In a hot, dilute, magnetized accretion flow, the electron mean-free path can be much greater than the Larmor radius, thus thermal conduction is anisotropic and along magnetic field lines. In this case, if the temperature decreases outward, the flow may be subject to a buoyancy instability (the magnetothermal instability, or MTI). The MTI amplifies the magnetic field, and aligns field lines with the radial direction. If the accretion flow is differentially rotating, the magnetorotational instability (MRI) may also be present. Using two-dimensional, time-dependent magnetohydrodynamic simulations, we investigate the interaction between these two instabilities. We use global simulations that span over two orders of magnitude in radius, centered on the region around the Bondi radius where the infall time of gas is longer than the growth time of both the MTI and MRI. Significant amplification of the magnetic field is produced by both instabilities, although we find that the MTI primarily amplifies the radial component, and the MRI primarily the toroidal component, of the field, respectively. Most importantly, we find that if the MTI can amplify the magnetic energy by a factor $F_t$, and the MRI by a factor $F_r$, then when the MTI and MRI are both present, the magnetic energy can be amplified by a factor of $F_t \cdot F_r$. We therefore conclude that amplification of the magnetic energy by the MTI and MRI operates independently. We also find that the MTI contributes to the transport of angular momentum, because radial motions induced by the MTI increase the Maxwell (by amplifying the magnetic field) and Reynolds stresses. Finally, we find that thermal conduction decreases the slope of the radial temperature profile. The increased temperature near the Bondi radius decreases the mass accretion rate.
At the end of their birth process, neutron stars can be subject to a magnetorotational instability in which a conversion of kinetic energy of differential rotation into radiation and kinetic energies is expected to occur at the Alfvén timescale of few ms. This birth energy conversion predicts the observed large velocity of neutron stars if during the evolving of this instability the periods are of few ms and the magnetic fields reach values of $10^{16}$G.
The magnetospheres around neutron stars should be very particular because of their strong magnetic field and rapid rotation. A study of the pulsar magnetospheres is of a crucial importance since it is the key issue to understand how energy inflow to the exterior is produced. In this paper, I discuss magnetohydrodynamic processes in the pulsar magnetosphere. I consider in detail the properties of magnetohydrodynamic waves that can exist in the magnetosphere and their instabilities.These instabilities lead to formation of magnetic structures and can be responsible for a short-term variability of…
Clusters of galaxies are embedded in halos of optically thin, gravitationally stratified, weakly magnetized plasma at the system's virial temperature. Due to radiative cooling and anisotropic heat conduction, such intracluster medium (ICM) is subject to local instabilities, which are combinations of the thermal, magnetothermal and heat-flux-driven buoyancy instabilities. If the ICM rotates significantly, its stability properties are substantially modified and, in particular, also the magnetorotational instability (MRI) can play an important role. We study simple models of rotating cool-core cl…
We investigate the stability of incompressible, exact, non-ideal magnetorotational (MRI) modes against parasitic instabilities. Both Kelvin-Helmholtz and tearing-mode parasitic instabilities may occur in the dissipative regimes accessible to current numerical simulations. We suppose that a primary MRI mode saturates at an amplitude such that its fastest parasite has a growth rate comparable to its own. The predicted alpha parameter then depends critically on whether the fastest primary and parasitic modes fit within the computational domain and whether non-axisymmetric parasitic modes are allo…
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…
Though usually treated in isolation, the magnetorotational and gravitational instabilities (MRI and GI) may coincide at certain radii and evolutionary stages of protoplanetary discs and active galactic nuclei. Their mutual interactions could profoundly influence several important processes, such as accretion variability and outbursts, fragmentation and disc truncation, or large-scale magnetic field production. Direct numerical simulations of both instabilities are computationally challenging and remain relatively unexplored. In this paper, we aim to redress this neglect via a set of 3D vertica…
