Recent hydrodynamical simulations of convection in a solar-like model suggest that penetrative convective flows at the boundary of the convective envelope modify the thermal background in the overshooting layer. Based on these results, we implement in one-dimensional stellar evolution codes a simple prescription to modify the temperature gradient below the convective boundary of a solar model. This simple prescription qualitatively reproduces the behaviour found in the hydrodynamical simulations, namely a local heating and smoothing of the temperature gradient below the convective boundary. We show that introducing local heating in the overshooting layer can reduce the sound-speed discrepancy usually reported between solar models and the structure of the Sun inferred from helioseismology. It also affects key quantities in the convective envelope, such as the density, the entropy, and the speed of sound. These effects could help reduce the discrepancies between solar models and observed constraints based on seismic inversions of the Ledoux discriminant. Since mixing due to overshooting and local heating are the result of the same convective penetration process, the goal of this work is to invite solar modellers to consider both processes for a more consistent approach.
We investigate the spectral evolution of white dwarfs by considering the effects of hydrogen mass in the atmosphere and convective overshooting above the convection zone. We notice the importance of the convective overshooting and suggest that the overshooting length should be proportional to the thickness of the convection zone to better fit the observations.
Mixing in the convective core is quite uncertain in core helium burning stars. In order to explore the overshooting mixing beyond the convective core, we incorporated the $k$-$ω$ proposed by Li (2012, 2017) into MESA, and investigated the overshooting mixing in evolution of sdB models. We found that the development of the convective core can be divided into three stages. When the radiative temperature gradient $\nabla_{\rm rad}$ monotonically decreases from the stellar center, the overshooting mixing presents a behaviour of exponential decay similar with Herwig (2000), and the overshooting dis…
Properties of semi-convection and core convective overshooting of stars with 15 $M_{\odot}$ and 30 $M_{\odot}$ are calculated in the present paper. New methods are used to deal with semi-convection. Different entropy gradient is used when adopting the Schwarzschild method and the Ledoux method which are used to confine the convective boundary and to calculate the turbulent quantities: $\frac{\partial \overline{s}}{\partial r}=-\frac{c_{p}}{H_P}(\nabla-\nabla_{\rm ad})$ when the Schwarzschild method is adopted and $\frac{\partial \overline{s}}{\partial r}=-\frac{c_{p}}{H_P}(\nabla-\nabla_{\rm a…
In this paper, four sets of evolutionary models are computed with different values of the mixing length parameter $α_{\rm p}$ and the overshooting parameter $δ_{\rm ov}$. The properties of the convective cores and the convective envelopes are studied in the massive stars. We get three conclusions: First, the larger $α_{\rm p}$ leads to enhancing the convective mixing, removing the chemical gradient, and increasing the convective heat transfer efficiency. Second, core potential $ϕ_{\rm c} = M_{\rm c} / R_{\rm c}$ describes sufficiently the evolution of a star, whether it is a red or blue superg…
We perform two-dimensional numerical simulations of core convection for zero-age-main-sequence stars covering a mass range from 3 $M_\odot$ to 20 $M_\odot$. The simulations are performed with the fully compressible time-implicit code MUSIC. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 $M_\odot$ models. The simulations cover hundreds to thousands of convective turnover timescales. Appl…
We estimate the extent of overshooting inwards from the bottom of the intershell convective zone in thermal pulses in (S)AGB stars. We find that the buoyancy is so strong that any overshooting should be negligible. The temperature inversion at the bottom of the convective zone adds to the stability of the region. Any mixing that occurs in this region is highly unlikely to be due to convective overshooting, and so must be due to another process.
