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 6.55 to 7.45 solar masses. 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 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. We also find that the models at the HP center are located within the resonance region but not on the 2:1 resonance line. 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. 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. 
G. Bono (Astron. Obs. of Roma), M. Marconi (Astron. Obs. of   Capodimonte), R. F. Stellingwerf (SC, 2229 Loma Linda, Los Alamos)