deletions | additions       diff --git a/Discussion2.tex b/Discussion2.tex  index 491dacc..a53a5d3 100644  --- a/Discussion2.tex  +++ b/Discussion2.tex 
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It is interesting to consider what angular momentum transport mechanisms, not included in our models, might be responsible for the strong coupling implied by the asteroseismic observations. One candidate are gravity waves excited by the convective envelope during the RGB, as these can potentially lead to some transport of angular momentum. While a similar process has been discussed in the context of the Sun's rotational profile \citep{Zahn:1997,Charbonnel:2005}, more work needs to be done to understand the details of the excitation and propagation of gravity waves \citep[See e.g.][]{Lecoanet:2013,Rogers:2013}  Another possibility is that some large scale magnetic field is present in and above the stellar core at the end of the main sequence, efficiently coupling core and envelope. This magnetic field could be either of fossil origin (similar to what has been discussed in the context of explaining the internal rotation profile of the Sun) or be generated by a convective dynamo in the H-burning core during the main sequence. Dynamo action is favorable as, given the typical rotational velocities of 1.5-3.0$\mso$ stars during the main sequence, Rossby numbers are usually < 1, implying an $\alpha\Omega$-dynamo could be at work in the core. The equipartition magnetic field is $B_{\rm{eq}} = \varv_c\,\sqrt{4\pi\rho}$, assuming $B_{\phi}\sim B_r\sim B_{\rm{eq}}$ the resulting magnetic stress is $S= \frac{B_r B_{\phi}}{4\pi}$ and the associated diffusivity is   $\nu \sim \frac{S}{\rho q \Omega}$, where $q=-\frac{\partial \log \Omega}{\partial \log r}$ is the shear. Typical convective velocities in the core of main sequence, low-mass stars are on the order $0.01\kms$ resulting in $B_{\rm{eq}}\sim 10^5 G$. During the early red giant branch the size of the region between the stellar core and the convective envelope is of order $\sim \rso$, implying the Alfven timescale is on the order $\tau_{\textrm{a}}\approx \frac{\rso}{v_{\textrm{a}}}< 10^4$yr R/v_{\textrm{a}}\approx (\frac{R}{\rso}\frac{B}{kG}\frac{\bar{\rho}}{\rho_{\odot}})$yr    Compared to the artificial diffusivity required to explain the early RGB asteroseismic observations... \textbf{TBD: Matteo complete this piece of the discussion putting in numbers. Depending on how promising the results are we might wanna keep this out of the paper.}