With the "post-processing" technique we explore the role of the convective overshooting on the production of s-nuclei in stellar models of different initial mass and metallicity ($15 \leq M_{ZAMS}/M_{\odot} \leq 25$; $10^{-4} \leq Z \leq 0.02$), considering a range of values for the parameter $f$, which determines the overall efficiency of convective overshooting.We find enhancements in the production of s-nuclei until a factor $\sim 6$ (measured as the average overproduction factor of the 6 s-only nuclear species with $60\lesssim A\lesssim90$) in all our models of different initial mass and m…
Turbulent convection models are thought to be good tools to deal with the convective overshooting in the stellar interior. However, they are too complex to be applied in calculations of stellar structure and evolution. In order to understand the physical processes of the convective overshooting and to simplify the application of turbulent convection models, a semi-analytic solution is necessary. We obtain the approximate solution and asymptotic solution of the turbulent convection model in the overshooting region, and find some important properties of the convective overshooting: I. The oversh…
Classical Cepheids are powerful probes of both stellar evolution and near-field cosmology thanks to their high luminosities, pulsations, and that they follow the Leavitt (Period-Luminosity) Law. However, there still exist a number of questions regarding their evolution, such as the role of rotation, convective core overshooting and winds. ln particular, how do these processes impact Cepheid evolution and the predicted fundamental properties such as stellar mass. In this work, we compare a sample of period change that are real-time observations of stellar evolution with new evolution models to …
As part of a larger program aimed at better quantifying the uncertainties in stellar computations, we attempt to calibrate the extent of convective overshooting in low to intermediate mass stars by means of eclipsing binary systems. We model 12 such systems, with component masses between 1.3 and 6.2 solar masses, using the detailed binary stellar evolution code STARS, producing grids of models in both metallicity and overshooting parameter. From these, we determine the best fit parameters for each of our systems. For three systems, none of our models produce a satisfactory fit. For the remaini…
Convective core overshooting has a strong influence on the evolution of stars of moderate and high mass. Studies of double-lined eclipsing binaries and stellar oscillations have renewed interest in the possible dependence of overshooting on stellar mass, which has been poorly constrained by observations so far. Here we have used a sample of 29 well-studied double-lined eclipsing binaries in key locations of the H-R diagram to establish the explicit dependence of f(ov) on mass, where f(ov) is the free parameter in the diffusive approximation to overshooting. Measurements of the masses, radii, a…
Convective core overshooting extends the main-sequence lifetime of a star. Evolutionary tracks computed with overshooting are quite different from those that use the classical Schwarzschild criterion, which leads to rather different predictions for the stellar properties. Attempts over the last two decades to calibrate the degree of overshooting with stellar mass using detached double-lined eclipsing binaries have been largely inconclusive, mainly due to a lack of suitable observational data. Here we revisit the question of a possible mass dependence of overshooting with a more complete sample…
Based on the turbulent convection model (TCM) of Li & Yang (2007), we have studied the characteristics of turbulent convection in the envelopes of 2 and 5M stars at the RGB and AGB phases. The TCM has been applied successfully in the whole convective envelopes including the convective unstable zone and the overshooting regions. We find that the convective motions become stronger and stronger when the stellar models are located upper and upper along the Hayashi line. In the convective unstable zone, we find that the turbulent correlations are proportional to functions of a common factor $(\nabl…
Overshooting occurs in stars when convective elements penetrate into adjacent radiative zones. In the Sun, it leads to the so-called `tachocline' at the base of the outer convection zone and this region is becoming a key ingredient of the standard solar dynamo model as strong toroidal magnetic fields may be generated there. However this overshoot is not predicted by the mixing-length theory of convection where convective elements must stop at the border of a convectively unstable region. I will review the main properties of this convective overshoot in stellar interiors, with in particular its…
The evolution of stars born with a convective core is highly dependent on the efficiency and extent of near core mixing processes, which effectively increases both the core mass and main-sequence lifetime. We investigate to what extent gravity-mode period spacings in slowly pulsating B-type stars observed by the Kepler mission can be used to constrain both the shape and extent of convective core overshoot and additional mixing in the radiative envelope. We compute grids of 1D stellar structure and evolution models for two different shapes of convective core overshooting and three shapes of rad…
