Rotation of Red Giants

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The internal rotation of post-main sequence stars is investigated, in response to the convective pumping of angular momentum toward the stellar core, combined with a tight magnetic coupling between core and envelope. The spin evolution is calculated using model stars of initial mass 1, 1.5 and $5\,M_\odot$, taking into account mass loss on the giant branches and the partitioning of angular momentum between the outer and inner envelope. We also include the deposition of orbital angular momentum from a sub-stellar companion, as influenced by tidal drag as well as the excitation of orbital eccentricity by a fluctuating gravitational quadrupole moment. A range of angular velocity profiles $\Omega(r)$ is considered in the deep convective envelope, ranging from solid rotation to constant specific angular momentum. We focus on the backreaction of the Coriolis force on the inward pumping of angular momentum, and the threshold for dynamo action in the inner envelope. Quantitative agreement with measurements of core rotation in subgiants and post-He core flash stars by Kepler is obtained with a two-layer angular velocity profile: uniform specific angular momentum where the Coriolis parameter ${\rm Co} \equiv \Omega \tau_{\rm con} \lesssim 1$ (here $\tau_{\rm con}$ is the convective time); and $\Omega(r) \propto r^{-1}$ where ${\rm Co} \gtrsim 1$. The inner profile is interpreted in terms of a balance between the Coriolis force and angular pressure gradients driven by the convective cell structure. Including the effect of angular momentum pumping on the surface rotation of subgiants also reduces the need for an additional magnetic wind torque. The co-evolution of internal magnetic fields and rotation is considered in Paper II, where we explain when and how a strong core-envelope coupling is established, and how it may break down as the result of stellar mass loss.