By performing local three-dimensional MHD simulations of stratified accretion disks, we investigate disk winds driven by MHD turbulence. Initially given weak vertical magnetic fields are effectively amplified by magnetorotational instability and winding due to differential rotation. Large scale channel flows develop most effectively at 1.5 - 2 times the scale heights where the magnetic pressure is comparable to but slightly smaller than the gas pressure. The breakup of these channel flows drives structured disk winds by transporting the Poynting flux to the gas. These features are universally observed in the simulations of various initial fields. This disk wind process should play an essential role in the dynamical evaporation of proto-planetary disks. The breakup of channel flows also excites the momentum fluxes associated with Alfvenic and (magneto-)sonic waves toward the mid-plane, which possibly contribute to the sedimentation of small dust grains in protoplanetary disks.
We investigate where in protoplanetary disks magnetorotational instability operates, which can cause angular momentum transport in the disks. We investigate the spatial distribution of various charged particles and the unstable regions for a variety of models for protoplanetary disks taking into account the recombination of ions and electrons at grain surfaces, which is an important process in most parts of the disks. We find that for all the models there is an inner region which is magnetorotationally stable due to ohmic dissipation. This must make the accretion onto the central star non-stea…
We examine the linear stability of a flow threaded by a weak, vertical magnetic field in a disk with a keplerian rotation profile and a vertical stratification of the ionization degree as that predicted for vast portions of protoplanetary disks. A quasi-global analysis is carried out, where the form of the perturbations in the vertical direction is determined. Considering the ohmic magnetic diffusivity of the gas, the conditions leading to the magnetorotational instability are analyzed as a function of the diffusivity at the disk surfaces, its vertical profile and the strength of the unperturb…
Neutrino radiation takes a major role in the momentum, heat, and lepton transports in proto-neutron stars (PNSs). These diffusive processes affect the growth of magnetorotational instability (MRI) in PNSs. We perform a local linear analysis for the axisymmetric and nonaxisymmetric MRI including the effects of neutrino transports and ohmic dissipation. We find that the MRI can grow even in the multi-diffusive situations that are realized in neutrino loaded PNSs. When the toroidal magnetic component dominates over the poloidal one, nonaxisymmetric MRI modes grow much faster than axisymmetric mod…
We investigate the stability of differentially rotating proto-neutron stars (PNSs) with a toroidal magnetic field. Stability criteria for nonaxisymmetric MHD instabilities are derived using a local linear analysis. PNSs are expected to have much stronger radial shear in the rotation velocity compared to normal stars. We find that nonaxisymmetric magnetorotational instability (NMRI) with a large azimuthal wavenumber $m$ is dominant over the kink mode ($m=1$) in differentially rotating PNSs. The growth rate of the NMRI is of the order of the angular velocity $Ω$ which is faster than that of the …
We analyze the ionization state of the magnetohydrodynamically turbulent protoplanetary disks and propose a new mechanism of sustaining ionization. First, we show that in the quasi-steady state of turbulence driven by magnetorotational instability in a typical protoplanetary disk with dust grains, the amount of energy dissipation should be sufficient for providing the ionization energy that is required for activating magnetorotational instability. Second, we show that in the disk with dust grains the energetic electrons that compose electric currents in weakly ionized gas can provide collision…
We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and dust grains are assumed to have settled towards the midplane, so charges are carried by electrons and ions only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, and disc surface density. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conducti…
We present results of 2D simulation of magnetorotational (MR) supernova accompanied by jet formation in the core collapse supernova explosion. Initial magnetic field used in the simulations has dipole-like symmetry. Contrary to the simulations of MR supernova with initial quadrupole-like magnetic field, where the matter was ejected mainly near the equatorial plane, in presence of the dipole-like initial magnetic field the supernova explosion is developing preferably along a rotational axis, and leads to formation of a protojet. We expect that protojet propagation through the envelope of the st…
The magnetorotational instability (MRI) (Balbus and Hawley 1991, Hawley and Balbus 1991) transports angular momentum radially outwards in accretion discs through the distortion of the magnetic field lines that connect fluid elements. In protostellar discs, low conductivity is important, especially in the inner regions (Gammie 1996, Wardle 1997). As a result, low k modes are relevant and vertical stratification is a key factor of the analysis. However, most models of the MRI in these environments have adopted either the ambipolar diffusion or resistive approximations and have not simultaneously…
We present the results of 2D simulations of the magnetorotational model of a supernova explosion. After the core collapse the core consists of rapidly a rotating proto-neutron star and a differentially rotating envelope. The toroidal part of the magnetic energy generated by the differential rotation grows linearly with time at the initial stage of the evolution of the magnetic field. The linear growth of the toroidal magnetic field is terminated by the development of magnetohydrodynamic instability, leading to drastic acceleration in the growth of magnetic energy. At the moment when the magnet…
We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionised accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and assumed constant with height. We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field…
Well before the existence of exo-solar systems was confirmed, it was accepted knowledge that most -- if not all -- stars possess circumstellar material during the first one-to-several million years of their pre-main sequence lives, and thus that they commonly have the potential to form planets. Here I summarize current understanding regarding the evolution of proto-planetary dust and gas disks, emphasizing the diversity in evolutionary paths.
