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VELOCE III. Reconstructing Radial Velocity Curves of Classical Cepheids

Giordano Viviani, Richard I. Anderson

TL;DR

We develop a PCA-based framework trained on VELOCE-I to reconstruct Cepheid radial velocity curves from sparsely sampled data by deriving priors for RV-curve components as a function of pulsation period. Using KDE-derived priors and MAP fitting, we recover the pulsation-averaged velocity $v_\gamma$ to roughly $0.35$ km s$^{-1}$ and the peak-to-peak amplitude $P2P$ to about $6-7\%$ with as few as three RV measurements, enabling multiplicity studies and galactic kinematic analyses in large surveys. Validation on LMC/SMC data shows SB1 detections and kinematic patterns consistent with prior work, with LMC Cepheids tracing rotation and the SMC exhibiting more complex dynamics. The approach is well suited for upcoming spectroscopic surveys (e.g., 4MOST, SDSS-V), providing robust, probabilistic Cepheid RV templates and expanding the scientific reach of time-domain spectroscopy in evolved intermediate-mass stars.

Abstract

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, $v_γ$, to within $20-30$m/s, and peak-to-peak amplitudes, $P2P$, to within $\sim 2\%$. Subsampling the initial data set, we show that $v_γ$ 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 $v_γ$ 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 $v_γ$ 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.

VELOCE III. Reconstructing Radial Velocity Curves of Classical Cepheids

TL;DR

We develop a PCA-based framework trained on VELOCE-I to reconstruct Cepheid radial velocity curves from sparsely sampled data by deriving priors for RV-curve components as a function of pulsation period. Using KDE-derived priors and MAP fitting, we recover the pulsation-averaged velocity to roughly km s and the peak-to-peak amplitude to about with as few as three RV measurements, enabling multiplicity studies and galactic kinematic analyses in large surveys. Validation on LMC/SMC data shows SB1 detections and kinematic patterns consistent with prior work, with LMC Cepheids tracing rotation and the SMC exhibiting more complex dynamics. The approach is well suited for upcoming spectroscopic surveys (e.g., 4MOST, SDSS-V), providing robust, probabilistic Cepheid RV templates and expanding the scientific reach of time-domain spectroscopy in evolved intermediate-mass stars.

Abstract

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, , to within m/s, and peak-to-peak amplitudes, , to within . Subsampling the initial data set, we show that and can be determined to within km/s and , 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 km/s. The typical total uncertainty on achieved for the SMC Cepheids is 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 and in the two galaxies, similar to the Milky Way's SB fraction of 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 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 and 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.

Paper Structure

This paper contains 25 sections, 3 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Data and methods
  3. VELOCE observations and FS models
  4. Principal Component Analysis of VELOCE FS models
  5. Turning PC coefficients into RV curve fitting priors
  6. Results
  7. Principal Components
  8. Evaluating PC Performance
  9. $\Delta v_\gamma = v_\gamma - v_{\gamma, \rm VELOCE}$
  10. $\Delta P2P = P2P - P2P_{\rm VELOCE}$
  11. $RMSE$
  12. RV curve fits based on PCs with Priors
  13. $\Delta v_\gamma = v_\gamma - v_{\gamma, \rm VELOCE}$
  14. $\Delta P2P = P2P - P2P_{\rm VELOCE}$
  15. $RMSE$
  16. ...and 10 more sections

Figures (12)

  • Figure 1: Cepheids' RV curves published in VELOCE-I. On the left panel, we report the sampled $\texttt{V}^{\rm FS}$ for both the training (blue) and test (orange) set. The solid black line indicates the mean curve of the training set, $\overline{\texttt{V}^{\rm FS}}$. The residual curves after subtracting $\overline{\texttt{V}^{\rm FS}}$ are reported in the second panel.
  • Figure 2: Variance ratio explained by each PC. The vertical orange dashed line separates the retained (left) and discarded (right) PCs. The total explained variance ratio of the retained PCs is shown in right top corner.
  • Figure 3: Distribution of the coefficients $p^{FS}_i$ of the $\mathcal{M}$ models as a function of the logarithm of the pulsation period, $\log{P}$. As for the previous plots, the training set is presented in blue, whereas the test set in orange. In the background, the KDE distributions obtained from the training set are shown in grayscale.
  • Figure 4: Performance of the obtained PCs when fitting VELOCE-I data. The training and test set members are colored in blue and orange respectively. The left panels from top to bottom: the difference in pulsation average velocity, $\Delta v_\gamma$, the difference in peak-to-peak amplitude, $\Delta P2P$, and $RMSE$. The right panels present the same quantities as percentage of the target's $P2P_{\rm VELOCE}$.
  • Figure 5: Performance of the PCs and priors applied to subsamples of size $N_{\rm RV}=3$. Each panel shows each target's mean and standard deviation of the results obtained for all combination. From top to bottom, the statistics reported are: $\Delta v_\gamma$, $\Delta P2P$ and $RMSE$.
  • ...and 7 more figures