Spin Evolution of Accreting Young Stars. I. Effect of Magnetic Star-Disk Coupling

We present a model for the rotational evolution of a young, solar mass star interacting with an accretion disk. The model incorporates a description of the angular momentum transfer between the star and disk due to a magnetic connection, and includes changes in the star's mass and radius and a decreasing accretion rate. The model also includes, for the first time in a spin evolution model, the opening of the stellar magnetic field lines, as expected to arise from twisting via star-disk differential rotation. In order to isolate the effect that this has on the star-disk interaction torques, we neglect the influence of torques that may arise from open field regions connected to the star or disk. For a range of magnetic field strengths, accretion rates, and initial spin rates, we compute the stellar spin rates of pre-main-sequence stars as they evolve on the Hayashi track to an age of 3~Myr. How much the field opening affects the spin depends on the strength of the coupling of the magnetic field to the disk. For the relatively strong coupling (i.e., high magnetic Reynolds number) expected in real systems, all models predict spin periods of less than $\sim3$ days, in the age range of 1--3~Myr. Furthermore, these systems typically do not reach an equilibrium spin rate within 3~Myr, so that the spin at any given time depends upon the choice of initial spin rate. This corroborates earlier suggestions that, in order to explain the full range of observed rotation periods of approximately $1$--$10$ days, additional processes, such as the angular momentum loss from powerful stellar winds, are necessary.