VELOCE III. Reconstructing Radial Velocity Curves of Classical Cepheids
We present a novel framework for accurately reconstructing radial velocity (RV) curves of classical Cepheids from sparsely sampled time-series data suitable for application in large spectroscopic surveys. The framework provides a prior 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, $v_γ$, to within $20-30$ m/s, and peak-to-peak amplitudes, $P2P$, to within $\sim 1.1\%$. Subsampling the initial data set, we show that $v_γ$ and $P2P$ can be determined to within $\sim 500$ m/s and $\sim 4\%$, respectively, from as few as three observations at random pulsation phases, with the phase of minimum radius fitted rather than assumed. We fitted existing time-series RV data of Cepheids in the LMC and SMC, obtaining typical residuals of $0.5-2.0$ km/s. The typical total uncertainty on $v_γ$ achieved for the SMC Cepheids is $\sim 0.84$ 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 single-lined SB fractions of $\sim 25\%$ and $27\%$ 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 (amplitude $>80$ km/s). The SMC's kinematics are more complex and not yet sufficiently sampled. Our framework is designed to yield accurate $v_γ$ 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.