Population synthesis to constrain Galactic and Stellar Physics- I- Determining age and mass of thin-disc red-giant stars
AAstronomy & Astrophysics manuscript no. article_pop_astroph c (cid:13)
ESO 2018October 8, 2018
Population synthesis to constrain Galactic and Stellar Physics
I- Determining age and mass of thin-disc red-giant stars
N. Lagarde , A.C. Robin , C. Reylé , and G. Nasello Institut UTINAM, CNRS UMR6213, Univ. Bourgogne Franche-Comté, OSU THETA Franche-Comté-Bourgogne, Observatoire deBesançon, BP 1615, 25010 Besançon Cedex, Francee-mail: [email protected]
Received 14 december 2016 / Accepted 5 February 2017
ABSTRACT
Context.
The cornerstone mission of the European Space Agency, Gaia, together with forthcoming complementary surveys (CoRoT,
Kepler , K2, APOGEE and Gaia-ESO), will revolutionize our understanding of the formation and history of our Galaxy, providingaccurate stellar masses, radii, ages, distances, as well as chemical properties for a very large sample of stars across di ff erent Galacticstellar populations. Aims.
Using an improved population synthesis approach and new stellar evolution models we attempt to evaluate the possibility ofderiving ages and masses of clump stars from their chemical properties.
Methods.
A new version of the Besançon Galaxy model (BGM) is used in which new stellar evolutionary tracks are computed fromthe stellar evolution code STAREVOL. These provide global, chemical and seismic properties of stars from the pre-main sequence tothe early-AGB. For the first time, the BGM can explore the e ff ects of an extra-mixing occurring in red-giant stars. In particular wefocus on the e ff ects of thermohaline instability on chemical properties as well as on the determination of stellar ages and masses usingthe surface [C / N] abundance ratio.
Results.
The impact of extra-mixing on He, carbon isotopic ratio, nitrogen, and [C / N] abundances along the giant branch is quanti-fied. We underline the crucial contribution of asteroseismology to discriminate between evolutionary states of field giants belonging tothe Galactic disc. The inclusion of thermohaline instability has a significant impact on C / C, He as well as on the [C / N] values. Weclearly show the e ffi ciency of thermohaline mixing at di ff erent metallicities and its influence on the determined stellar mass and agefrom the observed [C / N] ratio. We then propose simple relations to determine ages and masses from chemical abundances accordingto these models.
Conclusions.
We emphasize the usefulness of population synthesis tools to test stellar models and transport processes inside stars. Weshow that transport processes occurring in red-giant stars should be taken into account in the determination of ages for future Galacticarchaeology studies.
Key words.
Asteroseismology; Galaxy:stellar content, Galaxy:evolution, Galaxy:abundances, stars: evolution
1. Introduction
Galactic Archaeology explores the formation and evolution ofour Galaxy using the chemical properties, kinematics, and theirdependency on age, of di ff erent stellar populations, (Freeman &Bland-Hawthorn 2002; Turon et al. 2008). In this context, thedetermination of accurate stellar distances and ages along theGalactic disc is crucial to improving our understanding of theMilky Way.The Gaia space mission provided astrometry for more than2 million stars and photometry for 1 billion stars, with typicaluncertainties of about 0.3 mas for the positions and parallaxes,and about 1 mas / yr for the proper motions (first data release,Gaia Collaboration et al. 2016).Asteroseismology data of red-giants stars observed by the space missions CoRoT (Baglin &Fridlund 2006), Kepler (Gilliland et al. 2010) and K2 providecrucial constraints on the stellar properties such as masses, radii,and evolutionary states (e.g. Stello et al. 2008; Mosser et al.2012b; Bedding et al. 2011; Vrard et al. 2016), on the internalrotation profile (e.g. Mosser et al. 2012a; Beck et al. 2012), aswell as on the properties of helium ionization regions (Miglio et al. 2010). Thanks to asteroseismology, masses of red-giantstars can be directly related to stellar interior physics and stellarevolution (Lebreton et al. 2014a,b) allowing one to determineages, without being limited to surface properties. Seismic datacollected for more than 20,000 red-giant stars belonging to theGalactic-disc populations represent a huge sample to constrainstellar and Galactic physics (Miglio et al. 2013; Anders et al.2016). A broad e ff ort is ongoing with large spectroscopic sur-veys such as APOGEE (Majewski et al. 2015; SDSS Collabora-tion et al. 2016), ESO-Gaia (Gilmore et al. 2012), RAVE (Stein-metz et al. 2006), SEGUE (Yanny et al. 2009), LAMOST (Cuiet al. 2012), HERMES (Ackersta ff et al. 1998) and for the futurewith WEAVE, 4MOST and MOONS from which stellar param-eters, radial velocities and detailed chemical abundances can bemeasured for CoRoT, Kepler , and K2 targets.To exploit their full potential, it is crucial to perform a com-bined analysis of these di ff erent kinds of observations. The popu-lation synthesis approach is a powerful tool for such analysis, al-lowing the computation of mock catalogues under various modelhypothesis, and to statistically compare them with any type oflarge survey data. The Besançon Galaxy model (hereafter BGM)is a stellar population synthesis model (Robin et al. 2003; Czekaj Article number, page 1 of 9 a r X i v : . [ a s t r o - ph . S R ] F e b & A proofs: manuscript no. article_pop_astroph
Fig. 1.
