| project | SONATA BIS, 2018/30/E/ST9/00598 |
| funding | Polish National Science Center, NCN |
| PI | Radosław Smolec |
| Co-Is | Vincent Hocde, post-doc (till Sep 2023) |
| Rajeev Singh Rathour, PhD student (degree in Jun 2025) | |
| Oliwia Ziółkowska, PhD student | |
| dates | 04.2019 - 04.2026 |
Jump to project highlights, refereed publications, conference contributions, and presentations.
Estimating the metallicity of classical Cepheids is of prime importance for studying metallicity effects on stellar evolution and the chemical evolution of galaxies, as well as on the period-luminosity relation used on the extragalactic distance scale. Our aim was to establish new empirical relations for estimating the iron content of classical Cepheids for short and long periods based on Fourier parameters from the V- and I-band light curves. The empirical relations in the V and I bands allowed us to derive the mean metallicity of a sample of MW, SMC, and LMC Cepheids that is in agreement with literature values. We also showed that these relations are precise enough to reconstruct the radial metallicity gradients within the Milky Way from OGLE data.
More information: Hocde, V., Smolec, R., Moskalik, P., Ziółkowska, O., Singh Rathour, R. Metallicity estimation of MW, SMC and LMC classical Cepheids from the shape of the V- and I-band light curves; A&A, 671, A157 (2023);
doi:10.1051/0004-6361/202245038.
Left: metallicity distribution of the Milky Way. Right: estimated Cepheid metallicities versus the galactocentric distance for the Milky Way
Modelling of large-amplitude nonlinear pulsation of classical pulsator is challenging, but now new open access tool, Radial Stellar Pulsation (RSP) is available as part of the Modules for Experiments in Stellar Astrophysics (MESA). RSP is based on nonlinear convective pulsation codes developed by R. Smolec as part of PhD thesis, see also Smolec & Moskalik (2008).
More information: B. Paxton, R. Smolec, J. Schwab, A. Gautschy, et al. Modules for Experiments in Stellar Astrophysics (MESA): Pulsating Variable Stars, Rotation, Convective Boundaries, and Energy Conservation, ApJ Suppl. Ser. (2019).
doi:10.3847/1538-4365/ab2241.
The Figure shows a comparison between observed and modelled amplitudes and amplitude ratios for fundamental mode (RRab) and first overtone (RRc) RR Lyrae stars.
Y Ophiuchi (Y Oph) is a classical Cepheid with a pulsation period of 17.12 days. This star is reported to be as dim as a Cepheid of about half its pulsation period and it exhibits a low radial velocity and light-curve amplitude. For these reasons, Y Oph is not used to calibrate period-luminosity (PL) relation and its distance remains uncertain.
We find that all pulsation models at high effective temperatures are in remarkable agreement with the observations along the pulsation cycle. This result suggests that the low amplitude of Y Oph may be explained by proximal location to the blue edge of the instability strip (IS). We also find that a pulsational mass of about 7-8 solar masses is consistent with a non-canonical evolutionary model with moderate overshooting, PL relation and Gaia parallax. However, a much lower mass below 5 solar masses is required to match Baade-Wesselink (BW) distance measurements from the literature. We show that the combination of the impact of the CSE on the photometry, together with a projection factor of about 1.5, explains the discrepant distance and luminosity values obtained from BW methods.
More information: Hocde, V., Smolec, R., Moskalik, P., Singh Rathour, R., Ziółkowska, O.; Pulsation modeling of the Cepheid Y Ophiuchi with RSP/MESA. Impact of the circumstellar envelope and a high projection factor on the Baade-Wesselink method; A&A, 683, A233 (2024);
ADS, PDF, arXiv:2312.12046.
The Figure shows HR diagram comparing parameters of MESA-RSP models of Y Oph (crosses) with evolutionary tracks computed with MESA for different stellar masses. These models assume an overshooting parameter fov = 0.02. The vertical blue strip corresponds to the measured value of the mean effective temperature for Y Oph, i.e. Teff = 5800 ± 100K.
We conduct a systematic search for non-evolutionary period changes to look for Cepheids in likely binary configurations and quantify their incidence rates in the Magellanic Clouds. We collected over a decade's worth time series photometry from the publicly available Optical Gravitational Lensing Experiment (OGLE) with more than 7200 Cepheids altogether from the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). Our sample contains both fundamental-mode and first-overtone mode Cepheids. Then we calculated the observed minus calculated (O-C) diagrams to reveal the light-travel time effect (LTTE).
We found 52 candidate Cepheid binary systems in the LMC (30 fundamental and 22 first-overtone mode) and 145 in the SMC (85 fundamental and 60 first-overtone mode). The majority of the sample is characterized by orbital periods of 2000-4000 d and eccentricities of 0.2-0.5. Moreover, we report two candidates in each galaxy with the Cepheid likely existing with a giant companion. The incidence rate ratio for SMC to LMC calculated from our sample is in agreement with binary Cepheid population synthesis predictions.
