The Gaia-ESO survey: 3D NLTE abundances in the open cluster NGC 2420 suggest atomic diffusion and turbulent mixing at the origin of chemical abundance variations

Atomic diffusion and mixing processes in stellar interiors influence the structure and the surface composition of stars. Some of these processes cannot yet be modelled from the first principles. This limits their applicability in stellar models used for studies of stellar populations and Galactic evolution. Our main goal is to put constrains on the stellar structure and evolution models using new refined measurements of chemical composition in stars of Galactic open cluster. We use medium-resolution, 19 200<= R<= 21 500, optical spectra of the stars in the open cluster NGC 2420 obtained within the Gaia-ESO survey. The sample covers all evolutionary stages from the main-sequence to red giant branch. Stellar parameters are derived using a combined Bayesian analysis of spectra, 2MASS photometry, and astrometric data from Gaia DR2. The abundances of Mg, Ca, Fe, and Li are determined from non-local thermodynamic equilibrium (NLTE) synthetic spectra, computed using one-dimensional (1D) and averaged three-dimensional (3D) model atmospheres. We compare our results with a grid of Code d'Evolution Stellaire Adaptatif et Modulaire (CESTAM) stellar evolution models, which include atomic diffusion, turbulent and rotational mixing. We find prominent evolutionary trends in the abundances of Fe, Ca, Mg, and Li with the mass of the stars in the cluster. Fe, Mg, and Ca show a depletion at the cluster turn-off, but the abundances gradually increase and flatten near the base of the RGB. The abundance trend for Li displays a signature of rotational mixing on the main-sequence and abrupt depletion on the subgiant branch, which is caused by advection of Li-poor material to the surface. The analysis of abundances combined with the CESTAM model predictions allows us to place limits on the parameter space of the models and to constrain the zone in the stellar interior where turbulent mixing takes place.


Introduction
Models of stellar evolution and their predictions in terms of nucleosynthesis in stars form the basis of many studies in modern astrophysics. Measurements of chemical abundances from stellar spectra provide the most detailed and accurate observational diagnostic of chemical composition of stellar atmospheres, and Based on observations collected with the ESO Very Large Telescope at the La Silla Paranal Observatory in Chile for the  are, therefore, routinely used in studies of chemical evolution of stellar populations in the Milky Way and other galaxies.
Until recently, it was common to assume that the abundances measured in the atmospheres of late-type (FGK) stars reflected the composition of the material from which the stars were born. Selective modulations of surface abundances of Li, C, and N were known for red giant branch (RGB) stars and were canonically attributed to convective mixing and dredge-up episodes on the RGB (Salaris et al. 2015). Yet for most other evolutionary stages -the main-sequence (MS), turn-off (TO), and subgiant branch (SGB) -strong evidence for distinct chemical sig-Article number, page 1 of 15 arXiv:2007.09153v1 [astro-ph.SR] 17 Jul 2020 A&A proofs: manuscript no. aanda natures of self-processing in un-evolved stars was lacking. This suggested that star clusters are simple mono-metallic stellar populations (e.g. Gratton et al. 2001;Thévenin et al. 2001;Ramírez & Cohen 2003). These observations could not be reconciled with uncomfortably large effects of atomic diffusion -a term that is nowadays used to refer to a combined action of gravitational settling and radiative acceleration -theoretically predicted in early stellar structure calculations (e.g. Michaud et al. 1984;Turcotte et al. 1998;Richard et al. 2002). As a consequence, it has become common to associate the measured abundance patterns with the variations in the chemical properties of the interstellar matter, disregarding the subtle yet important influence of secular effects in stellar evolution on the surface chemical composition of stars.
However, we are now witnessing a paradigm shift in the field, which is driven both by new observational studies and theoretical results. Empirical evidence of the impact of atomic diffusion on the surface chemical composition of stars is continuously emerging from careful observational studies of Galactic clusters with modern space-and ground-based astronomical facilities (e.g. Korn et al. 2007;Gruyters et al. 2014;Blanco-Cuaresma et al. 2015;Gruyters et al. 2016;Husser et al. 2016;Gao et al. 2018;Bertelli Motta et al. 2018;Souto et al. 2018;Liu et al. 2019;Souto et al. 2019). For example, it is known that the abundances of light elements (Li, Be and B) can be depleted in main-sequence, turn-off and subgiant stars (Smiljanic et al. 2010;Deliyannis et al. 2019;Boesgaard et al. 2020) and these signatures have been linked to the effects of rotationinduced mixing, internal gravity waves, atomic diffusion, and thermohaline mixing. Large statistically significant samples of stars with high-resolution spectra and high-quality astrometry (e.g. the Gaia-ESO survey: Gilmore et al. (2012); Randich et al. (2013); Gaia DR2: Gaia Collaboration et al. (2016,2018) probing the full evolutionary sequence from the lower MS to upper RGB are now available for many open clusters in the Milky Way. This allows unambiguous membership classification, accurate analysis of evolutionary stages of stars, and, in turn, robust identification of systematic abundance variations along the evolutionary sequence of a cluster. One of the major results of the recent detailed investigations is a systematic depletion, of the order ∼ 0.15 dex, of the abundances of light (Mg, Ca) and Fegroup elements at the TO of several Galactic open clusters when compared with their lower MS and RGB stars, which is qualitatively consistent with theoretical predictions (Gao et al. 2018;Souto et al. 2018).
Major progress with the implementation of non-standard chemical mixing processes in stellar structure models was made over the past decade. These include micro-and macroscopic mixing processes. Microscopic mixing has a different impact on different chemical elements and it includes gravitational settling, thermal diffusion, and radiative acceleration among other effects. In contrast, macroscopic processes, such as rotational and thermohaline mixing, act on all chemical species in the same way. Earlier theoretical studies of atomic diffusion and mixing in stellar structure calculations (Richard et al. 2002;Deliyannis & Pinsonneault 1990;Proffitt & Michaud 1991;Richer et al. 1992;Vauclair 1999;Chaboyer et al. 2001;Richard 2005) are now being superseded by the new generation of stellar evolution models (e.g. Théado et al. 2009;Vick et al. 2013;Zhang et al. 2019;Deal et al. 2020) that include both atomic diffusion and transport processes as thermohaline convection, mass loss, rotation or accretion. A comprehensive review of the subject can be found in Salaris & Cassisi (2017).
Despite all the advances, major uncertainties in understanding of the physical mechanisms underlying the transport of elements in stellar interior remain. It has become clear that additional mixing processes, such as parametrised turbulent mixing, are necessary to reconcile observations with stellar evolution models (e.g. Richer et al. 2000;Richard et al. 2001;Michaud et al. 2011). Also observational studies are still limited and provide only a fragmented picture of secular stellar evolution and its relation to abundances in stellar atmospheres. Most studies, to date, focus on the analysis of small stellar samples, comprising not more than a dozen of stars in each evolutionary stage, and do not probe the critical regime of age and metallicity, where the combined effects of secular stellar evolution are expected to be at the maximum. M67 is the best-studied system in this respect, however this cluster is too old, and its turn-off is too cool, to reveal the fine difference in the abundance patterns caused by diffusion processes in the interior (e.g. Deal et al. 2018).
Motivated by the availability of new observational data, in this study we perform a detailed chemical abundance analysis of 70 stars in the open cluster NGC 2420 (also known as Collinder 154, Melotte 69). This relatively young, τ ∼ 2 Gyr (Bossini et al. 2019), cluster was recently observed within the Gaia-ESO large spectroscopic stellar survey (Gilmore et al. 2012;Randich et al. 2013). Accurate proper motions and parallaxes have also become available from the 2nd data release (Gaia DR2) of Gaia space mission (Gaia Collaboration et al. 2016, 2018. The observed sample of stars includes the full evolutionary sequence, from the lower MS to the RGB tip. NGC 2420 is an ideal ensemble to study the effects of atomic diffusion, as it is relatively metal-poor -which maximises the effect of radiative acceleration -and it hosts early F-type stars with T eff ≈ 6500 K at the TO region. These stars are luminous and have very thin convective envelopes and, as a consequence, the changes in surface composition caused by the combined effects of mixing, gravitational settling, and radiative acceleration, should remain easily detectable, in contrast to cooler G-type solar-like stars, which harbour more massive convective envelopes that efficiently mix the material and act as buffers that wash out the fine signatures of individual transport processes. The paper is organised as follows. In Sect. 2, we present the observed data, while in Sect. 3 we describe methods used to compute stellar parameters and provide a detailed discussion of three-dimensional (3D) and NLTE effects. Sect. 4 summarizes the key aspects of CESTAM stellar evolution models which are employed to model the impact of atomic diffusion, turbulent mixing and rotation on the surface enrichment, and to interpret the observed depletion and accumulation of chemical elements. In Sect. 5 we present the results of the abundance analysis and test them against the CESTAM models. We compare our findings with previous studies and discuss them in the context of stellar evolution and Galactic archaeology in Sect. 6. In Sect. 7 we outline the future perspectives of our findings. Finally, Sec. 8 provides a summary of our results.