Theoretical evolution of He and carbon isotopic ratio at the stellar surface as a function of surface gravity for stellar models of : left panels various masses (1.0 ; 1.2 ; 1.5 ; 1.8 ; 3.0 M (cid:12) represented by a black, red, blue, green and orange solid line, respectively) at Z = right panels various metallicities ([Fe / H] = = (cid:12) . These models include the e ff ects of thermohaline instability (bottom panels) and following standard evolution (top panels). These tracks areshown from the main sequence up to the early-AGB. et al. 2014) intended to meld the formation and evolution scenariiof the Galaxy, stellar formation and evolution theory, models ofstellar atmospheres, as well as dynamical constraints, in orderto make a consistent picture of the Galaxy in comparison withavailable observations (photometry, asteroseismology, astrome-try, and spectroscopy) at di ff erent wavelengths.To benefit from the combination of recent asteroseismicand spectroscopic surveys, we updated the evolutionary tracksthat are used as inputs in the BGM. These stellar evolutionmodels are computed with the code STAREVOL (e.g. Lagardeet al. 2012a), which follows the global, chemical and seismicproperties of stars all along their evolution. This is done fromthe pre-main sequence (along the Hayashi track) to the early-asymptotic giant branch (early-AGB). These models includethe e ff ects of di ff erent transport processes such as thermohalineinstability (discussed in this paper).The aim of this series of papers is to investigate the impactsof di ff erent hydrodynamic processes that occur inside the starson the chemical properties of Galactic stellar populations. Inthe context of the interpretation of large spectroscopic surveyssuch as APOGEE, or Gaia-ESO, we will perform comparisonbetween theoretical synthetic populations and spectroscopic sur-veys in forthcoming papers (Lagarde et al. in prep. Part II). Inthis paper, we focus on presenting and discussing the implemen-tation in the Besançon Galaxy model of stellar evolution mod-els that include the e ff ects of thermohaline instability on global,chemical and seismic properties. We discuss the determinationof stellar ages and masses from the [C / N] ratio. We plan to fo-cus on the e ff ects of rotation and the implementation of di ff er-ent prescriptions for thermohaline instability on stellar ages andchemical properties in a separate forthcoming paper (Part III).In Sect.2 we present the input physics of our stellar evolution Table 1.
Stellar Evolution models
Metallicity sets Stellar mass MixingZ ([Fe / H], [ α / Fe]) (M (cid:12) )Z = = = = = ff ects of ther-mohaline mixing or following the standard prescription. We alsopresent the new quantities that can be simulated by the BGM. InSect. 5, we discuss the determination of stellar ages and massesfrom the surface carbon and nitrogen abundances, and we pro-vide relations for three metallicity ranges. We conclude and ex-plore some perspectives in Sect. 6.
