Can Fu Orionis Outbursts Regulate the Rotation Rates of T Tauri Stars?

We propose that FU Orionis outbursts may play an important role in maintaining the slow rotation of classical disk-accreting T Tauri stars. Current estimates for the frequency and duration of FU Orionis outbursts and the mass accretion rates of T Tauri and FU Orionis stars suggest that more mass may be accreted during the outbursts than during the T Tauri phases. If this is the case, then the outbursts should also dominate the accretion of angular momentum. During the outbursts, the accretion rate is so high that the magnetic field of the star should not disrupt the disk, and the disk will extend all the way in to the stellar surface. Standard thin disk models then predict that the star should accrete large amounts of angular momentum, which will produce a secular spinup of the star. We present boundary layer solutions for FU Orionis parameters which show that the rotation rate of the accreting material reaches a maximum value which is far less than the Keplerian rotation rate at the stellar surface. This is due to the importance of radial pressure support at these high mass accretion rates. As a result, the rate at which the star accretes angular momentum from the disk drops rapidly as the stellar rotation rate increases. In fact, the angular momentum accretion rate drops below zero for stellar rotation rates which are always substantially below breakup, but depend on the mass accretion rate and on the adopted definition of the stellar radius. When the angular momentum accretion rate drops close to zero, the star will stop spinning up. Faster stellar rotation rates will produce negative angular momentum accretion which will spin the star down. Therefore, FU Orionis outbursts can keep the stellar rotation rate close to some equilibrium value for which the angular momentum accretion rate is small. We show that this equilibrium rotation rate may be similar to the observed rotation rates of T Tauri stars; thus we propose that FU Orionis outbursts may be responsible for the observed slow rotation of T Tauri stars. This mechanism is independent of whether the disk is disrupted by the stellar magnetic field during the T Tauri phase.