1. Multiple Stellar Populations: the evolutionary framework Santi Cassisi INAF - Astronomical Observatory of Teramo - Italy

2. The theoretical framework: a brief “historical” overview The study of Galactic globular clusters has always received a long-standing attention owing to its importance in retaining fundamental hints about the Galaxy formation and the age of the Universe Until the early 90’, almost all sets of stellar models were computed by adopting scaled- solar abundances for the elements heavier than He:...but... Castellani et al. (1989) Chieffi & Straniero (1991) Vandenberg & Bell (1984) Vandenberg et al. (1990)... Gratton, Sneden & Carretta (2004)

3. soon after..., the first sets of stellar models properly accounting for α-enhanced heavy element mixtures came to light (Vandenberg et al. 92, Salaris et al. 93,..., Pietrinferni et al. 06, Dotter et al. 08) At fixed iron content, increasing the α-element abundance makes the evolutionary tracks fainter and cooler with respect to the scaled-solar ones; so the isochrones...: The change in the radiative opacity contributes to about 60%; The variation of the CNO-cycle efficiency - induced by the O abundance change - provides the difference; for a fixed [Fe/H] value Δ[α/Fe]=+0.3 →δt ≃ −1Gyr

4. The “rescaling” solution Isochrones for α-enhanced element abundances are well mimicked by those for scaled-solar mixtures of heavy elements, simply by requiring the total abundance of heavy elements (Z) to be the same: This had the implication than α-enhanced stellar models are no mandatory for studying the stellar populations in GC!!! The peculiar chemical patterns associated with the multiple population phenomenon in GCs complicates the evolutionary theoretical framework

5. The multiple stellar population chemistry 1/3 light elements anti-correlations Na-O anti-correlation light elements abundances can affect the radiative opacity evaluations and the H-burning rate via a change of the CNO-cycle efficiency + C - N and N - O anti-correlations Mg-Al anti-correlation

6. The multiple stellar population chemistry 2/3 C+N+O enhancement (?) but there are some notable exceptions Marino et al. (2011) M22 + NGC1851(still contradictory... ) ω Centauri In general, the CNO sum seems to be constant Carretta et al. (2005) being C, N, and O the catalysts of the CNO-cycle a change of their sum affects the H-burning rate

7. The multiple stellar population chemistry 3/3 He enhancement the proofs: Direct spectroscopic measurements no possible, but for hot HB stars (but...), a small T eff window along the HB ( Villanova, Piotto & Gratton 09 ), and RGB stars via the NIR He110830 Å transition ( Dupree, Strader & Smith 11 ); Indirect estimates (Bragaglia, Carretta, Gratton et al. 10) by measuring differences in: effective temperature; [Fe/H]; RGB bump luminosity level;

8. The multiple stellar population chemistry 3/3 He enhancement the proofs: Reliable direct spectroscopic measurements possible only in a small T eff range along the HB ( Villanova, Piotto & Gratton 09 ), and RGB stars via the NIR He110830 Å transition ( Dupree, Strader & Smith 11 ); Indirect estimates ( Bragaglia et al. 2010 ) by measuring difference in: [Fe/H], T eff, RGB bump luminosity; Photometric evidence: ω Cen, NGC2808, NGC104, etc etc... King, Bedin, Cassisi et al. (2012)Piotto, Bedin, Anderson, et al. (2007)

9. How these chemical patterns affect evolution of Stars? Evolutionary and structural properties Stellar Spectra Let us consider separately the impact on:

10. The effect of a He enhancement on Stars When increasing the initial He content: radiative opacity decreases; the mean molecular weight μ increases; since so a ΔY≈0.1 implies As a consequence, for a given total mass and metallicity, the star becomes: brighter; bluer the H-burning rate increases; Yt H (Gyr) 0.24611.3 0.3007.7 0.3505.5 0.4003.8 He

11. He-enhanced stellar populations: the theoretical scenario He-rich MS loci run almost parallel; At fixed luminosity, when increasing the He content by ΔY≈0.15 the MS T eff increases by ≈350K; the mass@Turn-off is 0.806M ⊙ for Y≈0.25 and 0.610M ⊙ for Y=0.40. Much smaller...; for a given age, the SGB loci overlap perfectly...; The RGB bump the bump becomes brighter; increasing the He abundance the luminosity excursion ΔV strongly decreases...; isochrones