2. Stellar evolution models
Stellar evolution models are computed with the codeSTAREVOL (e.g. Lagarde et al. 2012b) for a range ofmasses between 0.6 M (cid:12) and 6.0 M (cid:12) at five metallicities Z = / H] = = / H] = = / H] = -0.23),Z = / H] = -0.54) and Z = / H] = -2.14). Thesemodels are computed from the pre-main sequence to the early-AGB phase. We use the same main physical ingredients that areused and fully described in Lagarde et al. (2012b), except for: Article number, page 2 of 9. Lagarde , A.C. Robin, C. Reylé, and G. Nasello: Population synthesis to constrain Galactic and Stellar Physics – the solar mixture, that comes from Asplund et al. (2009); – the treatment of convection, that is based on a classical mix-ing length formalism with α MLT = ff usionnor rotation.As discussed in Lagarde et al. (2012a), these stellar evolu-tion models follow the global asteroseismic properties using thescaling relations and asymptotic relations (Tassoul 1980), i.e. thelarge frequency separation, the frequency corresponding to themaximum oscillation power, the asymptotic period spacing ofg-modes, and di ff erent acoustic radii.To quantify the e ff ects of transport processes on the chemicalproperties of stellar populations in our Galaxy, we computedstellar evolution models assuming: (1) standard models (nomixing mechanism other than convection), (2) models thatinclude the e ff ects of thermohaline instability induced by He-burning. This instability develops as long thin fingers whoseaspect ratio is consistent with prediction by Ulrich (1972) andwith the laboratory experiments (Krishnamurti 2003). Althoughthe e ffi ciency of thermohaline instability in stellar interiors isstill discussed in the literature by hydrodynamical simulations(Denissenkov 2010; Traxler et al. 2011, Prat et al in prep.), weadopt an aspect ratio equal to 5, which might correspond to themaximum e ffi ciency of this instability.As discussed by Charbonnel & Lagarde (2010) and Angelouet al. (2011, 2012), this mechanism has a crucial e ff ect onsurface chemical properties of red-giant branch stars. Its e ff ect isconsistent with most of spectroscopic observations of low-massand intermediate-mass stars, especially in reproducing the low- C / C and the [C / N] ratio in open clusters (e.g. Tautvaišien˙eet al. 2016; Drazdauskas et al. 2016; Tautvaišien˙e et al. 2015,2013; Mikolaitis et al. 2010; Smiljanic et al. 2009) as well as inCoRoT targets (Morel et al. 2014; Lagarde et al. 2015). It hasalso a very significant impact on the chemical evolution of lightelements in the Milky Way (Lagarde et al. 2011) allowing theresolution of the long-standing ” He-problem" in our Galaxy(Lagarde et al. 2012b).In the following section, we briefly describe the evolutionof stars and present the e ff ects of thermohaline mixing on thesurface abundances of He and carbon isotopic ratio drawing thestellar evolution.
Figure 1 presents the theoretical evolution of Helium-3 and car-bon isotopic ratio for di ff erent initial masses and metallicitiesfrom the main sequence to the early-AGB. After the main sequence, a star experiences core contraction toincrease its central temperature, then evolves rapidly toward thered giant branch (RGB). During this phase, called the ”Sub giantbranch“ (SGB) when the stars cross HR diagram almost hor-izontally, the convective envelope grows in mass and deepensinside the star. This is the first dredge-up, where the convectiveenvelope is diluted with hydrogen-processed material, inducingchanges of the surface abundances. This episode occurs at higherluminosity when the metallicity decreases as well as when thestellar mass increases. The surface mass fractions of Li, Be,
Fig. 2.