Observations
The Gaia-ESO large spectroscopic survey was designed to obtain high quality spectroscopic observations of 100 000 field stars, as well as members of clusters down to the limiting magnitude V = 19 m . For further overview the reader is referred to Gilmore et al. (2012); Randich et al. (2013). In this work we make use of spectroscopic data obtained with the mediumresolution GIRAFFE spectrograph mounted at the Very Large Telescope (VLT). Although some targets in the cluster were also observed with the high-resolution UVES spectrograph, the spectra are only available for a few stars on the red giant branch. The pre-selection of targets in this cluster was based on the colour-magnitude diagram (CMD) from earlier photometric studies (Anthony-Twarog et al. 2006;Sharma et al. 2006). Postprocessing of raw observed spectra was done by the Gaia-ESO dedicated work groups. We use the spectra released within the 5th internal Data Release (iDR5), which contains 545 objects labelled as cluster candidates. The signal-to-noise (SNR) ratio of the spectra ranges from 10 to 150, and for our final sample the median SNR is in the open cluster NGC 2420 plotted as a function of their V magnitude. The best-fit GARSTEC isochrones are over-plotted (see text). Stars comprising the final sample are depicted with black asterisks. For selection criteria see main text. Some of the stars in the kinematically selected sample could be binaries. Bottom: Hertzsprung-Russell diagram of stars for which we perform detailed spectroscopic analysis.

Target selection
The recent Gaia DR2 estimate of the cluster parallax, π = 0.363 ± 0.064 milli-arcsec (mas), yields the distance of 2.55 kpc with an uncertainty of about 0.5 kpc (Cantat-Gaudin et al. 2018). Owing to the large distance, we refrain from membership analysis based on the proper motions of the stars and instead select cluster members by their apparent positions and radial velocities. We require the radial velocity to be within the range of 73 − 77 km/s and angular distance from the cluster center to be less then 10 arcmin, according to the observable size of the cluster as reported in Sharma et al. (2006). This procedure effectively eliminates 214 foreground and background stars and yields 331 cluster candidate members. We note that adding the proper motions in the analysis does not change our classification, as the uncertainties of proper motions are large. We explicitly avoid pre-selection on metallicity, as stellar structure models computed with atomic diffusion and mixing predict a dispersion in the chemical composition of the cluster, hence any preselection on the chemical composition carries a major danger to erase these astrophysically important signatures that are in the focus of our work.
Gaia photometry of the cluster reveals a characteristic broadening of the cluster MS. One of the viable explanations for this feature is the presence of unresolved binaries in our sample. it is a well-established fact (e.g. Maeder 1974;Bragaglia & Tosi 2006;Cordoni et al. 2018;El-Badry et al. 2018;Price-Whelan et al. 2020) that the unresolved binaries composed of two MS stars are redder and brighter than single MS stars of a similar mass. These unresolved binary systems may appear up to ∼ 0.75 mag brighter than the canonical main sequence that characterises evolution of single stars. However, it is not only the visual brightness, but also the color as a proxy for T eff that is affected (El-Badry et al. 2018). The effects become significant for binaries in which both components have similar masses (El-Badry et al. 2018). According to the statistical method by Cordoni et al. (2018), NGC 2420 has a significant, 33 %, fraction of unresolved MS-MS binaries. Binaries with mass ratio q > 0.7 constitute 10 % of NGC 2420 members. We, therefore, exclude those stars that have a high likelihood, based on the CMD position, of being binaries from the subsequent analysis.

