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In an earlier paper we showed that the combination of azimuthal magnetic fields and super-rotation in Taylor-Couette flows of conducting fluids can be unstable against non-axisymmetric perturbations if the magnetic Prandtl number of the fluid is $Pm\neq 1$. Here we demonstrate that the addition of a weak axial field component may allow axisymmetric perturbation patterns for $Pm$ of order unity depending on the boundary conditions. The axisymmetric modes only occur for magnetic Mach numbers (of the azimuthal field) of order unity, while higher values are necessary for non-axisymmetric modes. The typical growth time of the instability and the characteristic time scale of the axial migration of the axisymmetric mode are long compared with the rotation period, but short compared with the magnetic diffusion time. The modes travel in the positive or negative $z$-direction along the rotation axis depending on the sign of $B_\phi B_z$. We also demonstrate that the azimuthal components of flow and field perturbations travel in phase if $|B_\phi|\gg |B_z|$, independent of the form of the rotation law. Within a short-wave approximation for thin gaps it is also shown (in an Appendix) that for {\em ideal} fluids the considered helical magnetorotational instability (HMRI) only exists for rotation laws with negative shear., Comment: 18 pages, 10 Figures

High-frequency quasi-periodic oscillations (HFQPOs) observed in the emission of black-hole X-ray binary systems promise insight into strongly curved spacetime. `Discoseismic' oscillations with frequencies set by the intrinsic properties of the central black hole, in particular `trapped inertial waves' (r-modes), offer an attractive explanation for HFQPOs. To produce an observable signature, however, such oscillations must be excited to sufficiently large amplitudes. Turbulence driven by the magnetorotational instability (MRI) fails to provide the necessary amplification, but r-modes may still be excited via interaction with accretion disc warps or eccentricities. We present 3D global hydrodynamic simulations of relativistic accretion discs, which demonstrate for the first time the excitation of trapped inertial waves by an imposed eccentricity in the flow. While the r-modes' saturated state depends on the vertical boundary conditions used in our unstratified, cylindrical framework, their excitation is unambiguous in all runs with eccentricity >0.005 near the ISCO. These simulations provide a proof of concept, demonstrating the robustness of trapped inertial wave excitation in a non-magnetized context. In a companion paper, we explore the competition between this excitation, and damping by magnetohydrodynamic turbulence., 16 pages, 15 figures, accepted in MNRAS. Updated with grammatical and typographical corrections

Aims and Methods. Accretion bursts triggered by the magnetorotational instability (MRI) in the innermost disk regions were studied for protoplanetary gas-dust disks formed from prestellar cores of various mass $M_{\rm core}$ and mass-to-magnetic flux ratio $\lambda$. Numerical magnetohydrodynamics simulations in the thin-disk limit were employed to study the long-term ($\sim 1.0$~Myr) evolution of protoplanetary disks with an adaptive turbulent $\alpha$-parameter, which depends explicitly on the strength of the magnetic field and ionization fraction in the disk. The numerical models also feature the co-evolution of gas and dust, including the back-reaction of dust on gas and dust growth. Results. Dead zone with a low ionization fraction $x, Comment: Accepted for publication in Astronomy & Astrophysics

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., 26 pages, 16 figures, accepted for publication in the Astrophysical Journal

We consider a differentially rotating flow of an incompressible electrically conducting and viscous fluid subject to an external axial magnetic field and to an azimuthal magnetic field that is allowed to be generated by a combination of an axial electric current external to the fluid and electrical currents in the fluid itself. In this setting we derive an extended version of the celebrated Hain-Lüst differential equation for the radial Lagrangian displacement that incorporates the effects of the axial and azimuthal magnetic fields, differential rotation, viscosity, and electrical resistivity. We apply the Wentzel-Kramers-Brillouin method to the extended Hain-Lüst equation and derive a comprehensive dispersion relation for the local stability analysis of the flow to three-dimensional disturbances. We confirm that in the limit of low magnetic Prandtl numbers, in which the ratio of the viscosity to the magnetic diffusivity is vanishing, the rotating flows with radial distributions of the angular velocity beyond the Liu limit, become unstable subject to a wide variety of the azimuthal magnetic fields, and so is the Keplerian flow. In the analysis of the dispersion relation we find evidence of a new long-wavelength instability which is caught also by the numerical solution of the boundary value problem for a magnetized Taylor-Couette flow.

Previous axisymmetric investigations in two dimensions (2D) have shown that rings and gaps develop naturally in non-ideal magnetohydrodynamic (MHD) disk-wind systems, especially in the presence of ambipolar diffusion (AD). Here we extend these 2D simulations to three dimensions (3D) and find that rings and gaps are still formed in the presence of a moderately strong ambipolar diffusion. The rings and gaps form from the same basic mechanism that was identified in the 2D simulations, namely, the redistribution of the poloidal magnetic flux relative to the disk material as a result of the reconnection of a sharply pinched poloidal magnetic field lines. Thus, the less dense gaps are more strongly magnetized with a large poloidal magnetic field compared to the less magnetized (dense) rings. The rings and gaps start out rather smoothly in 3D simulations that have axisymmetric initial conditions. Non-axisymmetric variations arise spontaneously at later times, but they do not grow to such an extent as to disrupt the rings and gaps. These disk substructures persist to the end of the simulations, lasting up to 3000 orbital periods at the inner edge of the simulated disk. The longevity of the perturbed yet still coherent rings make them attractive sites for trapping large grains that would otherwise be lost to rapid radial migration due to gas drag. As the ambipolar diffusivity decreases, both the disk and the wind become increasingly turbulent, driven by the magnetorotational instability, with tightly-wound spiral arms becoming more prominent in the disk., Comment: 19 pages, 13 figures, accepted by MNRAS

Magnetic fields of planets, stars and galaxies are generated by self-excitation in moving electrically conducting fluids. Once produced, magnetic fields can play an active role in cosmic structure formation by destabilising rotational flows that would be otherwise hydro-dynamically stable. For a long time, both hydromagnetic dynamo action as well as magnetically triggered flow instabilities had been the subject of purely theoretical research. Meanwhile, however, the dynamo effect has been observed in large-scale liquid sodium experiments in Riga, Karlsruhe and Cadarache. In this paper, we summarise the results of liquid metal experiments devoted to the dynamo effect and various magnetic instabilities such as the helical and the azimuthal magnetorotational instability and the Tayler instability. We discuss in detail our plans for a precession-driven dynamo experiment and a large-scale Tayler–Couette experiment using liquid sodium, and on the prospects to observe magnetically triggered instabilities of flows with positive shear.

