1. Current uncertainties in Stellar Evolution Models Santi Cassisi INAF - Astronomical Observatory of Teramo, Italy

2. The “ingredients” An evolutionary code Numerics Boundary conditions 1D versus 3D Physical inputs Equation of State Radiative opacity Conductive opacity Nuclear reaction rates Neutrino energy losses Mixing treatment Overshooting Superadiabatic convection Non-canonical processes Microscopic mechanism Atomic diffusion Radiative levitation Additional mechanism Mass loss Rotation Magnetic field

3. Some pieces of evidence… Very Low Mass stars: King et al. (1998) Richer et al. (2008) Zoccali et al. (2000) Surface boundary conditions Equation of State Opacity ✓ ✓ ✓ Segransan et al. (2003)

4. Some pieces of evidence… Globular and Open star clusters: M67 Bedin et al.(2007) & Vandenberg et al. (2007) NGC188 Meibom et al.(2009) VdB modelsYale-Yonsei models

5. YY Dartmouth Victoria BaSTI Padua ≈1.5Gyr Eclipsing binary: an important benchmark 1/2 The case of V69 in the Galactic GC 47Tuc (Thompson et al. 2010) BaSTI Dartmouth Victoria When the differences (He content, heavy elements distribution, diffusion efficiency, etc…) are taken properly into account, the difference can be reduced to about 0.8Gyr,…

6. The Age – Luminosity calibration: the clock A comparison among the various stellar model libraries suggests that an uncertainty of about 1Gyr (i.e. ≈10%) do exist at the older ages…

7. Eclipsing binary: an important benchmark 2/2 The case of V20 in the Galactic Open Cluster NGC6791 (Grundahl et al. 2008) Kalirai et al.(2007) Victoria-Regina (t=8.5Gyr) Photometry by Stetson et al. (2003) (m-M) V =13.46 ± 0.10 E(B-V)=0.15 ± 0.02

8. Red Giant Branch Stars The location and slope are strongly dependent on the metallicity…; The RGB Tip brightness is one of the most important “primary” distance indicators; RGB star counts are quite important: to check the inner chemical stratification; being RGB stars among the brightest and cooler objects, their number (+ AGB stars)controls the integrated properties in the NIR bands; the RGB/AGB number ratio provides hints on the Star Formation History of complex stellar populations (Greggio 2002) ; Accurate RGB modeling is mandatory for interpreting data of unresolved stellar systems using population synthesis tools as well as for estimating the properties of resolved systems by means of isochrone fitting techniques 47 Tuc HST Snapshot Piotto et al. (1999)

9. Input physics affecting the RGB models Equation of State Low Temperature Radiative Opacity Efficiency of the convective energy transport Boundary conditions Abundances (He, Fe &  -elements) Conductive Opacity Neutrino energy losses Atomic diffusion efficiency Nuclear reaction rates Non standard physics… InputEvolutionary properties T eff  RGB location & shape He core mass@RGB Tip

10. The state-of-art of RGB models: the luminosity function Theoretical predictions about RGB star counts appear a quite robust result M13: Sandquist et al. (2010) RGB bump What is present situation about the level of agreement between between theory and observations concerning the RGB bump brightness?

11. The RGB bump brightness To overcome problems related to still-present indetermination on GC distance modulus and reddening, it is a common procedure to compare theory with observations by using the ΔV(Bump-HB) parameter Does it exist a real problem in RGB stellar models or is there a problem in the data analysis? Monelli et al. (2010)

12. The brightness of the Red Giant Branch Tip RGB tip The I-Cousin band TRGB magnitude is one of the most important primary distance indicators: age independent for t>2-3Gyrs; metallicity independent for [M/H]<−0.9 The TRGB brightness is a strong function of the He core mass at the He-burning ignition

13. TRGB: He core mass – luminosity Salaris, Cassisi & Weiss (2001) ≈ 0.03M  These differences are – often but not always…- those expected when considering the different physical inputs adopted in the model computations

14. The He core mass@TRGB Who is really governing the uncertainty in the M cHe predictions? 42% conductive opacity 36% diffusion efficiency 4% radiative opacity 8% 3 α reaction rate 10% plasma neutrinos  MAX M cHe ≈ 0.01M   M bol ~0.1 mag @TRGB @ZAHB

15. He CORE mass & conductive opacity: electron conduction is the dominant energy transport mechanism in the electron degenerate He core In order to obtain reliable κ cond estimates, one has to properly take into account the “real” physical conditions of the He core partial electron degeneracyintermediate ion coupling regime

