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Meredith L. Rawls edited Background2.tex
almost 10 years ago
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Compared to main-sequence stars, red giants oscillate with larger amplitudes and longer periods---several hours to days instead of minutes. There are two observable quantities that may be read directly from an oscillating star's power spectrum. The first is the large frequency separation, $\Delta \nu$, which is the separation in frequency space between modes of the same spherical order $l$. This is related to the sound speed, and therefore the average density of the star. As discussed in \citet{ulr86}, this suggests a scaling relation of the form
\begin{equation}\label{deltanu}
\langle \Delta \nu \rangle \propto \langle \rho \rangle^{1/2},
\end{equation}
\noindent where $\langle \rho \rangle \propto M/R^3$ is the average density of the star. It is generally reasonable to assume an average value for $\Delta \nu$ when considering p-modes of low radial order $n$. This is because geometric cancellation allows only low modes of spherical order $l$ to be observed, and we therefore can use an asymptotic approximation in the regime where $l/n \rightarrow 0$ \citep{chr10}.