Semi-Empirical Pulsation Reconstruction of Delta Cephei with Photometry, Radial Velocities, and Temperature Constraints

Abstract

We present a semi-empirical reconstruction of the pulsation behavior of the classical Cepheid delta Cephei using observed Johnson-V photometry, HARPS-N radial velocities, and published SPIPS pulsation-model curves. A cleaned AAVSO Johnson-V data set was phase folded with P = 5.366531 d, corrected for observer zero-point offsets, clipped for residual outliers, and fitted with a three-harmonic Fourier template. The resulting empirical template has Delta V about 0.833 mag, R21 about 0.382, R31 about 0.168, and a rise fraction about 0.287. After phase and vertical alignment, the published SPIPS V-band curve reproduces the empirical Johnson-V morphology with an RMS residual about 0.023 mag. A Fourier representation of the HARPS-N radial velocities gives a peak-to-peak velocity span about 40.82 km s^-1, corresponding to a preliminary radius-displacement amplitude about 4.81 solar radii for p = 1.317. Combining this radius curve with the SPIPS Teff(phi) curve yields a hybrid luminosity curve close to the published SPIPS luminosity curve. The adopted R0 = 43.7 solar radii scale gives a mean luminosity ratio L_hybrid/L_SPIPS about 1.04, while R0 = 44.9 solar radii gives about 1.10. A direct radius-scale comparison also favors the lower adopted radius scale, with an RMS offset of 0.864 solar radii relative to the SPIPS-implied radius, compared with 2.060 solar radii for the larger-radius case. These results show that the observed visual morphology, radial displacement, and temperature-driven luminosity variation are mutually consistent when placed on a common phase convention, while the absolute radius scale remains the dominant systematic.