We investigate the stability of partially ionised, differentially rotating, diffusive disc threaded by both azimuthal and vertical magnetic field. The general stability criterion of such a disc in the presence of axisymmetric fluctuations can be stated purely in terms of ambipolar and Hall diffusivities. It is shown that the disc is magnetorotationally unstable if the sum of scaled ambipolar and Hall diffusivities are larger than some numerical constant determined by the rotation profile of the disc. This criterion suggests that the diffusive discs are always unstable to almost radial fluctuations. The field geometry and obliqueness of wavevector (encapsulated together in the topological factor $g$), plays dual role of not only assisting MRI in ambipolar--Ohm dominated disc but also making otherwise stable region in Hall--ambipolar diffusion plane unstable.
The magnetorotational instability (MRI) is the most promising mechanism by which angular momentum is efficiently transported outwards in astrophysical discs. However, its application to protoplanetary discs remains problematic. These discs are so poorly ionised that they may not support magnetorotational turbulence in regions referred to as `dead zones'. It has recently been suggested that the Hall effect, a non-ideal magnetohydrodynamic (MHD) effect, could revive these dead zones by enhancing the magnetically active column density by an order of magnitude or more. We investigate this idea by …
The extent to which angular momentum transport in accretion discs is primarily local or non-local and what determines this is an important avenue of study for understanding accretion engines. Taking a step along this path, we analyze simulations of the magnetorotational instability (MRI) by calculating energy and stress power spectra in stratified isothermal shearing box simulations in several new ways. We divide our boxes in two regions, disc and corona where the disc is the MRI unstable region and corona is the magnetically dominated region. We calculate the fractional power in different qua…
The redistribution of angular momentum is a long standing problem in our understanding of protoplanetary disk (PPD) evolution. The magnetorotational instability (MRI) is considered a likely mechanism. We present the results of a study involving multifluid global simulations including Ohmic dissipation, ambipolar diffusion and the Hall effect in a dynamic, self-consistent way. We focus on the turbulence resulting from the non-linear development of the MRI in radially stratified PPDs and compare with ideal MHD simulations. In the multifluid simulations the disk is initially set up to transition …
We examine whether the magnetorotational instability (MRI) can serve as a mechanism of angular momentum transport in circumplanetary disks. For the MRI to operate the ionization degree must be sufficiently high and the magnetic pressure must be sufficiently lower than the gas pressure. We calculate the spatial distribution of the ionization degree and search for the MRI-active region where the two criteria are met. We find that there can be thin active layers at the disk surface depending on the model parameters, however, we find hardly any region which can sustain well-developed MRI turbulenc…
Whether the magnetorotational instability (MRI) can amplify initially weak magnetic fields to dynamically relevant strengths in core collapse supernovae is still a matter of active scientific debate. Recent numerical studies have shown that the first phase of MRI growth dominated by channel flows is terminated by parasitic instabilities of the Kelvin-Helmholtz type that disrupt MRI channel flows and quench further magnetic field growth. However, it remains to be prop- erly assessed by what factor the initial magnetic field can be amplified and how it depends on the initial field strength and t…
We study how the magnetorotational instability (MRI) in protoplanetary disks is affected by the electric discharge caused by the electric field in the resistive MHD. We have performed three-dimensional shearing box simulations with various values of plasma beta and electrical breakdown models. We find the self-sustainment of the MRI in spite of the high resistivity. The instability gives rise to the large electric field that causes the electrical breakdown, and the breakdown maintains the high ionization degree required for the instability. The condition for this self-sustained MRI is set by t…
Magnetorotational turbulence and magnetically driven disc winds are often considered as separate processes. However, realistic astrophysical discs are expected to be subject to both effects, although possibly at different times and locations. We investigate here the potential link between these two phenomena using a mixed numerical and analytical approach. We show in particular that large-scale MRI modes which dominate strongly magnetised discs (plasma beta~10) naturally produce magnetically driven outflows in the nonlinear regime. We show that these outflows share many similarities with local…