The nonaxisymmetric azimuthal magnetorotational instability is studied for hydromagnetic Taylor-Couette flows between cylinders of finite electrical conductivity. We find that the magnetic Prandtl number Pm determines whether perfectly conducting or insulating boundary conditions lead to lower Hartmann numbers for the onset of instability. Regardless of the imposed rotation profile, for small Pm the solutions for perfectly conducting cylinders become unstable for weaker magnetic fields than the solutions for insulating cylinders. The critical Hartmann and Reynolds numbers form monotonic functions of the ratio of the electrical conductivities of the cylinders and the fluid, such that a ratio of about 10 provides a very good approximation to perfectly conducting cylinders, and a ratio of about 0.1 a very good approximation to insulating cylinders. These results are of particular relevance for the super-rotating case where the outer cylinder rotates faster than the inner one; in this case the critical onset values are substantially different for perfectly conducting versus insulating boundary conditions. An experimental realization of the super-rotating instability, with liquid sodium as the fluid and cylinders made of copper, would require an electric current of at least 33.5 kAmp running along the central axis., Comment: 18 pages with 15 figures

Background: The velocity fluctuations grow dominantly by convective instability form 32 spiral vortices which are stationary with respect to the disk. However, recent researches suggest that the global instability plays a role in the boundary layer transition. Objective: The study looks into the relation between convective instability and global instability. Method: A finite difference method is used to carry out numerical simulation. The full Navier-Stokes perturbation equations and the continuity equation solved by simulation code. Results: A disturbance is continuatively introduced to excite the convectively unstable mode, which successfully generates a flow field with 32 spiral and stationary vortices. Next, a short-duration artificial disturbance with an azimuthal wavenumber of 64 is introduced at Reynolds number of 530 in order to introduce a velocity fluctuation of the traveling mode, which is globally unstable. It is shown that the source of vibration for the globally unstable mode exists between Reynolds number of 560 and 670. Finally, the global and traveling wavenumber 64 component is excited in a flow field which is dominated by the convective and stationary wavenumber 32 component. It is shown that the wavenumber 64 component grows by the global instability even when the excitation is very weak. Conclusion: The results suggest that the reason why the globally unstable mode has not been observed in experiments is because the boundary layer transition caused by the convective instability takes place before the globally unstable mode can start to grow by itself.

We show that on-off intermittency in solar and stellar cycles is a result of amplitude-phase synchronization in multiscale interactions in solar/stellar dynamos or magnetorotational instability which leads to the formation of kinematic and magnetic coherent structures, and the novel techniques of Lagrangian coherent structures can detect transport barriers and vortices such as magnetic flux tubes/ropes in solar and stellar turbulence with high accuracy.

Geometrically thick tori with constant specific angular momentum have been widely used in the last decades to construct numerical models of accretion flows onto black holes. Such discs are prone to a global non-axisymmetric hydrodynamic instability, known as Papaloizou-Pringle instability (PPI), which can redistribute angular momentum and also lead to an emission of gravitational waves. It is, however, not clear yet how the development of the PPI is affected by the presence of a magnetic field and by the concurrent development of the magnetorotational instability (MRI). We present a numerical analysis using three-dimensional GRMHD simulations of the interplay between the PPI and the MRI considering, for the first time, an analytical magnetized equilibrium solution as initial condition. In the purely hydrodynamic case, the PPI selects as expected the large-scale $m=1$ azimuthal mode as the fastest growing and non-linearly dominant mode. However, when the torus is threaded by a weak toroidal magnetic field, the development of the MRI leads to the suppression of large-scale modes and redistributes power across smaller scales. If the system starts with a significantly excited $m=1$ mode, the PPI can be dominant in a transient phase, before being ultimately quenched by the MRI. Such dynamics may well be important in compact star mergers and tidal disruption events., Comment: 15 pages, 13 figures, submitted to MNRAS

In the tandem planet formation regime, planets form at two distinct sites where solid particles are densely accumulated due to the on/off state of the magnetorotational instability (MRI). We found that tandem planet formation can reproduce the solid component distribution of the Solar System and tends to produce a smaller number of large planets through continuous pebble flow into the planet formation sites. In the present paper, we investigate the dependence of tandem planet formation on the vertical magnetic field of the protoplanetary disk. We calculated two cases of B z = 3.4 × 10 −3 G and B z = 3.4 × 10 −5 G at 100 AU as well as the canonical case of B z = 3.4 × 10 −4 G. We found that tandem planet formation holds up well in the case of the strong magnetic field ( B z = 3.4 × 10 −3 G). On the other hand, in the case of a weak magnetic field ( B z = 3.4 × 10 −5 G) at 100 AU, a new regime of planetary growth is realized: the planets grow independently at different places in the dispersed area of the MRI-suppressed region of r = 8−30 AU at a lower accretion rate of M ˙ 10 − 7.4 M ⊙ yr − 1 . We call this the “dispersed planet formation” regime. This may lead to a system with a larger number of smaller planets that gain high eccentricity through mutual collisions.

We present a brief survey of recent mathematical results on the stability and instability of magnetohydrodynamic flows in the presence of a gravitational field, which include the incompressible magnetic Rayleigh-Taylor instability, and the Parker instability (i.e., the magnetic buoyancy instability) in compressible magnetohydrodynamics. In particular, the stabilizing effect of some factors (e.g., steady magnetic fields, boundary conditions, domains) are analyzed. In addition, the mathematical results on the Rayleigh-Taylor instability problem in viscoelastic flows are discussed.

