Three‐dimensional Simulations of Disk Accretion to an Inclined Dipole. I. Magnetospheric Flows at Different Θ

Abstract

We present results of fully three-dimensional MHD simulations of disk accretion to a slowly rotating magnetized star with its dipole moment inclined at an angle Θ to the rotation axis of the disk (which is aligned with the spin axis of the star). The main goal was to investigate the pattern of magnetospheric flow and the disk-star interaction for a variety of inclination angles Θ. We observed that at Θ = 0°, the disk stops at magnetospheric radius rm, and matter flows to the star through axisymmetric funnel flows, as observed in earlier axisymmetric simulations. However, when the dipole moment of the star is inclined, then the flow becomes nonaxisymmetric. The nonaxisymmetry becomes notable at very small inclination angles, Θ ~ 2°-5°. The pattern of magnetospheric flow is different at different Θ. For relatively small angles, Θ ≲ 30°, the densest matter flows to the star mostly in two streams, which follow paths to the closest magnetic pole. The streams typically corotate with the star, but they may precess about the star for Θ ≲ 10°. At intermediate angles, 30° ≲ Θ ≲ 60°, the streams become more complicated and often split into four streams. For even larger angles, Θ ≳ 60°, matter accretes in two streams, but their geometry is different from that of the streams at small Θ. Magnetic braking changes the structure of the inner regions of the disk. It creates a region of lower density (a "gap") for rm ≲ r ≲ 4rm. A ring of higher density forms at r ~ rm for Θ ≲ 30°. For r ≲ (2–3)rm, the azimuthal velocities are sub-Keplerian. The inner region of the disk at r ~ rm is warped. The warping is due to the tendency of matter to corotate with an inclined magnetosphere. The normal of the inner warped part of the disk is close to the magnetic axis of the dipole. The accreting matter brings positive angular momentum to the (slowly rotating) star, tending to spin it up. The corresponding torque NZ depends only weakly on Θ. The angular momentum flux to the star near the star's surface is transported predominantly by the magnetic field; the matter component contributes ~1% of the total flux. The torques NX and NY are also calculated, and these may give a slow precession of the symmetry axis of the star. The angle Θ was fixed in simulations because the timescale of its evolution is much longer than that of the simulations. Results of simulations are important for understanding the nature of classical T Tauri stars, cataclysmic variables, and X-ray pulsars. These stars often show complicated spectral and photometric variability patterns, which may be connected with the structure of magnetospheric flows. The magnetospheric structure of stars with different Θ can give different variability patterns in observed light curves. This can provide information about inclination angles Θ in different stars. A notable result of the present simulations is the formation of multiple streams in the accretion flows near the star for intermediate inclination angles. This may give short-scale, quasi-periodic variability in the light curves of some stars.