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We present a model for the rotational evolution of a young, solar mass starinteracting with an accretion disk. The model incorporates a description of theangular momentum transfer between the star and disk due to a magneticconnection, and includes changes in the star's mass and radius and a decreasingaccretion rate. The model also includes, for the first time in a spin evolutionmodel, the opening of the stellar magnetic field lines, as expected to arisefrom twisting via star-disk differential rotation. In order to isolate theeffect that this has on the star-disk interaction torques, we neglect theinfluence of torques that may arise from open field regions connected to thestar or disk. For a range of magnetic field strengths, accretion rates, andinitial spin rates, we compute the stellar spin rates of pre-main-sequencestars as they evolve on the Hayashi track to an age of 3~Myr. How much thefield opening affects the spin depends on the strength of the coupling of themagnetic field to the disk. For the relatively strong coupling (i.e., highmagnetic Reynolds number) expected in real systems, all models predict spinperiods 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, sothat 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 rangeof observed rotation periods of approximately $1$--$10$ days, additionalprocesses, such as the angular momentum loss from powerful stellar winds, arenecessary.

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