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.     

Accretion disc coronae as magnetic reservoirs

Most astrophysical sources powered by accretion on to a black hole, either of stellar mass or supermassive, when observed with hard X-rays show signs of a hot Comptonizing component in the flow, the so-called corona , with observed temperatures and optical depths lying in a narrow range (0.1≲ τ ≲1 and 1×10⁹ K≲ T ≲3×10⁹ K). Here we argue that these facts constitute strong supporting evidence for a magnetically dominated corona. We show that the inferred thermal energy content of the corona, in all black hole systems, is far too low to explain their observed hard X-ray luminosities, unless either the size of the corona is at least of the order of 10³ Schwarzschild radii, or the corona itself is in fact a reservoir , where the energy is mainly stored in the form of a magnetic field generated by a sheared rotator (probably the accretion disc). We briefly outline the main reasons why the former possibility is to be discarded, and the latter preferred.     

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.     

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.     

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.     

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.     

Turbulent dynamo action in a shear flow

We consider the mean electromotive force and a dynamo-generated magnetic field, taking into account the stretching of turbulent magnetic field lines by a shear flow. Calculations are performed by making use of the second-order correlation approximation. In the presence of shear, the mirror symmetry of turbulence can be broken; thus turbulent motions become suitable for the generation of a large-scale magnetic field. Regardless of the shear law, turbulence can lead to a rapid amplification of the mean magnetic field. The growth rate of the mean magnetic field depends on the length-scale: it is faster for the fields with smaller length-scale. The mechanism considered is qualitatively different from the alpha dynamo, and can generate only a magnetic field that is inhomogeneous in the direction of flow. In contrast to the alpha dynamo, this mechanism also allows the generation of two-dimensional fields. The suggested mechanism may play an important role in the generation of magnetic fields in accretion discs, galaxies and jets.     

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.     

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 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.     

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.     

Magnetic and vertical shear instabilities in accretion discs

The stability properties of magnetized discs rotating with angular velocity Ω = Ω( s ,  z ), dependent on both the radial and the vertical coordinates s and z , are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Ω on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low.     

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.     

Launching of conical winds and axial jets from the disc–magnetosphere boundary: axisymmetric and 3D simulations

We investigate the launching of outflows from the disc–magnetosphere boundary of slowly and rapidly rotating magnetized stars using axisymmetric and exploratory 3D magnetohydrodynamic simulations. We find long-lasting outflows in the following cases. (1) In the case of slowly rotating stars , a new type of outflow, a conical wind , is found and studied in simulations. The conical winds appear in cases where the magnetic flux of the star is bunched up by the disc into an X-type configuration. The winds have the shape of a thin conical shell with a half-opening angle  θ∼ 30°–40°  . About 10–30 per cent of the disc matter flows from the inner disc into the conical winds. The conical winds may be responsible for episodic as well as long-lasting outflows in different types of stars. There is also a low-density, higher velocity component (a jet) in the region inside the conical wind. (2) In the case of rapidly rotating stars (the 'propeller regime'), a two-component outflow is observed. One component is similar to the conical winds. A significant fraction of the disc matter may be ejected into the winds. The second component is a high-velocity, low-density magnetically dominated axial jet where matter flows along the opened polar field lines of the star. The jet has a mass flux of about 10 per cent of that of the conical wind, but its energy flux (dominantly magnetic) can be larger than the energy flux of the conical wind. The jet's angular momentum flux (also dominantly magnetic) causes the star to spin down rapidly. Propeller-driven outflows may be responsible for the jets in protostars and for their rapid spin-down. The jet is collimated by the magnetic force while the conical winds are only weakly collimated in the simulation region. Exploratory 3D simulations show that conical winds are axisymmetric about the rotational axis (of the star and the disc), even when the dipole field of the star is significantly misaligned.