deletions | additions       diff --git a/MAYBE_REMOVE_NEXT_PARAGRAPH_AND__.tex b/MAYBE_REMOVE_NEXT_PARAGRAPH_AND__.tex  index e3626e2..f7a5ae7 100644  --- a/MAYBE_REMOVE_NEXT_PARAGRAPH_AND__.tex  +++ b/MAYBE_REMOVE_NEXT_PARAGRAPH_AND__.tex 
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Most stars fall on the ``normal" upper branch of visibilities around 1.5 in  agreement with previous results [ref Mosser2012LargeKepler].   The agreement with the theoretically predicted location of the  suppressed branch (black curve) is remarkable. This curve assumes that 100\% of the wave energy tunneling into the stellar core is trapped; the decrease of the suppression to lower \numax \numax\  is then a consequence of the increasingly weaker coupling between acoustic waves in the envelope and gravity waves in the core as stars evolve (Fuller et al. 2015). Interestingly, with this large stellar sample we can separate the stars by   mass into the five panels of Fig.2, which clearly shows that the relative  population on the lower branch (suppressed stars) is strongly mass dependent.