The Gaia-ESO survey: impact of extra-mixing on C- and N-abundances of giant stars

The GES survey using FLAMES at the VLT has obtained high-resolution UVES spectra for a large number of giant stars, allowing a determination of the abundances of the key chemical elements C and N at their surface. The surface abundances of these chemical species are well-known to change in stars during their evolution on the red giant branch after the first dredge-up episod, as a result of extra-mixing phenomena. We investigate the effects of thermohaline mixing on C and N abundances using the first comparison between the GES [C/N] determinations with simulations of the observed fields using a model of stellar population synthesis. We explore the effects of thermohaline mixing on the chemical properties of giants through stellar evolutionary models computed with the stellar evolution code STAREVOL. We include these stellar evolution models in the Besan\c{c}on Galaxy model to simulate the [C/N] distributions determined from the UVES spectra of the GES and compare them with the observations. Theoretical predictions including the effect of thermohaline mixing are in good agreement with the observations. However, the field stars in the GES with C and N-abundance measurements have a metallicity close to solar, where the efficiency of thermohaline mixing is not very large. The C and N abundances derived by the GES in open and globular clusters clearly show the impact of thermohaline mixing at low-metallicity, allowing to explain the [C/N] ratio observed in lower-mass and older giant stars. Using independent observations of carbon isotopic ratio in clump field stars and open clusters, we also confirm that thermohaline mixing should be taken into account to explain the behavior of 12C/13C ratio as a function of stellar age. Overall the current model including thermohaline mixing is able to reproduce very well the C- and N-abundances over the whole metallicity range investigated by the GES data.


Introduction
Over the last decade, the understanding of our Galaxy has dramatically increased thanks to the development of large spectroscopic surveys that provide fundamental properties of a large number of stars in different regions of our Galaxy (e.g. RAVE: Steinmetz et al. 2006;SEGUE: Yanny et al. 2009; Gaia-ESO: Gilmore et al. 2012; APOGEE: Blanton et al. 2017;LAMOST: Cui et al. 2012;GALAH: De Silva et al. 2015). Some of them provide abundances deduced from high-resolution spectra, allowing the determination of light chemical elements such as carbon, nitrogen, or lithium.
The carbon and nitrogen abundances, and also the carbon isotopic ratio, are key chemical tracers used to constrain the stellar evolution of giant stars. Indeed, lowmass stars experience the well-known first dredge-up at the bottom of the red giant branch (RGB), implying changes of the surface abundances of C and N (Iben 1967). After this episode, numerous spectroscopic observations show that an extra mixing occurs after the bump luminosity on the red giant branch changing the abundances of elements lighter than oxygen at the surface of bright red giant stars (e.g. Gilroy 1989;Gilroy & Brown 1991;Gratton et al. 2000;Luck 1994;Tautvaišienė et al. 2000Tautvaišienė et al. , 2001Tautvaišienė et al. , 2005Smiljanic et al. 2009;Mikolaitis et al. 2010Mikolaitis et al. , 2012. Different transport processes have been discussed in the literature to explain the abundance anomalies in giants. Parametric computations have been proposed to better understand the behaviour of chemical abundances at the stellar surface in lowand intermediate-mass stars. After showing that the hot bottom burning (HBB) process, which was previously proposed by Cameron & Fowler (1971) to allow Li production in AGB stars, can explain the oxygen isotopic ratios in AGB stars with initial stellar mass between 4.5 and 7.0 M, Boothroyd et al. (1995) introduced the notion of cool bottom processing (i.e. ad hoc transport material from the cool bottom of stellar convective envelope to deeper and hotter radiative regions where nuclear reactions occur) to explain surface abundances of giant stars with masses lower than 2.0 M (see also Wasserburg et al. 1995;.  suggested, as did Wasserburg et al. (1995), the presence of non-standard mixing of unknown physical origin, between the hydrogen burning and the base of convective envelope after the bump to explain abundances anomalies in red giant stars. To understand variations in surface abundances of giant stars, they proposed a deep diffusive mixing (e.g. Weiss et al. 1996;Denissenkov et al. 1998). Nevertheless, these two propositions of extra mixing are then not related to any physical mechanism to explain changes in surface abundances, and depend on free parameters. On the other hand, rotation has been investigated as a possible source of mixing in RGB stars by several authors (Sweigart & Mengel 1979;Charbonnel 1995;Denissenkov & Tout 2000;Palacios et al. 2006;Chanamé et al. 2005), showing that the total transport coefficient of rotation at this phase is too low to imply abundance variation on the first ascent giant branch as requested by observations of RGB stars brighter than the RGB bump.
