole, which represents systematically about $5\%$ of the averaged magnetic field strength. Interestingly, this dipole is tilted towards the equatorial plane. We find that local shearing box models can reproduce fairly well several characteristics of global MRI turbulence such as the kinetic and magnetic spectra. The turbulence is nonetheless more vigorous in the local models than in the global ones. Overall, our results support the ability of the MRI to form magnetar-like large-scale magnetic fields. They furthermore predict the presence of a stronger small-scale magnetic field. The resulting magnetic field could be important to power outstanding stellar explosions, such as superluminous supernovae and GRBs., Accepted for publication in A&A, 16 pages, 21 figures. Minor changes after referee report. Addition of a field line figure

Extensive simulations of the Princeton Magnetorotational Instability (MRI) Experiment with the Spectral/Finite Element code for Maxwell and Navier-Stokes Equations (SFEMaNS) have been performed to map the MRI-unstable region as a function of inner cylinder angular velocity and applied vertical magnetic field. The angular velocities of the outer cylinder and the end-cap rings follow the inner cylinder in fixed ratios optimized for MRI. We first confirm the exponential growth of the MRI linear phase using idealized conducting vertical boundaries (end caps) rotating differentially with a Taylor-Couette profile. Subsequently, we run a multitude of simulations to scan the experimental parameter space and find that the normalized volume-averaged mean-square radial magnetic field, our main instability indicator, rises significantly where MRI is expected. At various locations, the local radial components of fluid velocity and generated magnetic field are well correlated with the volume-averaged indicator. Based on this correlation, a diagnostic system that will measure the radial magnetic field at several locations on the inner cylinder is proposed as the main comparison between simulation and experiment. A detailed analysis of poloidal mode structures in the SFEMaNS code indicates that MRI, rather than Ekman circulation or Rayleigh instability, dominates the fluid behavior in the region where MRI is expected.