Helical and azimuthal magnetorotational instabilities operate in rotating magnetized flows with relatively steep negative or extremely steep positive shear. The corresponding lower and upper Liu limits of the shear, which determine the threshold of modal growth of these instabilities, are continuously connected when some axial electrical current is allowed to pass through the rotating fluid. We investigate the nonmodal dynamics of these instabilities arising from the non-normality of shear flow in the local approximation, generalizing the results of the modal approach. It is demonstrated that moderate transient/nonmodal amplification of both types of magnetorotational instability occurs within the Liu limits, where the system is stable according to modal analysis. We show that for the helical magnetorotational instability this magnetohydrodynamic behavior is closely connected with the nonmodal growth of the underlying purely hydrodynamic problem.

Context. Disks around pre-main-sequence stars evolve over time by turbulent viscous spreading. The main contender to explain the strength of the turbulence is the Magneto-Rotational-Instability (MRI) model, whose efficiency depends on the disk ionization fraction. Aims. We aim at computing self-consistently the chemistry including PAH charge chemistry, the grain charging and an estimate of an effective value of the turbulence alpha parameter in order to find observational signatures of disk turbulence. Methods. We introduced PAH and grain charging physics and their interplay with other gas-phase reactions in the physico-chemical code ProDiMo. Non-ideal magnetohydrodynamics effects such as Ohmic and ambipolar diffusion are parametrized to derive an effective value for the turbulent parameter alpha_eff . We explored the effects of turbulence heating and line broadening on CO isotopologue sub-millimeter lines. Results. The spatial distribution of alpha_eff depends on various unconstrained disk parameters such as the magnetic parameter beta_mag or the cosmic ray density distribution inside the protoplanetary disks. The inner disk midplane shows the presence of the so-called dead-zone where the turbulence is quasi-inexistent. The disk is heated mostly by thermal accommodation on dust grains in the dead-zone, by viscous heating outside the dead-zone up to a few hundred astronomical units, and by chemical heating in the outer disk. The CO rotational lines probe the warm molecular disk layers where the turbulence is at its maximum. However, the effect of turbulence on the CO line profiles is minimal and difficult to distinguish from the thermal broadening. Conclusions. Viscous heating of the gas in the disk midplane outside the dead-zone is efficient. The determination of alpha from CO rotational line observations alone is challenging., accepted to A&A. 29 pages