We study a process of slow mixing in stars with convective envelopes, which is driven by the settling of cool downward plumes below the base of the convection zone. If a small fraction (of order $10^{-7}$) of the material cooled at the surface retains a significant entropy deficit while descending in plumes, it can reach the depth where lithium burning takes place. The model calculates the thermal response and mixing below the convection zone due to the settling process, assuming that the plumes arrive at the base of the convection zone with a broad range of entropy contrasts. We obtain a good…
We revise the evolutionary status of the B-type supergiant HD\,163899 based on the new determinations of the mass-luminosity ratio, effective temperature and rotational velocity as well as on the interpretation of the oscillation spectrum of the star. The observed value of the nitrogen-to-carbon abundance fixes the value of the rotation rate of the star. Now, more massive models are strongly preferred than those previously considered and it is very likely that the star is still in the main sequence stage. The rotationally induced mixing manifests as the nitrogen overabundance in the atmosphere…
The convective kissing instability in low-mass M-dwarf models: convective overshooting, semi-convection, luminosity functions, surface abundances and star cluster age dating
We report differential photometric observations and radial-velocity measurements of the detached, 1.69-day period, double-lined eclipsing binary AQ Ser. Accurate masses and radii for the components are determined to better than 1.8% and 1.1%, respectively, and are M1 = 1.417 +/- 0.021 MSun, M2 = 1.346 +/- 0.024 MSun, R1 = 2.451 +/- 0.027 RSun, and R2 = 2.281 +/- 0.014 RSun. The temperatures are 6340 +/- 100 K (spectral type F6) and 6430 +/- 100 K (F5), respectively. Both stars are considerably evolved, such that predictions from stellar evolution theory are particularly sensitive to the degree…
KIC 10553698A is a hot pulsating subdwarf B (sdB) star observed by the Kepler satellite. It exhibits dipole (l = 1) and quadrupole (l = 2) gravity modes with a clear period spacing structure. The seismic properties of the KIC 10553698A provide a test of stellar evolution models, and offer a unique opportunity to determine mixing processes. We consider mixing due to convective overshooting beyond the boundary of the helium burning core. Very small overshooting ( f = 10^{-6} ) results in a progressive increase in the size of convective core. However, moderate ( f = 10^{-2} ) and small ( f = 10^{…
We perform 2D, fully compressible, time-implicit simulations of convection in a solar-like model with the MUSIC code. Our main motivation is to explore the impact of a common tactic adopted in numerical simulations of convection that use realistic stellar conditions. This tactic is to artificially increase the luminosity and to modify the thermal diffusivity of the reference stellar model. This work focuses on the impact of these modifications on convective penetration (or overshooting) at the base of the convective envelope of a solar-like model. We explore a range of enhancement factors for …
Many current stellar evolution models assume some dependence of the strength of convective core overshooting on mass for stars more massive than 1.1-1.2 solar masses, but the adopted shapes for that relation have remained somewhat arbitrary for lack of strong observational constraints. In previous work we compared stellar evolution models to well-measured eclipsing binaries to show that, when overshooting is implemented as a diffusive process, the fitted free parameter f(ov) rises sharply up to about 2 solar masses, and remains largely constant thereafter. Here we analyze a new sample of eight…
Helioseismic investigation has suggested to apply the turbulent convection models (TCMs) to the convective overshooting. Using the turbulent velocity in the overshooting region determined by the TCM, one can deal with the overshooting mixing as a diffusion process, which leads to incomplete mixing. It has been found that this treatment can improve the solar sound speed and the Li depletion in open clusters. In order to investigate whether the TCM can be applied to the overshooting mixing outside the stellar convective core, new observations of the eclipsing binary star HY Vir are adopted to ca…
Uncertainties on central mixing in main sequence (MS) and core He-burning (He-B) phases affect key predictions of stellar evolution such as late evolutionary phases, chemical enrichment, ages etc. We propose a test of the extension of extra-mixing in two relevant evolutionary phases based on period spacing Delta_P of solar-like oscillating giants. From stellar models and their corresponding adiabatic frequencies (respectively computed with ATON and LOSC codes) we provide the first predictions of the observable Delta_P for stars in the red giant branch (RGB) and in the red clump (RC). We find: …
