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Matteo Cantiello added Astero Observations.tex
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Space-based photometry from CoRoT and {\it Kepler} has detected radial and non-radial oscillations in over ten thousand red giants
\citep{deridder09,bedding10,2012A&A...548A..10M, stello13}.
These modes are present due to vigorous convection within the star (see
\citet{christen11}), and are predominantly acoustic waves (p-modes) at evenly spaced
frequencies, $\Delta \nu\propto (M/R)^{3/2}$, centered on the
frequency $\nu_{\rm max}\propto M/(R^2T_{\rm eff}^{1/2})$ of maximum power,
which is below the acoustic cutoff \citep{brown91}.
The measured $\nu_{\rm max}$, $T_{\rm eff}$ and $\Delta \nu$ then
yield $10\%$ measurements of $M$ and $R$
for over 10,000 red giants \citep{stello13} with $1M_\odot
though lower in mass than SNe progenitors, span
evolutionary states from red giant branch (RGB) stars to those undergoing core helium burning.
Most importantly, the detection of rotationally split internal gravity
waves (g-modes) provides a new probe of the stellar interior, enabling
stringent tests of the theoretical ideas of angular momentum transport within stars.
The first step in the chain of discoveries was the detection of
$\ell=1$ mixed modes, which have p-mode characteristics in the red giant envelope, but
g-mode characteristics in the helium core
\citep{aizenman77, dupret09, montalban10}. These modes are nearly evenly spaced in period, at
$\Delta P_{\rm obs}$ (see Figure
\ref{fig:keplerpower} where $\ell=0,\ell=2$ are not broken up, but
the $\ell=1$ are in 4 separate locations) and were identified by
\citet{beck11} as core sensitive gravity dominated mixed modes.
\citet{bedding11} and \citet{mosser11mixed} used this to separate RGB
stars (i.e. those with degenerate helium cores) from red clump stars (i.e. those with non-degenerate helium burning cores). \citet{2012ApJ...744L...6B}
highlighted the asteroseismic signatures of a star transitioning from the RGB tip to the clump due to the helium core flash
over $\approx 2$ Myrs.
\begin{wrapfigure}{l}{3.0in}
\vspace{-.350in}
\begin{center}
\epsfig{file=fig/powerspec,width=3.0in}
\vspace{-.35in}
\caption{ \textit{ {\it Kepler} power spectrum of an RGB star with $\Delta \nu=12.5{\mu}{\rm Hz}$}}\label{fig:keplerpower}
\vspace{-.35in}
\end{center}
\end{wrapfigure}
The most recent breakthrough \citep{2012Natur.481...55B,2012A&A...548A..10M} is the measurement of the interior stellar rotation, found by the measurement of the rotational splitting
of the $\ell=1$ modes highlighted by the triplet tick marks in Figure \ref{fig:keplerpower}.
\citet{2012A&A...548A..10M} showed that it is the rotation
of the material near the active hydrogen burning shell that is most directly inferred from
the splitting \citep[See also][]{2013A&A...549A..74M}. Those modes
identified as predominantly acoustic (with more inertia in the outer convective envelope)
showed rotational splitting indicative of a slower rotation rate than the core. This measurement
of the interior rotational state of an evolved star provides a new test for
theoretical ideas of angular momentum transport.
