deletions | additions       diff --git a/In_stars_with_field_strengths__.tex b/In_stars_with_field_strengths__.tex  index b0f8c8e..a8e4d9b 100644  --- a/In_stars_with_field_strengths__.tex  +++ b/In_stars_with_field_strengths__.tex 
...
In stars with field strengths exceeding $B_c$ (equation \ref{eqn:Bc}) somewhere in their core, incoming dipole gravity waves will become evanescent where $B>B_c$. At this point, the waves must either reflect or be transmitted into the strongly magnetized region as Alfv\'en waves.   {\bf The In either case, the  reflection/transmission process modifies the angular structure of the waves such that their energy is spread over a broad spectrum of $\ell$ values (supplementary online text).} Once a dipole wave has its energy spread to a broad spectrum of $\ell$, {\bf it will not substantially contribute to observable oscillations at the stellar surface}, because 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. 
...