The Event Horizon Telescope Collaboration, Recent developments in compact object astrophysics, especially the discovery of merging neutron stars by LIGO, the imaging of the black hole in M87 by the Event Horizon Telescope, and high- precision astrometry of the Galactic Center at close to the event horizon scale by the GRAVITY experiment motivate the development of numerical source models that solve the equations of general relativistic magnetohydrodynamics (GRMHD). Here we compare GRMHD solutions for the evolution of a magnetized accretion flow where turbulence is promoted by the magnetorotational instability from a set of nine GRMHD codes: Athena++, BHAC, Cosmos++, ECHO, H-AMR, iharm3D, HARM-Noble, IllinoisGRMHD, and KORAL. Agreement among the codes improves as resolution increases, as measured by a consistently applied, specially developed set of code performance metrics. We conclude that the community of GRMHD codes is mature, capable, and consistent on these test problems. © 2019. The American Astronomical Society. All rights reserved., R.N. thanks the National Science Foundation (NSF; grants OISE-1743747, AST-1816420) and acknowledges computational support from the NSF via XSEDE resources (grant TG-AST080026N). L.D.Z. acknowledges support from the PRIN-MIUR project Multi-scale Simulations of High-Energy Astrophysical Plasmas (Prot. 2015L5EE2Y) and from the INFN-TEONGRAV initiative. C.J.W. made use of thComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, ChileComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, Chilee Extreme Science and Engineering Discovery Environment (XSEDE) Comet at the San Diego Supercomputer Center through allocation AST170012. The H-AMR high-resolution simulation was made possible by NSF PRAC award Nos. 1615281 and OAC-1811605 at the Blue Waters sustained-petascale computing project and supported in part under grant No. NSF PHY-1125915 (PI A. Tchekhovskoy). K.C. and S.M. are supported by the Netherlands Organization for Scientific Research (NWO) VICI grant (No. 639.043.513); M.L. is supported by the NWO Spinoza Prize (PI M.B.M. van der Klis). The HARM-Noble simulations were made possible by NSF PRAC award No. NSF OAC-1515969, OAC-1811228 at the Blue Waters sustained-petascale computing project, and supported in part under grant No. NSF PHY-1125915. The BHAC CKS-GRMHD simulations were performed on the Dutch National Supercomputing cluster Cartesius and are funded by the NWO computing grant 16431. S.C.N. was supported by an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center administered by USRA through a contract with NASA. Y.M., H.O., O.P., and L.R. acknowledge support from the ERC synergy grant >BlackHoleCam: Imaging the Event Horizon of Black Holes> (grant No. 610058). M.B. acknowledges support from the European Research Council (grant No. 715368-MagBURST) and from the Gauss Centre for Supercomputing e.V. (www.Gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (www.lrz.de).P.C.F.was supported by NSF grant AST-1616185 and used resources from the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by NSF grant No. ACI-1548562. Work by P.A. was performed in part under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. The authors of the present paper further thank the following organizations and programs: the Academy of Finland (projects 274477, 284495, 312496); the Advanced European Network of E-infrastructures for Astronomy with the SKA (AENEAS) project, supported by the European Commission Framework Programme Horizon 2020 Research and Innovation action under grant agreement 731016; the Alexander von Humboldt Stiftung; the Black Hole Initiative at Harvard University, through a grant (60477) from the John Templeton Foundation; the China Scholarship Council; Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT, Chile, via PIA ACT172033, Fondecyt 1171506, BASAL AFB-170002, ALMA-conicyt 31140007); Consejo Nacional de Ciencia y Tecnologia (CONACYT, Mexico, projects 104497, 275201, 279006, 281692); the Delaney Family via the Delaney Family John A. Wheeler Chair at Perimeter Institute; Direccion General de Asuntos del Personal Academico-Universidad Nacional Autonoma de Mexico (DGAPA-UNAM, project IN112417); the European Research Council Synergy Grant >BlackHoleCam: Imaging the Event Horizon of Black Holes> (grant 610058); the Generalitat Valenciana postdoctoral grant APOSTD/2018/177; the Gordon and Betty Moore Foundation (grants GBMF-3561, GBMF-5278); the Istituto Nazionale di Fisica Nucleare (INFN) sezione di Napoli, iniziative specifiche TEONGRAV; the International Max Planck Research School for Astronomy and Astrophysics at the Universities of Bonn and Cologne; the Jansky Fellowship program of the National Radio Astronomy Observatory (NRAO); the Japanese Government (Monbukagakusho: MEXT) Scholarship; the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for JSPS Research Fellowship (JP17J08829); the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS, grants QYZDJ-SSW-SLH057, QYZDJ-SSW-SYS008); the Leverhulme Trust Early Career Research Fellowship; the Max-Planck-Gesellschaft (MPG); the Max Planck Partner Group of the MPG and the CAS; the MEXT/JSPS KAKENHI (grants 18KK0090, JP18K13594, JP18K03656, JP18H03721, 18K03709, 18H01245, 25120007); the MIT International Science and Technology Initiatives (MISTI) Funds; the Ministry of Science and Technology (MOST) of Taiwan (105-2112-M-001-025-MY3, 106-2112-M-001-011, 106-2119-M-001-027, 107-2119-M-001-017, 107-2119-M-001-020, and 107-2119-M-110-005); the National Aeronautics and Space Administration (NASA, Fermi Guest Investigator grant 80NSSC17K0649); the National Institute of Natural Sciences (NINS) of Japan; the National Key Research and Development Program of China (grant 2016YFA0400704, 2016YFA0400702); the National Science Foundation (NSF, grants AST-0096454, AST-0352953, AST-0521233, AST-0705062, AST-0905844, AST-0922984, AST-1126433, AST-1140030, DGE-1144085, AST-1207704, AST-1207730, AST-1207752, MRI-1228509, OPP-1248097, AST-1310896, AST-1312651, AST-1337663, AST-1440254, AST-1555365, AST-1715061, AST-1615796, AST-1716327, OISE-1743747, AST-1816420); the Natural Science Foundation of China (grants 11573051, 11633006, 11650110427, 10625314, 11721303, 11725312); the Natural Sciences and Engineering Research Council of Canada (NSERC, including a Discovery Grant and the NSERC Alexander Graham Bell Canada Graduate Scholarships Doctoral Program); the National Youth Thousand Talents Program of China; the National Research Foundation of Korea (the Global PhD Fellowship Grant: grants NRF-2015H1A2A1033752, 2015-R1D1A1A01056807, the Korea Research Fellowship Program: NRF-2015H1D3A1066561); the Netherlands Organization for Scientific Research (NWO) VICI award (grant 639.043. 513) and Spinoza Prize SPI 78-409; the New Scientific Frontiers with Precision Radio Interferometry Fellowship awarded by the South African Radio Astronomy Observatory (SARAO), which is a facility of the National Research Foundation (NRF), an agency of the Department of Science and Technology (DST) of South Africa; the Onsala Space Observatory (OSO) national infrastructure, for the provisioning of its facilities/observational support (OSO receives funding through the Swedish Research Council under grant 2017-00648); the Perimeter Institute for Theoretical Physics (research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development, and by the Province of Ontario through the Ministry of Research, Innovation and Science); the Russian Science Foundation (grant 17-12-01029); the Spanish Ministerio de Economia y Competitividad (grants AYA2015-63939-C2-1-P, AYA2016-80889-P); the State Agency for Research of the Spanish MCIU through the >Center of Excellence Severo Ochoa> award for the Instituto de Astrofisica de Andalucia (SEV-2017-0709); the Toray Science Foundation; the US Department of Energy (USDOE) through the Los Alamos National Laboratory (operated by Triad National Security, LLC, for the National Nuclear Security Administration of the USDOE (Contract 89233218CNA000001)); the Italian Ministero dell'Istruzione Universita e Ricerca through the grant Progetti Premiali 2012-iALMA (CUP C52I13000140001); the European Union's Horizon 2020 research and innovation programme under grant agreement No. 730562 RadioNet; ALMA North America Development Fund; the Academia Sinica; and Chandra TM6-17006X. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), supported by NSF grant ACI-1548562, and CyVerse, supported by NSF grants DBI-0735191, DBI-1265383, and DBI-1743442. XSEDE Stampede2 resource at TACC was allocated through TG-AST170024 and TG-AST080026N. XSEDE JetStream resource at PTI and TACC was allocated through AST170028. The simulations were performed in part on the SuperMUC cluster at the LRZ in Garching, on the LOEWE cluster in CSC in Frankfurt, and on the HazelHen cluster at the HLRS in Stuttgart. This research was enabled in part by support provided by Compute Ontario (http://computeontario.ca), Calcul Quebec (http://www.calculquebec.ca), and Compute Canada (http://www.computecanada.ca).

The evolution of a large-scale poloidal magnetic field in an accretion disc is an important problem because it determines the launching of winds and the feasibility of the magnetorotational instability to generate turbulence or channel flows. Recent studies, both semi-analytical calculations and numerical simulations, have highlighted the crucial role non-ideal MHD effects (Ohmic resistivity, Hall drift and ambipolar diffusion), relevant in the protoplanetary disc context, might play in magnetic flux evolution in the disc. We investigate the flux transport in discs through the use of two one-dimensional semi-analytic models in the vertical direction, exploring regimes where different physical source terms and effects dominate. The governing equations for both models are derived by performing an asymptotic expansion in the limit of a thin disc, with the different regimes isolated through setting the relative order of the leading terms between variables. Flux transport rates and vertical structure profiles are calculated for a range of diffusivities and disc magnetisations. We found that Ohmic and ambipolar diffusivities drive radially outward flux transport with an outwardly inclined field. A wind outflow drives inward flux transport, which is significantly enhanced in the presence of Hall drift in the positive polarity case, $\eta_H (\boldsymbol{B}_z \cdot \boldsymbol{\Omega}) > 0$, an effect which has only been briefly noted before. Coupled only with outward inclination, the Hall effect reduces the flux transport given by a background Ohmic and/or ambipolar diffusivity, but drives no flux transport when it is the only non-ideal effect present., Comment: In press. Accepted by MNRAS

