The radial disc structure around a magnetic neutron star: analytic and semi-analytic solutions

The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10⁴ stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfvén radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque.     

Magnetically moderated outbursts of WZ Sagittae

We argue that the quiescent value of the viscosity parameter of the accretion disc in WZ Sge may be  α_cold∼ 0.01  , in agreement with estimates of α_cold for other dwarf novae. Assuming the white dwarf in WZ Sge to be magnetic, we show that, in quiescence, material close to the white dwarf can be propelled to larger radii, depleting the inner accretion disc. The propeller therefore has the effect of stabilizing the inner disc and allowing the outer disc to accumulate mass. The outbursts of WZ Sge are then regulated by the (magnetically determined) evolution of the surface density of the outer disc at a radius close to the tidal limit. Numerical models confirm that the recurrence time can be significantly extended in this way. The outbursts are expected to be superoutbursts since the outer disc radius is forced to exceed the tidal (3:1 resonance) radius. The large, quiescent disc is expected to be massive, and to be able to supply the observed mass accretion rate during outburst. We predict that the long-term spin evolution of the white dwarf spin will involve a long cycle of spin-up and spin-down phases.     

An accretion disc model with a magnetic wind and turbulent viscosity

A model is presented for an accretion disc with turbulent viscosity and a magnetically influenced wind. The magnetic field is generated by a dynamo in the disc, involving the turbulence and radial shear. Disc-wind solutions are found for which the wind mass flux is sufficient to play a major part in driving an imposed steady inflow, but small enough for most material to be accreted on to the central object. Constraints arise for the magnetic Reynolds and Prandtl numbers in terms of the turbulent Mach number and vertical length-scale of the disc's horizontal magnetic field. It is shown that the imposition of a stellar boundary condition enhances the wind mass flux in the very inner region of the disc and may result in jet formation.     

Disc structure around strongly magnetic accretors: a full disc solution with turbulent diffusivity

The problem of the effect of a strongly magnetic star on a surrounding accretion disc is considered. For stellar rotation periods greater than a critical value, a numerical solution is found for a steady disc with turbulent magnetic diffusion, including electron scattering opacity and radiation pressure. Inside the corotation radius, the extraction of disc angular momentum by magnetic coupling to the star becomes strong and this leads to enhanced viscous stress and dissipation. The resulting elevated temperature causes electron scattering opacity and radiation pressure to become significant further from the star than in the absence of its magnetic field. The disc ends as its height increases rapidly due to the large central pressure, its density decreases and magnetically induced viscous instability occurs.     

A semi-analytic solution for the radial and vertical structure of accretion discs with a magnetic wind

A semi-analytic method is presented for solving for the radial and vertical structures of an accretion disc, with a magnetically channelled wind flowing from its surfaces. Both magnetic and turbulent viscous effects are taken into account, and the essential wind properties are related to the disc structure. The angular momentum removed by the wind plays a major part in driving the inflow through the disc, with photospheric temperatures being sufficient to generate the required wind mass flux. The magnetic field is generated by an αω-dynamo, but the method of solution should have application with other magnetic field sources. Self-consistent disc-wind solutions result, with rms turbulent Mach numbers which are in good agreement with those found in simulations of turbulence generated from magnetic shearing instabilities.     

Magnetic field bending in accretion discs with dynamos

We consider the problem of poloidal magnetic field advection and bending of an initially vertical field owing to radial inflow in thin accretion discs. For a ratio of kinematic viscosity to magnetic diffusivity of order unity, significant bending of an externally applied vertical field cannot occur in a disc with no internal dynamo. However, we show that if poloidal field is generated by a dynamo operating near its critical state, then significant field bending may be possible. Our results are of particular relevance to wind launching from accretion discs.     