Thermohaline instability driven by 3 He-burning through the pp-chain has been proposed to govern the photospheric compositions of bright low-mass red giant stars (e.g. Charbonnel & Zahn 2007;Charbonnel & Lagarde 2010). This double diffusive instability, induced by a mean molecular weight inversion due to the 3 He( 3 He,2p) 4 He reaction in the thin radiative layer between the convective envelope and the hydrogen-burning shell (Eggleton et al. 2008;Lattanzio et al. 2015), is a physical mechanism that best reproduces the observational abundances (e.g. of C and N) in giant stars (e.g. Charbonnel & Lagarde 2010;Angelou et al. 2011Angelou et al. , 2012Henkel et al. 2017). A few recent papers have suggested that magnetic fields might play a role in stellar mixing, alone (Busso et al. 2007) or in combination with thermohaline mixing (Denissenkov & Merryfield 2011;Palmerini et al. 2011). Since thermohaline also provides a physical solution of the 3 He problem, well-known in Galactic chemical evolution models (Lagarde et al. 2011(Lagarde et al. , 2012, we focus on this mechanism in this paper. To exploit all the potential of the spectroscopic data, Lagarde et al. (2017;hereafter L17) improved the Besançon Galaxy model (hereafter BGM) including the stellar evolution models that provide surface chemical and seismic properties of stars during their life. In addition to global properties, the BGM is now able to explore the effects of extra mixing on the surface abundances of different chemical species. The BGM allows us to compute the stellar component of our Galaxy taking into account errors and the selection function of the observations, drawing a consistent picture of the Galaxy with the formation and evolution scenarios of the Milky Way, stellar formation and evolution theory, models of stellar atmospheres, and dynamical constraints (Robin et al. 2003;Czekaj et al. 2014). This population synthesis model is a powerful tool that can improve current stellar evolution models and the physics of different transport processes occurring in stellar interiors using a comparison with observations of field stars at different stellar masses, metallicities, ages, evolutionary stages, or at different locations in the Galaxy.
In this paper, we study the effects of thermohaline mixing with metallicity and mass of giant stars, using the C and N abundances derived for the giants in the Gaia-ESO survey. To this end, we perform simulations using the BGM with and without the effects of thermohaline instability. The simulations and data used for this study are described in Sect. 2, while the theoretical effects of thermohaline instability with stellar mass and metallicity are discussed in Sect. 3. We start with field stars observed with UVES in Sect. 4, and then enlarge our study to the open and globular clusters observed by the Gaia-ESO survey and compiled from the literature (see Sect. 4.2). We draw our conclusions in Sect. 5.

Data set and simulations
The Gaia-ESO survey (Gilmore et al. 2012;Randich et al. 2013, hereafter GES) uses the Fibre Large Array Multi Element Spectrograph (FLAMES) multifibre facility (Pasquini et al. 2002) of the Very Large Telescope (VLT) to obtain a better understanding of the kinematic and chemical evolution of our Galaxy. Giraffe, the medium-resolution spectrograph (R ∼ 20000), and UVES (Dekker et al. 2000), the high-resolution spectrograph (R ∼ 47000), are used to observe up to 10 5 stars in the Milky Way.