16. Conductive opacity: an update So far, only 3 independent sources of  cond were available, each one with its own shortcomings (Catelan 2005) Recently, a set of κ cond (Cassisi et al. 2007) estimates has been provided based on: a full coverage of the parameter space; the inclusion of the e - e - scattering effects;

17. TRGB: He core mass & luminosity a n u p d a t e last generations of stellar models agree – almost all – within ≈ 0.003M  a fraction of the difference in M cHe is due to the various initial He contents – but in the case of the Padua models… the difference in M bol (TRGB) is of the order of 0.15 mag when excluding the Padua models…

18. The TRGB brightness as Standard Candle: theoretical calibrations The I-band theoretical calibrations appear sistematically brighter by about 0.15 mag ω Cen – Bellazzini et al. (2001)

19. The TRGB brightness: theory versus observations (an update) The reliability of this comparison would be largely improved by: increasing the GC sample…; reducing the still-existing uncertainties in the color-T eff transformations Updated RGB models are now in agreement with empirical data at the level of better than 0.5 σ In the near-IR bands, the same calibration is in fine agreement with empirical constraints (but in the J-band…)

20. Do we really need 3D stellar modeling? isosurface of the velocity field Mocak et al. (2008, 2010) radial downflow radial upflow isosurface of the chemical abundance Dearborn et al. (2006) temperature (10 8 K) 12 C mass fraction (10 -3 )radial velocity (10 5 cms -1 ) @top of the convection zone (Mocak et al. 2008) The He core at the peak of the core helium flash is a very turbulent environment at all heights of the convection zone

21. 1D versus 3D modeling of the He core flash same outcomes: the behavior is consistent with hydrostatic modeling even at the He flash peak; 3D models seem to retain more or less spherical symmetry; in 3D models, convection approaches but never exceedes the outer boundary of convection as determined from stability criterion in 1D models (overshoot…?); 3D models show significant mixing below the convective shell from downward overshoot…… it is possible that this process could reduce or eliminate the “miniflashes” present in 1D simulations; 3D models do not change the theoretical framework!!!

22. The Horizontal Branch The brightness: a primary standard candle the 2° parameter problem Star counts  The R parameter The ZAHB luminosity is mainly fixed by the mass size of the He core@TRGB Any physical inputs affecting the value of M cHe, has a strong impact on the ZAHB luminosity The color distribution: Peculiar “patterns”: rotation surface chemical abundances The color location along the HB DOES depend on the mass loss efficiency along the RGB

23. The ZAHB brightness: an update The difference among the most recent models is about 0.15 mag All models but the Dotter’s ones, predict the same dependence on [M/H] De Santis & Cassisi (1999)

24. The integrated magnitudes & colors of stellar systems can be largely affected by the HB morphology (see Conroy’s talk…) Mass loss along the RGB: the impact on the HB High mass-loss efficiency low mass-loss efficiency The impact of mass loss phenomenon on the evolutionary properties of RGB stars is (…not always!...) negligible, but…it is very important for the Horizontal Branch Dorman, Rood & O’Connell (1993)

25. Mass loss on the RGB: not good news “Investigations of the impact of RGB mass loss upon the HB morphology have mostly relied on the Reimers’s (1975) formula, and it is widely used as a LAW” (Catelan 2005) These formulae are not able to reproduce the mass-loss rates measured by Origlia et al. (2002, 2007)… But… various prescriptions do exist they predict quite different mass loss efficiency

26. HB stars show a number of peculiarities Discontinuities in the abundance ratios Diffusive processes (atomic diffusion + radiative levitation) are really at work in HB stars! What about stellar models…?

27. Stellar model predictions (Michaud et al. 2007,2008) Various masses to cover range of T eff along the HB; In color from 15 to 30 Myr after ZAHB; Same turbulence model for all masses; Data for M15 by Behr (2003) Stars with T eff < 11000 K have same metals as giants of cluster; Stars with T eff > 11000 K have X100 overabundance; Overabundances explained… but normal ones suggest something else also present since overbundances by X5 expected;

28. The detailed case of B315 in M15 T eff =13000 + 500 K All species observed by Behr (03) in B315: He, Na, Mg, Al, Si, P, S, Ca, Ti, Fe, Ni; Masses (0.60 to 0.63) and ages (20 and 30 Myr) chosen to reproduce approximately the observed T eff and span various HB evolution stages; All have same mixed mass fixed by Fe vs T eff; He, Na, Al, Si, P, S, Ca, Ti, Mn, and Fe reasonably reproduced within the error bars; Mg is a problem: Mg I is reproduced while Mg II is not while it should be more accurately observed; He has large error bars; while Ni is an upper limit;

29. Discontinuity in the rotation rates (Behr 00 + 03, Recio-Blanco et al. 02 + 04) Globular clusters Field Stars Some embarrassments: they rotate… some of them rotate fast… it seems to exist a discontinuity…

30. [Fe/H] and rotation along the HB: an observational link Data from Behr et al. (1999, 2003) - black: M3; red: M13; green: M15; blue: M68; brown: NGC 288; Stars with T eff < 11000 K have [Fe/H] as RGB stars; Stars with T eff > 11000 K have [Fe/H] values from 10 to 100 times larger; Stars with anomalies have slow rotation; note star with arrow; Any clues from stellar models?