Motion of charged particles in the magnetosphere

The adiabatic motion of charged particles in the magnetosphere has been investigated using Mead-Fairfield magnetospheric field model (Mead and Fairfield, 1975). Since the motion of charged particles in a dipolar field geometry is well understood, we bring out in this paper some important features in characteristic motion due to non-dipolar distortions in the field geometry. We look at the tilt averaged picture of the field configuration and estimate theoretically the parameters like bounce period, longitudinal invariant and the bounce averaged drift velocities of the charged particle in the Mead-Fairfield field geometry. These parameters are evaluated as a function of pitch angle and azimuthal position in the region of ring current (5 to 7 Earth radii from the centre of the Earth) for four ranges of magnetic activity. At different longitudes the non-dipolar contribution as a percentage of dipole value in bounce period and longitudinal invariant show maximum variation for particles close to 90° pitch angles. For any low pitch angle, these effects maximize at the midnight meridian. The radial component of the bounce averaged drift velocity is found to be greatest at the dawn-dusk meridians and the contribution vanishes at the day and midnight meridians for all pitch angles. In the absence of tilt-dependent terms in the model, the latitudinal component of the drift velocity vanishes. On the other hand, the relative non-dipolar contribution to bounce averaged azimuthal drift velocity is very high as compared to similar contribution in other characteristic parameters of particle motion. It is also shown that non-dipolar contribution in bounce period, longitudinal invariant and bounce averaged drift velocities increases in magnitude with increase in distance and magnetic activity.     

A comparison of DA white dwarf temperatures and gravities from Lyman and Balmer line studies

The stability of turbulent accretion discs is considered, in which a magnetically influenced wind plays a major role in driving the inflow. The magnetic field is generated by a dynamo operating in the disc, involving radial shear and turbulence. The steady angular momentum balance is found to be linearly stable for a range of radial boundary conditions, and an expression is derived for the adjustment time-scale as a function of the equilibrium ratio of the magnetic and viscous disc torques.     

Magnetic field dragging and the vertical structure of thin accretion discs

The presence of an imposed vertical magnetic field may drastically influence the structure of thin accretion discs. If the field is sufficiently strong, the rotation law can depart from the Keplerian one. We consider the structure of a disc for a given eddy magnetic diffusivity but neglect details of the energy transport. The magnetic field is assumed to be in balance with the internal energy of the accretion flow. The thickness of the disc as well as the turbulent magnetic Prandtl number and the viscosity, α , are the key parameters of our model. The calculations show that the radial velocity can reach the sound speed for a magnetic disc if the thickness is comparable to that of a non-magnetic one. This leads to a strong amplification of the accretion rate for a given surface density. The inclination angle of the magnetic field lines can exceed the critical value 30° (required to launch cold jets) even for a relatively small magnetic Prandtl number of order unity. The toroidal magnetic fields induced at the disc surface are smaller than predicted in previous studies.     

The fate of sub-micron circumplanetary dust grains I: Aligned dipolar magnetic fields

We study the stability of charged dust grains orbiting a planet and subject to gravity and the electromagnetic force. Our numerical models cover a broad range of launch distances from the planetary surface to beyond synchronous orbit, and the full range of charge-to-mass ratios from ions to rocks. Treating the spinning planetary magnetic field as an aligned dipole, we map regions of radial and vertical instability where dust grains are driven to escape or crash into the planet. We derive the boundaries between stable and unstable trajectories analytically, and apply our models to Jupiter, Saturn and the Earth, whose magnetic fields are reasonably well represented by aligned dipoles.     

High Energy Emissions from Young Stellar Objects

X-ray emissions from Young Stellar Objects (YSO) are detected by many X-ray missions that are providing important information about their properties. However, their emission processes are not fully understood. In this research note, we propose a model for the generation of emissions from a YSO on the basis of a simple interaction between the YSO and its surrounding circumstellar accretion disc containing neutral gas and charged dust. It is assumed that the YSO has a weak dipole type magnetic field and its field lines are threaded into the circumstellar disc. Considering the motion of ions and charged dust particles in the presence of neutral gas, we show that the sheared dust-neutral gas velocities can lead to a current along the direction of ambient magnetic field. Magnitude of this current can become large and is capable of generating an electric field along the magnetic field lines. It is shown how the particles can gain energy up to MeV range and above, which can produce high-energy radiations from the YSO.     