The large separation, ∆ ν , as a function of the e ff ective temper-ature, T e ff , for synthetic population computed with the BGM. Coloursindicate the ν max , the frequency at which the power spectrum is maxi-mum. C and O decrease while those of He, He, C, N, and Oincrease, implying a decrease at the surface of the isotopic ra-tios C / C, and C / N. Figure 1 clearly shows the signatureof this episode (e.g. at log(g) ∼ (cid:12) ).As shown by Charbonnel (1994), the first dredge-up e ffi -ciency (in terms of maximum depth of the convective envelope)decreases with decreasing metallicity. For a given stellar mass,Fig.1 (right panel) shows that the depletion of C / C and theincrease of He begin at lower gravity when the metallicity de-creases. The chemical variations during the first dredge-up de-pend on the initial stellar mass as well as on the metallicity. Fora given metallicity, when the initial stellar mass increases, Fig.1(left panels) shows that the post dredge-up values of carbon iso-topic ratio and He decrease, as well as at the given stellar masswhen the metallicity decreases (right panel). This dependence istrue for C / N, as well as for oxygen isotopic ratios. This isdue to the convective envelope reaching deeper regions duringthe first dredge-up. From the sub giant branch to the RGB tip,the temperature at the base of the convective envelope is alwaysinsu ffi cient to activate nuclear reactions. As a consequence, instandard models (top panels of Fig. 1) the only change in sur-face abundances is due to the first dredge-up on the SGB; afterthis episode the surface abundances remain constant along theRGB once the convective envelope recedes and until the seconddredge-up occurs at the end of the helium burning phase. Thermohaline mixing has recently been flagged as the mainmechanism that can govern the photospheric chemical compo-sition of low-mass bright giant stars (Charbonnel & Zahn 2007;Charbonnel & Lagarde 2010). In such stars, thermohaline in-stability is a double-di ff usive instability induced by the molec-ular weight inversion created by the He( He,2p) He reactionin the external region of the hydrogen-burning shell (Eggletonet al. 2006, 2008). As discussed by Charbonnel & Zahn (2007)and Charbonnel & Lagarde (2010), this instability is expected to
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Fig. 3.
Surface gravity as a function of e ff ective temperature for synthetic populations computed with the BGM including the e ff ects of thermoha-line instability (right panel) or not (left panel). The colour code represents the carbon isotopic ratio at the surface of stars in the thin disc. set in after the first dredge-up when the star reaches the RGB-bump (at log(g) ∼ He at the stellarsurface after the RGB-bump. C and N di ff use outwards,while C di ff uses inwards (see for more details Charbonnel &Lagarde 2010), implying a decrease of C / C and [C / N]. Thee ffi ciency of thermohaline instability decreases when the stellarmass or stellar metallicity increase (see Fig. 1). In addition,thermohaline mixing induces a slight decrease of He (Lagardeet al. 2011) and increase of nitrogen at lower metallicity duringthe central helium burning before the second dredge-up episode.Thermohaline instability does not change the evolutionarytracks in the HR-diagram and has not impact on stellar ages be-cause it has not significant e ff ect on the stellar structure.
3. The Besançon Galaxy Model
The Besançon Galaxy Model (hereafter BGM) is a model usingthe population synthesis approach that simulates observations ofthe sky with errors and biases. It is based on assumptions anda scenario for the Galaxy formation and evolution that reflectthe present knowledge about the Milky Way. Four stellar popu-lations are considered: a thin disc, a thick disc, a bar, and a halo,with each stellar population having a specific density distribu-tion. The stellar content of each population is modeled throughan Initial Mass Function (IMF) and a Star Formation History(SFH), which can di ff er from one population to the other. Tocompute the stellar distribution at a given time, the stars gener-ated by these IMFs and SFHs follow evolutionary tracks. Whenthey have reached their final age (the present time) their astro-physical parameters (mass, age, T e ff , log(g), metallicity, abun- dances...) are stored and used to compute their observationalproperties, using atmosphere models, and assuming a 3D extinc-tion map describing the interstellar extinction they su ff er. A dy-namical model is used to compute radial velocities and propermotions. In the simulations presented here, we make use of the3D extinction map from Marshall et al. (2006).For the time being, the metallicity of each star is the ini-tial metallicity of the gas when it was born, which is estimatedassuming a time dependent metallicity from Haywood (2008),and a radial metallicity gradient of -0.7 dex / kpc. In the future aproper chemical evolution model will be incorporated.The model takes into account the stellar binarity, by gener-ating secondary components at their birth, assuming a binarityprobability depending on mass (see Czekaj et al. (2014) for moredetails). Then, according to the estimated spatial resolution ofthe observations to simulate, stars in systems are merged or not(that is, their fluxes are added if the stars are too close, projectedon the plane of the sky).In the present version of the model, only the thin disc is mod-elled this way, while the thick disc, bar and stellar halo are gen-erated using a Hess diagram computed from a fixed evolutionaryscheme as described in Robin et al. (2003), which does not yettake into account binarity.The stellar densities in di ff erent regions of the Galaxy aremodulated by density laws for each population, which are givenin detail in Robin et al. (2003) for the thin disc, Robin et al.(2012) for the bar, and Robin et al. (2014) for the thick disc andhalo.In the model version presented here, we use the evolutionarytracks described in Sect.2, instead of the Padova tracks used inCzekaj et al. (2014), from which surface abundances and astero-sismic parameters are computed for each simulated star. For starsof mass lower than 0.6 solar mass, Chabrier & Bara ff e (1997)evolutionary tracks are still used, although those new propertiesare not computed yet.
