Absolute Magnitudes of Cepheids. III. Amplitude as a Function of Position in the Instability Strip: a Period-Luminosity Relation

The amplitude of Cepheid variation is maximum at the blue edge of the instability strip, and decreases monotonically toward the red in the period range 0.40 < log P <0.86. In this respect Cepheids resemble RR Lyrae stars where it is known that the largest-amplitude c and ab variables are bluest. For intermediate-period Cepheids (0.86 < log P < 1.3) the trend is reversed; it returns to the original sense for stars with log P > 1.3. The difference in behavior may be related to Christy's explanation of the Hertzsprung relation for stars with periods near 10 days. Amplitude as a function of strip position permits formulation of a period-luminosity-amplitude relation which is equivalent to, and nearly as accurate as, the usual period-luminosity-color relation. Its advantage is that no colors are necessary. What were previously considered fundamental differences between Cepheids in our Galaxy and those in the SMC have largely disappeared in the present formulation when the amplitude effect is considered. Revised moduli for the LMC [(no - M)AB = 18.91J, the SMC [(rn - Ai)M = 19.35], and M31 [(m - M)AB = 24.76] are adopted. A principal conclusion is that Cepheids form an adequate foundation upon which to build the calibration of those brighter distance indicators which must be used to obtain an eventual value for the Hubble constant.