Acceleration of particles by black hole with gravitomagnetic charge immersed in magnetic field

The collision of test charged particles in the vicinity of an event horizon of a weakly magnetized non-rotating black hole with gravitomagnetic charge has been studied. The presence of the external magnetic field decreases the innermost stable circular orbits (ISCO) radii of charged particles. The opposite mechanism occurs when there is nonvanishing gravitomagnetic charge. For a collision of charged particle moving at ISCO and the neutral particle falling from infinity the maximal collision energy can be decreased by gravitomagnetic charge in the presence of external asymptotically uniform magnetic field.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized 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 is assumed to be 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 and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

An analytic model for disc disruption by strong stellar magnetic fields

An analytic model is presented for the inner structure of an accretion disc in the presence of a strong stellar magnetic field. The model is valid inside the radius at which the electron scattering opacity starts to exceed the Kramers opacity. It illustrates how the increasing stellar poloidal field leads to an elevated disc temperature, ultimately causing a breakdown in the vertical equilibrium owing to rapidly increasing radiation pressure which cannot be balanced by the vertical stellar gravity. Viscous instability also occurs. The solution gives an accurate representation of numerical results, and enables useful expressions to be derived for the radius at which the disc is marginally thin and the radius at which viscous instability occurs. The disruption mechanism appears to have general validity for accretion discs around strongly magnetic stars.     

Sweeping-out of dust from spiral galaxy as a result of “magnetic sling” effect

A new mechanism of sweeping out of dust grains beyond galactic disks both in the radial direction along the galactic plane and in the vertical, cross-disk direction is proposed. The mechanism is driven by the interaction of dust grains with the bisymmetric nonstationary magnetic field of the galaxy, whose lines are curved and corotate with the stellar spiral density wave responsible for the arms. We attribute the radial transfer of interstellar dust grains in the plane of galactic disks to the fact that charged dust grains are “glued” to magnetic field lines and are therefore pushed outward because of the rotation of magnetic field lines and their tilt with respect to the radial direction parallel to the disk plane. In addition, dust is swept out vertically in the cross-disk direction because of the drift motion in crossed magnetic and gravitational fields (both are parallel to the galactic plane). Numerical computations of the motion of dust grains in real magneto-gravitational fields with the allowance for the drag force from interstellar gas show that the time scale of dust grain transport beyond galactic disks is on the order of 1 Gyr or shorter.     

Magnetic torques between accretion discs and stars

I show in this paper that two types of magnetic torques can appear in the interaction between an accretion disc and a magnetic accretor. There is the well-known torque resulting from the difference in angular velocity between the accretion disc and the star, but in addition there is a torque coming from the interaction between the stellar magnetic field and the disc's own magnetic field. The latter form of magnetic torque decreases in strength more slowly with increasing radius, and will therefore dominate at large radii. The direction of the disc field is not determined by the difference in angular velocity between the star and the disc as in the Ghosh &38; Lamb model, but rather is a free parameter. The magnetic torque may therefore either spin up or spin down the star, and the torque changes sign if the magnetic field in the disc reverses. I suggest that this mechanism can explain the torque reversals that have been observed in some disc-fed X-ray pulsars.     

The role of induced charges in the accretion of charged dust grains

The electrostatic interaction of charged dust grains is analysed by considering the interaction of two charged conducting spheres, rather than the hitherto considered model of a sphere and a point charge. Considerable mofification of the induced charge effects results when the nonzero radius of the second sphere is taken into account.In particular, it is shown that image charge or polarization effects can only be of significance as far as collision rates are concerned when modulus of the charge ratio of two colliding grains is very different from the ratio of their radii. Such a charge ratio deviates from the original Spitzer calculation, where grains have identical charge, irrespective of the grain material, for a given radius. This deviation may occur in cool gas clouds such as Hi regions and dense molecular clouds where the discreteness of electron charge is important, or in interstellar clouds where considerable photo-ionization of a mixture of grain materials of widely varying photoelectric efficiencies takes place.It is further argued that, with regard to the induced charge effects, the accretion rate will not be significantly different for dielectric as compared to conducting grains, regardless of the type of gas cloud under consideration.     

A model for the formation of spokes in Saturn's ring

We suggest that spokes consist of charged micron-sized dust particles elevated from the rings by radially moving dense plasma columns created by meteor impacts on the ring. Dense plasma causes electrostatic wall-sheaths at the ring and charging of the ring with electric fields strong enough to overcome the gravitational force on small dust particles. Under “ordinary” conditions only very few dust particles will be elevated as the probability of a dust particle having at least one excess electronic charge is very low. Dense plasma raises this probability significantly. The radial motion of the plasma column is due to an azimuthal polarization electric field built up by the relative motion between the corotating plasma and the negatively charged dust particles which move with a Keplerian speed.