Zones of anomalous activity of the magnetorotational instability in protostellar disks

A criterion for the magnetorotational instability of a protostellar disk in which the dust particles are assumed to be well mixed with the gas over the entire disk volume has been obtained within the framework of Hall magnetohydrodynamics. It is shown that the dusty plasma component affects significantly the Hall current and, under certain conditions, can cause its direction to be reversed compared to the case of a weakly ionized electron-ion plasma. A significant expansion of the range of wave numbers for unstable magnetic fluctuations is a consequence of the Hall current reversal. The spatial localization of the regions of protostellar disks in which not only the long-wavelength Alfvén disturbances but also the short-wavelength ones are subject to the magnetorotational instability is investigated. Possible physical consequences of the presence of anomalously active zones in cold disks for their structure and evolution are pointed out.     

On the first generation of stars

We argue that the first stars may have spanned the conventional mass range rather than be identified with the very massive objects  (∼100–10³ M_⊙)  favoured by numerical simulations. Specifically, we find that magnetic field generation processes acting in the first protostellar systems suffice to produce fields that exceed the threshold for magneto-rotational instability (MRI) to operate, and thereby allow the MRI dynamo to generate equipartition-amplitude magnetic fields on protostellar mass scales below  ∼50 M_⊙  . Such fields allow primordial star formation to occur at essentially any metallicity by regulating angular momentum transfer, fragmentation, accretion and feedback in much the same way as occurs in conventional molecular clouds.     

Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. We present the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. The disks are represented by a distribution of about 6 × 10⁴ point masses on a two-dimensional (r, φ) grid. The motions of the particles in the self-consistent gravity field are calculated, and the evolving density distributions are examined for instabilities. Two parameters that have major influences on stability are varied: the initial temperature of the disk (represented by an imposed velocity dispersion), and the mass of the protostar relative to that of the disk. It is found that a disk as massive as 1M_⊙, surrounding a 1M_⊙ protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300°K or greater. Stability of a cooler disk requires that it be less massive, but even at 100°K a stable disk can have an appreciable fraction ($\text{～}\text{1}\text{3}$) of a solar mass.     

On the formation of protostellar disks

An analysis is presented of the hydrodynamic aspects of the growth of protostellar disks from the accretion (or collapse) of a rotating gas cloud. The size, mass, and radiative properties of protostellar disks are determined by the distribution of mass and angular momentum in the clouds from which they are formed, as well as from the dissipative processes within the disks themselves. The angular momentum of the infalling cloud is redistributed by the action of turbulent viscosity on a shear layer near the surface of the disk (downstream of the accretion shock) and on the radial shear across cylindrical surfaces parallel to the rotation axis. The fraction of gas that is fed into a central core (protostar) during accretion depends on the ratio of the rate of viscous diffusion of angular momentum to the accretion rate; rapid viscous diffusion (or a low accretion rate) promotes a large core-to-disk mass ratio. The continuum radiation spectrum of a highly viscous disk is similar to that of a steady-state accretion disk without mass addition. It is possible to construct models of the primitive solar nebula as an accretion disk, formed by the collapse of a slowly rotating protostellar cloud, and containing the minimum mass required to account for the planets. Other models with more massive disks are also possible.     

The role of toroidal magnetic field in the stability of accretion disks with alpha viscosity and other viscosities

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 ? _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.     

Galactic dynamos and galactic winds

Spiral galaxies host dynamically important magnetic fields which can affect gas flows in the disks and halos. Total magnetic fields in spiral galaxies are strongest (up to 30 μG) in the spiral arms where they are mostly turbulent or tangled. Polarized synchrotron emission shows that the resolved regular fields are generally strongest in the interarm regions (up to 15 μG). Faraday rotation measures of radio polarization vectors in the disks of several spiral galaxies reveal large-scale patterns which are signatures of coherent fields generated by a mean-field dynamo. Magnetic fields are also observed in radio halos around edge-on galaxies at heights of a few kpc above the disk. Cosmic-ray driven galactic winds transport gas and magnetic fields from the disk into the halo. The halo scale height and the electron lifetime allow to estimate the wind speed. The magnetic energy density is larger than the thermal energy density, but smaller than the kinetic energy density of the outflow. There is no observation yet of a halo with a large-scale coherent dynamo pattern. A global wind outflow may prevent the operation of a dynamo in the halo. Halo regions with high degrees of radio polarization at very large distances from the disk are excellent tracers of interaction between galaxies or ram pressure of the intergalactic medium. The observed extent of radio halos is limited by energy losses of the cosmic-ray electrons. Future low-frequency radio telescopes like LOFAR and the SKA will allow to trace halo outflows and their interaction with the intergalactic medium to much larger distances.     