Evolutionary models of fast-rotating stars show that the stellar rotational velocity may approach the critical speed. Critically rotating stars cannot spin up more, therefore they lose their excess angular momentum through an equatorial outflowing disk. The radial extension of such disks is unknown, partly because we lack information about the radial variations of the viscosity. We study the magnetorotational instability, which is considered to be the origin of anomalous viscosity in outflowing disks. We used analytic calculations to study the stability of outflowing disks submerged in the mag…
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 diamagnetizati…
The magnetorotational instability (MRI), also known as the Balbus -- Hawley instability, is thought to have an important role on the initiation of turbulence and angular momentum transport in accretion discs. In this work, we investigate the effect of the magnetic field gradient in the azimuthal direction on MRI. We solve the magnetohydrodynamic equations by including the azimuthal component of the field gradient. We find the dispersion relation and calculate the growth rates of the instability numerically. The inclusion of the azimuthal magnetic field gradient produces a new unstable region o…
We calculate growth rates for nonaxisymmetric instabilities including the magnetorotational instability (MRI) throughout the Sun. We first derive a dispersion relation for nonaxisymmetric instability including the effects of shear, convective buoyancy, and three diffusivities (thermal conductivity, resistivity, and viscosity). We then use a solar model evolved with the stellar evolution code MESA and angular velocity profiles determined by Global Oscillations Network Group (GONG) helioseismology to determine the unstable modes present at each location in the Sun and the associated growth rates…
We discuss the relevance of the magnetorotational instability (MRI) in core-collapse supernovae (CCSNe). Our recent numerical studies show that in CCSNe, the MRI is terminated by parasitic instabilities of the Kelvin-Helmholtz type. To determine whether the MRI can amplify initially weak magnetic fields to dynamically relevant strengths in CCSNe, we performed three-dimensional simulations of a region close to the surface of a differentially rotating proto-neutron star in non-ideal magnetohydrodynamics with two different numerical codes. We find that under the conditions prevailing in proto-neu…
The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI that appear in the limits of infinite and vanishing magnetic Prandtl number. For the latter case we derive a new strict limit of the critical Rossby number. This new limit of ${\rm Ro_c}=-0.802$, which appears for a finite Lundquist number of ${\rm Lu}=0.618$, extends the formerly known inductionless Liu limit of ${\rm Ro_c}=-0.82…
We perform local, vertically stratified shearing-box MHD simulations of protoplanetary disks (PPDs) at a fiducial radius of 1 AU that take into account the effects of both Ohmic resistivity and ambipolar diffusion (AD). The magnetic diffusion coefficients are evaluated self-consistently from a look-up table based on equilibrium chemistry. We first show that the inclusion of AD dramatically changes the conventional picture of layered accretion. Without net vertical magnetic field, the system evolves into a toroidal field dominated configuration with extremely weak turbulence in the far-UV ioniz…
The nature of dynamo action in shear flows prone to magnetohydrodynamic instabilities is investigated using the magnetorotational dynamo in Keplerian shear flow as a prototype problem. Using direct numerical simulations and Newton's method, we compute an exact time-periodic magnetorotational dynamo solution to the three-dimensional dissipative incompressible magnetohydrodynamic equations with rotation and shear. We discuss the physical mechanism behind the cycle and show that it results from a combination of linear and nonlinear interactions between a large-scale axisymmetric toroidal magnetic…
The destabilising effect of Hall diffusion in a Keplerian disc allows the MRI to occur for much lower ionisation levels than would otherwise be possible. However, simulations suggest that the consequences for the saturated state are not as significant as suggested by the linear instability. Close inspection reveals that that the simulations have not yet probed the Hall-dominated regime. Here we revisit the effect of Hall diffusion on the MRI and the implications for the extent of MHD turbulence in protoplanetary discs. We conduct a local stability analysis for a vertical, weak magnetic field s…
A new non-dissipative mechanism is proposed for the saturation of the axisymmetric magnetorotational (MRI) instability in thin Keplerian disks that are subject to an axial magnetic field. That mechanism relies on the energy transfer from the MRI to stable magnetosonic (MS) waves. Such mode interaction is enabled due to the vertical stratification of the disk that results in the discretization of its MRI spectrum, as well as by applying the appropriate boundary conditions. A second order Duffing-like amplitude equation for the initially unstable MRI modes is derived. The solutions of that equat…