We develop a framework for magnetohydrodynamical (MHD) simulations in a local cylindrical shearing box by extending the formulation of the Cartesian shearing box. We construct shearing-periodic conditions at the radial boundaries of a simulation box from the conservation relations of the basic MHD equations, taking into account the explicit radial dependence of physical quantities. We demonstrate quasi-steady mass accretion, which cannot be handled by the standard Cartesian shearing box model, with an ideal MHD simulation in a vertically unstratified cylindrical shearing box up to 200 rotations. In this demonstrative run we set up (i) net vertical magnetic flux, (ii) a locally isothermal equation of state, and (iii) a sub-Keplerian equilibrium rotation, whereas the sound velocity and the initial Alfven velocity have the same radial dependence as that of the Keplerian velocity. Inward mass accretion is induced to balance with the outward angular momentum flux of the MHD turbulence triggered by the magnetorotational instability in a self-consistent manner. We discuss detailed physical properties of the saturated magnetic field, in comparison to the results of a Cartesian shearing box simulation., 27 pages, 10 figures, accepted by PASJ, movie is available at http://ea.c.u-tokyo.ac.jp/astro/Members/stakeru/research/cylshbx/

Fragmentation of highly differentially rotating massive stars that undergo collapse has been suggested as a possible channel for binary black hole formation. Such a scenario could explain the formation of the new population of massive black holes detected by the LIGO/VIRGO gravitational wave laser interferometers. We probe that scenario by performing general relativistic magnetohydrodynamic simulations of differentially rotating massive stars supported by thermal radiation pressure plus a gas pressure perturbation. The stars are initially threaded by a dynamically weak, poloidal magnetic field confined to the stellar interior. We find that magnetic braking and turbulent viscous damping via magnetic winding and the magnetorotational instability in the bulk of the star redistribute angular momentum, damp differential rotation and induce the formation of a massive and nearly uniformly rotating inner core surrounded by a Keplerian envelope. The core + disk configuration evolves on a secular timescale and remains in quasi-stationary equilibrium until the termination of our simulations. Our results suggest that the high degree of differential rotation required for $m=2$ seed density perturbations to trigger gas fragmentation and binary black hole formation is likely to be suppressed during the normal lifetime of the star prior to evolving to the point of dynamical instability to collapse. Other cataclysmic events, such as stellar mergers leading to collapse, may therefore be necessary to reestablish sufficient differential rotation and density perturbations to drive nonaxisymmetric modes leading to binary black hole formation., Comment: 11 pages, 5 figures. Minor changes, matches published version

The gas temperature in protoplanetary disks (PPDs) is determined by a combination of irradiation heating and accretion heating, with the latter conventionally attributed to turbulent dissipation. However, recent studies have suggested that the inner disk (a few AU) is largely laminar, with accretion primarily driven by magnetized disk winds, as a result of nonideal magnetohydrodynamic (MHD) effects from weakly ionized gas, suggesting an alternative heating mechanism by Joule dissipation. We perform local stratified MHD simulations including all three nonideal MHD effects (ohmic, Hall, and ambipolar diffusion) and investigate the role of Joule heating and the resulting disk vertical temperature profiles. We find that in the inner disk, as ohmic and ambipolar diffusion strongly suppress electrical current around the midplane, Joule heating primarily occurs at several scale heights above the midplane, making the midplane temperature much lower than that with the conventional viscous heating model. Including the Hall effect, Joule heating is enhanced/reduced when the magnetic fields threading the disks are aligned/anti-aligned with the disk rotation, but it is overall ineffective. Our results further suggest that the midplane temperature in the inner PPDs is almost entirely determined by irradiation heating, unless viscous heating can trigger thermal ionization in the disk innermost region to self-sustain magnetorotational instability turbulence., Comment: 23 pages, 11 figures; matches the published version

The magnetorotational instability (MRI) occurs when a weak magnetic field destabilises a rotating, electrically conducting fluid with inwardly increasing angular velocity. The MRI is essential to astrophysical disk theory where the shear is typically Keplerian. Internal shear layers in stars may also be MRI unstable, and they take a wide range of profiles, including near-critical. We show that the fastest growing modes of an ideal magnetofluid are three-dimensional provided the shear rate, $S$, is near the two-dimensional onset value, $S_c$. For a Keplerian shear, three-dimensional modes are unstable above $S\approx0.10S_c$, and dominate the two-dimensional modes until $S\approx2.05S_{c}$. These three-dimensional modes dominate for shear profiles relevant to stars and at magnetic Prandtl numbers relevant to liquid-metal laboratory experiments. Significant numbers of rapidly growing three-dimensional modes remain well past $2.05S_{c}$. These finding are significant in three ways. First, weakly nonlinear theory suggests that the MRI saturates by pushing the shear rate to its critical value. This can happen for systems, like stars and laboratory experiments, that can rearrange their angular velocity profiles. Second, the non-normal character and large transient growth of MRI modes should be important whenever three-dimensionality exists. Finally, three-dimensional growth suggests direct dynamo action driven from the linear instability., Comment: 15 pages, 5 figures. Proceedings of the Royal Society A, accepted

We investigate numerical convergence in simulations of magnetically arrested disks around spinning black holes. Using the general-relativistic magnetohydrodynamics code Athena++, we study the same system at four resolutions (up to an effective 512 by 256 by 512 cells) and with two different spatial reconstruction algorithms. The accretion rate and general large-scale structure of the flow agree across the simulations. This includes the amount of magnetic flux accumulated in the saturated state and the ensuing suppression of the magnetorotational instability from the strong field. The energy of the jet and the efficiency with which spin energy is extracted via the Blandford-Znajek process also show convergence. However the spatial structure of the jet shows variation across the set of grids employed, as do the Lorentz factors. Small-scale features of the turbulence, as measured by correlation lengths, are not fully converged. Despite convergence of a number of aspects of the flow, modeling of synchrotron emission shows that variability is not converged and decreases with increasing resolution even at our highest resolutions., Comment: 19 pages, 18 figures, to be published in ApJ

