VELOCE III. Reconstructing Radial Velocity Curves of Classical Cepheids

We present a novel framework for accurately reconstructing radial velocity (RV) curves of classical Cepheids (Cepheids) from sparsely sampled time-series data suitable for application in large spectroscopic surveys. The framework provides a set of priors for the principal components of RV curves established based on high-precision measurements from the VELOCE project; template RV curves of Cepheids can be readily extracted from our results. We demonstrate the ability of our framework to estimate unbiased pulsation average velocities, $v_\gamma$, to within $20-30$m/s, and peak-to-peak amplitudes, $P2P$, to within $\sim 2\%$. Subsampling the initial data set, we show that $v_\gamma$ and $P2P$ can be determined to within $\sim 0.35$ km/s and $\sim 6-7\%$, respectively, from as few as three observations. We fitted existing time-series RV data of Cepheids in the LMC and SMC using this framework and obtained typical RMSE of $0.5-2.0$ km/s. The typical total uncertainty on $v_\gamma$ achieved for the SMC Cepheids is $\sim 0.85$ km/s, providing sensitivity to spectroscopic binaries (SB). We identified 8 SB1 systems; two and one of which are new detections in the LMC and SMC, respectively. This yields a single-lined SB fraction of $\sim 25\%$ and $29\%$ in the two galaxies, similar to the Milky Way's SB fraction of $29\%$ established as part of VELOCE. Despite their relatively small number, LMC Cepheids reproduce the known line-of-sight component of the LMC's large-scale rotation, which differs in the extremes by more than $80$km/s. The kinematics of the SMC are more complex and not sufficiently sampled by the available Cepheids. Our framework is designed to yield accurate $v_\gamma$ and $P2P$ of Cepheids observed by large spectroscopic surveys, such as 4MOST, SDSS-V, and others, and will unlock new insights into the kinematics and multiplicity of evolved intermediate-mass stellar populations.