The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable rotating shear flows, e.g., in accretion disks. What laws of differential rotation are susceptible to the destabilization by axial, azimuthal, or helical magnetic field? The answer to this question, which is vital for astrophysical and experimental applications, inevitably leads to the study of spectral and geometrical singularities on the instability threshold. The singularities provide a connection between seemingly discontinuous stability criteria and thus…
In this paper we investigate the influence of radiative transport on the growth of the magnetorotational instability (MRI) in accretion discs. The analysis is performed by use of analytical and numerical means. We provide a general dispersion relation together with the corresponding eigenfunctions describing the growth rates of small disturbances on a homogeneous background shear flow. The dispersion relation includes compressibility and radiative effects in the flux-limited diffusion approximation. By introducing an effective speed of sound, all the effects of radiation transport can be subsu…
The magnetorotational instability (MRI) plays a crucial role for cosmic structure formation by enabling turbulence in Keplerian disks which would be otherwise hydrodynamically stable. With particular focus on MRI experiments with liquid metals, which have small magnetic Prandtl numbers, it has been shown that the helical version of this instability (HMRI) has a scaling behaviour that is quite different from that of the standard MRI (SMRI). We discuss the relation of HMRI to SMRI by exploring various parameter dependencies. We identify the mechanism of transfer of instability between modes thro…
Turbulence driven by magnetorotational instability (MRI) crucially affects the evolution of solid bodies in protoplanetary disks. On the other hand, small dust particles stabilize MRI by capturing ionized gas particles needed for the coupling of the gas and magnetic fields. To provide an empirical basis for modeling the coevolution of dust and MRI, we perform three-dimensional, ohmic-resistive MHD simulations of a vertically stratified shearing box with an MRI-inactive "dead zone" of various sizes and with a net vertical magnetic flux of various strengths. We find that the vertical structure o…
The acceleration of an outflow along inclined magnetic field lines emanating from an accretion disc can be studied in the local approximation, as employed in the computational model known as the shearing box. By including the slow magnetosonic point within the computational domain, the rate of mass loss in the outflow can be calculated. The accretion rates of mass and magnetic flux can also be determined, although some effects of cylindrical geometry are omitted. We formulate a simple model for the study of this problem and present the results of one-dimensional numerical simulations and suppo…
The magnetorotational instability (MRI) can be a powerful mechanism amplifying the magnetic field in core-collapse supernovae. Whether initially weak magnetic fields can be amplified by this instability to dynamically relevant strengths is still a matter of debate. One of the main uncertainties concerns the process that terminates the growth of the instability. Parasitic instabilities of both Kelvin-Helmholtz and tearing-mode type have been suggested to play a crucial role in this process, disrupting MRI channel flows and quenching magnetic field amplification. We perform two-dimensional and t…
Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the …
The magnetorotational instability (MRI) is a shear instability and thus its sensitivity to the shear parameter $q = - d\lnΩ/d\ln r $ is of interest to investigate. Motivated by astrophysical disks, most (but not all) previous MRI studies have focused on the Keplerian value of $ q=1.5$. Using simulation with 8 vertical density scale heights, we contribute to the subset of studies addressing the the effect of varying $q$ in stratified numerical simulations. We discuss why shearing boxes cannot easily be used to study $q>2$ and thus focus on $q<2$. As per previous simulations, which were either u…
This paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks. Optically thin lines from Keplerian planar disks are considered. Model line profiles are calculated for simple field topologies of axial fields (i.e., vertical to the disk plane) and toroidal fields (i.e., purely azimuthal). A scheme for discerning field strengths and geometries in disks is developed based on Stokes Q-U diagrams for the run of polarization across line profiles that are Doppler broadened by the disk rotation. A discussion of the Hanle effect for magnetized disks in which th…
