Reconstruction of Cepheid radial velocity curves from the shape of the V-band light curves

Radial velocity (RV) curves of Cepheids are essential for studying their pulsation properties and also for measuring their distance via the parallax-of-pulsation method. Although precise RV curves are available for hundreds of Cepheids, it is still not possible to predict the complete RV curve from other observables such as their pulsation period or metallicity. This paper aims to develop the first method of reconstructing the shape of the RV curves of short-period fundamental-mode Cepheids, based exclusively on their pulsation period and the morphology of their V-band light curves (LCs). We compiled a dataset of high-quality spectroscopic and photometric measurements from the literature for 81 short-period fundamental-mode Galactic Cepheids up to a pulsation period of 8, days, enabling the precise determination of the Fourier parameters and their uncertainties. By performing a detailed comparative analysis of their shapes, we investigated correlations between LC and RV Fourier parameters and used these relations to reconstruct the RV curves. We further assessed the accuracy of these reconstructions by examining potential metallicity effects with an additional dataset of 24 metal-poor Cepheids. For pulsation periods between 3. 5 and 7. 0, days, we found tight correlations between different combinations of LC and RV Fourier parameters up to order 7. In particular, we discovered that the ratios 21 (RV) /R_ 21 (LC) and R_ 31 (RV) /R_ 31 (LC) are tightly correlated with the pulsation period. These relationships enable the reconstruction of RV curves of Cepheids with their LC. The reconstructed curve has an uncertainty of about 0. 60, km, s ^ -1 relative to the Fourier fit of true spectroscopic RV measurements. For individual Cepheids, the reconstructed RV curves integrated along the pulsation cycle (i. e. the linear radius variations) are accurate to less than 1% and precise to within 4. 16% in comparison to the integrated true spectroscopic RV curves. Last, our sample of metal-poor Cepheids shows a good agreement with the empirical relations calibrated on Galactic pulsators, indicating that the method of reconstruction is weakly dependent on metallicity. For the first time, we present a method of reconstructing the shape of the RV curves of Cepheids using solely the V-band LC and the pulsation period. This approach provides a valuable tool for the reconstruction of RV curves for extragalactic Cepheids through photometric data alone. It opens the road to a purely photometric parallax-of-pulsation method in the context of photometric surveys, such as the Vera Rubin Telescope. Further calibration in different photometric bands and for a larger metallicity baseline will be useful to improve the method.