Despite extensive study, the mechanisms by which Be star disks acquire high densities and angular momentum while displaying variability on many timescales are still far from clear. In this paper, we discuss how magnetic torquing may help explain disk formation with the observed quasi-Keplerian (as opposed to expanding) velocity structure and their variability. We focus on the effects of the rapid rotation of Be stars, considering the regime where centrifugal forces provide the dominant radial support of the disk material. Using a kinematic description of the angular velocity, v ðrÞ, in the disk and a parametric model of an aligned field with a strength BðrÞ, we develop analytic expressions for the disk properties that allow us to estimate the stellar surface field strength necessary to create such a disk for a range of stars on the main sequence. The fields required to form a disk are compared with the bounds previously derived from photospheric limiting conditions. The model explains why disks are most common for main-sequence stars at about spectral class B2 V. The earlier type stars with very fast and high-density winds would require unacceptably strong surface fields (>10 3 G) to form torqued disks, while the late B stars (with their low mass-loss rates) tend to form disks that produce only small fluxes in the dominant Be diagnostics. For stars at B2 V the average surface field required is about 300 G. The predicted disks provide an intrinsic polarization and a flux at H comparable to observations. The radial extent of our dense quasi-Keplerian disks is compatible with typical estimates. We also discuss whether the effect on field containment of the time-dependent accumulation of matter in the flux tubes/disk can help explain some of the observed variability of Be star disks.

We consider rotating magnetic stars with winds and disks. We establish a theorem that relates the angular velocity of a disk region with no meridional motion to the angular velocity of the star. Also, we show that for a given value of the magnetic field strength, if the rotation rate is too high or the flow velocity into the shock boundary is too low, a Keplerian disk region will not be formed. We develop a model for the formation of disks in magnetic rotators through the processes of fill-up and diffusion into Keplerian orbits. At the end of the fill-up stage the density of the disk increases significantly and the magnetic force in the disk becomes negligible. We derive analytical expressions for the inner and outer radii of Keplerian disks in terms of the stellar rotation rate. A disk can form if the meridional component Bm of the field at the stellar surface is larger than a minimum value. The radial extent of the Keplerian region becomes larger for larger values of Bm and is largest when Bm equals an optimal value. The strengths of the minimum fields required for Keplerian disk formation in B-type stars varies from order 1G to 10G. In O-type stars they must be of order 500G. Also, we suggest that the stellar magnetic fields may be affected by rotationally driven meridional circulation leading to some of the the observed variations of disks with time.Comment: 44 pages, 1 figure, accepted by Ap

The puzzle of the origin of Be star disks is discussed. Contrary to recently published claims, it is argued that the magnetically torqued disk ( MTD) type models of Cassinelli et al. offer a viable scenario for a successful model with all the key ingredients. MTD models involve disk compression by equatorial collision of stellar wind streams that are steered and torqued by a dipole-like magnetic field. While the growing disk density tends to lead to the gas breaking out centrifugally from the field, it is proposed that the onset of viscous effects can lead to an eventual stable, slowly outflowing, Keplerian disk. It is then shown that the resulting very dense (wind compressed) disk need have only a very slow subsonic outflow to satisfy mass continuity. Consequently, line profile data do not preclude steadily expanding disks of high density. It is also shown that the time taken to reach the steady state would typically be of the order of 10 4 wind flow times R/v 1 . This is far longer than the run times of recent numerical MHD simulations that displayed bursty breakout behavior, which may therefore only be transients induced by unrealistic initial conditions.

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We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10 7 K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.