Discerning internal conditions of pulsating hot subdwarf B-type stars: Modeling multiple trapped modes in KIC 10001893

Context. The frequencies of gravity-mode oscillations are determined by the chemical, thermal, and structural properties of stellar interiors, which facilitates the study of internal mixing mechanisms in stars. We investigated the impact of discontinuities in the chemical composition induced by the formation of an adiabatic semi-convection region during the core helium (He)-burning phase of evolution of hot subdwarf B-type (sdB) stars. Aims. This study delves into the progression of convective core evolution, using a numerical approach to model the emergence of a semi-convection zone. We scrutinize the asteroseismic attributes of the evolutionary stages and assess the core He-burning phase by evaluating the parameter linked to the average interval between the deep trapped modes in both sdB evolutionary models and the observations of KIC 10001893. Methods. We performed evolutionary and asteroseismic analyses of sdB stars using MESA and GYRE to examine the properties of the semi-convection region. Additionally, we computed parameters related to gravity-mode period spacings and the interval between deep trapped modes to characterize the core He-burning phase at different stages of sdB evolution. Results. Using a numerical scheme in MESA to model the development of the semi-convection zone, we illustrate the evolution of the convective core in sdB stars. Our study addresses the challenges of relying solely on the average interval between oscillation mode periods with consecutive radial orders to identify the core He-burning stage. To improve identification, we propose a new parameter that represents the average interval between deep trapped modes during some of the stages of sdB evolutionary models. Additionally, we find that integrating convective penetration with convective premixing improves our models and yields comparable outcomes without the need for additional model parameters. Conclusions. Our results can advance the development of detailed evolutionary models for sdB stars by refining internal mixing schemes, increasing the accuracy of pulsation predictions, and improving alignment with observational data.