Age of the cluster
We estimate the age of the cluster by fitting the observed Johnsons-Cousin photometry (Sharma et al. 2006) and Gaia parallaxes 1 to a grid of stellar isochrones, as described below. The cluster is almost unaffected by reddening. According to the NASA/IPAC Infrared Science Archive service 2 , E(B-V) = 0.035 mag, in agreement with earlier studies (Anthony-Twarog et al. 2006). NGC 2420 has been considered to be a moderately metal-deficient open cluster, being a "transition" object between solar metallicity open clusters and more metal-poor globular clusters. Some of the recent studies targeting members of NGC 2420 report the average metallicity of the cluster at [Fe/H] = −0.05±0.10 (Pancino et al. 2010, , based on a few stars observed at high-resolution) or [Fe/H] = −0.2 ± 0.06 (Jacobson et al. 2011, based on stars observed with a medium-resolution spectrograph). (Siegel et al. 2019) suggest that lower-metallicity, by −0.1 dex, isochrones are needed to describe the photometry of the cluster turn-off stars.
We use the grid of GARSTEC stellar isochrones (Weiss & Schlattl 2008) based on the stellar models used in BeSPP (Serenelli et al. 2017). Synthetic photometry is computed using bolometric corrections based on ATLAS12/SYNTHE (Kurucz 1970(Kurucz , 1993 as implemented by Conroy et al. (in prep.) 3 . Zero point corrections were applied to reproduce the solar colors from Casagrande & VandenBerg (2018).
To break the age-metallicity degeneracy we assume the metallicity of the cluster to be the one of the most evolved stars in our sample, which are located on the RGB. Metallicity of those stars was computed with spectrum synthesis, see Sect. 3.3 for more details. Figure 1 shows two GARSTEC isochrones, which correspond to the age of 2.5 and 2.7 Gyr, respectively. We caution that the standard procedure of fitting the grid of isochrones to the CMD, although wide-spread in astronomy see i.e. Pont & Eyer (2004), assumes that the cluster is a mono-metallic coeval system. In fact, this contradicts our findings (Sect. 5) of a systematic depletion of elemental abundances at the cluster TO point, which we interpret as a signature of atomic diffusion and mixing. However, employing a different, more strict, approach is not feasible at this stage. Indeed, a systematic depletion of metallicity in principle requires an iterative procedure involving the full analysis of the observed spectra and Bayesian stellar evolution fitting. Developing such a model is beyond the scope of our study. However, in the next section we show that fundamental stellar parameters are not affected at any significant level by the assumed «average» metallicity of the cluster.

Stellar parameters and chemical abundances
We use several methods to constrain stellar parameters: analysis of photometry and parallaxes, fitting of the Balmer lines, and the full Bayesian approach employing stellar evolution models and parallaxes. All these methods are broadly used in the literature and have been verified in our previous studies with different families of synthetic spectral models (Bergemann et al. 2012;Ruchti et al. 2013;Serenelli et al. 2013). We follow this approach, rather than using the recommended Gaia-ESO parameters and abundances, because it allows us to remain fully consistent with our 1D NLTE and 3D NLTE calculations. First, 3D NLTE abundances are the quantities that we use for astrophysical interpretation (Section 5). Second, this allows an objective analysis of systematic and statistical uncertainties, which are associated with every step in stellar parameter determinations.
Photometric T eff are derived from the (V − K) colour using the Alonso et al. (1996) and Casagrande et al. (2010) calibration relations. We assume the same metallicity, [Fe/H] = −0.2, for all cluster members, but check that the variation of metallicity has no significant impact on the T eff estimates. These estimates of T eff are then employed as initial guesses for the spectroscopic analysis of H α line wings (see Ruchti et al. (2013) for the details of this method).
We use the SME 1D LTE code (Piskunov & Valenti 2017) and MARCS model atmospheres (Gustafsson et al. 2008) to generate synthetic model spectra and fit them to the observed spectra. Finally, we resort to the Bayesian code BeSPP ) to refine our photometric and spectroscopic estimates of T eff , and to derive estimates of log g for our targets. Assuming the Gaussian uncertainty of ±150 K on the spectroscopic values, we combine them with the 2MASS JHK magnitudes, Gaia parallaxes, and adopt a uniform metallicity prior ([Fe/H] = −0.20 ± 0.30). The final estimates of T eff and log g are determined from the analysis of the full posterior probability distribution functions (PDFs) as described in Serenelli et al. (2013).
3 http://waps.cfa.harvard.edu/MIST/model_grids.html# bolometric We note that the final estimates are not affected in any significant way by assuming a uniform metallicity for the cluster, see Thus we show that the derived fundamental parameters are not biased by the initial guess of the metallicity.
The analysis of metallicities and chemical abundances for individual stars is strictly spectroscopic, and we rely on the method of detailed spectrum synthesis. Although the GIRAFFE HR10 and HR15N spectra cover only a limited wavelength range, we have 15 Fe I and 2 Fe II relatively unblended spectrum features, as well as a few clean features of other chemical elements that are suitable for a high-quality abundance analysis. The parameters of these lines are provided in Table 1.
All atomic data are adopted from the official Gaia-ESO line list (see Heiter et al. 2015, for details). We note that some species (Mg and Li) are represented by one spectral feature in our observed spectral data. We have, therefore, taken a special care to assess all sources of error in the abundance analysis of the diagnostic features, including statistical and systematic uncertainties.
The assumption of 1D LTE is arguably the most severe source of systematic error in abundance estimates(e.g. Asplund 2005;Bergemann & Nordlander 2014). More than that, 3D and NLTE effects are function of the evolutionary stage. We therefore perform detailed calculations of NLTE abundances using canonical one-dimensional (1D) hydrostatic model atmospheres and 3D hydrodynamic model atmospheres. The detailed approach to NLTE computations is described in the following sections.

