The Hertzsprung progression in Cepheid calculations
The Hertzsprung bump in Cepheid models has been studied for models of a wide range of mass (M), radius (R), and effective temperature (T sub e). This study showed that the delay of the bump (in days) measured from the time of minimum radius preceding the bump by one plus period is dependent only on M and R and not on T sub e. Over a range of models from M/M solar mass approximately 0.5 and R/R solar radius = 10 to M/M solar mass = 13 and R/R solar radius = 160, the delay of the bump (in days) is approximately proportional to the radius. This is consistent with a picture that the bump results from an acoustic signal that traverses the star from the ionization zone into the center and out again to the surface. The bump and other nonlinear phenomena has been studied over a series of Cepheid models from a period of less than one day to a period of 150 days. The results show characteristic changes in amplitude and in the appearance of bumps and are in good correspondence to actual Cepheids. The masses in this series are, however, characteristically lower than evolutionary masses.