Evolutionary models of fast-rotating stars show that the stellar rotational
velocity may approach the critical speed. Critically rotating stars cannot spin
up more, therefore they lose their excess angular momentum through an
equatorial outflowing disk. The radial extension of such disks is unknown,
partly because we lack information about the radial variations of the
viscosity. We study the magnetorotational instability, which is considered to
be the origin of anomalous viscosity in outflowing disks. We used analytic
calculations to study the stability of outflowing disks submerged in the
magnetic field. The magnetorotational instability develops close to the star if
the plasma parameter is large enough. At large radii the instability disappears
in the region where the disk orbital velocity is roughly equal to the sound
speed. The magnetorotational instability is a plausible source of anomalous
viscosity in outflowing disks. This is also true in the region where the disk
radial velocity approaches the sound speed. The disk sonic radius can therefore
be roughly considered as an effective outer disk radius, although disk material
may escape from the star to the insterstellar medium. The radial profile of the
angular momentum-loss rate already flattens there, consequently, the disk
mass-loss rate can be calculated with the sonic radius as the effective disk
outer radius. We discuss a possible observation determination of the outer disk
radius by using Be and Be/X-ray binaries.Comment: 8 pages, accepted for publication in Astronomy & Astrophysic
