Simulation of accretion disks due to viscosity in semi-detached binary systems

A computation simulation of the motion of equilibrium particles in semi-detached binary systems is presented. We find that an accretion disk can be formed around the primary due to viscosity between moving particles. The calculated results are obtained for various factors and mass ratios. The results show that a part of the martter transferred from the secondary is accreted by the primary and the equilibrium mass transfer of moving particle depends on viscous factors and mass ratios.A part of the work has been performed during author's visit the Institute for Advanced Study, Princeton, N.J.     

Anomalous magnetic viscosity in accretion disks with q-distributed plasmas

Based on the equations of the self-generated magnetic field in the q-distributed plasmas, the studies show that the magnetic field is modulationally unstable by the perturbation method and the equations have self-similar collapse solution. The anomalous magnetic viscosity of accretion disks generates from highly spatially intermittent flux of the self-generated magnetic field. In addition, the anomalous viscosity coefficient is 8 orders more than the molecular viscosity and is modified by the adjustable index q, which may preferably explain the observations.     

The origin of Jovian and Saturnian satellites in accretion disks

The properties of gas-dust disks that surrounded Jupiter and Saturn during the final stage of their formation are analyzed. The sizes of the disks are determined by the total planetocentric angular momentum of the matter accreted by planets and correspond to the sizes of the orbits of their largest satellites. The mass of the solid component of disks is limited from below by the total mass of the Galilean satellites of Jupiter (no less than 4 × 10²⁶ g) and the mass of the largest Saturnian satellites (1.4 × 10²⁶ g), whereas the mass of the gaseous component is limited from above by the amount of hydrogen and helium that could have been later lost by the disks. Our analysis of the known mechanisms of dissipation of gas showed that its simultaneous content in the disks relative to the solid component was much lower than the corresponding gas-to-solid ratio in the Sun. A certain amount of solid compounds (including ice) could have been brought into the disks with planetesimals, which had undergone mutual collisions in the neighborhood of giant planets and served as germs of satellites. The bulk of solid matter appears to have been captured into disks when the latter were crossed by smaller and intermediate-sized planetesimals, which then became parts of the satellites.     

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.     

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)     

Thermomagnetic and magnetorotational instabilities of thin Keplerian discs in poloidal magnetic fields

Stability of thin hot Keplerian discs is investigated asymptotically in small disc's aspect ratio, ε. The study is carried out in the local approximation for short vertical waves in the disc‐thickness scale. Besides the radial rotation shear and the vertical magnetic field, the background configuration is characterized by a vertically near‐constant temperature profile with a small vertical gradient. The temperature‐gradient term in Ohm's law, which characterizes the thermomagnetic transport is found to be of the order of ε. The effect of the thermomagnetic transport slightly modifies the conventional magnetorotational instability (MRI), while a new thermomagnetic instability (TMI) emerges in regions of the wavenumber space where MRI is absent. Explicit solutions are obtained for a wide range of values of plasma beta, β, and thermomagnetic transport coefficient, λ. In particular, it is shown for λ ≪ 1 that the MRI dominates in weak magnetic fields, β ≫ 1, while the TMI is exhibited in strong magnetic fields, β ∼ 1, also with the growth rate of the order of inverse rotation period (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A magnetic scaleheight: the effect of toroidal magnetic fields on the thickness of accretion discs

We consider accreting systems in which the central object interacts, via the agency of its magnetic field, with the disc that surrounds it. The disc is turbulent and, so, has a finite effective conductivity. The field sweeps across the face of the disc, thereby forming a current that is directed radially within the disc. In turn, this disc current creates a toroidal field, where the interaction between the disc current and the toroidal field produces a Lorentz force that compresses the disc. We investigate this compression, which creates a magnetic scaleheight of the disc that can be much smaller than the conventional scaleheight. We derive an analytic expression for the magnetic scaleheight and apply it to fully ionized discs.     

Turbulent generation of magnetic fields in astrophysical jets

We consider evolution of the regular magnetic field in turbulent astrophysical jets. The observed lateral expansion of a jet is approximately described by a linear in coordinates regular velocity field (the Hubble flow). It is shown that in expanding turbulent jets with non-vanishing mean helicity of the turbulence temporal amplification and effective realignment of the regular magnetic field occurs with the field changing orientation from the transverse to the longitudinal one along the jet axis. The distance at which the realiggment occurs depends on parameters of the jet, in particular, on the power of the central source. Estimates for the jet in a weak source 3C 31 favourably agree with observations.     

