Classical Cepheid Pulsation Models. IX. New Input Physics

We constructed several sequences of classical Cepheid envelope models at solar chemical composition (Y=0.28,Z=0.02) to investigate the dependence of the pulsation properties predicted by linear and nonlinear hydrodynamic models on input physics. To study the dependence on the equation of state (EOS) we performed several numerical experiments by using the simplified analytical EOS originally developed by Stellingwerf and the recent analytical EOS developed by Irwin. Current findings suggest that the pulsation amplitudes, as well as the topology of the instability strip, marginally depend on the adopted EOS. To compromise between accuracy and numerical complexity we computed new EOS tables using the Irwin analytical EOS. We found that the difference between analytical and tabular thermodynamic quantities and their derivatives are smaller than 2% when adopting suitable steps in temperature and density. To improve the numerical accuracy of physical quantities, we are now adopting bicubic splines to interpolate both opacity and EOS tables. The new approach presents a substantial advantage to avoiding numerical derivatives in both linear and nonlinear models. The EOS first- and second-order derivatives are estimated by means of the analytical EOS or by means of analytical derivatives of the interpolating function. The opacity first-order derivatives are evaluated by means of analytical derivatives of the interpolating function. We also investigated the dependence of observables predicted by theoretical models on the mass-luminosity (ML) relation and on the spatial resolution across the hydrogen and the helium partial ionization regions. We found that nonlinear models are marginally affected by these physical and numerical assumptions. In particular, the difference between new and old models in the location as well as in the temperature width of the instability strip is, on average, less than 200 K. However, the spatial resolution somehow affects the pulsation properties. The new fine models predict a period at the center of the Hertzsprung progression (P_HP=9.65-9.84 days) that reasonably agrees with empirical data based on light curves (P_HP=10.0+/-0.5 days); and radial velocity curves (P_HP=9.95+/-0.05 days); they improve previous predictions by Bono, Castellani, & Marconi.