The physics of the "hot spots" on stellar surfaces and the associated variability of accreting magnetized rotating stars is investigated for the first time using fully three-dimensional magnetohydrodynamic simulations. The magnetic moment of the star µ is inclined relative to its rotation axis Ω by an angle Θ (we will call this angle the "misalignment angle") while the disk's rotation axis is parallel to Ω. A sequence of misalignment angles was investigated, between Θ = 0 • and 90 • . Typically at small Θ the spots are observed to have the shape of a bow which is curved around the magnetic axis, while at largest Θ the spots have a shape of a bar, crossing the magnetic pole. The physical parameters (density, velocity, temperature, matter and energy fluxes, etc.) increase toward the central regions of the spots, thus the size of the spots is different at different values of these parameters. At relatively low density and temperature, the spots occupy approximately 10 − 20% of the stellar surface, while at the highest values of these parameters this area may be less than 1% of the area of the star. The size of the spots increases with the accretion rate. The light curves were calculated for different Θ and inclination angles of the disk i. They show a range of variability patterns, including one maximum-per-period curves (at most of angles Θ and i), and two maximum-per-period curves (at large Θ and i). At small Θ, the funnel streams may rotate faster/slower than the star, and this may lead to quasi-periodic variability of the star. The results are of interest for understanding the variability and quasi-variability of Classical T Tauri Stars, millisecond pulsars and cataclysmic variables.

Magnetohydrodynamic (MHD) simulations have been used to study disk accretion to a rotating magnetized star with an aligned dipole moment. Quiescent initial conditions were developed in order to avoid the fast initial evolution seen in earlier studies. A set of simulations was performed for different stellar magnetic moments and rotation rates. Simulations have shown that the disk structure is significantly changed inside a radius r br where magnetic braking is significant. In this region the disk is strongly inhomogeneous. Radial accretion of matter slows as it approaches the area of strong magnetic field and a dense ring and funnel flow form at the magnetospheric radius r m where the magnetic pressure is equal to the total, kinetic plus thermal, pressure of the matter.Funnel flows (FF), where the disk matter moves away from the disk plane and flows along the stellar magnetic field, are found to be stable features during many rotations of the disk. The dominant force driving matter into the FF is the pressure gradient force, while gravitational force accelerates it as it approaches the star. The magnetic force is much smaller than the other forces. The funnel flow is found to be strongly sub-Alfvénic everywhere. The FF is subsonic close to the disk, but it becomes supersonic well above the disk. Matter reaches the star with a velocity close to that of free-fall.Angular momentum is transported to the star dominantly by the magnetic field. In the disk the transport of angular momentum is mainly by the matter, but closer to the star the matter transfers its angular momentum to the magnetic field and the magnetic field is dominant in transporting angular momentum to the surface of the star. For slowly rotating stars we observed that magnetic braking leads to the deceleration of the inner regions of the disk and the star spins up. For a rapidly rotating star, the inner regions of the disk rotate with a super-Keplerian velocity, and the star spins-down. The average torque is found to be zero when the corotation radius r cor ≈ 1.5r m .The evolution of the magnetic field in the corona of the disk depends on the ratio of magnetic to matter energies in the corona and in the disk. Most of the simulations were performed in the regime of a relatively dense corona where the matter energy density was larger than the magnetic energy density. In this case the coronal magnetic field gradually opens but the velocity and density of outflowing matter are small. In a test case where a significant part of the corona was in the field dominated regime, more dramatic opening of the magnetic field was observed with the formation of magneto-centrifugally driven outflows.Numerical applications of our simulation results are made to T Tauri stars. We conclude that our quasi-stationary simulations correspond to the classical T Tauri stage of evolution. Our results are also relevant to cataclysmic variables and magnetized neutron stars in X-ray binaries.

We present results of fully three-dimensional magnetohydrodynamic (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 assumed to be 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 r m , 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 non-axisymmetric. The non-axisymmetry 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 co-rotate 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 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 r m ∼ < r ∼ < 4r m . A ring of higher density forms at r ∼ r m for Θ ∼ < 30 • . For r ∼ < (2 − 3)r m , the azimuthal velocities are sub-Keplerian. The inner region of the disk at r ∼ r m is warped. The warping is due to the tendency of matter to co-rotate with 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 N z 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 N x and N y 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 time scale of its evolution is much longer that 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 ...

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.

We present results of axisymmetric magnetohydrodynamic simulations of the interaction of a rapidly rotating, magnetized star with an accretion disk. The disk is considered to have a finite viscosity and magnetic diffusivity. The main parameters of the system are the star's angular velocity and magnetic moment, and the disk's viscosity and diffusivity. We focus on the "propeller" regime where the inner radius of the disk is larger than the corotation radius. Two types of magnetohydrodynamic flows have been found as a result of simulations: "weak" and "strong" propellers. The strong propellers are characterized by a powerful disk wind and a collimated magnetically dominated outflow or jet from the star. The weak propellers have only weak outflows. We investigated the time-averaged characteristics of the interaction between the main elements of the system, the star, the disk, the wind from the disk, and the jet. Rates of exchange of mass and angular momentum between the elements of the system are derived as a function of the main parameters. The propeller mechanism may be responsible for the fast spinningdown of the classical T Tauri stars in the initial stages of their evolution, and for the spinning-down of accreting millisecond pulsars.