A Reproducible AAVSO Johnson-V Fourier Template for the Prototype Cepheid Delta Cephei

Abstract

We present an empirical Fourier reconstruction of the observed Johnson-V light curve of the prototype Classical Cepheid Delta Cephei. The goal is not to infer a full physical stellar model but to establish a reproducible observed-light-curve benchmark for later comparison with nonlinear pulsation, synthetic photometry, Baade-Wesselink/SPIPS, GYRE-supported, and independent hydrodynamic calculations. Using an adopted period of Pobs = 5.366531 d, 244 AAVSO Johnson-V measurements were filtered to a cleaned sample of 242 points after rejecting two extreme outliers. The cleaned data span 355.09259 d and were phase folded using an empirical bright-maximum epoch of JD = 2460851.395800. We fit a low-order Fourier model to the phased light curve and adopt a third-order template as the preferred empirical morphology representation. The adopted N = 3 fit gives A0 = 3.9031, A1 = 0.3434 mag, A2 = 0.1428 mag, and A3 = 0.0531 mag, corresponding to R21 = 0.4159 and R31 = 0.1547. The template has a full Johnson-V amplitude of Delta V = 0.8544 mag, a rise fraction of frise = 0.2885, and an asymmetry index of Aasym = 0.4230. Bootstrap uncertainties are reported in the manuscript. Fourier orders N = 4-6 reduce the RMS residual by only about 0.0012 mag relative to the N = 3 model, so the third-order representation is retained as the simplest adequate empirical template. Observer-level residual diagnostics show that the remaining scatter is not purely random. This paper provides an observational morphology target rather than a physical explanation of the pulsation.