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?

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

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 R

The effect of 12 C+  (adapted from Zoccali et al 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

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  or  Presumably Y pr =  0.005, corresponding to an uncertainty on R by  4%, a smaller effect. Y=0.245 Y=0.230 R (adapted from Zoccali et al and Cassisi et al. 2003)

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 about the influence of the treatments of convection on the chemical composition of the C/O core)

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)

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