The success of asteroseismology relies heavily on our ability to identify the
frequency patterns of stellar oscillation modes. For stars like the Sun this is
relatively easy because the mode frequencies follow a regular pattern described
by a well-founded asymptotic relation. When a solar like star evolves off the
main sequence and onto the red giant branch its structure changes dramatically
resulting in changes in the frequency pattern of the modes. We follow the
evolution of the adiabatic frequency pattern from the main sequence to near the
tip of the red giant branch for a series of models. We find a significant
departure from the asymptotic relation for the non-radial modes near the red
giant branch tip, resulting in a triplet frequency pattern. To support our
investigation we analyze almost four years of Kepler data of the most luminous
stars in the field (late K and early M type) and find that their frequency
spectra indeed show a triplet pattern dominated by dipole modes even for the
most luminous stars in our sample. Our identification explains previous results
from ground-based observations reporting fine structure in the Petersen diagram
and sub ridges in the period-luminosity diagram. Finally, we find `new ridges'
of non-radial modes with frequencies below the fundamental mode in our model
calculations, and we speculate they are related to f modes.Comment: 8 page, 5 figures, accepted by ApJL (ApJ, 788, L10