1D NLTE abundances
The 1D statistical equilibrium code MULTI2.3 (Carlsson 1986) is used to compute grids of 1D LTE and NLTE line profiles, and, consequently, NLTE abundance corrections, ∆ NLTE , via interpo- lation in the LTE and NLTE curves-of-growth as described in (Eitner et al. 2019). NLTE abundance correction describes the difference in abundance required to match a spectral line of a fixed equivalent width with LTE and NLTE models. This quantity generally depends on the atomic properties of the line, elemental abundance, and physical parameters of a stellar atmosphere. If ∆ NLTE is known, the NLTE abundance of an element A(X) NLTE is computed according to Eq. 1.
The NLTE correction ∆ NLTE is positive when the NLTE line profile is weaker than its LTE equivalent. Vice versa, ∆ NLTE < 0 implies that the NLTE line profile is stronger than its LTE counterpart, given all other parameters in calculations (abundance, model atmosphere parameters) are identical. In the latter case, the LTE abundance is higher compared to NLTE abundance. It should be stressed, however, that Fe is the only element for which ∆ NLTE is strictly differential: the input parameters of the model atmosphere in LTE and NLTE calculations are the same. The NLTE abundance corrections for the other chemical elements -Mg, Ca, and Li -are computed using NLTE-corrected metallicities, which implies, for a given T eff , log g, and v mic , so this implies that we correctly take into account the second-order dependence of their NLTE correction on that of Fe. The NLTE corrections on iron lines typically amount to +0.03 to +0.07 dex, which implies the sensitivity of the NLTE corrections for Mg and Ca is of the order 0.01 dex. Background opacity tables for each of these elements were computed using the Turbospectrum radiative transfer code (Plez 2012 Ca, and are based on the models presented in the earlier studies by (Bergemann et al. , 2012Mashonkina et al. 2017). Table 2 summarises the main properties of the atomic models, such as the number of energy levels and ionisation stages, the Article number, page 5 of 15 A&A proofs: manuscript no. aanda number of bound-bound, and the size of the frequency grid for radiative bound-free transitions. In this work, we update the reaction rates and cross-sections to more recent estimates available in the literature. In particular, we include the new photoionisation cross-sections for Fe I from Bautista et al. (2017), replace the semi-classical recipes for the rates of bound-bound and bound-free transitions cased by inelastic collisions between Fe+H (Barklem 2018) and Fe+e (Bautista et al. 2017). In the Ca model atom we update rates for transitions caused by inelastic Ca+H collisons ) and update the list of energy levels to include fine structure resolved levels and therefore, update radiative bound-bound transitions. The estimates of line broadening caused by elastic collisions with H atoms are taken from Barklem et al. (2000). We also reduce the complexity of the atomic models, in order to use them in the 3D NLTE calculations (Sect. 3.3.2). We cut the Mg photo-ionisation cross-sections at 1100 Å as radiative fluxes at bluer wavelengths is negligibly small. For Fe, we re-sample the photo-ionisation cross-sections, so that they consist of a factor of ∼ 10 less frequency points, but still contain all the important resonances. Numerous tests have been carried out to ensure that the atomic models with reduced complexity do not introduce any biases in 1D and 3D NLTE abundance corrections with respect to the original models. For Li we make use of 1D NLTE corrections published by Lind et al. (2009).
Our 1D NLTE abundance corrections are shown in Fig. 3. The NLTE corrections for the optical Fe I lines are moderate and do not exceed 0.15 dex, supporting previous estimates in the literature (Bergemann et al. 2012;Ezzeddine et al. 2018). For the Mg I 5528 Å line, the NLTE correction is small: it varies from 0.03 dex for the TO model to < 0.01 for the main-sequence and sub-giant models. Ca I lines are typically weaker in NLTE compared to LTE, therefore, the NLTE corrections are moderately positive and range from 0.05 dex on the main-sequence to −0.1 dex on the subgiant branch. NLTE corrections to Li I 6707 line is negative for main-sequence models, but it becomes positive on the RGB. We emphasize that in virtue of the metallicitydependence of the NLTE abundance corrections for every element other than iron, our estimates of NLTE effects for the NGC 2420 stars may not be directly comparable with other studies.

3D NLTE abundances
As a proxy of 3D structure of stellar atmospheres, we use averaged 3D atmospheric models taken from the STAGGER grid of stellar convection simulations (Magic et al. 2013). The procedure to compute the <3D> NLTE corrections is identical to that used for 1D NLTE calculations (3.3.1) and it follows our approach in Bergemann et al. (2012). To account for 3D convective motions we include turbulent velocity in otherwise 1D model atmosphere according to Eq.2 as proposed by Uitenbroek & Criscuoli (2011).
We emphasize that the <3D> models do not include any parametrisations of convection, and so there are no ad-hoc parameters, such as the mixing length or micro-and macroturbulence, which allows us to perform radiation transfer from the first principles. The estimates of ∆ <3D>NLTE for Fe, Ca, and Mg are shown in Fig. 3. Our results for <3D> NLTE corrections compare favourably well with the earlier estimates in the literature. For Ca this is the first study of <3D> NLTE effects for the stars other than the Sun. For Fe and Mg, the <3D> NLTE corrections are within 0.05 dex, which is consistent with the calculations by Bergemann et al. (2012) and Bergemann et al. (2017), respectively.
Our results for Ca in 1D NLTE are consistent with (Mashonkina et al. 2017), who predict modest and positive NLTE abundance corrections. The 3D effect, however, are insignificant, of order of 0.01 dex. For Li we estimate 3D NLTE corrections based on precomputed grid by (Harutyunyan et al. 2018). At [Fe/H] = −0.5 they predict 3D NLTE correction to be between 0.019 -0.049 for MS and TO stars. We note that this value is much smaller than our observational errors (∼ 0.1 dex) and 1D NLTE effects (∼ −0.15 to 0.15 dex).
The <3D> NLTE corrections are applied to abundances measured in 1D LTE to derive the final chemical abundance pattern of NGC 2420. A more detailed investigation of the NLTE effects for the studied elements and a technical description of computations will be presented in the follow-up paper (Semenova et. al in prep.).

Propagation of uncertainties
For all measured chemical elements we propagate corresponding abundance uncertainties using a Monte-Carlo approach. We construct a set of randomly sampled input parameters with respect to their errors and perform the spectrum fitting procedure with these input parameters fixed. The resulting error on derived abundances is defined as the standard deviation of the set of solution assuming a Gaussian distribution. Therefore, the errors presented account for fluctuations of the solutions due to noise component (signal-to-noise ratio of observed spectra) and systematic component (i.e. normalization procedure, errors of fundamental parameters).

