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In this paper, regarding the recent detection of significant azimuthal magnetic field in some accretion disks such as protostellar (Donati et al. in Nature 438:466, 2005), the multi-fluid model has been employed to analysis the stability of Keplerian rotational viscous dusty plasma system in a current-free helical magnetic field structure. Using the fluid-Maxwell equations, the general dispersion relation of the excited modes in the system has been obtained by applying the local approximation method in the linear perturbation theory. The typical numerical analysis of the obtained dispersion relation in the high-frequency regime shows that the presence of azimuthal magnetic field component in Keplerian flow has a considerable role in the stability conditions of the system. It also shows that the magnetic field helicity has a stabilization role against the magnetorotational instability (MRI) in the system due to contraction of the unstable wavelength region and decreasing the maximum growth rate of the instability. In this sense, the stabilization role of the viscosity term is more considerable for HMRI (instability in the presence of azimuthal magnetic field component) than the corresponding MRI (instability in the absence of azimuthal magnetic field component). Moreover, considering the discovered azimuthal magnetic field in these systems, the MRI can be arisen in the over-all range of dust grains construction values in contract with traditional MRI. This investigation can greatly contribute to better understanding the physics of some astrophysical phenomena, such as the main source of turbulence and angular momentum transport in protostellar and the other sufficiently ionized astrophysical disks, where the azimuthal magnetic field component in these systems can play a significant role.

The standard thin accretion disk model predicts that the inner regions of alpha model disks, where radiation pressure is dominant, are thermally and viscously unstable. However, observations show that the bright X-ray binaries and AGN accretion disks, corresponding to radiation-pressure thin disks, are stable. In this paper, we reconsider the linear and local instability of accretion disks in the presence of a toroidal magnetic field. In the basic equations, we consider physical quantities such as advection, thermal conduction, arbitrary viscosity, and an arbitrary cooling function also. A fifth order diffusion equation is obtained and is solved numerically. The solutions are compared to non-magnetic cases. The results show that the toroidal magnetic field can make the thermal instability in radiation pressure-dominated slim disks disappear if ϕ m ≥0.3. However, it causes a more thermal instability in radiation pressure alpha disks without advection. Also, we consider the thermal instability in accretion disks with other values of the viscosity and obtain a general criterion for thermal instability in the long-wavelength limit and in the presence of a toroidal magnetic field.

We explore the ability of a protostellar disc to fragment using an evolutionary disc model. Our disc model includes the mass influx from a molecular cloud core, the irradiation from the central star, the magnetorotational instability (MRI), and the gravitational instability (Kratter et al. in Astrophys. J. 681:375, 2008). We use the fragmentation criterion of Gammie (Astrophys. J. 553:174, 2001) and Rafikov (Astrophys. J. 621:L69, 2005) to judge whether or not a protostellar disc can fragment. We find that there is a link between whether a protostellar disc can fragment and the properties of the molecular cloud cores (angular velocity $\omega$ , temperature $T_{\mathrm{core}}$ , and mass $M_{\mathrm{core}}$ ). In the parameter space $\omega-M_{\mathrm{core}}$ , there is a critical value $\omega_{\mathrm{crit}}$ , which divides the parameter space into two regions: one is the fragmentation region, the other is the non-fragmentation region. The protostellar disc can only fragment when $\omega> \omega_{\mathrm{crit}}$ . The reason can be understood as follows. The protostellar disc is formed from the gravitational collapse of a molecular cloud core, the properties of the molecular cloud core determine the properties of the protostellar disc. Thus the two categories of protostellar discs correspond to two categories of molecular cloud cores. Moreover, we find that $\omega_{\mathrm{crit}}$ is approximately a linear function of $M_{\mathrm{core}}$ in log-scale coordinates.

On the basis of hydrodynamic equations and the new anomalous viscosity, we numerically calculate the steady state of geometrically thin accretion disk around a black hole, including surface density, temperature and radial velocity distribution. We found the density distribution, especially in the inner region, is greatly different from the one with conventional α-viscosity. The stability of the accretion disks with anomalous viscosity is also examined. The results show that the Outward–moving mode is unstable, and the viscous mode is stable throughout the disk. The instability of the Inward–moving mode depends on the wavelength. The results show that the prescription of viscosity has some influence on the stability properties of the disk.

2D numerical simulations of magnetorotational (MR) supernova mechanism are described. It is shown that magnetic field is amplified due to the differential rotation after core collapse. When magnetic pressure reaches some level, a compression wave starts to move outwards. Moving along steeply decreasing density profile the compression wave transforms quickly into fast MHD shock. The magnetorotational instability (MRI) was found in our simulations. MRI leads to the exponential growth of the components of the magnetic field. The MRI significantly reduces MR supernova explosion time. Configuration of the initial magnetic field qualitatively defines the shape of MR supernova explosion. For the quadrupole-like initial poloidal field the MR supernova explosion develops mainly along equatorial plane, the dipole-like initial field results in MR supernova developing as mildly collimated jet along axis of rotation. The explosion energy of MR supernova found in our simulations is ∼0.5–0.6×1051 erg.

