Precise Fourier parameters of Cepheid radial velocity curves: Towards refining the Hertzsprung progression models

¹ Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland
² Sternberg Astronomical Institute, Moscow State University, 119234 Moscow, Russia
³ Institute of Astronomy, Russian Academy of Sciences, 119017 Moscow, Russia

Received: 25 August 2023
Accepted: 20 June 2024

Abstract

Context. Radial velocity (RV) curves of Classical Cepheids allow precise determination of the resonant periods, which in turn help to constrain fundamental parameters of these stars. The RV curves of Cepheids are also useful for identifying their pulsation modes and for distance determination using the parallax-of-pulsation method.

Aims. The primary goal of this paper is to derive precise Fourier parameters of the RV curves for fundamental and first-overtone Galactic Cepheids. Our secondary objectives are then to analyze the progression of the Fourier parameters up to the seventh harmonic, and to propose an identification of the pulsation modes of the stars.

Methods. For each star, we carefully selected RV measurements available in the literature that yield the highest precision of Fourier parameters according to the procedure that follows. We performed a Fourier decomposition of the RV curves using the unweighted least-square method and the standard deviation of the fit was used to derive the uncertainty on the Fourier parameters. We corrected for zero-point differences between datasets and RV modulations caused by binary motion.

Results. With this study we have more than doubled the number of Cepheids with published RV curve Fourier parameters and with their uncertainty properly estimated. Our sample includes 178 fundamental-mode and 33 first-overtone pulsators, as well as 7 additional Cepheids whose pulsation mode is uncertain or undetermined according to our criteria. For the fundamental-mode Cepheids, the precision of the obtained low-order Fourier phases and amplitudes is about seven times and 25% better, respectively, as compared to the precision achieved in previously published Fourier parameter surveys. With highly accurate RV Fourier phases ϕ₂₁, we are able to firmly identify V495 Cyg as a new first-overtone Cepheid and we confirm the first-overtone nature of several other stars. In particular, α UMi should be firmly classified as a first-overtone pulsator. In three objects (VY Per, AQ Pup, and QZ Nor), we find significant γ-velocity variations, which for the first two objects (and possibly for QZ Nor as well) can be attributed to the spectroscopic binarity of these stars. Finally, the analysis of the fundamental mode Fourier parameters up to seventh order reveals tight progression of Fourier phases for all pulsation periods.

Conclusions. We provide new precise Fourier parameters of Cepheid RV curves determined from RV measurements available in the literature together with unpublished data. The pulsation period coverage and the precision obtained, in particular for Fourier phase ϕ₂₁, will be useful for studying the dynamics of Cepheid pulsations with the help of hydrodynamical models. Further RV measurements from modern high-resolution spectroscopic instruments will be important to improve these results.