Hall equilibrium of thin Keplerian discs embedded in mixed poloidal and toroidal magnetic fields

Axisymmetric steady-state weakly ionized Hall–magnetohydrodynamic (MHD) Keplerian thin discs are investigated by using asymptotic expansions in the small disc aspect ratio ε. The model incorporates the azimuthal and poloidal components of the magnetic fields in the leading order in ε. The disc structure is described by an appropriate Grad–Shafranov equation for the poloidal flux function ψ that involves two arbitrary functions of ψ for the toroidal and poloidal currents. The flux function is symmetric about the mid-plane and satisfies certain boundary conditions at the near-horizontal disc edges. The boundary conditions model the combined effect of the primordial as well as the dipole-like magnetic fields. An analytical solution for the Hall equilibrium is achieved by further expanding the relevant equations in an additional small parameter δ that is inversely proportional to the Hall parameter. It is thus found that the Hall equilibrium discs fall into two types: Keplerian discs with (i) small  ( R _d∼δ⁰)  and (ii) large  ( R _d≳δ^{− k} , k > 0)  radius of the disc. The numerical examples that are presented demonstrate the richness and great variety of magnetic and density configurations that may be achieved under the Hall–MHD equilibrium.     

Reorientation of global coronal magnetic fields due to differential rotation

Because of the progressive decrease in rotation rate of the solar plasma at increasing latitudes, the photospheric foot-points of large-scale closed magnetic structures in the corona, which are originally widely separated in longitude, may ultimately be brought into proximity. Magnetic mergers and reconnections between magnetic fields of opposite polarity are presumed to occur, producing major structural changes in the corona and in the locations of underlying filaments. Thus we believe that the differential rotation phenomenon is essential to understanding both gradual (evolutionary) and sudden (transient) changes in the corona, and that they can occur without any observable change in the photospheric magnetic flux. A process is suggested for the splitting or bifurcation of a high-latitude magnetic structure, producing two separate components at the same latitude, whose rotation rates are influenced by their respective magnetic linkages to other regions on the Sun.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The origin of the magnetic fields in white dwarfs

Magnetic white dwarfs with fields in excess of ∼10⁶ G (the high field magnetic white dwarfs; HFMWDs) constitute about ∼10 per cent of all white dwarfs and show a mass distribution with a mean mass of  ∼0.93 M_⊙  compared to  ∼0.56 M_⊙  for all white dwarfs. We investigate two possible explanations for these observations. First, that the initial–final mass relationship (IFMR) is influenced by the presence of a magnetic field and that the observed HFMWDs originate from stars on the main sequence that are recognized as magnetic (the chemically peculiar A and B stars). Secondly, that the IFMR is essentially unaffected by the presence of a magnetic field, and that the observed HFMWDs have progenitors that are not restricted to these groups of stars. Our calculations argue against the former hypothesis and support the latter. The HFMWDs have a higher than average mass because on the average they have more massive progenitors and not because the IFMR is significantly affected by the magnetic field. A requirement of our model is that ∼40 per cent of main-sequence stars more massive than  ∼4.5 M_⊙  must either have magnetic fields in the range of ∼10–100 G, which is below the current level of detection, or generate fields during subsequent stellar evolution towards the white dwarf phase. In the former case, the magnetic fields of the HFMWDs could be fossil remnants from the main-sequence phase consistent with the approximate magnetic flux conservation.     

A possible example of giant convective cells delineated by magnetic fields

A remarkable north-south pattern of symmetry in the location of filaments on 11 June, 1972 together with an analysis of surface magnetic field harmonics by Altschuler et al. (1974) is offered as evidence for the existence of giant convective cells. Both data suggest a longitudinal wave number of 5, a value which seems to exclude this symmetry being due to effects of a solar -dynamo. The lifetime of these cells was about 2–4 months. This was apparently the only instance from 1959 to 1973 of such cells being manifested in magnetic field patterns which were evident by harmonic analyses or by filament inspections.     

Evolutionary processes in protoplanetary accretion disks: the propagation of axisymmetric shock waves

