Cepheid Pulsation--III: Models Fitted to a new Mass-Luminosity Relation

A new mass-luminosity relation for classical Cepheids was chosen so that models, which exhibited a prominent secondary bump in the light and velocity curves, agreed well with the observed period-phase of bump relation. The high T e edge of the strip is sensitive to the helium content and comparison with observation gives a helium content of 45 per cent by mass, though it must be emphasized that this value depends critically on the assumed ( B–V ) – T e relation. The models which were examined in the fundamental, first and second modes covered a period range of 1–40 days. Due to the narrowness of the observed strip, a satisfactory guide as to which mode a star is pulsating in can be obtained simply from the period. In general Cepheids of period greater than 7 days pulsate in the fundamental, those of period between 2 and 7 days pulsate in the first mode and those of period less than two days pulsate in the second mode. In every case where a model exhibited a prominent secondary bump it was found to be pulsating in the fundamental mode. No satisfactory period–luminosity relation was found because of the finite width of the strip. However, the existence of a period–radius–mass relation automatically implies the existence of a period–luminosity–colour relation provided that classical Cepheids obey some mass-luminosity relation. This period-luminosity-colour relation was derived separately for the fundamental mode pulsators and the first mode pulsators.