4. Simulations of synthetic populations
As discussed in Part 2 and in the literature (Palacios et al. 2006;Lagarde et al. 2012a; Bossini et al. 2015), transport processesoccurring in stellar interiors have significant impact on global(e.g. luminosity, e ff ective temperature, age), chemical, and seis- Article number, page 4 of 9. Lagarde , A.C. Robin, C. Reylé, and G. Nasello: Population synthesis to constrain Galactic and Stellar Physics
Fig. 4.
Surface abundance of He (in mass fraction, top-left panel), C / C (top-right panel), [C / Fe] (bottom-left panel), and [N / Fe] (bottom-rightpanel) as a function of stellar mass for synthetic thin disc computed with the BGM. Stars have been selected to be in the clump according to their ∆Π (cid:96) = . The colour code represents the metallicity of stars. Simulations including or not the e ff ects of thermohaline instability are represented bycolour-dots and crosses respectively. mic properties. Population syntheses are powerful tools to studythese processes using survey data. In the context of our study,we discuss the impact of thermohaline mixing on the propertiesof thin disc giants observed by asteroseismic and spectroscopicsurveys. We shall consider in a future paper the thick disc pop-ulation, which di ff ers from the thin disc by its [ α / Fe] abundanceratio. For the present study we only consider stellar models ac-cording to solar α -abundance (i.e. [ α / Fe] = Kepler field. They provide astrophysical parameters, as-teroseismic properties and surface abundances for 54 stable andunstable species. We study in this section the impact on the prop-erties of the simulated fields of this new models.
The detection of solar-like oscillations with the space missionsCoRoT and
Kepler provides powerful constraints on stellar massand radius of giants stars. With the asymptotic period spacing of gravity modes, these observations provide information on stellarstructure (Mosser et al. 2012b; Lagarde et al. 2012a), as well asconstraints on transport processes (Lagarde et al. 2016). Usingthe scaling relations (Tassoul 1980; Mosser et al. 2010; Belka-cem et al. 2011), the asteroseismic parameters of large separa-tion, ∆ ν , and frequency of maximum oscillation power, ν max aredirectly related to stellar radii and masses: MM (cid:12) ≈ (cid:32) ν max ν max , (cid:12) (cid:33) (cid:32) ∆ ν ∆ ν (cid:12) (cid:33) − (cid:32) T e ff T e ff , (cid:12) (cid:33) / (1) RR (cid:12) ≈ (cid:32) ν max ν max , (cid:12) (cid:33) (cid:32) ∆ ν ∆ ν (cid:12) (cid:33) − (cid:32) T e ff T e ff , (cid:12) (cid:33) / (2)Solar reference values are ∆ ν (cid:12) = µ Hz; ν max , (cid:12) = µ Hz,and T e ff , (cid:12) = ff ect the mass and radius de-terminations of clump stars up to ∼
10% and ∼
6% respectively.Di ff erent temperature scales have been tested in Miglio (2012)and agree within the quoted uncertainty range.The population synthesis provides the seismic propertiessuch as the large separation, the frequency with the maximum Article number, page 5 of 9 & A proofs: manuscript no. article_pop_astroph amplitude, or the asymptotic period spacing of g-modes for starsin the thin disc (see Fig.2). It is well known that the age of gi-ant stars can be approximated by their lifetime on the main se-quence, which depends on the stellar mass and metallicity. In ad-dition, asteroseismology provides accurate stellar radii and thusallows the determination of distances. These observations of gi-ants belonging to the di ff erent populations of the Milky Way pro-vide additional constraints to study the formation and evolutionof our Galaxy (Miglio et al. 2013). To fully exploit the potentialof these observations, it is crucial to combine them with spectro-scopic surveys allowing the following of the chemical propertiesof the stars within the di ff erent stellar populations. Figure 3 shows the evolution