Nonlinear MESA-RSP Modeling of Delta Cephei: Period Matching, Amplitude Control, and Model-Acceptance Diagnostics

Delta Cephei is the prototype classical Cepheid and a useful target for testing whether a one-dimensional nonlinear radial-pulsation workflow can satisfy more than a period constraint. We present a target-specific, reproducible workflow using the Modules for Experiments in Stellar Astrophysics (MESA) Radial Stellar Pulsation (RSP) capability, hereafter MESA-RSP, to construct, tune, extend, and classify nonlinear radial-pulsation calculations for Delta Cephei. A tuned 200-period calculation with M = 5.0 solar masses, Teff = 6050 K, L = 2422.5 solar luminosities, X = 0.73, and Z = 0.007 gives P_model = 5.366622 d for the adopted target P_obs = 5.366531 d, a difference of 9.1 x 10^-5 d, or approximately 7.9 s. This agreement shows that the mean-density structure can be tuned successfully, but extended calculations demonstrate that period matching alone is not an adequate nonlinear model-acceptance criterion. When the period-matched model was continued with the default/weak-damping setup, the amplitude and cycle behavior became nonstationary. We therefore explored the MESA-RSP eddy-viscous damping parameter RSP_alfam as a first amplitude-control experiment. The RSP_alfam = 0.60 case is retained as a period-stable reference, while the RSP_alfam = 0.425, 500-period calculation is classified as the clean amplitude-enhanced candidate. A 700-period continuation is retained only as a diagnostic case because it produced an energy-error warning. The main contribution is a reproducible Delta Cephei workflow and a transparent classification scheme showing that acceptable nonlinear Cepheid models require period agreement, interpretable late-cycle amplitude behavior, controlled surface-velocity diagnostics, and the absence of serious numerical warnings.