Matteo Cantiello edited Conclusions.tex  about 10 years ago

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We identify the RGB as the evolutionary phase where some extra angular momentum transport mechanism is efficiently coupling the core to the stellar envelope. Potential candidates for such mechanism are internal gravity waves and fossil (or convective dynamo-generated) magnetic fields.   Ensemble asteroseismology is providing outstanding results regarding the internal rotation of low-mass stars. It is important, however, to keep in mind that only a fraction of the stars analyzed for seismology have identifiable mixed modes and rotational splittings   \citep[in the case of ][, for example, 313 out of 1399 stars, i.e. 22\%]{Mosser:2012}  %(in the case of Mosser et al. 2013a, for example, 313 out of 1399 stars, i.e., 22 %)  %It is  important however to keep in mind that only 22$\%$ of the red giant sample analyzed by seismologists have identifiable mixed modes and rotational splittings \citep[313 out of 1399 stars, see e.g.][]{Mosser:2012}. In particular confusion between mixed modes and rotational splittings could in principle have led to a bias toward stars with slower rotating cores (e.g. stars that did spin down due to binary interactions or because of a fossil magnetic fields). We believe these potential biases need to be carefully addressed as they could have important repercussion on the theoretical interpretations.   Nevertheless it is interesting to consider what angular momentum transport mechanisms could 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, providing some coupling between 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 $<$ replace_contentlt;$  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 $B_{\rm{eq}}\sim 10^4-10^5 G$. Some of the magnetic flux will diffuse in the radiative layers above the convective core, but this is expected to affect only a small fraction of the star as the Ohmic diffusion timescale is much longer than the main sequence timescale.   % Given the typical values of the density and shear in the region between contracting core and the expanding envelope, %we find that to match resulting magnetic diffusivity is of the order $. 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.}  Overall assessing if such mechanism can explain the observed rotation rates requires following the coupled evolution of shear and magnetic fields.