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Stothers, R.B., 1987: Second-overtone models of RR Lyrae stars. Astrophys. J., 319, 260-263, doi:10.1086/165451.
Linear models of RR Lyrae stars pulsating in the second overtone indicate that this mode is self-excited only for rather low luminosities if the masses are normal. An unstable second-overtone model has been selected from the linear survey and has been followed up to limiting amplitude by using a nonlinear hydrodynamical computer program. Deep splitting of the main light peak in the theoretical light curve occurs but does not resemble any observed feature. Moreover, the distribution of periods of RR Lyrae stars in globular clusters can be accounted for adequately by fundamental-mode and first-overtone pulsation. It is concluded that second-overtone pulsators probably do not exist among RR Lyrae stars.
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