For our study, we used the observations of giant stars made with UVES, and the carbon and nitrogen abundances derived from their spectra. These giant stars lie in different Galactic regions (see Fig. 1). All data used in this paper are included in the second, fourth, and fifth internal GES data releases (iDR2, iDR4, and iDR5) to have a sample that is as large as possible. The main atmospheric parameters of the stars were determined as described by Smiljanic et al. (2014), the carbon and nitrogen abundances were determined as described by Tautvaišienė et al. (2015). We separated the stars into two groups: -324 giant field stars with 173 stars located in the Galactic bulge; -Giants belonging to open and globular clusters (see Table 1). The simulations were made using the revised version of BGM (Paper I of this series, Lagarde et al. 2017), where a new grid of stellar evolution models computed with the code STAREVOL (e.g. Lagarde et al. 2012;Amard et al. 2016) has been implemented. This new grid provides the global properties (e.g. surface gravity, effective temperature) and chemical abundances (for 54 stable and unstable species). These models also take into account the effects of thermohaline instability during the red giant branch (e.g. Charbonnel & Lagarde 2010). As discussed in Paper I, thermohaline instability changes the photospheric composition of low-mass brighter giant stars, with a decrease in carbon and an increase in nitrogen. In addition to the simulations discussed in Lagarde et al. (2017), improvements have been extended to all populations other than the thin disc, implying the computation of stellar evolution models with different α-enhancements ([α/Fe] = 0.15 and 0.30), following the observational [α/Fe] versus [Fe/H] trend observed by Data Release 12 of APOGEE (Majewski et al. 2017). Namely, for [Fe/H] < 0.1, As discussed in Czekaj et al. (2014), the BGM also simulates the Poisson noise in the Monte Carlo generation of the simulated stars. We performed simulations in every GES field referred to in the iDR5 using this new version of the BGM. As shown in Fig. 2, all stars in the sample have 0.5 < J − K < 1.0 and 5.0 < J < 14, so we restricted our simulations to these colour and magnitude ranges. We did two sets of simulations, with and without the effects of thermohaline instability. The selection bias introduced by the additional requirement of measurable carbon and nitrogen abundances cannot be taken into account in our sample, which is why simulations produce more stars than are present in the sample. This difference does not affect the conclusions of this paper.

Physics
Thermohaline mixing, as discussed in Paper I, is a double diffusive process conducted in RGB stars by an inversion of mean molecular weight induced by 3 He( 3 He,2p) 4 He reaction (Charbonnel & Zahn 2007;Siess 2009;Charbonnel & Lagarde 2010;Henkel et al. 2017) and a temperature gradient. For this study we use the prescriptions advocated by Charbonnel & Zahn (2007) given by Ulrich (1972) with an aspect ratio of instability fingers α ∼ 6 as referred by Krishnamurti (2003). The thermohaline diffusion coefficient used in stellar evolution models includes the correction for non-perfect gas and is given by where K is the thermal diffusivity; ϕ = (∂ ln ρ/∂ ln µ) P,T ; δ = −(∂ ln ρ/∂ ln ν) P,µ ; ∇ = (∂ ln T/∂ ln P); ∇ µ and ∇ ad are respectively the molecular weight gradient and the adiabatic gradient; and with the non-dimensional coefficient The value of α is still discussed in the literature by hydrodynamic simulations in 2D or 3D (Denissenkov et al. 2009;Denissenkov 2010;Denissenkov & Merryfield 2011;Rosenblum et al. 2011;Traxler et al. 2011;Brown et al. 2013;Garaud & Brummell 2015). Although these simulations are still far from stellar conditions and do not take into account the coupling of this instability with other hydrodynamic processes occurring in red giant stars (e.g. rotation, magnetic field), they predict that thermohaline instability is not efficient enough to explain surface chemical abundances (Wachlin et al. 2014) with the thermohaline fingers becoming more like blobs. Future hydrodynamical simulations closer to the conditions met in stellar interiors (Prat et al. 2015) or including the effects of other hydrodynamical processes as recently by Sengupta & Garaud (2018) would shed light on this discrepancy. Hence, we choose to use the prescriptions described above to compare theoretical predictions with current observations at different masses and metallicities.

