deletions | additions       diff --git a/Late RGB.tex b/Late RGB.tex  index d7052b4..fafd67f 100644  --- a/Late RGB.tex  +++ b/Late RGB.tex 
...
\subsection{RGB past the luminosity bump}  The work of \citet{Mosser:2012} reveals that the cores of stars in the mass range 1.2...1.5$\mso$ spin down ascending the early RGB as $\approx R^{0.7\pm0.3}$. As stars keep climbing the RGB we expect departures from this law. As the degenerate He core grows in mass, its angular momentum content is determined by the rate of angular momentum transport and by the specific angular momentum of the advected material. Both quantities can in principle change as the star evolves on the RGB: this is because angular momentum transport mechanisms can be a function of, e.g., the rate of shear between the core and the envelope, which tend to increase as the star expands. Even if the torque was a constant, the value of the specific angular momentum of the advected material decreases rapidly as the core engulfs regions left by the retreating convective envelope. This occurs after the luminosity bump, which is created when the H-burning shell crosses the compositional gradient left by the first dredge up. Since the envelope expands and at the same time loses a considerable amount of mass through stellar winds (about $0.3\mso$ in the $M_{\rm Ini}=1.5\mso$ model), it loses angular momentum at an increasing rate. Since angular momentum is expected to be mixed efficiently in convective regions, the specific angular momentum of the material engulfed by the core after the luminosity bump is expected to be low and to decrease as the star climbs the RGB. Note that the disappearance of the steep compositional gradient after the luminosity bump is also  expected to enhance the efficiency of angular momentum transport mechanisms between core and envelope. Evidence of enhanced chemical mixing below the convective envelope (cold bottom process) comes from the observation of surface abundances in red giants, in particular a sudden drop in the carbon isotopic ratio $^{12}{\rm C}/^{13}{\rm C}$ and changes in $^7{\rm Li}$, carbon and nitrogen \citep{Gratton:2000}. The nature of this mixing is currently debated \citep[See e.g.][]{Palacios:2006,Charbonnel:2007,Nordhaus:2008,Cantiello:2010,Traxler:2011,Denissenkov:2011,Brown:2013}.   In our $1.5\mso$ calculations the luminosity bump occurs when the star has a radius of about 13.25$\rso$, corresponding to a value of the large separation of about 3.6$\mu$Hz. Regardless of the specific angular momentum transport mechanism included, we find a change in the exponent of the $\approx R^{\,\xi}$ relation. In particular for the model including magnetic torques and rotating with an initial surface velocity of $50\kms$, $\xi$ changes from -0.61 to -0.01 (while the same model only including angular momentum transport due to rotational instabilities have $\xi$ changing from -1.32 to -0.13. Different exponents are found for different initial rotational velocities, but we consistently find a break at the luminosity bump).  Therefore, regardless of the specific angular momentum transport mechanism operating in stars, in red giants ascending the RGB we expect that the rate of spindown should decrease past the luminosity bump, and depart from the relation $\approx R^{0.7\pm0.3}$ observed by \citet{Mosser:2012}.