Toward a Comprehensive Grid of Cepheid Models with MESA. III. Evolutionary and Pulsation Relations for Models with Core and Envelope Overshooting

Evolutionary tracks for 2-8M$_\odot$ models, covering a [Fe/H]=$-$1.0 ($Z=0.0014$) to [Fe/H]=+0.2 ($Z=0.02$) metallicity range are computed with Modules for Experiments in Stellar Astrophysics, MESA, to investigate evolutionary and pulsation properties of classical, fundamental mode Cepheids. We examine in detail the effects of convective overshooting from the Main Sequence core, as well as from the convective envelope on the Red Giant Branch. Mass loss is also included in a few model sets. Linear pulsation properties are derived consistently with a module of MESA, Radial Stellar Pulsation, RSP. We provide edges of the classical Instability Strip, as well as ages, crossing times through the Instability Strip and period change rates. Period-Luminosity, Mass-Luminosity, Period-Radius and Period-Age relations are provided, both in analytical and tabular form. Their dependence on metallicity, crossing number and overshooting parameters are investigated. Qualitative comparisons with classical Cepheids in the Milky Way and Magellanic Clouds as well as other theoretical relations are presented. We find satisfactory agreement for most of the observables and good match with other theoretical work, however reproducing short-period Cepheids in the Small Magellanic Cloud as well as Cepheid mass discrepancy pose a challenge for the presented models. Considering metallicity effect of the Period-Luminosity relation, we find $\gamma\approx -0.20$ mag dex$^{-1}$, nearly independent on photometric pass band and in good agreement with recent observational studies. The magnitude of this effect depends on the underlying mass-luminosity relation, being stronger for relations that predict higher luminosities at a given mass.