We compare the stellar wind torque calculated in a previous work ( Paper II ) to the spin-up and spin-down torques expected to arise from the magnetic interaction between a slowly rotating ( \sim 10 % of breakup ) pre-main-sequence star and its accretion disk .
This analysis demonstrates that stellar winds can carry off orders of magnitude more angular momentum than can be transferred to the disk , provided that the mass outflow rates are greater than the solar wind .
Thus , the equilibrium spin state is simply characterized by a balance between the angular momentum deposited by accretion and that extracted by a stellar wind .
We derive a semi-analytic formula for predicting the equilibrium spin rate as a function only of the ratio of \dot { M } _ { w } / \dot { M } _ { a } and a dimensionless magnetization parameter , \Psi \equiv B _ { * } ^ { 2 } R _ { * } ^ { 2 } ( \dot { M } _ { a } v _ { esc } ) ^ { -1 } , where \dot { M } _ { w } is the stellar wind mass outflow rate , \dot { M } _ { a } the accretion rate , B _ { * } the stellar surface magnetic field strength , R _ { * } the stellar radius , and v _ { esc } the surface escape speed .
For parameters typical of accreting pre-main-sequence stars , this explains spin rates of \sim 10 % of breakup speed for \dot { M } _ { w } / \dot { M } _ { a } \sim 0.1 .
Finally , the assumption that the stellar wind is driven by a fraction of the accretion power leads to an upper limit to the mass flow ratio of \dot { M } _ { w } / \dot { M } _ { a } \lesssim 0.6 .