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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.