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The R parameter Observational data on the R parameter The effect of 12 C+ The Helium abundance Differences in the treatment of convection The effect of other physical inputs So what?
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The observable The number of stars in the horizontal branch over the number of red giants with higher luminosity R= N HB/ N RGB (L>L HB ) N HB is a good indicator of the time spent in the HB phase, and thus to the fuel/energy available (role of 12 C+ ) N RGB (L>L HB ) moves as He abundance, fixing L HB, is varied, and thus it is dependent of Y. N HB N RGB
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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 L HB -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 2 1.5 1.0 R
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The effect of 12 C+ (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 12 C+ A change of S( 12 C+ ) by 100% changes R by 10% 2 Kunz Kunz 0.5Kunz R 2 1.5 1.0
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The effect of the Helium abundance Lower helium implies lower L HB 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 Y pr There are systematic uncertainties on Y pr, estimated at 0.234 0.003 or 0.244 0.002. Presumably Y pr = 0.239 0.005, corresponding to an uncertainty on R by 4%, a smaller effect. Y=0.245 Y=0.230 R 2 1.5 1.0 (adapted from Zoccali et al. 2000 and Cassisi et al. 2003)
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Different treatments of convection Influence on t HB while L HB is unaffected Canonical treatment of semiconvection uncertainty of ~5% on t HB Inclusion of breathing pulses increase of t HB by ~ 20% Inclusion of mechanical overshooting increase of t HB by ~ 25% Use of an additional parameter? R 2 =N AGB /N HB (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)
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The effect of other physical inputs Inclusion of microscopic diffusion L HB, t HB and t RGB are affected decrease of R by ~ 10% CO opacity only t HB is affected an overestimate of the uncertainty: from old (LAOL) to new (OPAL) opacity calcolations increase of t HB by about 8% (while L HB is unaffected)
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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 12 C+ by 100% changes R by 10% Change of Y pr within its uncertainty changes R by 4%, a smaller effect. convection treatment can strongly influence the R evaluation a precise evaluation of 12 C+ could help to discriminate among different mechanisms
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