Launching of accretion disc winds along dynamo-generated magnetic fields

The problem of magnetic field generation and advection in accretion discs is considered, in the context of wind launching and angular momentum extraction. A dipole-symmetry solution of the dynamo equations is found, with force-free boundary conditions appropriate for matching to a wind solution. Consideration of the curved field geometry and diffusive nature of the disc enables the position of the sonic point to be calculated and related to the field inclination at the disc surface. A critical inclination of 20° to the horizontal results, for which the sonic point lies in the disc surface and there is no potential barrier to wind launching. Hence the wind mass-loss rate will only become excessive, leading to disc disruption, for large field bending. The compressional effect of the horizontal magnetic field enhances the wind mass flux.     

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.     

The influence of magnetic fields on neutrino-dominated accretion disc

We consider the influence of magnetic fields on the model of neutrino-dominated accretion flows (NDAFs) for gamma-ray bursts (GRBs) via the assumption that the accretion rate of the disc is totally caused by the torque of the Lorentz force, i.e. the magnetic braking of large-scale magnetic fields and magnetic viscosity of small-scale magnetic fields. We calculate the structure, composition, luminosity of neutrino emission and the Poynting flux, and the rate of mass loss driven by neutrino heating or launched centrifugally by large-scale magnetic fields, based on the physical condition of the magnetized NDAFs. It is shown that the magnetized disc is favourable to interpret the diverse prompt emissions as well as the X-ray flares observed in the early afterglow of GRBs.     

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.     

Long-term nonlinear behaviour of the magnetorotational instability in a localized model of an accretion disc

For more than a decade, the so-called shearing-box model has been used to study the fundamental local dynamics of accretion discs. This approach has proved to be very useful because it allows high-resolution and long-term studies to be carried out, studies that would not be possible for a global disc.
Localized disc studies have largely focused on examining the rate of enhanced transport of angular momentum, essentially a sum of the Reynolds and Maxwell stresses. The dominant radial–azimuthal component of this stress tensor is, in the classic Shakura–Sunyaev model, expressed as a constant α times the pressure. Previous studies have estimated α based on a modest number of orbital times. Here we use much longer baselines, and perform a cumulative average for α. Great care must be exercised when trying to extract numerical α values from simulations: dissipation scales, computational box aspect ratio, and even numerical algorithms can all affect the result. This study suggests that estimating α becomes more, not less, difficult as computational power increases.     

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.     

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.     

The stability of accretion discs with inflow driven purely by magnetic winds

A model is presented for an accretion disc in which the inflow is driven purely by the angular momentum removed in a centrifugally accelerated magnetic wind. Turbulent discs around compact stars are considered, with the required magnetic field being generated in the disc by a simple dynamo. The turbulent magnetic Prandtl number, N _p, measures the ratio of turbulent viscosity to turbulent magnetic diffusivity. Formally, the hypothetical limit   N _p→ 0  corresponds to the magnetic wind torque dominating the viscous torque, but in practice the inflow is magnetically controlled for   N _p≲ 0.1  .
The suggestion by previous authors that purely magnetic wind-driven discs may be unstable is investigated. A detailed steady solution is found which allows perturbations to the thermal balance and vertical equilibrium to be calculated, and hence the effect of perturbations to the magnetic diffusivity, η, to be assessed. For a standard parametrized form of η, the wind-driven angular momentum balance is found to be linearly unstable. An increase in the inflow rate leads to increased bending of the poloidal magnetic field and an enhanced wind mass loss rate. This increases the angular momentum loss rate which drives further inflow. There is a resultant increase in η, due to the temperature perturbation, but this does not relieve field bending sufficiently to prevent the instability.     

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.     

Accretion disc viscosity: how big is alpha?

We consider observational and theoretical estimates of the accretion disc viscosity parameter α. We find that in thin, fully ionized discs, the best observational evidence suggests a typical range α∼ 0.1–0.4, whereas the relevant numerical simulations tend to derive estimates for α which are an order of magnitude smaller. We discuss possible reasons for this apparent discrepancy.     