In collisionless and weakly collisional plasmas, such as hot accretion flows onto compact objects, the magnetorotational instability (MRI) can differ significantly from the standard (collisional) MRI. In particular, pressure anisotropy with respect to the local magnetic-field direction can both change the linear MRI dispersion relation and cause nonlinear modifications to the mode structure and growth rate, even when the field and flow perturbations are small. This work studies these pressure-anisotropy-induced nonlinearities in the weakly nonlinear, high-ion-beta regime, before the MRI satura…
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…
We present results from the first 3D kinetic numerical simulation of magnetorotational turbulence and dynamo, using the local shearing-box model of a collisionless accretion disc. The kinetic magnetorotational instability grows from a subthermal magnetic field having zero net flux over the computational domain to generate self-sustained turbulence and outward angular-momentum transport. Significant Maxwell and Reynolds stresses are accompanied by comparable viscous stresses produced by field-aligned ion pressure anisotropy, which is regulated primarily by the mirror and ion-cyclotron instabili…
We investigate the explosion of stars with zero-age main-sequence masses between 20 and 35 solar masses and varying degrees of rotation and magnetic fields including ones commonly considered progenitors of gamma-ray bursts (GRBs). The simulations, combining special relativistic magnetohydrodynamics, a general relativistic approximate gravitational potential, and two-moment neutrino transport, demonstrate the viability of different scenarios for the post-bounce evolution. Having formed a highly massive proto-neutron star (PNS), several models launch successful explosions, either by the standard…
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…
Non-axisymmetric modes of magnetorotational and possible hydrodynamical instabilities in the upcoming DRESDYN-MRI experiments -- linear and nonlinear dynamics
We explore the influence of non-axisymmetric modes on the dynamics of the collapsed core of rotating, magnetized high-mass stars in three-dimensional simulations of a rapidly rotating star with an initial mass of $M_{ZAMS}$ = 35 solar masses endowed with four different pre-collapse configurations of the magnetic field, ranging from moderate to very strong field strength and including the field predicted by the stellar evolution model. The model with the weakest magnetic field achieves shock revival due to neutrino heating in a gain layer characterized by a large-scale, hydrodynamic m = 1 spira…
We study the influence of numerical methods and grid resolution on the termination of the magnetorotational instability (MRI) by means of parasitic instabilities in three-dimensional shearing-disc simulations reproducing typical conditions found in core-collapse supernovae. Whether or not the MRI is able to amplify weak magnetic fields in this context strongly depends, among other factors, on the amplitude at which its growth terminates. The qualitative results of our study do not depend on the numerical scheme. In all our models, MRI termination is caused by Kelvin-Helmholtz instabilities, co…
Magnetohydrodynamic (MHD) turbulence is of key importance in many high-energy astrophysical systems, where MHD instabilities can amplify local magnetic field over very short time scales. Specifically, the magnetorotational instability (MRI) and dynamo action have been suggested as a mechanism to grow magnetar-strength magnetic field ($\ge10^{15} G$) and magnetorotationally power the explosion of a rotating massive star. Such stars are progenitor candidates for type Ic-bl hypernova explosions and make up all supernovae connected to long gamma-ray bursts (GRBs). The MRI has been studied with loc…
Magnetohydrodynamic instabilities play an important role in accretion disks systems. Besides the well-known effects of the magnetorotational instability (MRI), the Parker-Rayleigh-Taylor instability (PRTI) also arises as an important mechanism to help in the formation of the coronal region around an accretion disk and in the production of magnetic reconnection events similar to those occurring in the solar corona. In this work, we have performed three-dimensional magnetohydrodynamical (3D-MHD) shearing-box numerical simulations of accretion disks with an initial stratified density distribution…
It is likely that nearly all central galactic massive and supermassive black holes are nonradiative: their accretion luminosities are orders of magnitude below what can be explained by efficient black hole accretion within their ambient environments. These objects, of which Sagittarius A* is the best-known example, are also dilute (mildly collisional to highly collisionless) and optically thin. In order for accretion to occur, magnetohydrodynamic instabilities must develop that not only transport angular momentum, but also gravitational energy generated through matter infall, outwards. A class…