Accretion disk instabilities

Basic properties of accretion disk instabilities are summarized. We first explain the standard disk model by Shakura and Sunyaev. In this model, the dominant sources of viscosity are assumed to be chaotic magnetic fields and turbulence in gas flow, and the magnitude of viscosity is prescribed by so-called model. It is then possible to build a particular disk model. In the framework of the standard model, accretion disks are stationary, but when some of the basic assumptions are relaxed, various kinds of instabilities appear. In particular, we focus on the thermal limit-cycle instability caused by partial ionization of hydrogen (and helium). We demonstrate that the disk instability model well accounts for the basic observed features of outbursts of dwarf novae and X-ray nova. We then introduce other kinds of instabilities based on the viscosity model. They are suspected to produce time variabilities observed on a wide range of timescales in close binaries and active galactic nuclei.     

Mechanisms of the vertical secular heating of a stellar disk

We investigate the nonlinear growth stages of the bending instability in stellar disks with exponential radial density profiles. We found that the unstable modes are global (the wavelengths are larger than the disk scale lengths) and that the instability saturation level is much higher than that following from a linear criterion. The instability saturation time scales are of the order of one billion years or more. For this reason, the bending instability can play an important role in the secular heating of a stellar disk in the z direction. In an extensive series of numerical N-body simulations with a high spatial resolution, we were able to scan in detail the space of key parameters (the initial disk thickness z₀, the Toomre parameter Q, and the ratio of dark halo mass to disk mass M_h/M_d). We revealed three distinct mechanisms of disk heating in the z direction: bending instability of the entire disk, bending instability of the bar, and heating on vertical inhomogeneities in the distribution of stellar matter.     

Bending instability of stellar disks: The stabilizing effect of a compact bulge

The saturation conditions for bending modes in inhomogeneous thin stellar disks that follow from an analysis of the dispersion relation are compared with those derived from N-body simulations. In the central regions of inhomogeneous disks, the reserve of disk strength against the growth of bending instability is smaller than that for a homogeneous layer. The spheroidal component (a dark halo, a bulge) is shown to have a stabilizing effect. The latter turns out to depend not only on the total mass of the spherical component, but also on the degree of mass concentration toward the center. We conclude that the presence of a compact (not necessarily massive) bulge in spiral galaxies may prove to be enough to suppress the bending perturbations that increase the disk thickness. This conclusion is corroborated by our N-body simulations in which we simulated the evolution of near-equilibrium, but unstable finite-thickness disks in the presence of spheroidal components. The final disk thickness at the same total mass of the spherical component (dark halo + bulge) was found to be much smaller than that in the simulations where a concentrated bulge is present.     

Observations of disks around protostellar sources with nobeyama millimeter array

We present results from a survey observation of circumstellar disks around protostellar sources associated with the Taurus molecular cloud. Our result shows that the 98 GHz continuum emission tends to be weaker for embedded sources than for visible T Tauri stars, which is consistent with our previous interpretation of disk formation. Direct observations of the formation of a centrifugally supported viscous accretion disk around HL Tau is discussed.     

Magnetic fields in protoplanetary disks

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary disks. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface. Magnetically-driven mixing has implications for disk chemistry and evolution of the grain population, and the effective viscous response of the disk determines whether planets migrate inwards or outwards. However, the weak ionisation of protoplanetary disks means that magnetic fields may not be able to effectively couple to the matter. I examine the magnetic diffusivity in a minimum solar nebula model and present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas, except at the disk surfaces where the low density of neutrals permits the ions to remain attached to the field lines. For a standard population of 0.1 μm grains the active surface layers have a combined column Σ_active≈2 g cm⁻² at 1 AU; by the time grains have aggregated to 3 μm, Σ_active≈80 g cm⁻². Ionisation in the active layers is dominated by stellar X-rays. In the absence of grains, X-rays maintain magnetic coupling to 10% of the disk material at 1 AU (i.e. Σ_active≈150 g cm⁻²). At 5 AU the Σ_active≈Σ_total once grains have aggregated to 1 μm in size.     

