1. Omega Centauri, Cambridge 2001 1 The RR Lyrae of  Centauri: a theoretical route The RR Lyrae of  Centauri: a theoretical route (progress report) Castellani V. 1, Degl’Innocenti S. 1, Marconi M. 2 1 Physics Department, University of Pisa, Italy 2 Capodimonte Astronomical Observatory, Naples, Italy

2. Omega Centauri, Cambridge 2001 2  Cen RR Lyrae  Rich sample by Kaluzny et al. (1997)  Metallicity by Rey et al. (2000) An exciting possibility……However : ? [Fe/H]?

3. Omega Centauri, Cambridge 2001 3 Bearing in mind such a “warning” let us try to move along a theoretical route…. Sub-sample of the Kaluzny et al. RR Lyrae for which the metallicity evaluation from Rey et al. is available  Cen RR Lyrae

4. Omega Centauri, Cambridge 2001 4 Is theory consistent with observations? Z peaked at  0.0004 (Rey et al. 2000, Suntzeff & Kraft 1996)

5. Omega Centauri, Cambridge 2001 5 Visual magnitude distribution The bulk of RR Lyrae has a mean visual magnitude in the range 14.45  14.60 mag. By adopting: (m v -M v ) =14.05  0.11 (Thompson et al. 2001) Kaluzny et al. sample approximately in the range 0.4  0.55 mag

6. Omega Centauri, Cambridge 2001 6 Evolutionary theory Consistent with observations…nothing more until more precise [Fe/H] and will be available

7. Omega Centauri, Cambridge 2001 7 Pulsational theory The strongest constraint:  Light curve (P,  31, A are only a partial parametrization of the light curve) Let us recall the scenario: UComae : a field RRc  observations: P=0.29 days, E(B-V)  0

8. Omega Centauri, Cambridge 2001 8 (Bono, Castellani, Marconi, 2000, ApJ 532, L129) ________________________ (see Bono & Stellingwerf, 1994, for a description of the adopted non linear, convective, hydrodinamical code) Comparison between theory and observation for UComae light curve by assuming the mass in the range predicted by evolutionary theory for the observed P the fitting exists  L, T e * (in agreement with independent evaluations available in the literature) * We recall the Bono et al. (1997) relations: LogP F =11.627 +0.823 LogL -0.582 LogM -3.506 LogT e LogP FO =10.789 +0.800 LogL -0.594 LogM -3.309 LogT e

9. Omega Centauri, Cambridge 2001 9 To appreciate the sensitivity of the method: varying the temperature by 50 o K and by  0.03 mag.

10. Omega Centauri, Cambridge 2001 10  Centauri: a different approach   Let us assume a distance modulus (DM=14.05  0.11) and thus for RR Lyrae   Given the period, for each T e, one finds a mass and a light curve morphology  RR ab type  light curve 99B P=0.627 days, [Fe/H]= -1.74  0.05 (however the results are barely sensitive to the metallicity value within the metal poor range * ) * see e.g. Bono, Incerpi & Marconi 1996, Bono et al. 1997

11. Omega Centauri, Cambridge 2001 11 For the given DM (DM=14.05  =0.38) the temperature is fixed mainly by the required amplitude, in fact: Light curves at fixed period and but with different T e T e  A  : For RRab the amplitude increases by increasing the effective temperature (at fixed period) One obtains the pulsator mass

12. Omega Centauri, Cambridge 2001 12 What happens if DM is changed? A different distance modulus has been applied to each light curve to obtain the observed  14.43 for the light curve 99 The amplitude is almost constant..but the light curve shape changes Light curves at fixed period and T e but with different

13. Omega Centauri, Cambridge 2001 13 Best fit In this case pulsational theory is consistent with observations and stellar evolution DM=14.05 …. The fit is not perfect, but satisfactory.....at least to characterize a method Summarising: By fitting A v One finds T e DMBest fit of the light curve (In agreement with the DM estimate by Thompson et al. 2001) Note that the estimated stellar mass agrees with the one predicted by stellar evolution! mass

14. Omega Centauri, Cambridge 2001 14 If one changes the DM by about 0.1 mag. the light curve fit appears less satisfactory upper limit for a DM variation

15. Omega Centauri, Cambridge 2001 15 A variation of the distance modulus by  0.15 mag. can be definitely ruled out

16. Omega Centauri, Cambridge 2001 16 This is the “theoretical truth”… ….how true is this truth? Pulsational computations are quite sophisticated: one has to account for difficult mechanisms as eddy viscosity, overshooting and so on.... The true truth: we were already surprised of the rather beautiful agreement…. We would like to test deeper the theory:  Firmer T e  Better [Fe/H]  Velocity curve A strong test! Details of LC depend on Z a further prediction Goal * : a well tested and well calibrated theory promises to provide reliable distance modulus from just one (or few) RR! …the work is in progress... ________ *These results confirm a similar analysis on a LMC bump Cepheid by Wood et al. (1997)