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.     

On spin-up/spin-down torque reversals in disc accreting pulsars

The recent BATSE observations of the spin-up and spin-down of accreting pulsars have shown that the standard formulation for the accretion torque as proposed by Ghosh &38; Lamb may need to be revised. The observations indicate alternate spin-up and spin-down phases driven by torques of similar magnitude and typically larger than the mean torque. The variations of the torque in systems such as Cen X-3 are difficult to explain in terms of changes of the mass accretion rate. The implication is that the torque does not depend on the accretion rate as in the GL model. In this paper we argue that the observed changes in the spin rate can result from stochastic transitions between two magnetospheric states. In particular, we show that intermediate magnetospheric systems are not admissible, because of a disc-induced magnetospheric instability which exists in a star–disc magnetic interaction system. This explains why torque reversal occurs in disc accreting pulsars with similar magnitudes.     

On the effects of the stellar magnetic field on the structure of T Tauri accretion discs

The structure of accretion discs around magnetic T Tauri stars is calculated numerically using a particle hydrodynamical code, in which magnetic interaction is included in the framework of King's diamagnetic blob accretion model. Setting up the calculation so as to simulate the density structure of a quasi-steady disc in the equatorial plane of a T Tauri star, we find that the central star's magnetic field typically produces a central hole in the disc and spreads out the surface density distribution. We argue that this result suggets a promising mechanism for explaining the unusual flatness (IR excess) of T Tauri accretion disc spectra.     

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.     

Burial of the polar magnetic field of an accreting neutron star – II. Hydromagnetic stability of axisymmetric equilibria

The theory of polar magnetic burial in accreting neutron stars predicts that a mountain of accreted material accumulates at the magnetic poles of the star, and that, as the mountain spreads equatorward, it is confined by, and compresses, the equatorial magnetic field. Here, we extend previous, axisymmetric, Grad–Shafranov calculations of the hydromagnetic structure of a magnetic mountain up to accreted masses as high as   M _a= 6 × 10⁻⁴ M_⊙  , by importing the output from previous calculations (which were limited by numerical problems and the formation of closed bubbles to   M _a < 10⁻⁴ M_⊙  ) into the time-dependent, ideal-magnetohydrodynamic code zeus-3d and loading additional mass on to the star dynamically. The rise of buoyant magnetic bubbles through the accreted layer is observed in these experiments. We also investigate the stability of the resulting hydromagnetic equilibria by perturbing them in zeus-3d . Surprisingly, it is observed that the equilibria are marginally stable for all   M _a≤ 6 × 10⁻⁴ M_⊙  ; the mountain oscillates persistently when perturbed, in a combination of Alfvén and acoustic modes, without appreciable damping or growth, and is therefore not disrupted (apart from a transient Parker instability initially, which expels <1 per cent of the mass and magnetic flux).     

Accretion to magnetized stars through the Rayleigh–Taylor instability: global 3D simulations

We present results of 3D simulations of magnetohydrodynamics (MHD) instabilities at the accretion disc–magnetosphere boundary. The instability is Rayleigh–Taylor, and develops for a fairly broad range of accretion rates and stellar rotation rates and magnetic fields. It manifests itself in the form of tall, thin tongues of plasma that penetrate the magnetosphere in the equatorial plane. The shape and number of the tongues changes with time on the inner disc dynamical time-scale. In contrast with funnel flows, which deposit matter mainly in the polar region, the tongues deposit matter much closer to the stellar equator. The instability appears for relatively small misalignment angles, Θ≲ 30°, between the star's rotation and magnetic axes, and is associated with higher accretion rates. The hotspots and light curves during accretion through instability are generally much more chaotic than during stable accretion. The unstable state of accretion has possible implications for quasi-periodic oscillations and intermittent pulsations from accreting systems, as well as planet migration.     

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.     

Accretion in stellar clusters and the initial mass function

We present a simple physical mechanism that can account for the observed stellar mass spectrum for masses M ∗≳0.5 M_⊙ . The model depends solely on the competitive accretion that occurs in stellar clusters where each star's accretion rate depends on the local gas density and the square of the accretion radius. In a stellar cluster, there are two different regimes depending on whether the gas or the stars dominate the gravitational potential. When the cluster is dominated by cold gas, the accretion radius is given by a tidal-lobe radius. This occurs as the cluster collapses towards a ρ  ∝  R ⁻² distribution. Accretion in this regime results in a mass spectrum with an asymptotic limit of γ =−3/2 (where Salpeter is γ =−2.35) . Once the stars dominate the potential and are virialized, which occurs first in the cluster core, the accretion radius is the Bondi–Hoyle radius. The resultant mass spectrum has an asymptotic limit of γ =−2 with slightly steeper slopes ( γ ≈−2.5) if the stars are already mass-segregated. Simulations of accretion on to clusters containing 1000 stars show that, as expected, the low-mass stars accumulate the majority of their masses during the gas-dominated phase whereas the high-mass stars accumulate the majority of their masses during the stellar-dominated phase. This results in a mass spectrum with a relatively shallow γ ≈3/2 power law for low-mass stars and a steeper power law for high-mass stars −2.5≲ γ ≤−2 . This competitive accretion model also results in a mass-segregated cluster.     

Reconnection X-winds: spin-down of low-mass protostars

We investigate the interaction of a protostellar magnetosphere with a large-scale magnetic field threading the surrounding accretion disc. It is assumed that a stellar dynamo generates a dipolar-type field with its magnetic moment aligned with the disc magnetic field. This leads to a magnetic neutral line at the disc mid-plane and gives rise to magnetic reconnection, converting closed protostellar magnetic flux into open field lines. These are simultaneously loaded with disc material, which is then ejected in a powerful wind. This process efficiently brakes down the protostar to 10–20 per cent of the break-up velocity during the embedded phase.     

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.     

Continuous frequency spectrum of the global hydromagnetic oscillations of a magnetically confined mountain on an accreting neutron star

We compute the continuous part of the ideal-magnetohydrodynamic (ideal-MHD) frequency spectrum of a polar mountain produced by magnetic burial on an accreting neutron star. Applying the formalism developed by Hellsten & Spies, extended to include gravity, we solve the singular eigenvalue problem subject to line-tying boundary conditions. This spectrum divides into an Alfvén part and a cusp part. The eigenfunctions are chirped and anharmonic with an exponential envelope, and the eigenfrequencies cover the whole spectrum above a minimum ω_low. For equilibria with accreted mass  1.2 × 10⁻⁶≲ M _a/M_⊙≲ 1.7 × 10⁻⁴  and surface magnetic fields  10¹¹≲ B _*/G ≲ 10¹³, ω_low  is approximately independent of   B _*  , and increases with M _a. The results are consistent with the Alfvén spectrum excited in numerical simulations with the zeus-mp solver. The spectrum is modified substantially by the Coriolis force in neutron stars spinning faster than ∼100 Hz. The implications for gravitational-wave searches for low-mass X-ray binaries are considered briefly.