12. He-enhanced Horizontal Branch Stars In comparison with a “He-normal” ZAHB, He- rich ZAHBs are: 1) brighter for T eff ≲ 20000K; 2) fainter at larger T eff ; Cassisi & Salaris (2012) (1) ⇐ larger H-burning efficiency (2) ⇐ smaller He-core mass He-enhanced HB stars perform more extended blue-loops during the core He-burning stage

13. He-enhanced HB Stars: “HB morphology” implications Increasing the He-enhancement, in the optical bands the HB appears to be tilted: the luminosity increases moving from “red” to “blue”; The larger the He enhancement, the bluer the HB morphology, for any given assumption about the average mass- loss efficiency;

14. The effects of “light-element” abundance changes: the general framework There is a rich literature concerning the analysis of the effects on stellar evolution induced by a change of the heavy element abundances in the mixture: from Iben & Simoda (70).... to Salaris et al. (06), Dotter et al. (07), Pietrinferni et al. (09), Vandenberg et al. (12) Vandenberg et al. (2012) - by enhancing the abundances of several metals by 0.4 dex, in turn O has the biggest impact; It is the most abundant metal; It affects both the opacity and the nucleosynthesis (as C & N); In order of decreasing influence, other important elements are: Si, Mg, Ne, S and C; The RGB location is affected only by the changes of Mg and Si ( very efficient electron donors ); ∼ 100K

15. The impact of these selective enhancements on stellar isochrones The different impact of the selective enhancement of the various elements on the MS/SGB and the RGB loci strongly suggests that: a self-consistent comparison between theory and GC data has to take into account the (fine) details of the chemical pattern; the “horizontal method” for GC age estimates could be affected by deceptive light-element abundance differences between GCs ( see also Marin-Franch et al. 10 ); Vandenberg et al. (2012) 18Gyr 14Gyr 10Gyr  (V-I) @2.5

16. The impact of light-element anti-correlations on the evolutionary framework “extreme” light-element anti-correlations versus a “reference” α-enhanced mixture (Salaris et al. 06, Cassisi et al. 08, Ventura et al. 08, Pietrinferni et al. 09) change (dex)/ mixture CNONa(C+N+O) (CNO)Na-0.6+1.44-0.8+0.8 as in the reference mixture (CNO) ext Na-0.6+1.8-0.8+0.8 a factor of 2 larger The T eff changes on the MS and RGB are marginal (lower than 20K); The effect on the SGB is mainly due to change in the nuclear network; The change in the core H-burning lifetime is ≈1%

17. The impact on the isochrones A 11Gyr-old CNO-enhanced isochrone is perfectly matched by an α-enhanced isochrone with an age of 13Gyr... there is an age-offset of about 1.5-2 Gyr CNO-enhanced HB stars CNO-enhanced HB stars are brighter ( ≃ 0.12 mag on average)...; at fixed total mass, their ZAHB location is cooler; they perform more extended blue loops during the core He-burning stage

18. The photometric appearance of multiple stellar populations: the fundamental rôle of model atmospheres In the H-R diagram, at fixed [Fe/H], a clear separation (split) of an evolutionary sequence can be obtained: for the MS, only as a consequence of a huge He-enhancement; for the SGB, only as a consequence of an increase of the (C+N+O) sum; in the case of the RGB, only as a consequence of an He increase;...but multi-band observations suggest that the changes in the stellar Spectral Energy Distribution induced by the peculiar chemical patterns are important...;

19. Sbordone et al. (2011) RGB T eff =4476K, logg=1.2 TO MS T eff =6490K, logg=4.22 low MS T eff =4621K, logg=4.47 The light-element changes affect mainly the portion of the spectra short of about 400 nm owing to the changes in molecular bands (...,NH, CN, and OH in the fainter MS stars...) black: reference mixture red: (CNO) ext Na

20. The impact on the color-T eff relations The magnesium abundance (and to a lesser extent oxygen and silicon) is mainly responsible for these differences; V-band and near-IR bands (...!) are not affected by chemical element varations, the same does not hold for U and B bands; scaled-solar versus α-enhanced mixtures Cassisi et al. (2004)

21. Strömgren bands Johnson-Cousin bands He-enhanced mixture The impact on the color-T eff relations Any photometric band “bluer” than the standard B band is hugely affected by the multiple populations chemical patterns... also (!!!) when the CNO sum is constant... (Sbordone et al. 2011, see also Cassisi et al. 2004) ; He enhancement - strongly affecting the stellar structures - is irrelevant for the atmospheric structure; (CNO)Na mixture Johnson-Cousin bands Strömgren bands

