  The cores of luminous B and A-type (BA) supergiant stars are the seeds of
later core collapse supernovae. Thus, constraining the near-core conditions in
this class of stars can place tighter constraints on the size, mass and
chemical composition of supernova remnants. Asteroseismology of these massive
stars is one possible approach into such investigations. Recently, Moravveji et
al. (2012, hereafter Paper I) extracted 19 significant frequencies from a
6-year radial velocity monitoring or Rigel (\beta Ori, B8 Ia). The periods they
determined broadly range from 1.22 to 74.74 days. Based on our differentially
rotating stellar structure and evolution model, Rigel, at it's current
evolutionary state, is undergoing core He burning and shell H burning. Linear
fully non-adiabatic non-radial stability analyses result in the excitation of a
dense spectrum of non-radial gravity-dominated mixed modes. The fundamental
radial mode (\ell=0) and its overtones are all stable. When the hydrogen
burning shell is located even partially in the radiative zone, a favorable
condition for destabilization of g-modes through the so-called
\epsilon-mechanism becomes viable. Only those g-modes that have high relative
amplitudes in the hydrogen burning (radiative) zone can survive the strong
radiative damping. From the entire observed range of variability periods of
Rigel (found in Paper I), and based on our model, only those modes with periods
ranging between 21 to 127 days can be theoretically explained by the
\epsilon-mechanism. The origin of the short-period variations (found in Paper
I) still remain unexplained. Because Rigel is similar to other massive BA
supergiants, we believe that the \epsilon-mechanism may be able to explain the
long-period variations in \alpha Cygni class of pulsating stars.
