Classical Cepheid pulsation models VI. The Hertzsprung progression

We present the results of an extensive theoretical investigation on the pul sation behavior of Bump Cepheids. We constructed several sequences of full amplitude, nonlinear, convective models by adopting a chemical composition typical of Large Magellanic Cloud (LMC) Cepheids (Y=0.25, 2=0.008) and stel lar masses ranging from M/M. =6.55 to 7.45. We find that theoretical light and velocity curves reproduce the HP, and indeed close to the blue edge the bump is located along the descending branch, toward longer periods it cros ses at first the luminosity/velocity maximum and then it appears along the rising branch, In particular, we find that the predicted period at the HP c enter is P-HP = 11.24 +/- 0.46 d and that such a value is in very good agre ement with the empirical value estimated by adopting the Fourier parameters of LMC Cepheid :light curves i.e. P-HP = 11.2 +/- 0.8 d (Welch et al. 1997 ). Moreover, light and velocity amplitudes present a "double-peaked" distri bution which is in good qualitative agreement with observational evidence o n Bump Cepheids. It turns out that both the skewness and the acuteness typi cally show a well-defined minimum at the HP center and the periods range fr om P-HP = 10.73 +/- 0.97 d to P-HP = 11.29 +/- 0.53 d which are in good agr eement with empirical estimates. We also find that the models at the HP cen ter are located within the resonance region but not on the 2:1 resonance li ne (P-2/P-0 = 0.5), and indeed the P-2/P-0 ratios roughly range from 0.51 ( cool models) to 0.52 (hot models). Interestingly enough, the predicted Bump Cepheid masses, based on a Mass-Lu minosity (ML) relation which neglects the convective core overshooting, are in good agreement with the empirical masses of Galactic Cepheids estimated by adopting the Baade-Wesselink method (Gieren 1989). As a matter of fact, the observed mass at the HP center -P approximate to 11.2 d- is 6.9 +/- 0. 9 M., while the predicted mass is 7.0 +/- 0.45 M.. Even by accounting for t he metallicity difference between Galactic and LMC Cepheids, this result se ems to settle down the longstanding problem of the Bump mass discrepancy. Finally, the dynamical behavior of a cool Bump Cepheid model provides a pla in explanation of an ill-understood empirical evidence. In fact, it turns o ut that toward cooler effective temperatures the bump becomes the main maxi mum, while the true maximum is the bump which appears along the rising bran ch. 1:his finding also supplies a plain explanation of the reason why the p ulsation amplitudes of Bump Cepheids present a "double-peaked" distribution .