In this paper we investigate both the global and the local hydrodynamics of axisymmetric accretion disks around young stellar objects under the simultaneous action of viscosity, self-gravity and pressure forces. For simplicity, we take for the global model a polytropic equation of state, make the infinitely thin disk approximation and characterize the surface density and temperature profiles in the disk as power laws in the radial distance r from the protostar. We solve the problem of the general density profile of a Keplerian disk showing that self-gravity could not be an important factor for the fast formation of the rocky cores of giant gaseous planets in our solar system. Under the hypothesis that the unperturbed rotation curve of the disk is nearly Keplerian throughout the radial extent, we can estimate with our polytropic model a lower limit for the resulting masses M_d(r) of stable disks up to 100 AU. These masses are in the range of the so-called minimum mass solar nebular (_d/M_s ≈ 0.01–0.02).By adopting a simplified viscosity model, where the height-integrated turbulent dynamical viscosity ν is a function of the surface density σ like η ∝ σ^Γ, we derive in the local shearing sheet model linearized evolution equations for small density perturbations describing both a diffusion process and the propagation of acoustic density waves. We solve a special initial value problem and calculate the appropriate Green's function. The analytical solutions so obtained describe in the case Γ < 0 the successive formation of quasi-stationary ring-shaped density structures in a disk with a definite mode of maximum instability, whereas in the case Γ > Γ_c the density wave equation describes the propagation of an “overstable” ring-shaped acoustic density wavelet to the outer ranges of the accretion disk. Whereas the group velocity of the wave packet is subsonic, the phase velocities of individual wave crests in the wave packet are supersonic. The mode of maximum instability, the growth rate and the number of growing waves in the wavelet are controlled by Γ and α. Our present knowledge concerning turbulent viscosity in protoplanetary disks is not sufficient to decide whether or not the case Γ > Γ_c is realized.The suggested structuring processes in the linear theory should initiate in the non-linear regime the formation of narrow ring-shaped density shock waves moving through the protoplanetary disk. These non-linear waves could produce extremely spatially and temporally heterogeneous temperature regions in the disk. We speculate that ring-shaped density waves, excited by inner boundary conditions and which have dominated the disk's evolution at early times, are responsible both for the fast growth of dust to planetesimals and at least for the rapid accretion of the rocky cores of giant gaseous planets in the protoplanetary accretion disk (shock wave trigger hypothesis). We derive provisional scaling rules for planetary systems regarding the spacing of orbits as a function of the mass ratio of the protoplanetary disk to the protostar. However, further analytical work and linear as well as nonlinear numerical simulations of density waves excited by inner boundary conditions are needed to consolidate the results and speculations of our linear wave mechanics in the future.     

Mass loss from the inner regions of accretion discs due to centrifugally driven magnetic wind flows

Wind flows and collimated jets are believed to be a feature of a range of disc accreting systems. These include active galactic nuclei, T Tauri stars, X-ray binaries and cataclysmic variables. The observed collimation implies large-scale magnetic fields and it is known that dipole-symmetry fields of sufficient strength can channel wind flows emanating from the surfaces of a disc. The disc inflow leads to the bending of the poloidal magnetic field lines, and centrifugally driven magnetic winds can be launched when the bending exceeds a critical value. Such winds can result in angular momentum transport at least as effective as turbulent viscosity, and hence they can play a major part in driving the disc inflow.
It is shown here that if the standard boundary condition of vanishing viscous stress close to the stellar surface is applied, together with the standard connection between viscosity and magnetic diffusivity, then poloidal magnetic field bending increases as the star is approached with a corresponding increase in the wind mass loss rate. A significant amount of material can be lost from the system via the enhanced wind from a narrow region close to the stellar surface. This occurs for a Keplerian angular velocity distribution and for a modified form of angular velocity, which allows for matching of the disc and stellar rotation rates through a boundary layer above the stellar surface. The enhanced mass loss is significantly affected by the behaviour of the disc angular velocity as the stellar surface is approached, and hence by the stellar rotation rate. Such a mechanism may be related to the production of jets from the inner regions of disc accreting systems.     

Charged particle transport in turbulent magnetic fields: The perpendicular diffusion coefficient

The diffusion of charged particles in a static turbulent magnetic field, which is superimposed on a constant magnetic fieldB ₀ k, is considered. Previous calculations of the particle flux in a direction perpendicular tok have related the fluxS to the particle number densityf byS = – (f) where is found from the power spectrum of the turbulent magnetic field. It is shown that this formula is inconsistent with the notion, developed by Jokipii and Parker (1969), that the perpendicular particle flux primarily arises because of random-walking of magnetic field lines across the directionk. For a simple example of a turbulent magnetic field it is shown that the above expression forS is incorrect; the particle fluxS is recalculated and a new relationship betweenS andf is found. This new expression forS is shown to be consistent with particle diffusion across the directionk being due to random-walking of the magnetic field lines.     

The appearance of polarization in radiation from hot stars due to the faraday rotation effect as a possible method of determining stellar magnetic fields

The effect of Faraday rotation is shown to lead to the appearance of linear polarization of stellar radiation scattered in an optically-thin circumstellar electron-magnetized shell, even in the case when the shell is spherical. The spectral dependence of the polarization degree is evaluated for scattering in (i) a spherically-symmetric magnetized shell with a power-law radial dependence of the electron density, and (ii) a non-spherical ellipsoidal uniform envelope. The position of maximum in the polarization spectrum permits us to determine the magnetic field magnitude on a star surface. If the rotational and magnetic axes do not coincide, the periodic variability of the polarization will be observed with the period of stellar rotation. Some Be-stars, such as Cas, 48 Lib, EW Lac, Aqr, HD 45677, X Per, are proposed as candidates to be investigated for magnetic fields, as well as some stars of the T Tau-type. This method may be also applied to supernovae shells.