31. Meridional circulation in HB stars Dotted curve: ~max observed Vsin i; Circulation wipes out anomalies below about 11000 K; Dark gray region: no anomalies observed; White region: anomalies observed; Trend with the T eff of the limiting rotational velocity for He settling in presence of meridional circulation for two cases: Ciculation enters the He convection zone (dots); Circulation does not enter into the convection zone (triangles); Quievy et al. (2009) but NO clues on why HB stars rotate…

32. Rotation in HB stellar models: the state-of-the-art Many uncertainties exist: how to treat the internal redistribution of angular momentum from the TO to the TRGB? the rotation law in the convective regions the internal redistribution of angular momentum on the HB mixing processes associated to rotation These models fail to simultaneously predict the high-rotation rate observed around 11,000K and the low rotation observed at higher T eff V rot (Turn-off)~1Km/sV rot (Turn-off)~4Km/s Sills & Pinsonneault (2000)

33. The Asymptotic Giant Branch The AGB evolutionary phase is very important for many reasons as: Neutron Capture Nucleosynthesis Population tracers Integrated properties of resolved & unresolved stellar populations Marigo et al. (2008)

34. But… it is in the age regime when AGB stars dominate the SED, where different population synthesis models give - quite - different results In some cases - as in Maraston (2005) - the AGB contribution to both the bolometric and near-IR light of a stellar population, is much larger (a factor of 2 or more…) than in other models… SED for SSP see the talks by Bruzual and Conroy

35. Some piece of evidence Gonzales et al. (2004) Kyeong et al. (2003) Models (for Z=0.01) by: Maraston (2005) Marigo & Girardi (2008, Padua) Percival et al. (2009, BaSTI) (also for Z=0.008, 0.004, 0.0008) see the talks by Bruzual and Conroy All these population synthesis models rely on Synthetic AGB computations

36. AGB stellar models: why a THORNY problem? Nucleosynthesis Brightness Effective temperature scale  colors Evolutionary lifetime Initial – Final mass relation Mass loss opacitymixing burning(s) pulsations

37. The 1 th problem: the Third Dredge Up efficiency The mixing efficiency during the TDU has important effects on: C/O~10 Radiative burning of 13 C(α,n) 16 O reaction C/O=1.0 – C star!!!C/O=0.7 the rate of surface C-enhancement; the mass loss efficiency and, in turn, the TP stage lifetime; the amount of s-elements @ the stellar surface ; the effective temperature scale and colors;

38. The TDU efficiency: an unsettled issue Problem: How to treat the mixing during the TDU? Solution(s): Bare Schwarzschild criterion Envelope overshoot Time dependent mixing Diffusive process Free (!) parameter(s) The mixing efficiency during the TDU has important effects on: the rate of surface C-enhancement; the mass loss efficiency and, in turn, the TP stage lifetime; the amount of s-elements @ the stellar surface ; the effective temperature scale and colors;

39. The 2 th problem: opacity for C-enhanced mixtures Long time ago, Scalo & Ulrich (1975) showed that: TiO and H 2 O are the most important molecules in the oxygen-rich regime (C/O 1 Fundamental further steps ahead have been NOW made (Lederer & Aringer 2008, Marigo & Aringer 2009, Weiss & Ferguson 2009) What is the impact on the AGB stars effective temperature scale? A crucial issue!

40. The importance of an appropriate treatment of C-rich mixture opacity Marigo & Girardi (2007) Direct effect: huge decrease of the effective temperature strong increase of the mass loss efficiency… Indirect effect:

41. Fully evolutionary AGB models: is there a general consensus? A comparison among independent “fully AGB models” shows that: relevant differences exist both in the TP lifetimes and TPs number; sometime the differences have no explanation ( as between K93 and WV93… ); significant differences do exist also for the He core mass predictions…; Weiss & Ferguson (2009) versus Karakas (2003) and Wassiliadis & Wood (1993) No overshooting Overshooting + WF09

42. Conclusions Can I trust stellar evolutionary models? If the models does not fit the data, maybe… this means that the data are wrong…