In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid., Comment: 44 pages, 28 figures

We analyze the sustaining mechanism of nonlinear perturbations/turbulence in spectrally stable smooth shear flows. The essence of the sustenance is a subtle interplay of linear transient growth of Fourier harmonics and nonlinear processes. In spectrally stable shear flows, the transient growth of perturbations is strongly anisotropic in spectral (k-)space. This, in turn, leads to anisotropy of nonlinear processes ink-space and, as a result, the main (new) nonlinear process appears to be not a direct/inverse, but rather a transverse/angular redistribution of harmonics in Fourier space referred to as the nonlinear transverse cascade. It is demonstrated that nonlinear state is sustained owing to the interplay of the linear nonmodal growth and the transverse cascade. The possibility of such course of events has been described ink-space byG. Chagelishvili, J.-P. Zahn, A. Tevzadze and J. Lominadze, A&A, 402, 401 (2003)that reliably exemplifies the well-known bypass scenario of subcritical turbulence in spectrally stable shear flows. We present selected results of the simulations performed in different (HD and MHD; 2D and 3D; plane and Keplerian) shear flows to demonstrate the transverse cascade in action.

Fast magnetic reconnection events can play an important role in accretion disk systems. A potential model to explain the non-thermal very-high-energy (VHE) emission (from GeV to TeV) observed in black-hole binaries (BHBs) and Active Galatic Nuclei (AGNs) can be attributed to fast magnetic reconnection induced in the turbulent corona of accretion disks and/or jets. In this work, we will discuss the results of global general relativistic MHD (GRMHD) simulations of accretion disks around black holes, whose turbulence is naturally driven by MHD instabilities, such as the magnetorotational instability (MRI). We will also present studies of magnetic reconnection driven by kink instabilities inside jets employing special relativistic MHD (SRMHD) simulations. As we expect, our simulations reveal the development of a nearly steady-state turbulence driven by these instabilities. We have performed a detailed statistical analysis to identify the presence of current sheets in the turbulent regions of both the accretion flow and jet. We then determined the magnetic reconnection rates in these locations obtaining average reconnection velocities in Alfv\'{e}n speed units of the order of $0.01-0.7$, which are consistent with the predictions of the theory of turbulence-induced fast reconnection., Comment: Proceeding at the International Conference on Black Holes as Cosmic Batteries: UHECRs and Multimessenger Astronomy - BHCB2018, 12-15 September 2018, Foz du Iguazu, Brasil, in press in Procs. of Science

In the laboratory, the magnetorotational instability (MRI) can be observed in azimuthal (AMRI) or helical (HMRI) magnetic field configurations. In both variants, the shear flow between the two cylinders is operating in the hydrodynamically stable regime (Ωo∕Ωi >0.25). AMRI occurs then as an m=1 -symmetric wave with a characteristic drift and spatial frequency. First evidence of AMRI was obtained some years ago by Seilmayer et al. [1]. A Taylor Couette (TC) setup, filled with liquid metal (GaInSn), was exposed to a magnetic field Bφ∝r^(-1), which lead to instability of the flow. In that previous setup, the necessary current was supplied by a large frame of copper rods which also caused a residual m=1 magnetic field disturbance producing a stationary dominant background flow. Since then, several changes took place to circumvent external asymmetries and influences. The main improvement was the symmetric current return path which eliminates the m=1 background flow and reduces stray fields. This optimized magnetic field system leads to a symmetric B_φ distribution. However, remaining mechanical misalignments of each axis (two cylinder axes, central rod axis) still impose a weak residual m=1 modulation of magnetic field with respect to the liquid metal flow. Nevertheless, the field displacement could be minimized to a value in the order of 1 mm by the present installation. We observe a reasonable energy dependence of the dominant m=1 mode on the Hartmann number. But drift and spatial distribution differ from theory [2] and may depend on current and/or B_φ. The main feature is a symmetry breaking, which leads to an AMRI wave which is mainly located at the top of the cylinder. This is surprising since the theoretical prediction point to a symmetric wave with m=± 1 configuration. However, the wave component in the lower half of the cylindrical volume remained missing until now. The measured velocity in the range of v=O(1 mm/s) is inferred from an Ultrasound Doppler Velocimetry (UDV) system. Recent observations indicate that thermal convection could be a possible source of symmetry breaking. It turns out that a minimal radial heat flux q ̇≈0.1 W⋅m^(-2) or a temperature difference of about Δϑ≈10^(-2) K across the cylindrical gap can cause a significant convection flow in the present TC-setup. Here, significant Rayleigh numbers Ra≈10^(4…5) can be achieved right from the beginning because of the liquid metal properties with a typically low Prandtl number of Pr=0.033 in conjunction with the low viscosity ν=3.4⋅10^(-7) m^2⋅s^(-1). As the driving heat source the radiation of the inner current carrying rod could be identified. Figure 2 (left) summarizes different convective flow regimes, which occur for a hydrodynamic stable TC configuration with Ωi=0, Ωo≈0 and Irod=20 kA driving the convection due to radiation from the central rod. The thermal boundary condition is then defined by the vacuum insulation (Fig. 1 (1)) and the inner boundary of the vessel (Fig. 1 (8)) forming a small cylindrical gap with 3 mm in width and 0.4 m in height. The combinations of different insulation schemes (top/bottom/open chimney) indicate a connection between heat transport features and thermal convection. The solid line in Figure 2 (left) is the result of an axisymmetric MHD-simulation to verify the “convective” flow pattern, which was gained experimentally by UDV. Figure 2 (right) illustrates an ARMI run with Ω_o⁄Ω_i =0.26 and I=12.87 kA (Ha=100) when the yellow coil (see Fig. 1) heated the fluid to ϑ_Fluid≈30°C prior which also corresponds to a heat flux pointing radially inward. The AMRI wave then travels upwards as seen in the left part. Right after the switch off event at t=0 the hot copper coil starts to cool down. In the moment the heat flux points radially outwards again at t≈3000 s, the wave at the bottom is suppressed and the wave in the upper half starts to evolve as usual. Here convection reverses to normal operation which corresponds to a heated-from-inside regime. We like to present experimental results giving evidence of the dependence of AMRI mode on thermal boundary conditions which affect the symmetry breaking of AMRI in a TC-setup. [1] M. Seilmayer, V. Galindo, G. Gerbeth, T. Gundrum, F. Stefani, M. Gellert, G. Rüdiger, M. Schultz, and R. Hollerbach, Phys. Rev. Lett. 113, 024505 (2014). [2] G. Rüdiger, R. Hollerbach, M. Gellert, and M. Schultz, Astron. Nachrichten 328, 1158 (2007).