Stellar structure code
The primary goal of this paper is to study radial transport of chemical elements in stellar interiors. This physical phenomenon is caused by the competition and coupling between atomic diffusion and macroscopic transport processes. Atomic diffusion represents a balance between gravitational settling and radiative levitation forces (Meynet et al. 2004). Although usually not accounted for in calculations of stellar structure and evolution, the underlying mechanism is well-understood and the accuracy, with which it can be modelled in stellar structure, is roughly 20%, being limited by approximations in the atomic diffusion formalism and cross-sections (see Michaud et al. 2015, for a detailed overview). Other macroscopic transport processes of diffusive (e.g. rotation, thermohaline convection) or advective (e.g. mass loss) nature, are not yet well-constrained and, therefore, their effects are usually modelled using simple parametric recipes (e.g. Richer et al. 2000;Richard et al. 2001;Michaud et al. 2011). These processes can mitigate the effects of atomic diffusion on surface abundances.
In this work, we use the CESTAM code (Code d'Evolution Stellaire Adaptatif et Modulaire, the "T" stands for transport) (Morel & Lebreton 2008;Marques et al. 2013;Deal et al. 2018) in order to compute stellar evolutionary tracks including atomic Article number, page 6 of 15 E. Semenova, et al.: Abundance variations in NGC 2420. diffusion and additional parametrized mixing to provide quantitative predictions for the behaviour of the surface chemical composition for different evolutionary phases of a star. The code adopts the OPAL2005 equation of state (Rogers & Nayfonov 2002) and the OP opacity tables (Seaton 2005). These are complemented by the Wichita opacity data at low temperatures (Ferguson et al. 2005). We use opacity tables for a fixed solar mixture. We have verified that the error related to this assumption (not recomputing the Rosseland mean opacity taking into account mixture variations due to atomic diffusion) is never larger than 0.01 dex. This is due to the variations of chemical element abundances being relatively small, as they are inhibited by an additional transport process in our models. Nuclear reaction rates are adopted from the NACRE compilation (Angulo 1999), except for the 14 N(p, γ) 15 O reaction, which is taken from the Laboratory for Underground Nuclear Astrophysics (LUNA) compilation (Imbriani et al. 2004). We use the Canuto-Goldman-Mazzitelli formalism for convection (Canuto et al. 1996) with the mixing-length parameter α CGM = 0.68 calibrated on the Sun. The models also include the core overshoot of 0.15 H P . The stellar atmosphere, which represents the outer boundary condition in stellar structure models, is computed in the grey approximation. Following the recommendation of Serenelli (2010) we adopt the AGSS09 ) mixture for the refractory elements. The initial hydrogen, helium, and metal mass fractions -X 0 , Y 0 and Z 0 respectivelyare determined from the solar calibration, following the ∆Y/∆Z slope of 0.9 as determined in Deal et al. (2018). We do not take mass loss or magnetic fields into account. The evolution is computed from the pre-main-sequence up to the age of 2.5 Gyr.

Modelling transport processes
The diffusion equation of a trace element i at a given depth is expressed as following: where X i is the mass fraction of element i; A i its atomic mass; m p the mass of a proton; ρ the density in the considered layer; D turb the turbulent diffusion coefficient; and r i j the rate of the reaction that transforms the element i into j. The competition between macroscopic transport processes and atomic diffusion is given by the first two terms in the right-hand side of Eq. 3. The atomic diffusion velocity v i can be expressed as where D ip is the diffusion coefficient of element i relative to protons; g rad,i the radiative acceleration on element i; g the local gravity;Z i the average charge (in proton charge units) of element i (roughly equal to the charge of the 'dominant ion'); k the Boltzmann constant; T the local temperature; and κ T the thermal diffusivity. CESTAM computes atomic diffusion, including radiative acceleration, taking into account partial ionization for H, 3 He, 4 He, 6 Li, 7 Li, 9 Be, 11 B, 12 C, 13 C, 14 N, 15 N, 15 O, 16 O, 17 O, 22 Ne, 23 Na, 24 Mg, 27 Al, 28 Si, 31 P (without radiative acceleration), 32 S, 40 Ca, and 56 Fe. Radiative accelerations for light elements (below carbon) are not computed because they are negligible. Radiative accelerations are computed using the Single Valued Parameters (SVP) approximation (Alecian & LeBlanc 2002;LeBlanc & Alecian 2004). The uncertainty of g rad,i provided by this method is about 30% (Georges Alecian, private communication).
When rotation is included in the models, the turbulent diffusion coefficient is added to D turb . A description of the treatment of rotation in the CESTAM code can be found in Marques et al. (2013). We considered the magnetized wind braking of Matt et al. (2015Matt et al. ( , 2019 and an additional vertical viscosity of ν v = 10 8 cm 2 s −1 as calibrated by Ouazzani et al. (2019) to take into account the fact that the current rotation theory underestimates the transport of angular momentum. The other aspects of these models are the same than the ones presented in Deal et al. (2020). These models are only used to show that rotation may explain lithium depletion on the main-sequence.
The implementation of turbulent mixing D turb follows the standard phenomenological recipe (Richer et al. 2000;Richard et al. 2001Richard et al. , 2002Michaud et al. 2011). The prescription for D turb is not grounded in any ab-initio model, but is chosen to not affect the transport of the chemical elements close to the center, as the efficiency of mixing drops with ρ −n : where ω and n are constants, ρ is the density, and D He (T 0 ) the atomic diffusion coefficient of helium at the reference temperature T 0 . We assume ω = 400 and n = 3. The atomic diffusion coefficient of helium was obtained using an analytical approximation as described by Eq. 6. (Michaud et al. 2011) and depends therefore on local conditions. As Richard (2005) and Gruyters et al. (2016) showed, these values provide a good fit to the observed data of metal-poor clusters. The parameter ρ(T 0 ) represents the density at the reference temperature. By choosing different values of T 0 , we effectively change the spatial extension of the zone, in which the turbulent mixing takes place. In other words, the larger the T 0 the deeper is the base of the zone subject to this extra mixing. dex. The convective core is located at log T > 7.145 for the 1.4 M model and is not shown in the plot. In the top panels, we have colour-coded the profiles of D turb by their corresponding T 0 values. The T 0 = 10 6.0 K model (solid red line) corresponds to the maximum penetration of the deep mixing zone, down to R/R * ∼ 0.4 in both models. On the other hand, the log T 0 = 10 5.50 K model (blue line) has a very shallow mixing zone, which only reaches down to R/R * ∼ 0.7. The atomic diffusion coefficient of He is marked with the dashed line; this quantity represents a mean efficiency of atomic diffusion. Also the profile of rotational mixing, D rot , with zero-age MS velocities of υ = 2.2 and 7.0 km/s are indicated.

