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The R parameter

The R parameter. Observational data on the R parameter The effect of 12 C+ a The Helium abundance Differences in the treatment of convection The effect of other physical inputs So what?. The observable. N RGB.

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The R parameter

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  1. The R parameter • Observational data on the R parameter • The effect of 12C+a • The Helium abundance • Differences in the treatment of convection • The effect of other physical inputs • So what?

  2. The observable NRGB • The number of stars in the horizontal branch over the number of red giants with higher luminosity R= NHB/NRGB(L>LHB) • NHB is a good indicator of the time spent in the HB phase, and thus to the fuel/energy available (role of 12C+a) • NRGB(L>LHB) moves as He abundance, fixing LHB, is varied, and thus it is dependent of Y. NHB

  3. 2 1.5 1.0 R The Data • Large scattering of data • A constant R is fixed within ± 20% • Source of uncertainties: (from Zoccali et al. 2000) -”statistical” error -observational uncertainties, definition of LHB -dynamical effects • Possible solutions: • Select a small sample: few globular clusters, observed with high photometric accuracy, rich in HB stars, without “symptoms” of dynamical effects. • In this way there is the hope to fix R within ± few percent

  4. R 2 1.5 1.0 2 Kunz Kunz 0.5Kunz The effect of 12C+a (adapted from Zoccali et al. 2000 and Cassisi et al. 2003) • Good fit of all data obtained with standard convection, Y=0.245 and Kunz value for 12C+a • A change of S(12C+a) by ±100% changes R by ± 10%

  5. Lower helium implies lower LHB and consequently lower R. A change of Y by ±6% implies a change of R by ± 10% Stars in metal poor old GC should have primordial Helium abundance Ypr There are systematic uncertainties on Ypr, estimated at 0.234±0.003 or 0.244±0.002. Presumably Ypr= 0.239±0.005, corresponding to an uncertainty on R by ± 4%, a smaller effect. Y=0.245 Y=0.230 The effect of the Helium abundance R 2 1.5 1.0 (adapted from Zoccali et al. 2000 and Cassisi et al. 2003)

  6. Different treatments of convection Influence on tHB while LHB is unaffected • Canonical treatment of semiconvectionuncertainty of ~5% on tHB • Inclusion of breathing pulses increase of tHBby ~ 20% • Inclusion of mechanical overshooting  increase of tHB by ~ 25% • Use of an additional parameter? R2=NAGB/NHB (sensitive to the treatment of convection) (see also the discussion in Straniero et al. 2003 about the influence of the treatments of convection on the chemical composition of the C/O core)

  7. The effect of other physical inputs • Inclusion of microscopic diffusion  LHB ,tHBand tRGB are affected  decrease of Rby ~ 10% • CO opacity only tHB is affected an overestimate of the uncertainty: from old (LAOL) to new (OPAL) opacity calcolations  increase of tHB by about 8% (while LHB is unaffected)

  8. Conclusions • By using a well selected sample the observational uncertainty on the R parameter could be reduced to the level of few percent • Change of 12C+a by ±100% changes R by ± 10% • Change of Ypr within its uncertainty changes R by ± 4%, a smaller effect. • convection treatment can strongly influence the R evaluation a precise evaluation of 12C+a could help to discriminate among different mechanisms

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