We investigate the linear growth and vertical structure of the MRI in protoplanetary discs when dust grains are well mixed with the gas over the entire disc thickness. All the grains have the same radius (a = 0.1, 1 or 3 micron) and constitute 1 % of the total mass of the gas. Solutions are obtained at R = 5 and 10 AU for a minimum-mass solar nebula model and different choices of the initially vertical magnetic field strength (B), configuration of the diffusivity tensor and grain sizes. We find that when no grains are present, or they are > 1 micron, the midplane remains magnetically coupled f…
We consider the linear axisymmetric stability of a differentially rotating collisionless plasma in the presence of a weak magnetic field; we restrict our analysis to wavelengths much larger than the proton Larmor radius. This is the kinetic version of the magnetorotational instability explored extensively as mechanism for magnetic field amplification and angular momentum transport in accretion disks. The kinetic calculation is appropriate for hot accretion flows onto compact objects and for the growth of very weak magnetic fields, where the collisional mean free path is larger than the wavelen…
We investigate the conditions for the presence of a magnetically inactive dead zone in protostellar disks, using 3-D shearing-box MHD calculations including vertical stratification, Ohmic resistivity and time-dependent ionization chemistry. Activity driven by the magnetorotational instability fills the whole thickness of the disk at 5 AU, provided cosmic ray ionization is present, small grains are absent and the gas-phase metal abundance is sufficiently high. At 1 AU the larger column density of 1700 g/cm^2 means the midplane is shielded from ionizing particles and remains magnetorotationally …
The effect of the Hall term on the evolution of the magnetorotational instability (MRI) in weakly ionized accretion disks is investigated using local axisymmetric simulations. First, we show that the Hall term has important effects on the MRI when the temperature and density in the disk is below a few thousand K and between 10^13 and 10^18 cm^{-3} respectively. Such conditions can occur in the quiescent phase of dwarf nova disks, or in the inner part (inside 10 - 100 AU) of protoplanetary disks. When the Hall term is important, the properties of the MRI are dependent on the direction of the ma…
Accretion disks in which angular momentum transport is dominated by the magnetorotational instability (MRI) can also possess additional, purely hydrodynamic, drivers of turbulence. Even when the hydrodynamic processes, on their own, generate negligible levels of transport, they may still affect the evolution of the disk via their influence on the MRI. Here, we study the interaction between the MRI and hydrodynamic turbulence using local MRI simulations that include hydrodynamic forcing. As expected, we find that hydrodynamic forcing is generally negligible if it yields a saturated kinetic ener…
We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to show that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations, as the disk-in-a-box models presented here develop and sustain MHD turbulence. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnet…
Core-collapse supernovae are connected with formation of neutron stars. Part of the gravitation energy is transformed into the energy of the explosion, observed in SN II, SN Ib,c type supernovae. The mechanism of transformation is not simple, because the overwhelming majority of the energy is going into weakly interacting neutrino. The attempts to use this energy for the explosion were not successful during about 40 years of investigation. We consider the explosion mechanism in which the source of energy is the rotation, and magnetic field serves for the transformation of the rotation energy i…
(Abridged) In this paper we have used the RIEMANN code for computational astrophysics to study the interaction of a realistic distribution of dust grains with gas in a vertically stratified protostellar accretion disc. The disc was modeled to have the density and temperature of a minimum mass solar nebula, and was driven to a fully-developed turbulence via the magnetorotational instability (MRI). We find that the inclusion of standard dust to gas ratios does not have any significant effect on the MRI even when the dust sediments to the midplane of the accretion disc. The density distribution o…