More information: Singh Rathour, R., et al.; Non-evolutionary effects on period change in Magellanic Cepheids. I. New binary systems revealed from light travel time effects; A&A, 686, A268 (2024);
Full paper.
The Figure shows exemplary O-C diagrams from our study.
Contemporary one-dimensional stellar evolution codes, like Modules for Experiments in Stellar Astrophysics (MESA), come with a large number of free parameters that allow us to model the physical processes in stellar interiors under many assumptions. The uncertainties that arise from this freedom are rarely discussed in the literature despite their impact on the evolution of the model.
We have calculated a grid of evolutionary models with MESA, varying several controls, like solar mixture of heavy elements, mixing-length theory prescription, nuclear reaction rates, the scheme to determine convective boundaries, atmosphere model, and temporal and spatial resolution, and quantify their impact on age and location of the evolutionary track on the H-R diagram from the main sequence until the end of core helium burning.
Our investigation was conducted for a full range of masses and metallicities expected for classical Cepheids. The uncertainties are signi cant, especially during core helium burning, reaching or exceeding the observational uncertainties of logTeff and logL for detached eclipsing binary systems.
More information: Ziolkowska, et al.; Toward a Comprehensive Grid of Cepheid Models with MESA I. Uncertainties of the Evolutionary Tracks of Intermediate-mass Stars; ApJ Suppl. Ser., 274, 30 (2024);
Full paper.
Median (solid line) along with 25th and 75th percentiles (colored regions) for the maximum recorded relative difference distributions for log age (top panels), logTeff (middle panels), and logL (bottom panels) at progressing evolutionary phases (horizontal axis). The two colors correspond to models with (orange right-slanted lines) and without convective core overshooting (blue left-slanted lines).
We provide new precise Fourier parameters of Cepheid radial velocity (RV) curves determined from RV measurements available in the literature together with unpublished data. Our sample includes 178 fundamental-mode and 33 first-overtone pulsators. 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.
More information: Hocde, V., et al.; Precise Fourier parameters of Cepheid radial velocity curves: Towards refining the Hertzsprung progression models; A&A, 689, A224 (2024);
Full paper.
The Figure shows low-order Fourier parameters for RV curves of fundamental-mode and first-overtone Cepheids.
We provide a systematic and quantitative description of irregular period changes in Cepheids. Such a study is crucial for a complete understanding of period changes in Cepheids and is key to decoupling the evolutionary aspects from the non-evolutionary ones.
In our investigation, 33.5±7% of analysed stars show irregular period changes. Considering the pulsation mode, irregular period changes were detected in 16.5±0.7% of the analysed fundamental mode stars and in 68.1±1.2% of the first overtone stars. The amplitude of variability in the O-C diagrams increases with the pulsation period, and at a given pulsation period, it is larger for first overtone stars. While the increase is linear for first overtone stars, for fundamental mode stars it becomes steeper as the pulsation period increases. Time scales of the observed variability range from a few hundred to a few thousand days.
More information: Singh Rathour, R., et al.; Non-evolutionary effects on period change in Magellanic Cepheids. II. Empirical constraints on non-linear period changes; A&A, 695, A114 (2025);
Full paper.
The Figure shows exemplary O-C diagrams for LMC first overtone Cepheids with irregular period changes.
Evolutionary tracks for 2−8M☉ models, covering a [Fe/H]=−1.0 (Z=0.0014) to [Fe/H]=+0.2 (Z=0.02) metallicity range are computed with Modules for Experiments in Stellar Astrophysics, MESA, to investigate evolutionary and pulsation properties of classical, fundamental mode Cepheids. We examine in detail the effects of convective overshooting from the Main Sequence core, as well as from the convective envelope on the Red Giant Branch.
Period-Luminosity, Mass-Luminosity, Period-Radius and Period-Age relations are derived, both in analytical and tabular form. Their dependence on metallicity, crossing number and overshooting parameters are investigated.Considering metallicity effect of the Period-Luminosity relation, we find γ≈−0.20 mag dex−1 , nearly independent on photometric pass band and in good agreement with recent observational studies.
The full library of computed evolutionary models is available at Zenodo.
More information: Smolec, R., et al.; Toward a Comprehensive Grid of Cepheid Models with MESA. III. Evolutionary and Pulsation Relations for Models with Core and Envelope Overshooting; ApJ Suppl. Ser., in press (2026);
Full paper at arXiv.
Example of relations derived in the paper: Period-Radius relations for models without overshooting (top) and including overshooting (bottom), for Milky Way, LMC and SMC metallicities (in the left, middle, and right panels, respectively), confronted with observational determinations