The impact of atomic diffusion and mixing on chemical abundances
The lower panel of Figure 4 shows the profiles of Li abundances corresponding to all aforementioned models. To aid the interpretation of this figure, we also show the surface convective zone of the model with T 0 = 10 6 K (grey area) and the Li destruction zone (T> 2.5 × 10 6 K, green area). The radial extent of the surface convective zone is slightly different for the models with other T 0 values. This figure helps to understand why the surface abundance of Li is so sensitive to the exact prescription adopted for turbulent and rotational mixing. In particular, the surface abundance of Li decreases faster with either (a) decreasing the size of the turbulent mixing zone (decreasing T 0 ) or (b) increasing the depth of the convective envelope (or decreasing the mass of a star). In the former case, the larger the T 0 , the stronger is the mixing below the convective envelope, that counterbalances the effects of atomic diffusion (driven by gravitational settling) on lithium. In the latter case, the model with a lower mass (1.0 M ) has a deeper convective envelope that acts as a source of efficient mixing and, therefore, quenches atomic diffusion. Turbulent mixing helps to avoid strong surface abundance variations of all chemical elements, but it is not efficient enough to bring Li down to its nuclear destruction region. On the contrary, rotation is able to induce a lithium destruction but not to reduce strong surface abundance variations of chemical elements (Deal et al. 2020). Indeed, the 1.0 M model, which includes rotational mixing, reduces the surface Li abundance by more than one order of magnitude. This effect is much less important for more massive stars, owing to their shallower convective envelopes.  By comparing the profiles of g rad and g grav , we can see how the balance of two forces modifies the behaviour of the elemental abundances with depth. In general, owing to g rad > g grav at the bottom of the surface convective zone, heavy elements tend to accumulate at the surface of a star (or inside if the accumulation occurs deeper, Richard et al. 2001;Théado et al. 2009;Deal et al. 2016), more so in the more massive model with 1.4 M . And even if g rad < g grav , radiative acceleration will moderate the efficiency of gravitational settling. The behavior at larger depths is very non-linear, which is caused by the complex dependence of the opacity on the ionization state of the elements, and, consequently on the density and temperature profiles in the interior ). If we consider no additional transport processes in the 1.4 M model, iron and magnesium should be accumulated at the surface and calcium would be depleted. Figure 6 shows D turb at the bottom of the surface convective zone for different T 0 (colored solid lines) and, D He (T 0 ) the helium diffusion coefficient at the temperature T 0 = 10 5.7 K (dashed line), according to the mass of stellar models. D turb increases at the bottom of surface convective zone with increasing stellar mass for two reasons. The first one is due to the shallower convective zone in the more massive stars, which implies that the reference temperature T 0 is far deeper from the bottom of the surface convective zone, which induces a large turbulent diffusion coefficient according to Eq. 5. The second reason is the D He (T 0 ) increasing with the stellar mass as the internal struc- ture in varying with mass at a given internal temperature, among other things ρ, which induces a D He (T 0 ) value varying of two order of magnitude between 0.8 and 1.4 M . The model predictions for the surface abundances of Fe, Mg, Ca, and Li are shown in Fig. 7. All models correspond to the age of 2.5 Gyr, consistent with our observational constraints. Considering an age uncertainty of 0.2 Gyr leads to the difference in the predicted surface abundances of maximum 0.005 dex in the models for which atomic diffusion is the most efficient. The models differ in the value of T 0 . Not surprisingly, the surface element abundances do not remain constant with the evolutionary phase of a star, unless extreme values of turbulent mixing, T 0 superior to 10 6 K (equivalent to D turb > 10 8 cm 2 .s −1 at the bottom of the surface convective zone for the 1.4 M model as shown in Fig. 6), are adopted. Similarly, the effect of radiative levitation is to prevent for some chemical elements the 'metal sink' effect of gravitational settling, allowing the model to avoid critical surface under-abundances of metals.
The evolution of Mg and Fe along the isochrone is very similar. The abundances of both elements are significantly depleted at the TO point of the cluster, which corresponds to log g ≈ 4.3 dex for the most metal-poor model and to log g ≈ 4.1 dex for the solar metallicity model. Ca, in contrast, displays a modest overabundance at the TO point, although this behaviour can be inverted for certain combinations of log T 0 and initial abundances. Increasing log T 0 generally flattens the tracks of [A/H] towards the initial abundances as the value of D turb is increasing at the bottom of the surface convective zone (Fig. 6). The transition from the main sequence to the sub-giant phase is associated with a large depletion of Li, as the surface convective envelope deepens and Li-poor material is advected to the surface.
Of note is the non-linear behaviour of the models in the domain of inefficient turbulent mixing, log T 0 ≤ 5.50. In this regime, turbulent mixing, is no longer sufficient to balance the outward radiation force. This imbalance induces a relative accumulation of an element at the surface, which may even result in an over-abundance of the element relative to its initial unperturbed value. This process is responsible for the characteristic bump in the behavior of Ca abundances in the transition region between the TO point and the subgiant branch and globally re- log 10 T 0 = 5.50 log 10 T 0 = 5.70 log 10 T 0 = 6.0 log 10 T 0 = 6.50 duces the Fe and Mg depletion. This kind of effect can also be seen on iron in Fig. 7.

Results
Over the past decade, several observational studies reported clear and systematic evolutionary trends in the chemical abundances in open and globular clusters. These trends are commonly attributed to the effect of atomic diffusion. However, it was also shown that atomic diffusion alone is not sufficient to explain the observations of different chemical elements. Therefore, additional mixing processes of macroscopic nature were put forward (e.g. Mucciarelli et al. 2011;Korn et al. 2007;Nordlander et al. 2012;Gruyters et al. 2016).
In this section, we compare our new observational data with different models described in Sect. 4 and discuss the results in the context of other empirical and theoretical studies.

Intra-cluster abundance variations
Our 3D NLTE distributions of chemical abundances in NGC 2420 stars are shown in Fig. 8. The measured abundances of Fe, Ca, and Mg are significantly lower at the cluster TO point, with a maximum depletion of −0.2 dex relative to the lower MS or RGB stars. This prominent under-abundance gradually disappears along the SGB and the abundances attain their original (birth composition) values at the base of the RGB, around log g ≈ 3.3 dex. The depletion at the cluster TO is also predicted by stellar models computed with atomic diffusion and turbulent mixing. One of such models, computed using the T 0 of 10 5.8 K and several values of initial metallicity, is overplotted onto the observed data. The undulations of theoretical profiles for stars in the mass range from 1.1 to 1.3 M (log g range from 4.5 to 3.5) are caused by the interplay of gravitational settling, radiative pressure, and turbulent mixing, as described in Sect. 4.3. However our data are not accurate enough to resolve these tiny signatures, which would require the abundance accuracy of better than 0.05 dex. Nonetheless, the global systematic trends in the data agree very closely with the models. On the RGB, the deepening of the surface convective zone after the MS stage quickly restores the surface abundances of elements, which are not affected by nuclear reactions (Fe, Ca, Mg), to their initial value.

