Reconstruction of Cepheid Radial Velocity Curves from the shape of the V-band Light Curves

Abstract

This paper aims to develop the first method to reconstruct 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 precise determination of the Fourier parameters and their uncertainties. 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 23 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 $R_{21}(RV)/R_{21}(LC)$ and $R_{31}(RV)/R_{31}(LC)$ are 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${\rm km\,s}^{-1}$ 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. 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.

Figures (13)

• Figure 1: (a) Histogram of the pulsation period of the calibrating sample in yellow and of the metal-poor sample in red. (b) Histogram of the metallicity of the calibrating sample only (see Sect. \ref{['sect:calibration']}).
• Figure 2: (a) Histogram of the order of the Fourier fits for the $V$-band LCs and RV curves of the initial calibrating sample (81 Cepheids up to a pulsation period of 8 days). (b) 2D histogram of the LC Fourier order versus RV Fourier order.
• Figure 3: Fourier amplitude ratios and phase parameters ($R_{21}$ to $R_{61}$ and $\phi_{21}$ to $\phi_{61}$) of Cepheid RV curves (a) and LCs (b) as a function of the period. Models for MU Cep and OGLE-LMC-CEP-227 are shown to illustrate the difference between solar and subsolar metallicity around $P=4\,$day. The solar and sub-solar metallicity variables are plotted with yellow and red error bars (resp. magenta and green) for the RV curves (resp. LCs). Fourier parameters are derived with decomposition analysis presented in Sect. \ref{['sect:fourier']}.
• Figure 4: Amplitude of the first harmonic $A_1$ for RV curves (left panel) and for LCs (right panel). Cepheids of solar metallicity are plotted with yellow and green symbols and those of sub-solar metallicity with red and magenta symbols.
• Figure 5: Fourier parameters of RV curves as a function of pulsation period and $V$-band LC shape: (a) $\phi_{21}$, (b) $\phi_{31}$, (c) $\phi_{41}$, (d) $\phi_{51}$, (e) $\phi_{61}$, (f) $\phi_{71}$, (g) $R_{21}$, (h) $R_{31}$, (i) $R_{41}$, (j) $R_{51}$, (k) $R_{61}$, (l) $R_{71}$. Yellow circles (calibrating sample) are used to produce the fits between 3.45 and 7 days (blue lines, see Sect. \ref{['sect:templates']}); red circles show metal-poor Cepheids; grey points above $P > 7$ days are ignored in the fit; violet points are metal-poor Cepheid outside the pulsation period range 3.4 to 7 days.