Implications of a turbulent convection model for classical Cepheids

¹ INAF-Osservatorio astronomico di Capodimonte, Via Moiariello 16, I-80131 Napoli, Italy
² Department of Physics, Cotton University, Panbazar, Guwahati 781001, Assam, India
³ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Straße 1, 85748 Garching, Germany
⁴ Heidelberg Institute for Theoretical Studies (HITS), Schloss-Wolfsbrunnen Weg 35, Heidelberg, Germany
⁵ Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539 Munich, Germany

^⋆ Corresponding author: mami.deka@inaf.it

Received: 27 February 2025
Accepted: 5 June 2025

Abstract

Context. The appearance of blue loops in the evolutionary tracks of intermediate-mass core He-burning stars is essential for explaining the observed characteristics of Cepheïds. The blue loops for lower mass Cepheïds cannot always be reproduced when only classical, local mixing length theory (MLT) is used. Additionally, classical models result in a mass discrepancy compared to pulsational and dynamical mass determinations. Both problems can be resolved through an ad hoc extension of the MLT for convection.

Aims. We use the nonlocal Kuhfuss turbulent convection model (TCM), which allows us to explain the overshooting directly by solving the TCM equations. The primary objective of this study is to test the predictions of the Kuhfuss TCM when applied to intermediate-mass core He-burning stars and validate the model predictions against observations of Cepheïds.

Methods. We used the state-of-the-art 1D stellar evolution code GARSTEC with the implementation of the Kuhfuss TCM and computed evolutionary tracks for intermediate-mass core He-burning stars. We compared these tracks with those computed with MLT, including and excluding ad hoc overshooting and with observations of five Cepheïds in detached binary systems obtained from the literature.

Results. The stellar evolution tracks generated using the Kuhfuss TCM and MLT with ad hoc overshooting exhibit similar appearances. Overshoot mixing from the convective boundaries and the occurrence of the Cepheïd blue-loop have been achieved naturally as solutions to the equations of the Kuhfuss TCM. Furthermore, the evolutionary models, including the Kuhfuss TCM, have been successful in reproducing the observed stellar parameters, including mass, luminosity, radius, and effective temperature.

Conlcusions. We successfully generated Cepheïds’ blue loops with a TCM without any fine-tuning of the involved numerical parameters and with overshooting predicted directly from the convection theory. Beyond the achievement of blue loops, our approach which treats convection more physically has also been able to reproduce the observations of Cepheïds in eclipsing binary systems, with a similar level of accuracy as MLT models with ad hoc overshooting.