Distribution of Li abundances
The behaviour of Li in the cluster is qualitatively different from the behaviour of other elements. In contrast to other elements, the profile of Li with log g cannot be fully described by our standard models that include atomic diffusion and turbulent mixing only. As seen in the bottom right panel of Fig. 8, the observed abundances of Li on the MS (at log g ∼ 4.3 dex) are lower, compared to standard models. However, this problem can be solved by including, in addition, internal rotation, because this physical mechanism acts throughout the entire star and, therefore, allows for mixing in the deeper regions, which are hot enough to destroy Li. In the model computed with υ ≈ 7.0 km/s, transport induced by internal rotation leads to earlier destruction of Li and results in the characteristic depletion of Li abundance on the MS, in agreement with the observations.
In addition, at log g ∼ 4.3 dex, there are a few data points that suggest the presence of the Li dip (Deliyannis et al. 2019), that is the depletion of Li abundances compared to stars with higher and lower log g values. This dip was also seen in other light elements, like Be (Smiljanic et al. 2010), but its origin is still debated.
The abrupt depletion of the Li abundance on the subgiant branch, predicted by the model, is also seen in our observational data. The first dredge-up brings highly-processed Li-poor material from the interior to the surface of a star. Consequently, the Li abundance drops by two orders of magnitude at the base of the RGB. CESTAM models with rotation predict a lower abundance of lithium on the SGB phase due to the deeper mixing induced by rotation.
The effect on the other elements is much smaller as rotation only impacts the size of the region where the chemical composi-  tion is homogenized. In the case of the T 0 = 10 5.8 K the region is extended by only a few % in mass, which leads to the change of observed abundance of ∼0.07 dex. In contrast to that, atomic diffusion and the parametrize mixing lead to depletion of Fe by 0.2 dex. The impact of adding rotation on the other element will be investigated in a forthcoming paper. Figure 9 depicts the probability maps, which we employ to constrain the models consistent with our data. The maps were constructed by using a grids of CESTAM tracks for a cluster of a given age and different initial metallicities as described in Sect. 4. We perform the comparison between the observed abundance trends in NGC 2420 and a grid of CESTAM models by computing a likelihood for each of these models as described by Eq. 7, where χ 2 k is a chi-square per degree of freedom showing the goodness of fit by a certain model and [X/H] Obs/Mod i are observed and theoretically predicted abundances respectively. Statistical and systematic observational uncertainties described in Sect. 3.3.3 were taken into account. To ease the comparison between different elements we present normalised values of the likelihoods on the maps. This representation doesn't affect our conclusions.

Combined statistical analysis of data and models
Clearly each chemical element shows a different sensitivity to the input parameter space of the models. For some elements, i.e. Ca, it is barely possible to distinguish stellar models with different levels of physical complexity. One should also take into account that the response to transport processes is different for every element. In Sect. 4.3 we show that the Li abundance on the MS is very sensitive to rotation, while for other elements the effect of rotation is negligibly small. Thus the abundance of Li alone would not be sufficient to identify the most likely model. The degeneracy can be broken by combining the constraints from all four chemical elements simultaneously.
The combined analysis of all elements in our data set suggests that the model that is favoured by our data the most has a modest mixing efficiency of log T 0 = 5.8 (Fig. 10). This model reproduces the intra-cluster distributions of the abundances of all measured chemical elements against fundamental parameters of stars. Other models computed assuming significantly higher (log T 0 = 6.0) or significantly lower (log T 0 = 5.5) efficiency of turbulent mixing or assuming no atomic diffusion at all, are not supported by our data.
In summary, our observational data for NGC 2420 yields strong constraints on the physical processes in stellar interiors.
A&A proofs: manuscript no. aanda  Combining four chemical elements -Fe, Ca, Mg, and Li -we are able to confine the parameter space of the stellar models and to identify the most probable range of values that characterise the efficiency of turbulent mixing at the bottom of the stellar convective envelope. The CESTAM model, which includes atomic diffusion, turbulent mixing with log T 0 = 5.8, and rotational mixing is best supported by our data. Other stellar models, in particular including those computed without atomic diffusion, are ruled out at a high level of confidence.

Discussion
Similar attempts to constrain the transport of chemical elements in the stellar interior using observations were carried out in several other studies (e.g. Korn et al. 2006Korn et al. , 2007Mucciarelli et al. 2011;Nordlander et al. 2012;Gruyters et al. 2014Gruyters et al. , 2016. However, most of these studies are limited to the analysis of old (over 10 Gyr) and metal-poor ([Fe/H] −1 dex) Galactic clusters. Using the globular clusters NGC 6397 ([Fe/H] = −2 dex) and M 30 ([Fe/H] = −2.3 dex) they constrained log T 0 = 6. This value is at the upper boundary of our estimated range of log T 0 from 5.70 to 6.00. The difference with our results, which are based on the young cluster with a slightly sub-solar metallicity NGC 2420, may indicate a metallicity dependence of the efficiency of mixing processes, such as rotational and turbulent mixing, competing with atomic diffusion. This metallicity dependence is clearly present in the stellar evolution models (Fig. 8, compare models computed with [Fe/H] = -0.15 and 0.05 dex) and combining the results from the afore-mentioned studies, we can conclude that there is a significant evidence for a different efficiency of T 0 at lower metallicities.
Comparing our results with previous studies of open clusters, we find a good agreement in the slopes of abundance trends and behaviour of individual chemical elements. M67 -a 4 Gyr old solar-metallicity cluster -is arguably the best-studied system in this respect (Yong et al. 2005;Randich et al. 2006;Önehag et al. 2014;Bertelli Motta et al. 2018;Souto et al. 2018;Gao et al. 2018). The last study is similar to our work in that it is based on the NLTE analysis of abundances of several chemical elements. They use the MESA stellar models from Dotter et al. (2017) computed with account for atomic diffusion, radiative ac-celeration, overshoot, and turbulent mixing calibrated on the observed data for NGC 6397 from Korn et al. (2007). However, although their findings are generally consistent with the MESA models, they stress non-negligible differences on the RGB and red clump, especially for the key elements, such as Mg, Na, and Fe. This conclusion is corroborated by Souto et al. (2019), who also include odd-Z species, such as N, K, V, Mn, in the analysis. They confirm systematic depletion of metals at the cluster TO, as seen in previous studies. They also find a non-negligible abundance spread at all evolutionary phases. The most recent study of M67 by Liu et al. (2019) based on 3D NLTE and 1D NLTE for selected chemical elements confirms chemical inhomogeneity in M67, reinforcing evidence for signatures of atomic diffusion in the cluster. Whereas they make no attempt to quantitatively constrain the mixing processes, they emphasise the need to include such models in studies of stellar populations and chemical evolution.
Verma & Silva Aguirre (2019) showed that the analysis of acoustic glitches in asteroseismic data can be used to constrain turbulent mixing. Their results for three Kepler targets yield log T 0 in the range from 5.9 to 6.0, when comparing the effect on surface abundances, which is also slightly higher compared to our results. We note, however, that their parametrization of turbulent mixing (and hence, their definition of T 0 ) is not exactly the same as ours. Nevertheless, overall the conclusions of our and their study are similar taking into account both models and observations uncertainties. This fact is re-assuring, because the two methods to constrain the efficiency of mixing processes in stellar interiors are entirely independent.

