Spin-up of Be stars in the pre-main sequence phase

In an attempt to explain faster than average rotation of Be stars, a model for rotational evolution of a pre-main sequence (PMS) star with a weak primordial magnetic field was applied to stars with masses between 3 and 7 solar mass. The model takes into account the accretion of matter along the magnetic field lines, the stellar field-disk interaction and a magnetized wind. Evolutionary changes of the stellar moment of inertia are also included. The stellar mass and magnetic flux were assumed constant during the PMS evolution. The results indicate that magnetic accretion spins up a star early in its PMS life and if the star has a short PMS life time (i.e. high enough mass), it may keep faster rotation until the zero age main sequence (ZAMS). Detailed calculations show that typically a factor of two faster rotation is achieved compared to the conserved angular momentum case. This requires an intense accretion going on for a substantial fraction of the PMS phase in the presence of a surface magnetic field not exceeding 400 G. Stronger fields slow down the stellar rotation very efficiently by the magnetic field-disk locking mechanism. Low mass stars with PMS life time significantly longer than the time scale of spin down by the magnetic wind may be efficiently braked by the wind operating after the disappearance of the disk. They can retain faster than average rotation only under very special conditions. It is postulated that ZAMS progenitors of Be stars possess fossil magnetic fields with surface intensity between 40 and 400 G. The fields result in rotation rates about two times higher than those of normal stars in full agreement with the observations. If the observed Be stars have already evolved from ZAMS, their present magnetic fields should be correspondingly weaker due to the evolutionary increase of the stellar radius. ZAMS stars with magnetic fields weaker than about 40 G should have normal rotation and those with fields significantly stronger than 400 G should become slowly rotating Ap-Bp magnetic stars. The case of beta Cephei, with its present surface magnetic field close to 400 G, is a special case of an intermediate field, strong enough to slow down the star's rotation in the PMS phase but apparently not strong enough to develop Bp star characteristics.