<p>Non-linear calculations of intermediate amplitude to investigate stability have been carried out for one hundred RR Lyrae models of varying composition, mass, luminosity, and effective temperature. Of these, the calculations have been extended to the maximum amplitude for fifty models. The dependence of the location of the instability strip on composition, mass, and luminosity has been explored. In particular, the high-temperature boundary of the strip increases by 500° K for each 15 per cent increase in the mass fraction of helium.</p>\ud \ud <p>The dependence on effective temperature of the phase shift, the ratio of radius and luminosity amplitudes, and the shape of the light-curve has been explored, and the correlations of these three measures have been found. These measures may then be applied to observed variables to determine their location in the instability strip and the helium content of their envelopes. The examples studied give best agreement at about 30 per cent helium by mass.</p>\ud \ud <p>The calculations reveal many details of the shapes of the light- and velocity-curves which may be compared to observation. A number of features of these curves of known variables are discussed, and the underlying explanation is investigated.</p>\ud \ud <p>The sources of the driving energy of these models have been explored. In the models of the most favored composition, 30 per cent helium, the hydrogen ionization region is almost as important to the driving as is the He II ionization. The effects that cause the amplitude to cease growing and level off at the observed maximum amplitude are explored: they appear to involve several non-linear effects, particularly a steep velocity front, in the He II ionization zone.</p>\ud \ud <p>A new kind of period-luminosity relation has been discovered. The shortest period at which the fundamental mode persists, before it changes to the first harmonic, has been found to be independent of mass and composition and to depend only on the luminosity. This relation was found to be P<sub>tr</sub> = 0 057 (L/L☉)<sup>0.6</sup> days. This has been used to interpret the varying period distributions of RR Lyrae stars in clusters and in the field with the result that the luminosities are found to vary from M<sub>bol</sub> = 0.57 for very metal-weak clusters to M<sub>bol</sub> = 0.96 for clusters only slightly weak in metals. Metal-rich variables are slightly less luminous still. These results lead to the conclusion that the masses of RR Lyrae stars are near 0.5 M☉, which must imply a significant mass loss. These conclusions appear to be consistent with the possible interior models.</p
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