22. Johnson-Cousin bands He-enhanced mixture The impact on the color-T eff relations Johnson-Cousin bands Strömgren bands (CNO) ext Na mixture Any photometric band “bluer” than the standard B band is hugely affected by the multiple populations chemical patterns... also (!!!) when the CNO sum is constant... (Sbordone et al. 2011, see also Cassisi et al. 2004) ; He enhancement - strongly affecting the stellar structures - is irrelevant for the atmospheric structure; (CNO)Na mixture Johnson-Cousin bands Strömgren bands

23. isochrones for multiple population: a self-consistent approach In the “optical bands”, a splitting of sequence along the MS up to the TO (and the RGB) can be achieved only in case of a huge He-enhancement; When “bluer filters are used, CNONa anti-correlations and He differences can produce multiple sequences from the MS up to the RGB: This does not depend on the CNO sum; He-enhancements work in the opposite direction of light-element anti-correlations; Marino et al. (2008) blue solid: reference mixture red dash: CNONa magenta dash: (CNO) enh Na - normal He blue dot: (CNO) enh Na - Y=0.40

24. Strömgren photometric filters blue solid: reference mixture red dash: CNONa magenta dash: (CNO) enh Na - normal He blue dot: (CNO) enh Na - Y=0.40 c y =c 1 -(b-y) c 1 =(u-v)-(v-b) In this plane: being c 1 very sensitive to N, the larger the light-element anti- correlation, the redder the RGB location; an increase of He moves further to the red the RGB; Marino et al. (2009) =(v-b)-(b-y)

25. The insensitivity of the optical bands on light-element anti-correlations: a “lucky” occurrence!!! King, Bedin, Cassisi et al. (2012) The case of ω Centauri the most accurate He-enhancement estimate in a MPs GC Y=0.385

26. The near-infrared bands: a still largely unexplored window NGC2808 Milone et al. (2012) Milone, et al. (2012) The H 2 O molecule has the strongest effect... This flux variation in the spectral window corresponding to the F160W@WFC3 filter makes the He-enhanced VLM sequence redder than the normal-He sequence by: Δ(M F110W -M F160W )=0.10 in agreement with the observations (≈0.06 mag) Y=0.38 Y=0.25 bMS rMS

27. The Horizontal Branch: constraints from HB stellar models D’Antona et al. (2005) The HB morphology in the optical bands has been used to constrain the He abundances of the various sub- populations, but... Dalessandro et al. (2011) It is quite better to use UV photometric bands due to their quite larger sensitivity to T eff The case of NGC2808

28. The Horizontal Branch: constraints from evolutionary and pulsational models The SGB splitting can be interpreted as due to an age difference or a (CNO) sum difference (Cassisi et al. 08) Combining photometric evidence and spectroscopy (for both RGB - Yong+ 09, Carretta+ 11 -, SGB - Gratton+ 12. Lardo+ 12 -, and HB stars - Gratton+ 12) one can try to model the observed HB stellar distribution... The case of NGC1851 Gratton et al. (2012) blue dot: =0.67M ⊙, Y=0.28 red dot: =0.64M ⊙, Y=0.265 red square: =0.67M ⊙, Y=0.248 cyan triangle: =0.65M ⊙, Y=0.248, CNO enh... further constraints are required...

29. ...NGC1851 hosts a quite rich population of RR Lyrae stars... combining all together the hints coming from spectroscopy/photometry and pulsational properties of variable stars & comparing them with appropriate Synthetic HB models is “the best” approach for tracing the MPs properties Kunder et al. (2012) Period/Amplitude distribution

30. Final remarks The evidence of multiple stellar populations in Galactic GCs severely challenges stellar model “producers”; In order to compute stellar models suitable for reproducing the properties of stars in a given GC, the (fine) details of the observed chemical pattern have to be taken into account: Accurate radiative opacity evaluations accounting for the various heavy element enhancements are mandatory; Appropriate color - T eff transformations and Bolometric Corrections are needed in order to perform a self-consistent comparison between theory and observations; Depending on the issue under scrutiny (age determination, mass function estimates, etc.), an appropriate set of photometric filters has to be selected in order to minimize the uncertainties associated with models (atmospheres...) and undetected peculiarities in the chemical patterns;