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On the Effect of Rotation on Populations of Classical Cepheids II. Pulsation Analysis for Metallicities 0.014, 0.006, and 0.002

Classical Cepheid variable stars are high-sensitivity probes of stellar evolution and fundamental tracers of cosmic distances. While rotational mixing significantly affects the evolution of Cepheid progenitors (intermediate-mass stars), the impact of the resulting changes in stellar structure and composition on Cepheids on their pulsational properties is hitherto unknown. Here we present the first detailed pulsational instability analysis of stellar evolution models that include the effects of rotation, for both fundamental mode and first overtone pulsation. We employ Geneva evolution models spanning a three-dimensional grid in mass (1.7 - 15 $M_\odot$), metallicity (Z = 0.014, 0.006, 0.002), and rotation (non-rotating, average & fast rotation). We determine (1) hot and cool instability strip (IS) boundaries taking into account the coupling between convection and pulsation, (2) pulsation periods, and (3) rates of period change. We investigate relations between period and (a) luminosity, (b) age, (c) radius, (d) temperature, (e) rate of period change, (f) mass, (g) the flux-weighted gravity-luminosity relation (FWGLR). We confront all predictions aside from those for age with observations, finding generally excellent agreement. We tabulate period-luminosity relations (PLRs) for several photometric pass-bands and investigate how the finite IS width, different IS crossings, metallicity, and rotation affect PLRs. We show that a Wesenheit index based on H, V, and I photometry is expected to have the smallest intrinsic PLR dispersion. We confirm that rotation resolves the Cepheid mass discrepancy. Period-age relations depend significantly on rotation (rotation increases Cepheid ages), offering a straightforward explanation for evolved stars in binary systems that cannot be matched by conventional isochrones assuming a single age. Finally, we show that Cepheids obey a tight FWGLR.