Perspectives
Our findings of the relevance of atomic diffusion and mixing in stellar evolution are important in the context of other areas of astrophysics.
The most obvious consequence of our study is that accurate identification of membership in stellar associations, open and globular clusters, cannot rely on metallicity. This is still a common procedure in studies of stellar clusters (e.g. Blanco-Cuaresma & Fraix-Burnet 2018; Donor et al. 2020). However, it obviously leads to biases in the population statistics and determination of the age of cluster and its metallicity.
Next interesting consequence arises in the context of chemodynamical structure and evolution of the Galaxy. It is common to associate the present-day position of a star and its observed abundance pattern to its initial chemical composition, corresponding to that of the interstellar matter or star-forming region in which the star formed (Casagrande et al. 2011;Bensby et al. 2014;Recio-Blanco et al. 2014;Hansen et al. 2019;Hayden et al. 2020), modulo the effects of kinematic mixing and radial migration (e.g. Schönrich & Binney 2009). This information is used to infer quantities describing the present-day Galactic structure, ignoring the significant systematic effects that secular stellar evolution has on the photospheric abundances of stars. In turn, this causes a systematic bias in radial gradients, metallicity distribution functions, and even age-metallicity relationships, because the determinations of stellar ages by means of isochrone fitting are also affected by the problem of selective enhancement or depletion of abundances in different evolutionary phases (e.g. Jofré & Weiss 2011;Salaris 2016;Dotter et al. 2017).
Our results suggest that stellar abundances can be used to constrain the history of the Galaxy under the condition that stellar evolution models, and therefore, the stellar yields, implemented in Galactic Chemical Evolution (GCE) models, take atomic diffusion and mixing into account. An alternative solution is to restrict the analysis to the samples of stars, for which observed abundances patterns are not significantly affected by diffusion and mixing. The available evidence suggests that RGB stars, young (< 1 Gyr) and slowly rotating (< 5 km/s) stars, as well as low mass stars (< 0.9M ), are relatively robust tracers of the initial composition of the interstellar matter, whereas solar-like main-sequence stars, turn-off stars, subgiants -which dominate local Galactic neighbourhood and are very populous in samples like the GALAH (Buder et al. 2019) -are to be treated with caution. Moreover, this selective approach requires accurate determination of stellar masses and robust statistical modelling of selection functions in order to quantify the bias in the population statistics arising from target selection.

Conclusions
We presented a homogeneous analysis of Gaia-ESO spectra of stars in the open cluster NGC 2420 -a relatively young (2.5 ±0.5 Gyr) and metal-rich massive cluster at a distance of ∼ 2.5 kpc (Cantat-Gaudin et al. 2018). About 30% of stars in the cluster could be unresolved main-sequence binaries according to method discribed in Cordoni et al. (2018).
The spectra were taken with the Giraffe medium-resolution (19 200 ≤ R ≤ 21 500) spectrograph at the VLT. We combined our spectroscopic analysis with photometry and astrometry from Gaia DR2. Our sample includes ∼ 84 stars and covers the full evolutionary sequence in the cluster, from G-type stars on the main-sequence to K-type red giants. We used NLTE atomic models, as well as 1D hydrostatic (MARCS) and averaged 3D hydrodynamical (STAGGER) model atmospheres, to determine the abundances of Fe, Ca, and Mg in the cluster stars. The abundances of Li were measured using 1D LTE models and corrected for 3D NLTE effects using literature values.
We find that the chemical abundance distributions in the cluster display significant trends with the evolutionary stages of the stars. Fe, Mg, and Ca show a ∼ 0.1 to 0.2 dex depletion at the cluster turn-off point, but the abundances gradually increase and flatten near the base of the RGB. The abundances of Li are low for stars with M 1M , but increase for higher-mass stars and remain relatively constant at the level of A(Li) = 2.8 dex at the cluster turn-off. This value is close to the value predicted by the the standard models of big bang nucleosynthesis (SBBN). Li abundances drop by two orders of magnitude on the subgiant branch, attaining A(Li) = 1.3 dex on the RGB.
We attribute the systematic difference in abundances in the cluster to atomic diffusion and mixing. Comparing our findings with CESTAM stellar evolution models (Deal et al. 2018), we find that only RGB stars with masses 1.5M (log g 3.5 dex) can be viewed as robust tracers of the initial composition of the cluster. Also low-mass stars, M 0.9M are not expected to display self-processed photospheric abundances. Therefore, the initial chemical composition of NGC 2420 is A(Fe) = 7.35 ± 0.1 dex, A(Mg) = 7.3 ± 0.1 dex, A(Ca) = 6.4 ± 0.1 dex, A(Li) = 2.8 ± 0.1 dex. The present-day composition at the cluster turnoff is significantly different: A(Fe) = 7.15 ± 0.1 dex, A(Mg) = 7.15 ± 0.1 dex, A(Ca) = 6.14 ± 0.1 dex. We emphasize that these chemical offsets between the low-mass and higher-mass stars are caused by physical processes during stellar evolution, and are, consequently, essential to take into account in any study that uses stellar abundances for detailed diagnostics of stellar structure, exoplanet characterisation, or Galaxy history and formation.