Global structure of self-excited magnetic fields arising from the magnetic shear instability

The global structure of a self-excited magnetic field arising from the magnetic shear instability has been simulated in spherical geometry by a 3D fully non-linear approach. In order to model the structure of an accretion disc we prescribe a rotation profile of the Brandt type which is Keplerian in the outer regions but yields rigid rotation at the inner core. We performed a whole series of runs at different dynamo numbers with an increasing number of modes in spectral space, thereby checking the influence of the numerical resolution in our simulations. Starting from arbitrary small perturbations, the magnetic and kinetic energies grow by several orders of magnitude as soon as a certain azimuthal resolution of at least m =15 was used at a dynamo number of order C =10⁵. Several phases of the transition to turbulence are realized and interpretations are given for the respective effects occurring at each stage. The resulting magnetic field is highly non-axisymmetric and possesses a pronounced inhomogeneous vortex structure of twisted flux tubes. The flow is almost axisymmetric but shows a Kolmogorov-like behaviour for small scales. The outer surface of the shell is penetrated by magnetic field lines in spot-like regions, which are located mainly in the equatorial plane. For very high dynamo numbers we find a cyclic behaviour of the averaged magnetic field amplitude. The problem of angular momentum transport is discussed in terms of the ShakuraSunyaev viscosity alpha , which depends exponentially on the radial distance and adopts values in the range 10³10⁵.     

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

A full numerical solution is found for the effect of a strongly magnetic star on its accretion disc, for the case of magnetic buoyancy diffusion. As in the previously considered case of turbulent diffusion, the disc becomes disrupted when magnetic and viscous stresses become comparable. A magnetically induced temperature elevation leads to electron scattering opacity and radiation pressure becoming significant far from the stellar surface, with consequent viscous instability and vertical disruption of the disc. This, together with the previous turbulent case, suggests that such a disruption mechanism owing to strongly magnetic accretors is generally operable.     

Accretion disc dynamics in extreme mass ratio compact binaries

An analysis is presented of a numerical investigation of the dynamics and geometry of accretion discs in binary systems with mass ratios   q = M ₂/ M ₁ < 0.1  , applicable to ultracompact X-ray binaries, AM CVn stars and very short period cataclysmic variables. The steady-state geometry of the disc in the binary reference frame is found to be quite different from that expected at higher mass ratios. For   q ∼ 0.1  , the disc takes on the usual elliptical shape, with the major axis aligned perpendicular to the line of centres of the two stars. However, at smaller mass ratios the elliptical gaseous orbits in the outer regions of the disc are rotated in the binary plane. The angle of rotation increases with gas temperature, but is found to vary inversely with q . At   q = 0.01  , the major axis of these orbits is aligned almost parallel to the line of centres of the two stars. These effects may be responsible for the similar disc structure inferred from Doppler tomography of the AM CVn star GP Com, which has   q = 0.02  . The steady-state geometry at low mass ratios is not predicted by an inviscid, restricted three-body model of gaseous orbits; it is related to the effects of tidal-viscous truncation of the disc near the Roche lobe boundary. Since the disc geometry can be inferred observationally for some systems, it is proposed that this may offer a useful diagnostic for the determination of mass ratios in ultracompact binaries.     

An unconventional accretion disc dynamo

In the light of recent results from numerical simulations of accretion disc MHD turbulence, we revisit the problem of the configuration of large-scale magnetic fields resulting from an α Ω dynamo operating in a thin accretion disc. In particular, we analyse the consequences of the peculiar sign of the α -effect suggested by numerical simulations . We determine the symmetry of the fastest-growing modes in the kinematic dynamo approximation and, in the framework of an ' α -quenched' dynamo model, study the evolution of the magnetic field. We find that the resulting field for this negative polarity of the α -effect generally has dipole symmetry with respect to the disc midplane, although the existence of an equilibrium configuration depends on the properties of the turbulence. The role of magnetic field dragging is discussed and, finally, the presence of an external uniform magnetic field is included to address the issue of magneto centrifugal wind launching from accretion discs.