The protostellar collapse of a molecular cloud core is usually accompanied by outflow phenomena. The latter are thought to be driven by magnetorotational processes from the central parts of the protostellar disc. While several 3D AMR/nested grid studies of outflow phenomena in collapsing magnetically supercritical dense cores have been reported in the literature, so far no such simulation has been performed using the Smoothed Particle Hydrodynamics (SPH) method. This is mainly due to intrinsic numerical difficulties in handling magnetohydrodynamics within SPH, which only recently were partly r…
The r-process nucleosynthesis in core-collapse supernovae (CC-SNe) is studied, with a focus on the explosion scenario induced by rotation and strong magnetic fields. Nucleosynthesis calculations are conducted based on magneto-hydrodynamical explosion models with a wide range of parameters for initial rotation and magnetic fields. The explosion models are classified in two different types: i.e., prompt-magnetic-jet and delayed-magnetic-jet, for which the magnetic fields of proto-neutron stars (PNSs) during collapse and the core-bounce are strong and comparatively moderate, respectively. Followi…
The linear instability of thin, vertically-isothermal Keplerian discs, under the influence of axial magnetic field is investigated. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio of the disc. It is shown that the perturbations are decoupled into in-plane and vertical modes. Exact expressions for the growth rates as well as the number of unstable modes are derived. Those are the discrete counterpart of the continuous infinite homogeneous cylinder magnetorotational (MRI) spectrum. In addition, a weakly nonlinear analysis of the MRI is p…
We investigate the global nonaxisymmetric Rossby vortex instability in a differentially rotating, compressible magnetized accretion disk with radial density structures. Equilibrium magnetic fields are assumed to have only the toroidal component. Using linear theory analysis, we show that the density structure can be unstable to nonaxisymmetric modes. We find that, for the magnetic field profiles we have studied, magnetic fields always provide a stabilizing effect to the unstable Rossby vortex instability modes. We discuss the physical mechanism of this stabilizing effect. The threshold and pro…
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 $α$, when convection is though…
The mechanism of angular momentum transport in accretion discs has long been debated. Although the magnetorotational instability appears to be a promising process, poorly ionized regions of accretion discs may not undergo this instability. In this letter, we revisit the possibility of transporting angular momentum by turbulent thermal convection. Using high-resolution spectral methods, we show that strongly turbulent convection can drive outward angular momentum transport at a rate that is, under certain conditions, compatible with observations of discs. We find however that the angular moment…
We study the stability properties of Rayleigh unstable flows both in the purely hydrodynamic and magnetohydrodynamic (MHD) regimes for two different values of the shear $q=2.1, 4.2$ ($q = - d\lnΩ/ d\ln r$) and compare it with the Keplerian case $q=1.5$. We find that the $q>2$ regime is unstable both in the hydrodynamic and in the MHD limit (with an initially weak magnetic field). In this regime, the velocity fluctuations dominate the magnetic fluctuations. In contrast, in the $q<2$ (magnetorotational instability (MRI)) regime the magnetic fluctuations dominate. This highlights two different pa…
Black hole--neutron star (BHNS) binary mergers can form disks in which magnetorotational instability (MRI)-induced turbulence may drive accretion onto the remnant BH, supporting relativistic jets and providing the engine for a short-hard gamma-ray burst (SGRB). Our earlier study of magnetized BHNSs showed that NS tidal disruption winds the magnetic field into a toroidal configuration, with poloidal fields so weak that capturing MRI with full-disk simulations would require $\sim 10^8$ CPU-hours. In that study we imposed equatorial symmetry, suppressing poloidal magnetic fields that might be gen…
According to Rayleigh's criterion, rotating flows are linearly stable when their specific angular momentum increases radially outward. The celebrated magnetorotational instability opens a way to destabilize those flows, as long as the angular velocity is decreasing outward. Using a short-wavelength approximation we demonstrate that even flows with very steep positive shear can be destabilized by azimuthal magnetic fields which are current-free within the fluid. We illustrate the transition of this instability to a rotationally enhanced kink-type instability in case of a homogeneous current in …
The neutrino magnetic moment and supernovae with strong magnetic fields
GSI Helmholtz-Zentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心有限公司）；CNRS, Université Paris Cité, Astroparticule et Cosmologie（法国国家科学研究中心，巴黎西岱大学，粒子与宇宙学）；Universitat de València（瓦伦西亚大学）
