1. Current uncertainties in Red Giant Branch stellar models: Basti & the “Others” Santi Cassisi INAF - Astronomical Observatory of Teramo, Italy

2. Stellar models & Asteroseismic analysis 2 Huber et al. (2010) Kallinger et al. (2010) based on BaSTI models To assess the accuracy and reliability of the evolutionary scenario is mandatory!

3. Setting the (evolutionary) “scenario” massive stars Intermediate-mass stars low-mass stars M up M HeF Intermediate-mass starsLow-mass stars Physical Properties: Microscopical Mechanisms: Macroscopical Mechanisms:

4. Input physics affecting models for RGB low-mass stars 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 InputEvolutionary properties T eff  RGB location & shape He core mass@RGB Tip  RGB Tip brightness He-burning stage luminosity

5. The effect of the EOS Models computed by using some of the most commonly adopted EOS show: Different RGB slope Even if the ml is calibrated on the Sun, differences in the T eff of the order of 100K exist solar-calibrated ml

6. Low-temperature radiative opacity RGB models predict the same location and shape for the RGB until the T eff is larger than ~4000K; For lower T eff, computations based on the most updated opacity, predict cooler models (the difference is of the order of 100K); Current sets of stellar models employ mainly the low-T opacity computations by Ferguson et al. (2005) The largest improvement in low-T opacity has been the proper treatment of molecular absorption… and grains… Ferguson et al. 2005 Ferguson et al. 05

7. 7 Treatment of superadiabatic convection The mixing length is usually calibrated on the Sun: is this approach adequate for RGB stars? The solar-calibration of the ml guarantes that the models always predict the “right” T eff of at least solar-type stars; However, it is important to be sure that a solar ml is also suitable for RGB stars of various metallicities These results seem to point to the fact that the solar-calibrated ml is a priori adequate also for RGB stars Basti models Ferraro et al. (2006)

8. 8 Outer Boundary conditions 1/2 What is the most adequate approach for fixing the boundary conditions? The RGB based on model atmospheres shows a slightly different location with respect the models computed by using the Krishna-Swamy solar T(  ) The difference is of the order of 100K at solar metallicity

9. 9 Outer Boundary conditions 2/2 What about at lower metallicities? The RGB based on model atmospheres shows a slightly different slope, crossing over models computed using the KS66 solar T(  ) …but… The difference is always within ~  50K or less Kurucz

10. 10 Outer Boundary conditions 3/2 The trend of various thermodynamic quantities, opacity, convective velocity and the fraction of the total flux carried by convection in the subphotospheric layers of a solar model Vandenberg et al. (2008) T(τ) versus “model atmosphere”: structural predictions Solid line – model atmosphere Dashed line – evolutionary code integration but fixing the outer boundary conditions from the model atmosphere Despite the significant differences in the two approaches quite similar results are obtained…

11. 11 Models from different libraries, based on a solar-calibrated ml, can show different RGB effective temperatures This is probably due to some differences in the input physics, such EOS and/or boundary conditions which is not compensated by the solar recalibration of the ml Red Giant Branch models: the state-of-the-art 200K The difference in the RGB location can be also significantly larger (…up to 400 K…) when accounting from less updated model libraries

12. 12 Red Giant Branch models: the state-of-the-art

13. 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 InputEvolutionary properties T eff  RGB location & shape He core mass@RGB Tip  RGB Tip brightness He-burning stage luminosity  T eff ~100K  T eff ~150K  T eff ≤80K Solar calibrated ml

14. Eclipsing binaries can represent an important benchmark for model libraries The case of V20 in the Galactic Open Cluster NGC6791 (Grundahl et al. 2008) 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 A crucial issue: the color – T eff relations

15. The RGB luminosity function: the state-of-the-art Theoretical predictions about the RGB star counts appear a quite robust result! Evolutionary lifetimes for the RGB stage are properly predicted; There is no “missing physics” in the model computations; M13: Sandquist et al. (2010) What is present situation about the level of agreement between between theory and observations concerning the RGB bump brightness? Bertelli et al. 08 (Padua)

16. 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)

17. The RGB bump brightness: an independent check In order to avoid any problem associated to the estimate of the HB luminosity level from both the theoretical and observational point of view, we decided to use the ΔV(Bump-Turn Off) parameter ( see also Meissner & Weiss 06 ) a clear discrepancy between theory and observations is present, the theoretical RGB bump magnitudes being too bright by on average ~0.2 mag Cassisi et al. (2010) BaSTI models …any hint from asteroseismology…?

18. 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 InputEvolutionary properties T eff  RGB location & shape He core mass@RGB Tip  RGB Tip brightness He-burning stage luminosity

19. 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 Being M cHe @TRGB strongly dependent on the adopted “physical framework”, it has been often used as benchmark for testing “fundamental theory” The TRGB brightness is a strong function of the He core mass at the He-burning ignition

20. 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

21. The He core mass@TRGB Who is really governing the uncertainty in the M cHe predictions? 0.8M  Z=0.0002 – Y=0.23 M cHe Δ M cHe No diffusion 0.5110-0.0043 Stand. diffusion 0.5153// Plasma  +5% 0.5166+0.0013 Plasma  -5% 0.5141-0.0012 3  +15% 0.5143-0.0010 3  -15% 0.5166+0.0013  +5% 0.5158+0.0005  -5% 0.5147-0.0006  cond (HL) 0.5148-0.0050 Diffusion  1/2 0.5136-0.0017 Diffusion  2 0.5187+0.0034 42% conductive opacity 36% diffusion efficiency 4% radiative opacity 8% 3 α reaction rate 10% plasma neutrinos Δ MAX M cHe ≈ 0.01M  Δ M bol ~0.1 mag @TRGB @ZAHB Cassisi et al. (1998) – Michaud et al. (2010)

22. 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

23. 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;

24. TRGB: He core mass & luminosity 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…

25. The TRGB brightness as Standard Candle: theoretical calibrations  Cen – Bellazzini et al. 04 The I-band theoretical calibrations appear sistematically brighter by about 0.15 mag The effect of updated conductive opacity

26. 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 seems to be in fine agreement with empirical constraints (but in the J-band…)

27. M cHe & ZAHB brightness 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)

28. Future perspectives for the BaSTI archive Pulsational models to update the database, taking into account all the improvements in the physical framework; to improve the parameter-space coverage…; to check the accuracy & reliability by comparing the models with suitable empirical constraints such as eclipsing binaries, star clusters…; collaborations with reseachers working in the asteroseismology field are very welcomed!; The BaSTI archive is available @ http://www.oa-teramo.inaf.it/BASTI