Classical Cepheid pulsation models --- VI. The Hertzsprung progression

We present the results of an extensive theoretical investigation on the pulsation 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, Z=0.008) and stellar 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 crosses 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 center is P_HP = 11.24∓0.46 d and that such a value is in very good agreement 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" distribution which is in good qualitative agreement with observational evidence on Bump Cepheids. It turns out that both the skewness and the acuteness typically show a well-defined minimum at the HP center and the periods range from P_HP = 10.73 ∓ 0.97 d to P_HP = 11.29 ∓ 0.53 d which are in good agreement with empirical estimates. We also find that the models at the HP center are located within the resonance region but not on the 2:1 resonance line (P₂/P₀ = 0.5), and indeed the P₂/P₀ ratios roughly range from 0.51 (cool models) to 0.52 (hot models). Interestingly enough, the predicted Bump Cepheid masses, based on a Mass-Luminosity (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 ≈ 11.2 d- is 6.9 ∓ 0.9 M_⊙, while the predicted mass is 7.0 ∓ 0.45 M_⊙. Even by accounting for the metallicity difference between Galactic and LMC Cepheids, this result seems to settle down the long-standing problem of the Bump mass discrepancy. Finally, the dynamical behavior of a cool Bump Cepheid model provides a plain explanation of an ill- understood empirical evidence. In fact, it turns out that toward cooler effective temperatures the bump becomes the main maximum, while the true maximum is the bump which appears along the rising branch. This finding also supplies a plain explanation of the reason why the pulsation amplitudes of Bump Cepheids present a "double-peaked" distribution.