Overshooting from the convective cores of stars more massive than about 1.2 M(Sun) has a profound impact on their subsequent evolution. And yet, the formulation of the overshooting mechanism in current stellar evolution models has a free parameter (f[ov] in the diffusive approximation) that remains poorly constrained by observations, affecting the determination of astrophysically important quantities such as stellar ages. In an earlier series of papers we assembled a sample of 37 well-measured detached eclipsing binaries to calibrate the dependence of f[ov] on stellar mass, showing that it inc…
The frequency ratios $r_{01}$ and $r_{10}$ of KIC 11081729 decrease firstly and then increase with the increase in frequency. For different spectroscopic constraints, all models with overshooting parameter $δ_{\mathrm{ov}}$ less than 1.7 can not reproduce the distributions of the ratios. However, the distributions of the ratios can be directly reproduced by models with $δ_{\mathrm{ov}}$ in the range of about $1.7-1.8$. The estimations of mass and age of the star can be affected by spectroscopic results, but the determination of the $δ_{\mathrm{ov}}$ is not dependent on the spectroscopic result…
Recent investigations have shown that the extended main-sequence turnoffs (eMSTOs) are a common feature of intermediate-age star clusters in the Magellanic Clouds. The eMSTOs are also found in the color-magnitude diagram (CMD) of young-age star clusters. The origin of the eMSTOs is still an open question. Moreover, asteroseismology shows that the value of the overshooting parameter $δ_{\rm ov}$ of the convective core is not fixed for the stars with an approximatelly equal mass. Thus the MSTO of star clusters may be affected by the overshooting of the convective core (OVCC). We calculated the e…
The extent of mixed regions around convective zones is one of the biggest uncertainties in stellar evolution. 1D overshooting descriptions introduce a free parameter ($f_{ov}$) that is in general not well constrained from observations. Especially in small central convective regions the value is highly uncertain due to its tight connection to the pressure scale height. Long-term multi-dimensional hydrodynamic simulations can be used to study the size of the overshooting region and the involved mixing processes. Here we show how one can calibrate an overshooting parameter by performing 2D Maestr…
We attempt to constrain the initial helium abundance, the age and the efficiency of the convective core overshooting of the binary system TZ Fornacis. Our main aim is in pointing out the biases in the results due to not accounting for some sources of uncertainty. We adopt the SCEPtER pipeline, relying on stellar models computed with two stellar evolutionary codes (FRANEC and MESA). We found multiple independent groups of solutions. The best one suggests a system of age 1.10 $\pm$ 0.07 Gyr (primary star in the central helium burning stage, secondary in the sub-giant branch), with a helium-to-me…
We present a framework to simultaneously constrain the values and uncertainties of the strength of convective core overshooting, metallicity, extinction, distance, and age in stellar populations. We then apply the framework to archival Hubble Space Telescope observations of six stellar clusters in the Large Magellanic Cloud that have reported ages between ~1-2.5 Gyr. Assuming a canonical value of the strength of core convective overshooting, we recover the well-known age-metallicity correlation, and additional correlations between metallicity and extinction and metallicity and distance. If we …
An attempt at understanding downward overshooting in the convective envelopes of post-main-sequence stars has been made on the basis of three-dimensional large-eddy simulations, using artificially modified OPAL opacity and taking into account radiation and ionization in the equation of state. Two types of star, an intermediate-mass star and a massive star, were considered. To avoid a long thermal relaxation time of the intermediate-mass star, we increased the stellar energy flux artificially while trying to maintain a structure close to the one given by a 1D stellar model. A parametric study o…
Context: It is well known that the so-called s-process is responsible for the production of neutron-rich trans-iron elements, that form the bulk of the "heavy nuclides" (i.e. nuclides more massive than the iron-group nuclei) in the solar-system composition, considered as "standard of reference" dataset for cosmic abundances. In particular, the s-process produces about half of all the trans-iron isotopes by moving along the "valley of stability" through a series of neutron capture reactions and beta decays. More than one s-process "component" (i.e. a nucleosynthesis event with a single set of p…
We explore the role of mass loss and convective core overshoot in the evolution of Classical Cepheids. Stellar evolution models are computed with a recipe for pulsation-driven mass loss and it is found that mass loss alone is unable to account for the long-standing Cepheid mass discrepancy. However, the combination of mass loss and moderate convective core overshooting does provide a solution, bringing the amount of convective core overshooting in Cepheids closer to that found for other stars.