of carbon isotopic ratio along thelog(g) vs T e ff diagram in a simulation computed with the BGM.This figure clearly shows the impact of thermohaline instabilityon the C / C. The brighter-RGB and clump stars have a lower C / C at the surface when thermohaline instability is included.Figure 4 shows the surface chemical properties of thin discstars as a function of stellar mass, including or not the e ff ectsof thermohaline mixing. This figure focuses on clump starsselected by their asymptotic period spacing of g-modes ∆Π ( (cid:96) = .As shown by Charbonnel & Lagarde (2010) and recalled in Part2, thermohaline mixing changes the surface chemical propertiesof stars more evolved than the RGB-bump. The e ffi ciency ofthis mechanism with the metallicity and the stellar mass is alsoshown in Fig.4. Due to the strong e ff ect of thermohaline mixingon its abundances, Helium-3 and C / C are the best indicatorsto constrain this mechanism during the RGB. Fig.4 shows alsoan impact on [C / Fe] and [N / Fe] but less important especially forupper metallicities.Very recently, Masseron et al. (2016) used stellar models(at given mass and metallicity) to compare directly with theAPOGEE observations. They claim that stellar evolution mod-els including transport processes (e.g. thermohaline instabilityand rotation-induced mixing) overestimate the N-abundance inred-clump stars. However this study only considers models witha given mass and does not account for the range of masses andmetallicities that are present in observational data. To comparelarge surveys including stars at di ff erent masses and metallici-ties, synthetic population analysis is the most e ffi cient methodto validate the models by comparing the data with simulations,accounting for a realistic range of mass, metallicities and for ob-servational biaises. A detailed comparison between our syntheticpopulations and large surveys will be done in the Part II of thisseries (Lagarde et al in prep.).
5. Determination of age and mass using [C/N] ratio
Recent studies (e.g. Martig et al. 2015; Masseron & Gilmore2015) have proposed to use [C / N] to determine stellar ages andmasses of red-giant stars. However, these studies do not take intoaccount the e ff ects of mixing occurring in the stellar interiors,stellar input physics and possible changes of these relations atdi ff erent evolutionary stages. Figure 5 shows [C / N]-dependencywith stellar masses and ages, with and without thermohaline in-stability. Giant stars are divided into three groups: (1) Lower-RGB stars, stars ascending the red-giant branch before the RGB-bump (log(g) > ≤ ∆Π ( (cid:96) = values. Considering standard stellar evolution models only (graydots on Fig. 5), [C / N] seems to be a good proxy to determine stel-lar masses along the red giant branch and during the He-burningphase. Standard models show a more important dispersion of[C / N] with stellar age than with mass for the first ascent red-giantstars (lower-RGB and upper-RGB). Although [C / N] ratio at thestellar surface is directly related to the stellar properties (massor metallicity), we point out the di ffi culty to determine an accu-rate stellar age from these properties. As discussed by Lebretonet al. (2014a) stellar evolution models are still a ff ected by severaluncertainties (e.g. [Fe / H], α -enhancement, solar mixture, initialHe-abundances, transport processes) which can significantly af-fect the determination of stellar ages from the chemical proper-ties of stars. Fig. 6.
Surface abundance of [C / N] for clump stars as a function ofstellar ages (top panel) and stellar masses (bottom panel) for a syntheticthin disc computed with the BGM. Stars are divided in three metallicity-bins: -0.20 ≤ [Fe / H] ≤ -0.10 (blue dots), -0.05 ≤ [Fe / H] ≤ + + ≤ [Fe / H] ≤ + / N]and mass and age (Eq. 3 and 4) are also shown with the solid lines.