Nonaxisymmetric instabilities in self-gravitating disks. II. Linear and quasi-linear analyses

We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary systems. We examined equilibrium disk models varying three parameters: the ratio of the inner to outer equatorial radii, the ratio of star mass to disk mass, and the rotation law exponent q. We took the polytropic index n=1.5 and examined the exponents q=1.5 and 2, and the transitional one q=1.75. For each of these sets of parameters, we examined models with inner to outer radius ratios from 0.1 to 0.75, and star mass to disk mass ratios from 0 to 10³. We numerically calculated the growth rates and oscillation frequencies of low-order nonaxisymmetric disk modes, modes with azimuthal dependence ∝e ^im? . Low-m modes are found to dominate with the character and strength of instability strongly dependent on disk self-gravity. Representatives of each mode type are examined in detail, and torques and mass transport rates are calculated.     

Turbulence in Accretion Disks

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.     

Jets from young stars

Most stars produce spectacular jets during their formation. There are thousands of young stars within 500 pc of the Sun and many power jets. Thus protostellar jets may be the most common type of collimated astrophysical outflow. Shocks powered by outflows excite many emission lines, exhibit a rich variety of structure, and motions with velocities ranging from 50 to over 500 km s⁻¹. Due to their relative proximity, proper motions and structural changes can be observed in less than a year. I review the general properties of protostellar jets, summarize some results from recent narrow-band imaging surveys of entire clouds, discuss irradiated jets, and end with some comments concerning outflows from high-mass young stellar objects. Protostellar outflows are ideal laboratories for the exploration of the jet physics.     

Evolution of protoplanetary discs driven by the MRI, self-gravity and hydrodynamical turbulence

We study the viscous evolution of protoplanetary discs driven by the combined action of magnetohydrodynamic turbulence, resulting from the magneto-rotational instability (MRI), self-gravity torques, parametrized in terms of an effective viscosity and an additional viscous agent of unspecified origin. The distribution of torques driving the evolution of the disc is calculated by analysing where in the disc the MRI develops and, to incorporate the effect of self-gravity, calculating the Toomre parameter. We find that, generally, discs rapidly evolve towards a configuration where the intermediate regions, from a fraction of an au to a few au, are stable against the MRI due to their low-ionization degree. As an additional source of viscosity is assumed to operate in those regions, subsequent evolution of the disc is eruptive. Brief episodes of high mass accretion ensue as the criterion for the development of the MRI is met in the low-ionization region. The radial distribution of mass and temperature in the disc differs considerably from disc models with constant α parameter or layered accretion models, with potentially important consequences on the process of planet formation.     

The interstellar chemistry of protostellar disks

A study has been undertaken of the gas-grain chemistry of protostellar disks which are sufficiently cool that in the outer regions, where the gas density is less than 10¹³ cm^–3 and the ionization rate highest, a bimolecular chemistry resembling that of dark clouds can occur. Since the gas-grain collision rate is so high, outgassing mantle molecules effectively determine the gas phase composition at any position in the disk. In contrast to previous work, a detailed gas phase chemistry is considered along with the accretion and desorption of mantle species which is controlled locally by the dust temperature.     

Magnetic fields of accretion disks and outflows in prograde and retrograde black holes

We show that for the accretion disk with equipartition between magnetic and radiative pressures, prograde black holes generate outflowing energy in jets more efficiently than retrograde black holes do. Both viscous radiative and irradiative disks provide more efficient outflow jets in the case of a prograde black hole than in the case of a retrograde black hole. Our results confirm the conclusion of Tchekhovskoy & McKinney (2012) that, for the same absolute value of the spin, prograde black holes with geometrically thick accretion disks generate outflows several times more efficiently than retrograde black holes do. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)