Modeling properly the interface between convective cores and radiative interiors is one the most challenging and important open questions in modern stellar physics. The rapid development of asteroseismology, with the advent of space missions partly dedicated to this discipline, has provided new constraints to progress on this issue. We here give an overview of the information that can be obtained from pressure modes, gravity modes and mixed modes. We also review some of the most recent constraints obtained from space-based asteroseismology on the nature and the amount of mixing beyond convecti…
Thanks to their past history on the main sequence phase, supergiant massive stars develop a convective shell around the helium core. This intermediate convective zone (ICZ) plays an essential role in governing which g-modes are excited. Indeed a strong radiative damping occurs in the high density radiative core but the ICZ acts as a barrier preventing the propagation of some g-modes into the core. These g-modes can thus be excited in supergiant stars by the kappa-mechanism in the superficial layers due to the opacity bump of iron, at log T=5.2. However massive stars are submitted to various co…
As part of an ongoing program to measure detailed chemical abundances in nearby galaxies, we use a sample of young to intermediate age clusters in the Large Magellanic Cloud with ages of 10 Myr to 2 Gyr to evaluate the effect of isochrone parameters, specifically core convective overshooting, on Fe abundance results from high resolution, integrated light spectroscopy. In this work we also obtain fiducial Fe abundances from high resolution spectroscopy of the cluster individual member stars. We compare the Fe abundance results for the individual stars to the results from isochrones and integrat…
Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars. A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds str…
The stratification near the base of the Sun's convective envelope is governed by processes of convective overshooting and element diffusion, and the region is widely believed to play a key role in the solar dynamo. The stratification in that region gives rise to a characteristic signal in the frequencies of solar p modes, which has been used to determine the depth of the solar convection zone and to investigate the extent of convective overshoot. Previous helioseismic investigations have shown that the Sun's spherically symmetric stratification in this region is smoother than that in a standar…
Based on the turbulent convection model (TCM), we investigate chemical mixing in the bottom overshooting region of the convective envelope of intermediate-mass stars, focusing on its influence on the formation and extension of blue loops in the Hertzsprung-Russell (HR) diagram. A diffusive mixing model is adopted during the Red Giant Branch (RGB) phase. The properties of the blue loop are changed by modification of the element profiles above the H-burning shell, which results from the incomplete mixing in the bottom overshooting region when stellar model evolves up along the RGB. Such modifica…
Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. Our aim is to use asteroseismology to consistently measure the extent of convective cores in a sample of main-sequence stars whose masses lie around the mass-limit for having a convective core. We first test and validate a seismic diagnostic that was proposed to probe in a model-dependent way the extent of convective cores using the so-called $r_{010}$ ratios, which are built with $l=0$ and $l=1$ modes. We apply this procedure to 24 low-mass stars ch…
Slowly pulsating B stars (SPB) and $γ$ Dor stars pulsate in high-order gravity (g-) modes. The frequencies of g-modes are sensitive to the detailed structure and evolution history of stars having convective cores. Receding convective cores in OB-type stars leave behind a chemically inhomogenous $\nabla_μ>0$ radiative zone. Once a g-mode has radial nodes near the boundaries of these layers, the mode gets trapped and its period deviates from asymptotic period spacing. Careful study of such trapped modes allows constraining the extent of such layers by fitting individual pulsation frequencies. We…
Convective overshoot mixing is a critical ingredient of stellar structure models, but is treated in most cases by ad hoc extensions of the mixing-length theory for convection. Advanced theories which are both more physical and numerically treatable are needed. Convective flows in stellar interiors are highly turbulent. This poses a number of numerical challenges for the modelling of convection in stellar interiors. We include an effective turbulence model into a 1D stellar evolution code in order to treat non-local effects within the same theory. We use a turbulent convection model which relie…
The red-giant branch bump provides valuable information for the investigation of the internal structure of low-mass stars. Because current models are unable to accurately predict the occurrence and efficiency of mixing processes beyond convective boundaries, one can use the luminosity of the bump --- a diagnostic of the maximum extension of the convective envelope during the first-dredge up --- as a calibrator for such processes. By combining asteroseismic and spectroscopic constraints, we expand the analysis of the bump to masses and metallicities beyond those previously accessible using glob…