In this context, Figure 5 (colour-dots) shows the impact ofthermohaline instability on the [C / N] vs age and vs mass di-agrams. As thermohaline instability changes the surface abun-dances in carbon and nitrogen after the bump, large dispersionsof [C / N] with mass and age are noticeable for upper-RGB stars.Since this mechanism does not significatively a ff ect the surfacechemical properties of clump stars, relationships between [C / N]with masses and ages can be establish. These relationships canbe determined at a given metallicity for clump stars contrary toupper-RGB stars.Figure 6 shows thin-disc clump stars divided in three [Fe / H]-bins: (1) lower metallicity (-0.20 ≤ [Fe / H] ≤ -0.10) ; (2) solarmetallicity (-0.05 ≤ [Fe / H] ≤ + + ≤ [Fe / H] ≤ + / N] abundance ratio, in each metallicity range, assum-
Article number, page 6 of 9. Lagarde , A.C. Robin, C. Reylé, and G. Nasello: Population synthesis to constrain Galactic and Stellar Physics ing the stellar physics described above taking into account thee ff ects of thermohaline mixing. M / M (cid:12) = . · [ C / N ] + . · [ C / N ] + . − . ≤ [ Fe / H ] ≤ − . . · [ C / N ] + . · [ C / N ] + . − . ≤ [ Fe / H ] ≤ + . . · [ C / N ] + . · [ C / N ] + . + . ≤ [ Fe / H ] ≤ + .
25 (3) log ( Age [ yr ]) = . · [ C / N ] + . · [ C / N ] + . − . ≤ [ Fe / H ] ≤ − . . · [ C / N ] + . · [ C / N ] + . − . ≤ [ Fe / H ] ≤ + . − . · [ C / N ] + . · [ C / N ] + . + . ≤ [ Fe / H ] ≤ + .
25 (4)Importantly, the relation with age depends on the stellarmodel used. It is then crucial to validate the models and the mix-ing processes before using ages for Galactic archeology. In aforthcoming paper, we shall discuss the e ff ects of rotation onthese relations and estimate the accuracy of age and mass deter-minations using surface chemical properties.
6. Conclusions
In this paper, we have presented a new version of the Besançonstellar population synthesis model of the Galaxy including anew grid of stellar evolution models computed with the codeSTAREVOL. This new stellar grid of single-star evolution mod-els is computed for five metallicities in the mass range between0.6 and 6.0 M (cid:12) , including the e ff ects of thermohaline instabil-ity during the red-giant branch. These models provide the global(e.g. surface gravity, e ff ective temperature,...), chemical (surfaceproperties for 54 stable and unstable species) as well as seismicproperties ( ∆ ν , ν max , ∆Π ( (cid:96) = ). Thermohaline mixing occuring inthin disc giants has been shown to produce measurable e ff ectson the chemical properties, in particular on C / C and [C / N]ratios. Stellar evolution models at di ff erent α -enhancement arebeing computed to study the older populations, such as the thickdisc, the halo and the bulge, and will be presented in a forthcom-ing paper.By comparing the BGM simulations with observations fromlarge spectroscopic and seismic surveys, we are able to constrainthe physics of the transport processes occurring in stellar interi-ors. Red giants observed from asteroseismology can be now usedas new cosmic clock, allowing age calibration from chemicalobservations. Applying the new version of the BGM, we derivemean relations between [C / N] and age, usable to estimate agesfor thin-disc red-clump giants, knowing their metallicity. Con-trarily to previously derived relationships, ours take into accountthe natural spread in mass and metallicity of the underlying pop-ulation, and allows to include selection biases in the surveys. In aforthcoming paper of this series, we shall investigate the impactof di ff erent prescriptions for thermohaline instability on theserelations, as well as the e ff ect of rotation-induced mixing.Thanks to WEAVE, 4MOST, and PLATO the future looksextremely promising in terms of collecting spectroscopic andseismic data for a large number of stars. The Besançon Galaxy model will be a key tool to prepare these future instruments andmissions as well as to exploit a large amount of data from Gaia,given a better understanding of stellar and Galactic evolution. Acknowledgements.
We acknowledge financial support from "Programme Na-tional de Physique Stellaire" (PNPS) of CNRS / INSU, France. N.L. acknowl-edges financial support from the CNES fellowship.
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Article number, page 8 of 9. Lagarde , A.C. Robin, C. Reylé, and G. Nasello: Population synthesis to constrain Galactic and Stellar Physics
Fig. 5.
Surface abundance of [C / N] as a function of stellar ages (left panels) and stellar masses (right panels), colour-coded by metallicity, for asynthetic thin disc computed with the BGM. Stars have been selected to be in the clump according to their ∆Π (cid:96) = , as well as before and after theRGB-bump according to their log(g) values. Simulations including or not the e ffff