In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform magnetic field with the vertical temperature gradient is investigated. In the approximation of geometrical optics a dispersion equation for small axisymmetric perturbations is obtained with the effects of viscosity, ohmic and heat conductive dissipation taken into account. The stability criteria for azimuthal plasma flows are obtained in the presence of the vertical temperature gradient and the constant magnetic field. The Rayleigh-Benard problem for stationary convection in the non-uniformly rotating layer of the electrically conducting fluid in the axial uniform magnetic field is considered. In the linear theory of stationary convection the critical value of the Rayleigh number subject to the profile of the inhomogeneous rotation (Rossby number) is obtained. It is shown that the negative values of the Rossby number have a destabilizing effect, since the critical Rayleigh number becomes smaller, than in the case of the uniform rotation , or of the rotation with positive Rossby numbers . To describe the nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer was represented as the rotation with a constant angular velocity and azimuthal shear with linear dependence on the coordinate. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of the finite amplitude of perturbations by utilizing the solution of the Ginzburg-Landau equation. It is shown that the weakly nonlinear convection based on the equations of the six-mode Lorentz model transforms into the identical Ginzburg-Landau equation. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various profiles of the angular velocity of the rotation of electrically conductive fluid.

Lunar rocks are severely depleted in moderately volatile elements such as Rb, K, and Zn relative to Earth. Identifying the cause of this depletion is important for understanding how the Earth-Moon system evolved in the aftermath of the Moon-forming giant impact. We measured the Rb isotopic compositions of lunar and terrestrial rocks to understand why moderately volatile elements are depleted in the Moon. Combining our new measurements with previous data reveals that the Moon has an 87Rb/85Rb ratio higher than Earth by +0.16 permil. This isotopic composition is consistent with evaporation of Rb into a vapor medium that was ~99 percent saturated. Evaporation under this saturation can also explain the previously documented isotopic fractionations of K, Ga, Cu and Zn of lunar rocks relative to Earth. We show that a possible setting for achieving the same saturation upon evaporation of elements with such diverse volatilities is through viscous drainage of a partially vaporized protolunar disk onto Earth. In the framework of an alpha-disk model, the alpha-viscosity needed to explain the ~99% saturation calculated here is 0.001 to 0.01, which is consistent with a vapor disk where viscosity is controlled by magnetorotational instability., Comment: 28 pages, 8 figures, 2 tables

Magnetorotational instability (MRI) in complex quantum plasma, which comprises electron, ion, and dust grains, is investigated. Electrons are considered to be degenerate while ions and dust grains are taken as nondegenerate. The general dispersion relation for MRI with the effect of spin magnetization is derived using local approximations. The instability criteria for spin quantum plasma are derived using low-frequency approximations. Due to the complex nature of the dispersion relation, MHD assumptions are used to define the instability criteria. The dust mass plays a significant role in both the dispersion and growth rate of the magnetorotational mode. The complex mass of dust modifies the instability criteria. Spin magnetization force arises due to electron Pauli spin matrices and has an important role in low-temperature and highly dense plasmas that are found mainly in white dwarfs, neutron stars, and in core-collapse supernovae. It is found that spin magnetization influences the criteria for instability and hence the properties of MHD waves in the degenerate plasma.

We solve the two-dimensional hydrodynamic equations of hot accretion flow in the presence of the thermal conduction. The flow is assumed to be in steady-state and axisymmetric, and self-similar approximation is adopted in the radial direction. In this hydrodynamic study, we consider the viscous stress tensor to mimic the effects of the magnetorotational instability for driving angular momentum. We impose the physical boundary conditions at both the rotation axis and the equatorial plane and obtain the solutions in the full $ r-\theta $ space. We have found that thermal conduction is indispensable term for investigating the inflow-wind structure of the hot accretion flows with very low mass accretion rates. One of the most interesting results here is that the disc is convectively stable in hot accretion mode and in the presence of the thermal conduction. Furthermore, the properties of wind and also its driving mechanisms are studied. Our analytical results are consistent with previous numerical simulations of hot accretion flow., Comment: 20 pages, 10 figures, accepted for publication in ApJ

We investigate evolution of an accretion disc in binary black hole (BBH) systems and possible electromagnetic counterparts of the gravitational waves from mergers of BBHs. Perna et al. (2016) proposed a novel evolutionary scenario of an accretion disc in BBHs in which a disc eventually becomes "dead", i.e., the magnetorotational instability (MRI) becomes inactive. In their scenario, the dead disc survives until {\it a few seconds before} the merger event. We improve the dead disc model and propose another scenario, taking account of effects of the tidal torque from the companion and the critical ionization degree for MRI activation more carefully. We find that the mass of the dead disc is much lower than that in the Perna's scenario. When the binary separation sufficiently becomes small, the mass inflow induced by the tidal torque reactivates MRI, restarting mass accretion onto the black hole. We also find that this disc "revival" happens {\it more than thousands of years before} the merger. The mass accretion induced by the tidal torque increases as the separation decreases, and a relativistic jet could be launched before the merger. The emissions from these jets are too faint compared to GRBs, but detectable if the merger events happen within $\lesssim 10$ Mpc or if the masses of the black holes are as massive as $\sim 10^5 M_{\odot}$., Comment: 8 pages, 3 figures, accepted for publication in MNRAS

The correlation between frequency variations in the Earth’s rotation and geomagnetic jerks is analyzed on the interval from 1900 to 2008. It is found that jerks precede changes in the rate of the Earth’s rotation frequency in the interval of periods ranging from 5 to 8 years. A mechanism of jerks generation is suggested in which the jerks are considered as the result of the excitation of magnetorotational instability in the Earth’s core with the subsequent generation of torsional oscillations causing a change in the Earth’s rotation frequency.