Context. Mixing by convective overshooting has long been suggested to play an important role for the amount of hydrogen available to nuclear burning in convective cores of stars. The best way to model this effect is still debated. Aims. We suggest an improved model for the computation of the dissipation rate of turbulent kinetic energy which can be used in non-local models of stellar convection and can readily be implemented and self-consistently used in 1D stellar evolution calculations. Methods. We review the physics underlying various models to compute the dissipation rate of turbulent kine…
We study the dynamics associated with the extension of turbulent convective motions from a convection zone (CZ) into a stable region (RZ) that lies below the latter. For that purpose, we have run a series of three-dimensional direct numerical simulations solving the Navier-Stokes equations under the Boussinesq approximation in a spherical shell geometry. We observe that the overshooting of the turbulent motions into the stably stratified region depends on three different parameters: the relative stability of the RZ, the transition width between the two, and the intensity of the turbulence. In …
We study lithium depletion in low-mass and solar-like stars as a function of time, using a new diffusion coefficient describing extra-mixing taking place at the bottom of a convective envelope. This new form is motivated by multi-dimensional fully compressible, time implicit hydrodynamic simulations performed with the MUSIC code. Intermittent convective mixing at the convective boundary in a star can be modeled using extreme value theory, a statistical analysis frequently used for finance, meteorology, and environmental science. In this letter, we implement this statistical diffusion coefficie…
In a robust statistical way, we quantify the uncertainty that affects the calibration of the overshooting efficiency parameter $β$ that is owing to the uncertainty on the observational data in double-lined eclipsing binary systems. We also quantify the bias that is caused by the lack of constraints on the initial helium content and on the efficiencies of the superadiabatic convection and microscopic diffusion. We adopted a modified grid-based SCEPtER pipeline using as observational constraints the effective temperatures, [Fe/H], masses, and radii of the two stars. In a reference scenario of mi…
The size of convective cores remains uncertain, despite its substantial influence on stellar evolution, and thus on stellar ages. The seismic modeling of young subgiants can be used to obtain indirect constraints on the core structure during main sequence, thanks to the high probing potential of mixed modes. We selected the young subgiant KIC10273246, observed by Kepler, based on its mixed-mode properties. We thoroughly modeled this star, with the aim of placing constraints on the size of its main sequence convective core. We first extracted the parameters of the oscillation modes of the star …
(abridged) Context: Convective motions overshooting to regions that are formally convectively stable cause extended mixing. Aims: To determine the scaling of overshooting depth ($d_{\rm os}$) at the base of the convection zone as a function of imposed energy flux ($\mathscr{F}_{\rm n}$) and to estimate the extent of overshooting at the base of the solar convection zone. Methods: Three-dimensional Cartesian simulations of compressible non-rotating convection with unstable and stable layers are used. The simulations use either a fixed heat conduction profile or a temperature and density dependen…
We have investigated the role of the convective overshooting on the production of s-nuclei during core He-burning phase in stellar models with different initial mass and metallicity ($15 \leq M_{ZAMS}/M_{\odot} \leq 25$; $10^{-4} \leq Z \leq 0.02$), considering a diffusive approach to model the convective overshooting. The results and their possible consequences on some open questions linked to the s-process weak component efficiency are discussed.
Overshooting of turbulent motions from convective regions into adjacent stably stratified zones plays a significant role in stellar interior dynamics as this process may lead to mixing of chemical species, and contribute to the transport of angular momentum and magnetic fields. We present a series of fully non-linear, three-dimensional (3D) anelastic simulations of overshooting convection in a spherical shell which are focused on the dependence of the overshooting dynamics on the density stratification and the rotation, both key ingredients in stars which however have not been studied systemat…
The treatment of convective boundaries remains an important source of uncertainty within stellar evolution, with drastic implications for the thermally-pulsing stars on the Asymptotic Giant Branch (AGB). Various sources are taken as motivation for the incorporation of convective boundary mixing during this phase, from s-process nucleosynthesis to hydrodynamical models. In spite of the considerable evidence in favour of the existence of convective boundary mixing on the pre-AGB evolution, this mixing is not universally included in models of TP-AGB stars. The aim of this investigation is to asce…
Current standard solar models neither account properly for the photospheric lithium abundance nor reproduce the inferred solar sound speed profile. Diffusive overshooting at the base of the solar convective envelope has previously been shown to solve either of these model inadequacies. In this paper, we present an analysis of solar models with four different parametrizations of diffusive overshooting. We find that these models are able to recover the correct lithium depletion, regardless of the parametrization, if overshooting is suppressed, during the early evolutionary stages. Further, param…