Impact along the evolution
This double diffusive instability develops starting from the luminosity of the bump during the RGB (e.g. Charbonnel & Lagarde 2010, and Paper I). Indeed, the steady increase in the stellar luminosity along the RGB momentarily stops when the hydrogen burning shell (HBS) crosses the molecular weight barrier left behind by the first dredge-up. At that moment the mean molecular weight of the HBS becomes smaller, which implies a decrease in the total stellar luminosity. This is called a bump in the luminosity function. When the region of nuclear energy production has passed this discontinuity, the mean molecular weight slightly increases and the stellar luminosity increases again. This variation in the luminosity causes an accumulation of stars in the colour-magnitude diagram leading to a bump in the luminosity distribution (e.g. Iben 1967Iben , 1968Fusi Pecci et al. 1990;Charbonnel 1994;Christensen-Dalsgaard 2015). The impact of thermohaline instability on the theoretical [C/N] 1 distributions at different evolutionary states are shown in Fig. 3. With stellar models, giant stars are divided into three groups: (1) low-RGB stars: stars ascending the red giant branch before the Notes. For GES clusters, the approximate turn-off masses were evaluated using the theoretical PARSEC isochrones (Bressan et al. 2012) with the corresponding ages and metallicities. For globular clusters see the text; for clusters already published, we use the turn-off mass and age indicated in the corresponding article.
RGB bump 2 . These stars have not yet undergone thermohaline mixing; (2) upper-RGB: RGB stars brighter than the RGBbump (with logg 2.2); (3) clump stars selected according to their asymptotic period spacing of g-modes ∆Π =1 . As discussed by Charbonnel & Lagarde (2010) and Paper I, thermohaline instability occurring at the RGB-bump luminosity changes the surface abundances of C and N for giant stars brighter than the RGB-bump and along the red giant branch, resulting in a decrease in [C/N] (see middle panel of Fig. 3). While thermohaline mixing is no longer happening in red clump stars, they have the lowest [C/N] (as shown in Fig. 3) because they have undergone a full RGB phase of extra mixing.
2 Since the gravity (and thus luminosity) of the RGB-bump changes with the metallicity of stars, we establish a simple empirical relation based on stellar evolution models (without the effects of rotation on the evolutionary path) allowing the distinction of low-RGB and upper-RGB stars: log g RGBbump = 0.32·[Fe/H]+2.44.

Impact as a function of stellar mass
As discussed and explained by Charbonnel & Lagarde (2010;see Sect. 3.1.2), the global efficiency of thermohaline mixing increases when considering less massive stars at a given metallicity or more metal-poor stars at a given stellar mass. This results from the combination of several factors like the thermohaline diffusion timescale compared to the secular timescale, the compactness of the hydrogen burning shell and of the thermohaline unstable region, and the amount of 3 He available to power the thermohaline instability.  [C/N] distribution is larger for 1.0 M stars than for 2.0 M stars. On the other hand, the RGB-bump occurs on the evolution of low-and intermediate-mass stars only, and depends on the metallicity of these stars. More massive stars (HMS, M 2.2 M ) ignite central helium burning in a non-degenerate core at relatively low luminosity on the RGB, well before the hydrogen burning shell reaches the mean molecular weight discontinuity caused by the first dredge-up. Consequently, these objects do not go through the bump on their short ascent of the RGB, and thus thermohaline instability does not develop in this kind of star.

Impact as a function of metallicity
In low-mass, low-metallicity giants the thermohaline unstable region is more compact and has a steeper temperature gradient, resulting in a higher diffusion coefficient and then a more efficient transport process (see Fig. 6 of Lagarde et al. 2011).
The effect of thermohaline mixing at two metallicities on the [C/N] value at the surface of clump stars simulated by the BGM is shown on Fig. 5 (top and middle panels). The mass distributions for each metallicity range are also shown in Fig. 5 (bottom panel). Although thermohaline mixing has a larger impact on [C/N] when the metallicity decreases, the figure also clearly shows a non-negligible impact at solar metallicity.
