deletions | additions       diff --git a/Past the bump.tex b/Past the bump.tex  index 58d895e..a768ea3 100644  --- a/Past the bump.tex  +++ b/Past the bump.tex 
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Moreover during the RGB the H-burning shell moves up in mass coordinate and at some point crosses the compositional discontinuity left by the first dredge up (luminosity bump).  Since the envelope expands and at the same time loses a considerable amount of mass through stellar winds (about $0.3\mso$ in the $1.5\mso$ model), it loses angular momentum at an increasing rate. As 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 $R \simeq 13.25\rso$, corresponding to a value of the large separation $\Delta\nu \simeq 3.6\mu$Hz and frequency of maximum oscillation power $\nu_{\rm max}\simeq 30.5\mu$Hz. Regardless of the specific angular momentum transport mechanism included, we find a change in the exponent of the $P_c\propto R^{\,\xi}$ relation. relation associated with the luminosity bump.  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). This is because the value of the specific angular momentum of the advected material decreases rapidly as the core engulfs regions left by the retreating convective envelope.  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}.