The stability properties of inviscid protostellar disks are examined taking into account the Hall effect and buoyancy. Depending on the parameters, different types of instabilities can exist in different regions of disks. In a very low ionized region, the instability associated with baroclinic effects of buoyancy is likely most efficient. The Hall-driven shear instability can lead to destabilization of regions with a higher ionization. The magnetorotational instability modified by buoyancy can only be a destabilizing factor in regions with strong magnetic field or a relatively high conductivit…
We study the effect of an imposed vertical magnetic field on the turbulent mass diffusion properties of magnetorotational turbulence in protoplanetary discs. It is well-known that the effective viscosity generated by the turbulence depends strongly on the magnitude of such an external field. In this letter we show that the turbulent diffusion of the flow also grows, but that the diffusion coefficient does not rise with increasing vertical field as fast as the viscosity does. The vertical Schmidt number, i.e. the ratio between viscosity and vertical diffusion, can be close to 20 for high field …
When the ion mean free path much exceeds the Larmor radius in a plasma, the viscous stress tensor is altered dramatically, and depends only upon quantities measured along the field lines. This regime corresponds to typical interstellar medium conditions in galaxies and protogalaxies, even if the magnetic field is extremely weak, with a negligible Lorentz force on all scales of interest. In this work, the only role of the magnetic field is to channel angular momentum transport along its lines of force. We show that differential rotation in such a gas is highly unstable, with a maximum growth ra…
We study magnetohydrodynamic (MHD) effects arising in the collapse of magnetized, rotating, massive stellar cores to proto-neutron stars (PNSs). We perform axisymmetric numerical simulations in full general relativity with a hybrid equation of state. The formation and early evolution of a PNS are followed with a grid of 2500 x 2500 zones, which provides better resolution than in previous (Newtonian) studies. We confirm that significant differential rotation results even when the rotation of the progenitor is initially uniform. Consequently, the magnetic field is amplified both by magnetic wind…
These notes provide an introduction to the theory of the formation and early evolution of planetary systems. Topics covered include the structure, evolution and dispersal of protoplanetary disks; the formation of planetesimals, terrestrial and gas giant planets; and orbital evolution due to gas disk migration, planetesimal scattering, planet-planet interactions, and tides.
The processes of planet formation and migration depend intimately on the interaction between planetesimals and the gaseous disks in which they form. The formation of gaps in the disk can severely limit the mass of the planet and its migration toward the protostar. We investigate the process of gap formation through magnetohydrodynamic simulations in which internal stress arises self-consistently from turbulence generated by the magnetorotational instability. The simulations investigate three different planetary masses and two disk temperatures to bracket the tidal (thermal) and viscous gap ope…
The most efficient energy sources known in the Universe are accretion disks. Those around black holes convert 5 -- 40 per cent of rest-mass energy to radiation. Like water circling a drain, inflowing mass must lose angular momentum, presumably by vigorous turbulence in disks, which are essentially inviscid. The origin of the turbulence is unclear. Hot disks of electrically conducting plasma can become turbulent by way of the linear magnetorotational instability. Cool disks, such as the planet-forming disks of protostars, may be too poorly ionized for the magnetorotational instability to occur,…
The effects of Hall electromotive forces (HEMFs) on the linear stability of protostellar disks are examined. Earlier work on this topic focused on axial field and perturbation wavenumbers. Here we treat the problem more generally. Both axisymmetric and nonaxisymmetric cases are investigated. Though seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron whistler waves, and since these have right-handed polarization, a helicity factor is also introduced into the stability problem. This factor is the produc…