Because of their large mass and metallicity ranges, field stars provide key data to constrain the efficiency of thermohaline instability occurring in giant stars. In the next section, we study the effects of thermohaline instability with mass and metallicity, comparing the population synthesis and the GES observations.  In the same figure, the [C/N] value derived from the observed field stars are also shown (red dots). Since UVES is centred on solar neighbourhood MSTO stars (plus bulge, see Fig. 1 prescriptions directly. However, Fig. 7 allows a quantitative comparison and shows the necessity of extra mixing to reproduce the observations even at higher metallicities. In this case, information on stellar masses and evolutionary states of field stars are required to add more constraints on the efficiency of extra mixing with stellar mass. This is now possible with asteroseismology, which can be combined with astrometry from Gaia (Gaia Collaboration 2016), and will be discussed in a forthcoming paper. In addition, the right panel of Fig. 7 shows the simulation performed specifically for NGC 104 (with and without extra mixing), focussing on cluster region in the sky and the specific metallicity range.

C and N abundances in clusters
The GES has observed many different clusters in different regions of our Galaxy (see red circles in Fig. 1), providing the homogeneous observational data needed to constrain stellar and Galactic evolution. We investigate the [C/N] value derived in giant members of those open and globular clusters. We do not want to study each cluster in detail; instead, clusters are used here as tracers of extra mixing. Since stars belonging to a cluster were formed together, we can assume that they have the same age, distance, and metallicity, resulting in stronger constraints of thermohaline efficiency.     Table 1). A typical error bar is indicated.  Table 1). A typical error bar is indicated.  Table 1). clusters were acquired by two complementary programmes, and were analysed in a homogeneous way by the same group that produces C and N determinations in GES, resulting in a robust comparison with our models. Individual stars are attributed the turn-off mass and age of their host clusters (e.g. VandenBerg et al. 2013, Chantereau's priv. comm. using stellar models discussed in Charbonnel & Chantereau 2016, and Drazdauskas et al., in prep.). Synthetic populations with and without the effects of thermohaline instability are shown (right and left panels, respectively) for low-RGB, upper-RGB, and clump stars (as defined in Sect. 4). Simulations and observations in each cluster are a mix of giant stars at different evolutionary states (i.e. at different luminosities or gravities on the RGB), implying a wide [C/N] range for the synthetic populations and for the determination in each cluster.
As discussed by Charbonnel & Lagarde (2010) and described in Sect. 3, three mass ranges can be evoked to quantify the efficiency of thermohaline instability: -For low-mass and low-metallicity stars, thermohaline instability is the most efficient transport process that can change the C and N surface abundances, which is why the simulations presented here (which take into account thermohaline mixing only) reproduce very well the observed [C/N] in this mass range (see Fig. 9) including a very good fit for stars older than ∼1 Gyr (see Fig. 10). -For intermediate-mass stars (1.7 M 2.2 M ), our simulations present a slightly higher [C/N] than observations (see right panel of Fig. 9). Charbonnel & Lagarde (2010) show that in addition to thermohaline mixing, rotation-induced mixing plays an equivalent role in changing the surface abundances of the stars in this mass range, resulting in a slightly  . 9) and younger than 0.5 Gyr (see Fig. 10). As known for a long time (e.g. Meynet & Maeder 2002;Palacios et al. 2006;Charbonnel & Lagarde 2010), rotation-induced mixing has an impact on the internal chemical structure of main sequence stars, although its signatures are revealed later, at the beginning of the RGB. This results in a decrease in the surface abundances of C while N increases. We plan to focus on the effects of rotation on stellar ages and chemical properties in a forthcoming paper. We note that using the Data Release 12 of the APOGEE survey, Masseron & Gilmore (2015) showed that extra mixing has occurred in thin disc stars, but indicated that thick disc stars do not show any evidence of this extra mixing process. They proposed that the thick disc stars could be formed with a different initial abundances than thin disc stars. We also note that our simulations reproduce very well observations in clusters having metallicity corresponding to the thick disc or halo population assuming the same initial abundances for all populations. However, our comparison is based on clusters members, and complementary to this study it is crucial to consider a larger sample of thick disc field stars such as those observed by the APOGEE survey. In addition, the chemical evolution model and the population synthesis model should be combined to study the effects of different initial abundances for the different populations before drawing any conclusions.

