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The efficiency of convection in stars affects many aspects of their evolution and remains one of the key-open questions in stellar modelling. In particular, the size of the mixed core in core-He-burning low-mass stars is still uncertain and impacts the lifetime of this evolutionary phase and, e.g., the C/O profile in white dwarfs. One of the known observables related to the Horizontal Branch (HB) and Asymptotic Giant Branch (AGB) evolution is the AGB bump. Its luminosity depends on the position in mass of the helium-burning shell at its first ignition, that is affected by the extension of the central mixed region. In this preliminary work we show how various assumptions on near-core mixing and on the thermal stratification in the overshooting region affect the luminosity of the AGB bump, as well as the period spacing of gravity modes in core-He-burning models.

The calculation of the thermal stratification in the superadiabatic layers of stellar models with convective envelopes is a long-standing problem of stellar astrophysics, and has a major impact on predicted observational properties such as radius and effective temperature. The mixing length theory, almost universally used to model the superadiabatic convective layers, contains one free parameter to be calibrated (αml) whose value controls the resulting effective temperature. Here we present the first self-consistent stellar evolution models calculated by employing the atmospheric temperature stratification, Rosseland opacities, and calibrated variable αml (dependent on effective temperature and surface gravity) from a recently published large suite of three-dimensional radiation hydrodynamics simulations of stellar convective envelopes and atmospheres for solar stellar composition. From our calculations (with the same composition of the radiation hydrodynamics simulations), we find that the effective temperatures of models with the hydro-calibrated variable αml (that ranges between ~1.6 and ~2.0 in the parameter space covered by the simulations) present only minor differences, by at most ~30-50 K, compared to models calculated at constant solar αml (equal to 1.76, as obtained from the same simulations). The depth of the convective regions is essentially the same in both cases. We also analyzed the role played by the hydro-calibrated T(τ) relationships in determining the evolution of the model effective temperatures, when compared to alternative T(τ) relationships often used in stellar model computations. The choice of the T(τ) can have a larger impact than the use of a variable αml compared to a constant solar value. We found that the solar semi-empirical T(τ) by Vernazza et al. (1981, ApJS, 45, 635) provides stellar model effective temperatures that agree quite well with the results with the hydro-calibrated relationships. [ABSTRACT FROM AUTHOR]

A new scenario - early disc accretion - has been proposed very recently to explain the origin of the multiple population phenomenon in Galactic globular clusters. It envisages the possibility that a fraction of low- and very low-mass cluster stars may accrete the ejecta of interacting massive binary (and possibly also fast rotating massive) stars during the fully convective, pre-main sequence stage, to reproduce the CN and ONa anticorrelations observed among stars in individual clusters. This scenario is assumed to be able to explain the presence (and properties) of the multiple populations in the majority of globular clusters in the Milky Way. Here we have considered the well studied cluster NGC 2808, which displays a triple main sequence with well defined and separate He abundances. Knowledge of these abundances allowed us to put strong constraints on the He mass fraction and amount of matter to be accreted by low-mass pre-main sequence stars. We find that the minimum He mass fraction in the accreted gas has to be ~0.44 to produce the observed sequences and that at fixed initial mass of the accreting star, different efficiencies for the accretion are required to produce stars placed onto the multiple main sequences. This may be explained by differences in the orbital properties of the progenitors and/or different spatial distribution of intracluster gas with varying He abundances. Both O-Na and C-N anticorrelations appear naturally along the main sequences, once considering the predicted relationship between He and CNONa abundances in the ejecta of the polluters. As a consequence of the accretion, we predict no discontinuity between the abundance ranges covered by intermediate and blue main sequence stars, but we find a sizeable (several 0.1 dex) discontinuity of the N and Na abundances between objects on the intermediate and red main sequences. There is in principle enough polluting gas with the right He abundances to explain the observed main sequences by early accretion (hence no need to invoke a much higher cluster mass at birth, as required by scenarios envisaging multiple star formation bursts), however the matter ejected by the polluters must not be fully mixed before being accreted otherwise, according to the models, the average He abundance of the polluting gas is too low to produce the observed multiple main sequences. [ABSTRACT FROM AUTHOR]