deletions | additions       diff --git a/Asteroseismic Calculations.tex b/Asteroseismic Calculations.tex  index 4450cc1..e5096a1 100644  --- a/Asteroseismic Calculations.tex  +++ b/Asteroseismic Calculations.tex 
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%For KEPLER, the sampling rate of the long-cadence mode restricts the sensitivity to frequencies below $\sim 280\mu$Hz (Nyquist frequency).  Rotation is known to lift lifts  the degeneracy between the non-radial modes of the same radial order n and degree l but different azimuthal order m. In the case where If  the rotation of the star is slow enough so that enough, one can neglect  the effects of the centrifugal force can be neglected, and use  a first-order perturbation approximates well the effects of rotation on the mode frequencies. approximation.  Assuming a spherically symmetric rotation profile one can writethe frequency of the $(n,l,m)$ mode as  \begin{equation}  \nu_{n,l,m}=\nu_{n,l,0}+m\delta\nu_{n,l}  \label{e.split1}  \end{equation}  here for the frequency of the $(n,l,m)$ mode. Here  $\delta\nu_{n,l}$ is the \textit{rotational splitting}, rotational splitting,  a weighted measure of the star's rotation rate $\Omega(r)$ $\Omega(r)$.  \begin{equation}  \delta\nu_{n,l} = (2\pi)^{-1} \int_0^R K_{n,l}(r) \Omega(r) \,\hbox{d}r  \label{e.split2}  \end{equation}    The functions $K_{n,l}(r)$ are called rotational kernels of the modes and depend on the star's equilibrium structure and on the mode eigenfunctions.   Therefore rotational splittings are basically a weighted measure of the star’s rotation rate through the  rotational Kernels.