12 C/ 13 C in field stars and clusters
The GES cannot derive the carbon isotopic ratio due to the wavelength regions observed with no good 13 CN features, thus in this part we use data from other studies to investigate the importance of 12 C/ 13 C to constrain extra mixing on the red giant branch. Figures 11 and 12 present the carbon isotopic ratio as a function of C/N and as function of stellar masses and ages, for synthetic populations computed with the BGM taking into account the effects of thermohaline mixing (grey dots) or not (green dots). The carbon isotopic ratio decreases abruptly when the thermohaline mixing develops in RGB stars, as already shown by Charbonnel & Lagarde (2010). This is in agreement with the observed abundance ratios found in field stars and open clusters, shown with symbols in the figures (Mikolaitis et al. 2012;Drazdauskas et al. 2016;Tautvaišienė et al. 2016). Even though the range of [C/N] values agrees with both models in the observed range, the low values of 12 C/ 13 C cannot be reproduced without extra mixing process. As discussed below in the [C/N] case, thermohaline mixing explains very well the low-mass (and older) giants stars, but not the higher mass stars. This proves that 12 C/ 13 C is a more powerful parameter for constraining extra mixing on the RGB than [C/N], including for solar metallicity stars.

Conclusions
In this paper, we present the first comparison between synthetic populations computed with the Besançon Galaxy model and  Table 1). the C and N abundances derived by the Gaia-ESO survey in field stars and in different clusters, both globular and open. We conclude from this work that it is crucial to take into account thermohaline mixing to understand the C and N observed at the surface of low-mass stars, and in the determination of the stellar mass and age from their chemical properties (Martig et al. 2015;Ness et al. 2016).
We compared data from the Gaia-ESO survey with predictions computed using the Besançon Galaxy model in which we included stellar evolution models taking into account (and not) the effects of thermohaline instability (Paper I). To date, this mixing is the only physical process proposed in the literature to explain the photospheric composition of evolved red giant stars. We focus in the first part of this paper on field stars because of their wide-coverage properties (e.g. mass, metallicity, and ages) to deduce an observational trend between [C/N] and stellar mass, metallicity, or age. Due to the lack of C and N determinations in field stars at low metallicity, we cannot investigate further the observational constraints in the metallicity domain where thermohaline instability is more efficient. Nevertheless, the theoretical distribution of [C/N] predicted by the BGM including the effects of thermohaline instability is in better agreement than the distribution predicted by the standard model at metallicity close to solar.
We also investigate the [C/N] derived in giant members of open and globular clusters by the Gaia-ESO survey and literature. This comparison shows a very good agreement with stellar evolution models including thermohaline mixing over the whole scrutinized metallicity range, explaining the [C/N] observed in lower mass and older giant stars. This confirms that thermohaline instability is crucial to understand the chemical properties of giant stars. The next step is to use a larger sample of field stars to strengthen this encouraging result. On the other hand, we show that the observed behaviour of 12 C/ 13 C with stellar ages is clearly reproduced by models which A24, page 9 of 11  Table 1).
include the effect of thermohaline mixing. This confirms the importance, amongst others, of extra mixing when deducing stellar ages from the chemical properties of giant stars.
Additionally, and independently of spectroscopy, asteroseismology paves the way to a better understanding of stellar interiors, providing valuable and independent constraints on current stellar evolution models and on the physics of different transport processes. The space missions CoRoT (Baglin et al. 2006), Kepler, and K2 (Borucki et al. 2010) observed a large number of giant stars in different regions in our Galaxy, allowing a unique opportunity to derive some fundamental properties (e.g. stellar mass, radius, age and gravity, and evolutionary stage of giants) by observation of mixed modes in red giants (e.g. Chaplin & Miglio 2013). To obtain the most information possible from the data sample, the asteroseismic properties must be combined with the observations of the surface chemical abundances and especially the surface 12 C/ 13 C. Future studies of CoRoT inner-field stars (Valentini et al., in prep.) and K2 giants (campaign 3) already observed by GES, will provide complementary results for the development of stellar evolution models.