Richard V. E. Lovelace

We present a new study of the Rayleigh–Taylor unstable regime of accretion on to rotating magnetized stars in a set of high grid resolution three-dimensional magnetohydrodynamic simulations performed in low-viscosity discs. We find that the boundary between the stable and unstable regimes is determined almost entirely by the fastness parameter ω_s = Ω_⋆/Ω_K(r_m), where Ω_⋆ is the angular velocity of the star and Ω_K(r_m) is the angular velocity of the Keplerian disc at the disc–magnetosphere boundary r = r_m. We found that accretion is unstable if ω_s ≲ 0.6. Accretion through instabilities is present in stars with different magnetospheric sizes. However, only in stars with relatively small magnetospheres, r_m/R_⋆ ≲ 7, do the unstable tongues produce chaotic hotspots on the stellar surface and irregular light curves. At even smaller values of the fastness parameter, ω_s ≲ 0.45, multiple irregular tongues merge, forming one or two ordered unstable tongues that rotate with the angular frequency of the inner disc. This transition occurs in stars with even smaller magnetospheres, r_m/R_⋆ ≲ 4.2. Most of our simulations were performed at a small tilt of the dipole magnetosphere, Θ = 5°, and a small viscosity parameter α = 0.02. Test simulations at higher α values show that many more cases become unstable, and the light curves become even more irregular. Test simulations at larger tilts of the dipole Θ show that instability is present, however, accretion in two funnel streams dominates if Θ ≳ 15°. The results of these simulations can be applied to accreting magnetized stars with relatively small magnetospheres: Classical T Tauri stars, accreting millisecond X-ray pulsars, and cataclysmic variables.

We describe a Godunov-type magnetohydrodynamic (MHD) code based on the Miyoshi and Kusano (2005) solver which can be used to solve various astrophysical hydrodynamic and MHD problems. The energy equation is in the form of entropy conservation. The code has been implemented on several different coordinate systems: 2.5D axisymmetric cylindrical coordinates, 2D Cartesian coordinates, 2D plane polar coordinates, and fully 3D cylindrical coordinates. Viscosity and diffusivity are implemented in the code to control the accretion rate in the disk and the rate of penetration of the disk matter through the magnetic field lines. The code has been utilized for the numerical investigations of a number of different astrophysical problems, several examples of which are shown.

An analytic model is developed for the erosion of protoplanetary gas discs by high velocity magnetized stellar winds. The winds are centrifugally driven from the surface of rapidly rotating, strongly magnetized young stars. The presence of the magnetic field in the wind leads to Reynolds numbers sufficiently large to cause a strongly turbulent wind/disk boundary layer which entrains and carries away the disc gas. The model uses the conservation of mass and momentum in the turbulent boundary layer. The time-scale for significant erosion depends on the disc accretion speed and accretion rate and on the wind mass loss rate and the wind velocity. The time-scale is estimated to be 2E6 yr. A significant contribution to the disc erosion can come from frequent powerful coronal mass ejections (CMEs) where the average mass loss rate in CMEs and velocities have values comparable to those for the steady wind.

A brief review of the origin of jets from disc-accreting rotating magnetized stars is given. In most models, the interior of the disc is characterized by a turbulent viscosity and magnetic diffusivity (‘alpha’ discs) whereas the coronal region outside the disc is treated using ideal magnetohydrodynamics (MHD). Extensive MHD simulations have established the occurrence of long-lasting outflows in the case of both slowly and rapidly rotating stars. (1) Slowly rotating stars exhibit a new type of outflow, conical winds. Conical winds are generated when stellar magnetic flux is bunched up by the inward motion of the accretion disc. Near their region of origin, the winds have a thin conical shell shape with half opening angle of ∼30^∘. At large distances, their toroidal magnetic field collimates the outflow forming current carrying, matter dominated jets. These winds are predominantly magnetically and not centrifugally driven. About 10-30% of the disc matter from the inner disc is launched in the conical wind. Conical winds may be responsible for episodic as well as long lasting outflows in different types of stars. (2) Rapidly rotating stars in the ‘propeller regime’ exhibit twocomponent outflows. One component is similar to the matter dominated conical wind, where a large fraction of the disc matter may be ejected in this regime. The second component is a high-velocity, low-density magnetically dominated axial jet where matter flows along the open polar field lines of the star. The axial jet has a mass flux of about 10% that of the conical wind, but its energy flux, due to the Poynting flux, can be as large as for the conical wind. The jet’s magnetically dominated angular momentum flux causes the star to spin down rapidly. Propeller-driven outflows may be responsible for protostellar jets and their rapid spin-down.When the artificial requirement of symmetry about the equatorial plane is dropped, the conical winds are found to come alternately from one side of the disc and then the other, even for the case where the stellar magnetic field is a centered axisymmetric dipole.Recent MHD simulations of disc accretion to rotating stars in the propeller regime have been done with no turbulent viscosity and no diffusivity. The strong turbulence observed is due to the magneto-rotational instability. This turbulence drives accretion in the disc and leads to episodic conical winds and jets.

We have carried out and analysed a set of axisymmetric magnetohydrodynamic (MHD) simulations of the evolution of a turbulent/diffusive accretion disc around an initially unmagnetized star. The disc is initially threaded by a weak magnetic field where the magnetic pressure is significantly less than the kinetic pressure in the disc. The viscosity and magnetic diffusivity are modelled by two ‘alpha’ parameters, while the coronal region above the disc is treated using ideal MHD. The initial magnetic field is taken to consist of three poloidal field loops threading the disc. The motivation for this study is to understand the advection of disc matter and magnetic field by the turbulent/diffusive disc. At early times ( ≲ 400 orbits of the inner disc), the innermost field loop twists and its field lines become open. The twisting of the opened field lines leads to the formation of both an inner collimated, magnetically dominated jet, and at larger distances from the axis a matter-dominated uncollimated wind. For later times (>1000), the strength of the magnetic field decreases owing to field reconnection and annihilation in the disc. For the early times, we have derived from the simulations both the matter accretion speed in the disc u_m and the accretion speed of the magnetic field u_B which is determined by measuring the speed of the inward motion of the inner O-point of the magnetic field in the equatorial plane. We show that the derived u_m agrees approximately with the predictions of a model where the accretion speed is the sum of two terms, first due to the disc's viscosity (which gives a radial outflow of angular momentum in the disc), and a second due to the twisted magnetic field at the disc's surface (which gives a vertical outflow of angular momentum). At later times the magnetic contribution to u_m becomes small compared to the viscous contribution. For early times we find that u_m is larger than the magnetic field accretion speed u_B by a factor of ∼2 for the case where both the alpha parameters are equal to 0.1.