deletions | additions       diff --git a/In_stars_with_field_strengths__.tex b/In_stars_with_field_strengths__.tex  index f82bd49..755ce44 100644  --- a/In_stars_with_field_strengths__.tex  +++ b/In_stars_with_field_strengths__.tex 
...
In RGB cores, the reflection/transmission process modifies the waves such that they will become trapped in the radiative zone (supplementary online text). Incoming $\ell=1$ magneto-gravity waves can transmit energy into a continuous spectrum \cite{Reese_2004,Levin_2006} of Alfven waves with a broad spectrum of $\ell$ values \cite{Rincon_2003}. The same effect occurs for reflected waves. The location of $r_{\rm MG}$ is a function of latitude, because the magnetic field cannot be spherically symmetric. Even in the simplest case of a purely dipolar magnetic field, any resulting oscillation modes will contain a broad spectrum of $\ell$ \cite{Lee_2007,Lee_2010}. In reality, the field will likely have a complex geometry containing both poloidal and toroidal components \cite{Braithwaite_2004,Braithwaite_2006,Duez_2010}, and dipole waves will inevitably scatter into higher $\ell$ waves in the presence of a strong magnetic field.   Once a dipole wave has its energy spread to a broad spectrum of $\ell$, {\bf  it is doomed will not contribute  to remain within observable oscillations at  the core until it dissipates. stellar surface.}  The reason is that higher $\ell$ waves are trapped within the radiative core by a thicker evanescent region (see equation \ref{eqn:integral2}) separating the core from the envelope, preventing wave energy from tunneling back to the surface. Even if some wave energy does eventually return to the surface to create an oscillation mode, the increased time spent in the core results in a very large mode inertia, greatly reducing the mode visibility. Additionally, high $\ell$ waves will not be detected in {\it Kepler} data due to the geometric cancellation which makes $\ell \gtrsim 3$ modes nearly invisible. We emphasize that the magnetic greenhouse effect arises not from the alteration of incoming wave frequencies, but rather due to modification of the wave angular structure. Such angular modification originates from the inherently non-spherical structure (because $\nabla \cdot {\bf B} = 0$) of even the simplest magnetic field configurations.