We study the dynamo generation (exponential growth) of large scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal ($x$-$y$) averaging, we demonstrate the presence of large scale fields when either horizontal or vertical ($y$-$z$) averaging is employed. By computing planar averaged fields and power spectra, we find large scale dynamo action in the early MRI growth phase---a previously unidentified feature. Fast growing horizontal low modes and fiducial vertical modes over a narrow range of wave numbers amplify these planar averaged fields in the MRI growth phase, before turbulence sets in. The large scale field growth requires linear fluctuations but not nonlinear turbulence (as defined by mode-mode coupling) and grows as a direct global mode of the MRI. Only by vertical averaging, can it be shown that the growth of horizontal low wavenumber MRI modes directly feed-back to the initial vertical field providing a clue as to why the large scale vertical field sustains against turbulent diffusion in the saturation regime. We compute the terms in the planar averaged mean field equations to identify the individual contributions to large scale field growth for both vertical and horizontal averaging. The large scale fields obtained from such vertical averaging are found to compare well with global cylindrical simulations and quasilinear analytical analysis from a previous study by Ebrahimi \& Blackman. We discuss the potential implications of these new results for understanding large scale MRI dynamo saturation and turbulence., 12 pages, 9 figues, submitted to MNRAS, comments are welcome

The circumnuclear disc (CND) orbiting the Galaxy's central black hole is a reservoir of material that can ultimately provide energy through accretion, or form stars in the presence of the black hole, as evidenced by the stellar cluster that is presently located at the CND's centre. In this paper, we report the results of a computational study of the dynamics of the CND. The results lead us to question two paradigms that are prevalent in previous research on the Galactic Centre. The first is that the disc's inner cavity is maintained by the interaction of the central stellar cluster's strong winds with the disc's inner rim, and second, that the presence of unstable clumps in the disc implies that the CND is a transient feature. Our simulations show that, in the absence of a magnetic field, the interaction of the wind with the inner disc rim actually leads to a filling of the inner cavity within a few orbital time-scales, contrary to previous expectations. However, including the effects of magnetic fields stabilizes the inner disc rim against rapid inward migration. Furthermore, this interaction causes instabilities that continuously create clumps that are individually unstable against tidal shearing. Thus the occurrence of such unstable clumps does not necessarily mean that the disc is itself a transient phenomenon. The next steps in this investigation are to explore the effect of the magnetorotational instability on the disc evolution and to test whether the results presented here persist for longer time-scales than those considered here., 18 pages, 11 figures, accepted by MNRAS

The dynamics of solid bodies in protoplanetary disks are subject to the properties of any underlying gas turbulence. Turbulence driven by disk self-gravity shows features distinct from those driven by the magnetorotational instability (MRI). We study the dynamics of solids in gravito-turbulent disks with two-dimensional (in the disk plane), hybrid (particle and gas) simulations. Gravito-turbulent disks can exhibit stronger gravitational stirring than MRI-active disks, resulting in greater radial diffusion and larger eccentricities and relative speeds for large particles (those with dimensionless stopping times $t_{stop} \Omega > 1$, where $\Omega$ is the orbital frequency). The agglomeration of large particles into planetesimals by pairwise collisions is therefore disfavored in gravito-turbulent disks. However, the relative speeds of intermediate-size particles $t_{stop} \Omega \sim 1$ are significantly reduced as such particles are collected by gas drag and gas gravity into coherent filament-like structures with densities high enough to trigger gravitational collapse. First-generation planetesimals may form via gravitational instability of dust in marginally gravitationally unstable gas disks., Comment: MNRAS accepted

Aims. The response of a protoplanetary disk to luminosity bursts of various durations is studied with the purpose to determine the effect of the bursts on the strength and sustainability of gravitational instability in the disk. A special emphasis is paid to the spatial distribution of gas and grown dust (from 1 mm to a few centimetres) during and after the burst. Methods. Numerical hydrodynamics simulations were employed to study the dynamics of gas and dust in the thin-disk limit. Dust-to-gas friction, including back reaction and dust growth, were also considered. Bursts of various durations (from 100 yr to 500 yr) were initiated in accordance with a thermally ignited magnetorotational instability. Luminosity curves for constant- and declining-magnitude bursts were adopted to represent two typical limiting cases for FU Orionis-type eruptions. Results. The short-term effect of the burst is to reduce the strength of gravitational instability by heating and expanding the disk. The longest bursts with durations comparable to the revolution period of the spiral can completely dissolve the original two-armed spiral pattern in the gas disk by the end of the burst, while the shortest bursts only weaken the spiral pattern. The reaction of grown dust to the burst is somewhat different. The spiral-like initial distribution with deep cavities in the inter-armed regions transforms into a ring-like distribution with deep gaps. This transformation is mostly expressed for the longest-duration bursts. The long-term effect of the burst depends on the initial disk conditions at the onset of the burst. In some cases, vigorous disk fragmentation sets in several thousands of years after the burst, which was absent in the model without the burst. Several clumps with masses in the giant-planet mass range form in the outer disk regions. After the disk fragmentation phase, the spatial distribution of grown dust is characterized by multiple sharp rings located from tens to hundreds of astronomical units. The arrangement and sharpness of the rings depends on the strength of dust turbulent diffusion. The wide-orbit rings are likely formed as the result of dust-rich clump dispersal in the preceding gravitationally unstable phase. Conclusions. Luminosity bursts similar in magnitude to FU Orionis-type eruptions can have a profound effect on the dynamics of gas and dust in protoplanetary disks if the burst duration is comparable to, or longer than, the dynamical timescales. In this context, the spatial morphology of the gas-dust disk of V883 Ori, a FU Orionis-like object that is thought to be in the outburst phase for more than a century with an unknown onset date, may be used as test case for the burst models considered in this work. The potential relation of the obtained ring structures to a variety of gaps and rings observed in T Tauri disks remains to be established.