We examine the properties of strongly magnetized accretion discs in a global framework, with particular focus on the evolution of magnetohydrodynamic instabilities such as the magnetorotational instability (MRI). Work by Pessah and Psaltis showed that MRI is stabilized beyond a critical toroidal field in compressible, differentially rotating flows and, also, reported the appearance of two new instabilities beyond this field. Their results stemmed from considering geometric curvature effects due to the suprathermal background toroidal field, which had been previously ignored in weak-field studi…
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 instabil…
We study the linear stability of weakly magnetized differentially rotating plasmas in both collisionless kinetic theory and Braginskii's theory of collisional, magnetized plasmas. We focus on the very weakly magnetized limit that is important for understanding how astrophysical magnetic fields originate and are amplified at high redshift. We show that the single instability of fluid theory - the magnetorotational instability mediated by magnetic tension - is replaced by two distinct instabilities, one associated with ions and one with electrons. Each of these has a different way of tapping int…
In weakly-collisional plasmas such as the intracluster medium (ICM), heat and momentum transport become anisotropic with respect to the local magnetic field direction. Anisotropic heat conduction causes the slow magnetosonic wave to become buoyantly unstable to the magnetothermal instability (MTI) when the temperature increases in the direction of gravity and to the heat-flux--driven buoyancy instability (HBI) when the temperature decreases in the direction of gravity. The local changes in magnetic field strength that attend these instabilities cause pressure anisotropies that viscously damp m…
The magnetorotational instability (MRI) is considered a key process for driving efficient angular momentum transport in astrophysical disks. Understanding its non-linear saturation constitutes a fundamental problem in modern accretion disk theory. The large dynamical range in physical conditions in accretion disks makes it challenging to address this problem only with numerical simulations. We analyze the concept that (secondary) parasitic instabilities are responsible for the saturation of the MRI. Our approach enables us to explore dissipative regimes that are relevant to astrophysical and l…
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…
Simulations of the magnetorotational instability (MRI) in 'unstratified' shearing boxes exhibit powerful coherent flows, whereby the fluid vertically splits into countermoving planar jets or `channels'. Channel flows correspond to certain axisymmetric linear MRI modes, and their preponderance follows from the remarkable fact that they are approximate nonlinear solutions of the MHD equations in the limit of weak magnetic fields. We show in this paper, analytically and with one-dimensional numerical simulations, that this property is also shared by certain axisymmetric MRI modes in vertically-st…
Based on the characteristics of the magnetorotational instability (MRI) and the MRI-driven turbulence, we construct a steady model for a geometrically thin disk using "non-standard" $α$-prescription. The efficiency of the angular momentum transport depends on the magnetic Prandtl number, $Pm = ν/η$, where $ν$ and $η$ are the microscopic viscous and magnetic diffusivities. In our disk model, Shakura-Sunyaev's $α$-parameter has a power-law dependence on the magnetic Prandtl number, that is $α\propto Pm^δ$ where $δ$ is the constant power-law index. Adopting Spitzer's microscopic diffusivities, th…
The intracluster medium (ICM) is stably stratified in the hydrodynamic sense with the entropy $s$ increasing outwards. However, thermal conduction along magnetic field lines fundamentally changes the stability of the ICM, leading to the "heat-flux buoyancy instability" when $dT/dr>0$ and the "magnetothermal instability" when $dT/dr<0$. The ICM is thus buoyantly unstable regardless of the signs of $dT/dr$ and $ds/dr$. On the other hand, these temperature-gradient-driven instabilities saturate by reorienting the magnetic field (perpendicular to $\hat{\bf r}$ when $dT/dr>0$ and parallel to $\hat{…
In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because the hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. Here, we calculate the vertical profiles of the {\it stationary} accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the s…
Galaxy clusters host a large reservoir of diffuse plasma with radially-varying temperature profiles. The efficiency of thermal conduction in the intracluster medium (ICM) is complicated by the existence of turbulence and magnetic fields, and has received a lot of attention in the literature. Previous studies suggest that the magnetothermal instability developed in outer regions of galaxy clusters would drive magnetic field lines preferentially radial, resulting in efficient conduction along the radial direction. Using a series of spherically-symmetric simulations, here we investigate the impac…