MHD turbulence driven by magnetorotational instability (MRI) in accretion disks is investigated using the local shearing box calculations. The growth of many short-wavelength MRI modes, which are called “channel flows”, is found in the spatial distribution of the current density. These small channel flows can be regarded as a unit structure of MRI driven turbulence. Nonlinear evolution of the channel flow affects the saturation amplitude and time variability of the Maxwell stress. Exponential growth of a channel mode is stopped by the Kelvin-Helmholtz type instability which triggers the subsequent magnetic reconnection. The characteristics of the magnetic reconnection are consistent with the Sweet-Parker model. These studies of the nonlinear evolution of the channel flow are required to understand the saturation mechanism of the MRI.

In this contribution I review the main challenges for theory and numerical simulation of accretion turbulence in disks. I then present briefly a solution we have elaborated in recent years to a part of these questions: we have found an MHD instability which occurs in the inner region of a disk in the configuration (poloidal field of the order of equipartition with the gas pressure) used for MHD jet models. This instability has the unique characteristic that it re-emits toward the corona a fraction of the energy and angular momentum it extracts from the disk. It is a good candidate to explain the low-frequency Quasi-Periodic Oscillation observed in X-ray binaries, and we believe that it might occur also in YSO.

An accretion disk is an inevitable part of the star forming process. Recent years have witnessed dramatic progress in our understanding of how turbulence arises and transports angular momentum in astrophysical accretion disks. The key conceptual point is that the combination of a subthermal magnetic field and outwardly decreasing differential rotation is subject to the magnetorotational instability. This rapidly generates magnetohydrodynamical (MHD) turbulence, leading to greatly enhanced angular momentum transport. Purely hydrodynamic disks, on the other hand, are stable. Disks that are too cool to couple effectively to the magnetic field will not be turbulent. Fully global three dimensional MHD simulations are now beginning to probe the properties of accretion disks from first principles.

We present the first global simulations of self-gravitating magnetized tori. The simulations are performed with Zeus-2D and GLOBAL. We find the magnetorotational instability (MRI) to behave similarly in a self-gravitating environment as in previous simulations of non self-gravitating systems: enhancement of turbulent angular momentum transport follows the linear phase. The torus quickly develops a two component structure composed of an inner thick disk in Keplerian rotation and an outer massive disk. We compare this result with zero mass global simulations in 2D, and also present preliminary results of 3D simulations., Comment: 6 pages, 6 figures, kluwer.cls, To appear in the proceedings of "Magnetic fields and star formation: Theory versus observations", Madrid,April 21-25 2003

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 treated stratification and Hall conductivity. We present here a linear analysis of the MRI, including the Hall effect, in a stratified disc., Comment: 6 pages, 3 figures, latex, kluwer.cls. To appear in the proceedings of "Magnetic fields and star formation: Theory versus observations", Madrid, April 21-25 2003

We have constructed self-consistent temperature and density profiles of irradiated active protoplanetary disks, using a two-dimensional radiative transfer calculation. By means of these profiles we have studied the stabilization of the convective instability by radiative heating and the magnetorotational instability (MRI) via ohmic dissipation, taking into account the effect of dust particle growth. Simple chemistry such as ionization by cosmic rays and recombination on dust grains are used to calculate the ionization degree of gas in the disks. Our results show that the dust growth stabilizes the convective instability due to the 2D effect of radiative transfer, while it enhances the MRI through the decrease in the recombination of ions on the dust grains. In addition, the influences of the dust settling toward the midplane of the disks on the instabilities are discussed.

This is the first paper to consider the effects of both magnetic field and self-gravity on the pulsational instability. Our main new results are that the self-gravity enhances the instability of the magneto-acoustic mode in the outer disk strongly, and also affects the instability in the inner disk, but stabilized the viscous mode. The effect of self-gravity is much greater than that of magnetic field in the outer disk, while the effect of magnetic field on the instability is weaker than that in the previous work's (Wuet al., 1995; Yanget al., 1995), in which the self-gravity has not been considered. Finally, we discuss our results.

The oscillations and stability of a homogeneous self-gravitating rotating cylinder in a toroidal magnetic field are investigated. It is assumed that the field is proportional to the distance to the axis of the cylinder. We show the existence of four infinite discreta spectra of magnetic (or rotational) modes. Rotation stabilizes the magneticm=1 instability. The magnetic field decreases the growth rate of rotational instability and reduces the interval of unstable wavenumbers. Ifm=1, instability always occurs with the exception of the equipartition state. Ifm>1, the instability can be suppressed by a sufficiently large magnetic field. Resistivity decreases the growth rate of magnetic instability, but increases the growth rate of rotational instability. For zero wavenumber perturbations secular instability occurs due to the action of resistivity before a neutral point is attained where a second secular instabiliity initiates due to the action of resistivity.

The thermal-convective instability of a composite stellar atmosphere is considered in the presence of rotation, variable horizontal magnetic field, and collisional effects. The criteria for monotonic instability are obtained which generalize the criterion derived for thermal-convective instability in the absence of above effects.

The problem of contrastreaming instability in collisionless anisotropic plasmas is investigated both for electrostatic and electromagnetic perturbations propagatingalong the ambient magnetic field. Both electron-electron and ion-ion streams are considered. It is found that the electromagnetic instability may, under certain conditions, be characterised by larger growth rates than the electrostatic instability.